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\begin{isabellebody}%
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\def\isabellecontext{Build{\isaliteral{5F}{\isacharunderscore}}Inverse{\isaliteral{5F}{\isacharunderscore}}Z{\isaliteral{5F}{\isacharunderscore}}Transform}%
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\isadelimtheory
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\isanewline
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\isanewline
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\endisadelimtheory
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\isatagtheory
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\isacommand{theory}\isamarkupfalse%
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\ Build{\isaliteral{5F}{\isacharunderscore}}Inverse{\isaliteral{5F}{\isacharunderscore}}Z{\isaliteral{5F}{\isacharunderscore}}Transform\ \isakeyword{imports}\ Isac\isanewline
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\ \ \isanewline
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\isakeyword{begin}%
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\endisatagtheory
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{\isafoldtheory}%
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\isadelimtheory
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\begin{isamarkuptext}%
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We stepwise build \ttfamily Inverse\_Z\_Transform.thy \normalfont as an
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exercise. Because Subsection~\ref{sec:stepcheck} requires
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\ttfamily Inverse\_Z\_Transform.thy \normalfont as a subtheory of \ttfamily
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Isac.thy\normalfont, the setup has been changed from \ttfamily theory
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Inverse\_Z\_Transform imports Isac \normalfont to the above one.
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\par \noindent
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\begin{center}
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\textbf{Attention with the names of identifiers when going into internals!}
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\end{center}
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Here in this theory there are the internal names twice, for instance we have
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\ttfamily (Thm.derivation\_name \isa{rule{\isadigit{1}}} =
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"Build\_Inverse\_Z\_Transform.rule1") = true; \normalfont
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but actually in us will be \ttfamily Inverse\_Z\_Transform.rule1 \normalfont%
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\end{isamarkuptext}%
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\isamarkuptrue%
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\isamarkupsection{Trials towards the Z-Transform\label{sec:trials}%
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}
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\isamarkuptrue%
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\isadelimML
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\endisadelimML
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\isatagML
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\isacommand{ML}\isamarkupfalse%
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\ {\isaliteral{7B2A}{\isacharverbatimopen}}val\ thy\ {\isaliteral{3D}{\isacharequal}}\ %
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\isaantiq
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theory\ Isac{}%
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\endisaantiq
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{\isaliteral{3B}{\isacharsemicolon}}{\isaliteral{2A7D}{\isacharverbatimclose}}%
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\endisatagML
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{\isafoldML}%
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\isamarkupsubsection{Notations and Terms%
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}
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\isamarkuptrue%
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\begin{isamarkuptext}%
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\noindent Try which notations we are able to use.%
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\end{isamarkuptext}%
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\isamarkuptrue%
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\isatagML
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\isacommand{ML}\isamarkupfalse%
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\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
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\ \ %
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\isaantiq
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term\ {\isaliteral{22}{\isachardoublequote}}{\isadigit{1}}\ {\isaliteral{3C}{\isacharless}}\ {\isaliteral{7C}{\isacharbar}}{\isaliteral{7C}{\isacharbar}}\ z\ {\isaliteral{7C}{\isacharbar}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}{}%
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\endisaantiq
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{\isaliteral{3B}{\isacharsemicolon}}\isanewline
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\ \ %
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\isaantiq
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term\ {\isaliteral{22}{\isachardoublequote}}z\ {\isaliteral{2F}{\isacharslash}}\ {\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{1}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}{}%
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\endisaantiq
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{\isaliteral{3B}{\isacharsemicolon}}\isanewline
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\ \ %
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\isaantiq
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term\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{2D}{\isacharminus}}u\ {\isaliteral{2D}{\isacharminus}}n\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}{}%
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\endisaantiq
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{\isaliteral{3B}{\isacharsemicolon}}\isanewline
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\ \ %
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\isaantiq
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term\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{2D}{\isacharminus}}u\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{2D}{\isacharminus}}n\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{1}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}{}%
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\endisaantiq
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{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{5B}{\isacharbrackleft}}\ {\isaliteral{5D}{\isacharbrackright}}\ denotes\ lists\ {\isaliteral{21}{\isacharbang}}{\isaliteral{21}{\isacharbang}}{\isaliteral{21}{\isacharbang}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
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\ \ %
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\isaantiq
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term\ {\isaliteral{22}{\isachardoublequote}}z\ {\isaliteral{2F}{\isacharslash}}{\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{1}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{2D}{\isacharminus}}u\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{2D}{\isacharminus}}n\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{1}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}{}%
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\endisaantiq
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{\isaliteral{3B}{\isacharsemicolon}}Isac\isanewline
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\ \ %
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\isaantiq
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term\ {\isaliteral{22}{\isachardoublequote}}{\isadigit{1}}\ {\isaliteral{3C}{\isacharless}}\ {\isaliteral{7C}{\isacharbar}}{\isaliteral{7C}{\isacharbar}}\ z\ {\isaliteral{7C}{\isacharbar}}{\isaliteral{7C}{\isacharbar}}\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\ z\ {\isaliteral{2F}{\isacharslash}}\ {\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{1}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{2D}{\isacharminus}}u\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{2D}{\isacharminus}}n\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{1}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}{}%
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\endisaantiq
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{\isaliteral{3B}{\isacharsemicolon}}\isanewline
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\ \ term{\isadigit{2}}str\ %
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\isaantiq
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term\ {\isaliteral{22}{\isachardoublequote}}{\isadigit{1}}\ {\isaliteral{3C}{\isacharless}}\ {\isaliteral{7C}{\isacharbar}}{\isaliteral{7C}{\isacharbar}}\ z\ {\isaliteral{7C}{\isacharbar}}{\isaliteral{7C}{\isacharbar}}\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\ z\ {\isaliteral{2F}{\isacharslash}}\ {\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{1}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{2D}{\isacharminus}}u\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{2D}{\isacharminus}}n\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{1}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}{}%
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\endisaantiq
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{\isaliteral{3B}{\isacharsemicolon}}\isanewline
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{\isaliteral{2A7D}{\isacharverbatimclose}}%
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\endisatagML
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{\isafoldML}%
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\isadelimML
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\begin{isamarkuptext}%
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\noindent Try which symbols we are able to use and how we generate them.%
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\end{isamarkuptext}%
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\isamarkuptrue%
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\isadelimML
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\isatagML
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\isacommand{ML}\isamarkupfalse%
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\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
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\ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}alpha\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{3C}{\isacharless}}{\isaliteral{2F}{\isacharslash}}alpha{\isaliteral{3E}{\isachargreater}}{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
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\ \ %
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\isaantiq
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term\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ {\isaliteral{22}{\isachardoublequote}}{}%
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\endisaantiq
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{\isaliteral{3B}{\isacharsemicolon}}\isanewline
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\ \ %
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\isaantiq
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term\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C64656C74613E}{\isasymdelta}}\ {\isaliteral{22}{\isachardoublequote}}{}%
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\endisaantiq
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{\isaliteral{3B}{\isacharsemicolon}}\isanewline
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\ \ %
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\isaantiq
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term\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C7068693E}{\isasymphi}}\ {\isaliteral{22}{\isachardoublequote}}{}%
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\endisaantiq
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{\isaliteral{3B}{\isacharsemicolon}}\isanewline
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\ \ %
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\isaantiq
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term\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C72686F3E}{\isasymrho}}\ {\isaliteral{22}{\isachardoublequote}}{}%
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\endisaantiq
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{\isaliteral{3B}{\isacharsemicolon}}\isanewline
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\ \ term{\isadigit{2}}str\ %
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\isaantiq
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term\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C72686F3E}{\isasymrho}}\ {\isaliteral{22}{\isachardoublequote}}{}%
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\endisaantiq
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{\isaliteral{3B}{\isacharsemicolon}}\isanewline
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{\isaliteral{2A7D}{\isacharverbatimclose}}%
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\endisatagML
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{\isafoldML}%
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\isamarkupsubsection{Rules%
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}
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\isamarkuptrue%
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\isacommand{axiomatization}\isamarkupfalse%
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\ \isakeyword{where}\ \isanewline
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\ \ rule{\isadigit{1}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isadigit{1}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5C3C64656C74613E}{\isasymdelta}}{\isaliteral{5B}{\isacharbrackleft}}n{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{and}\isanewline
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\ \ rule{\isadigit{2}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{7C}{\isacharbar}}\ z\ {\isaliteral{7C}{\isacharbar}}{\isaliteral{7C}{\isacharbar}}\ {\isaliteral{3E}{\isachargreater}}\ {\isadigit{1}}\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\ z\ {\isaliteral{2F}{\isacharslash}}\ {\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{1}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ u\ {\isaliteral{5B}{\isacharbrackleft}}n{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{and}\isanewline
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\ \ rule{\isadigit{3}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{7C}{\isacharbar}}\ z\ {\isaliteral{7C}{\isacharbar}}{\isaliteral{7C}{\isacharbar}}\ {\isaliteral{3C}{\isacharless}}\ {\isadigit{1}}\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\ z\ {\isaliteral{2F}{\isacharslash}}\ {\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{1}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{2D}{\isacharminus}}u\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{2D}{\isacharminus}}n\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{1}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{and}\ \isanewline
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\ \ rule{\isadigit{4}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{7C}{\isacharbar}}\ z\ {\isaliteral{7C}{\isacharbar}}{\isaliteral{7C}{\isacharbar}}\ {\isaliteral{3E}{\isachargreater}}\ {\isaliteral{7C}{\isacharbar}}{\isaliteral{7C}{\isacharbar}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ {\isaliteral{7C}{\isacharbar}}{\isaliteral{7C}{\isacharbar}}\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\ z\ {\isaliteral{2F}{\isacharslash}}\ {\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{2D}{\isacharminus}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}n\ {\isaliteral{2A}{\isacharasterisk}}\ u\ {\isaliteral{5B}{\isacharbrackleft}}n{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{and}\isanewline
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\ \ rule{\isadigit{5}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{7C}{\isacharbar}}\ z\ {\isaliteral{7C}{\isacharbar}}{\isaliteral{7C}{\isacharbar}}\ {\isaliteral{3C}{\isacharless}}\ {\isaliteral{7C}{\isacharbar}}{\isaliteral{7C}{\isacharbar}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ {\isaliteral{7C}{\isacharbar}}{\isaliteral{7C}{\isacharbar}}\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\ z\ {\isaliteral{2F}{\isacharslash}}\ {\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{2D}{\isacharminus}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}n{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2A}{\isacharasterisk}}\ u\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{2D}{\isacharminus}}n\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{1}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{and}\isanewline
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\ \ rule{\isadigit{6}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{7C}{\isacharbar}}\ z\ {\isaliteral{7C}{\isacharbar}}{\isaliteral{7C}{\isacharbar}}\ {\isaliteral{3E}{\isachargreater}}\ {\isadigit{1}}\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\ z{\isaliteral{2F}{\isacharslash}}{\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{1}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}{\isadigit{2}}\ {\isaliteral{3D}{\isacharequal}}\ n\ {\isaliteral{2A}{\isacharasterisk}}\ u\ {\isaliteral{5B}{\isacharbrackleft}}n{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequoteclose}}%
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\begin{isamarkuptext}%
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\noindent Check the rules for their correct notation.
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(See the machine output.)%
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\end{isamarkuptext}%
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\isamarkuptrue%
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\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
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\ \ %
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\isaantiq
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thm\ rule{\isadigit{1}}{}%
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\endisaantiq
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{\isaliteral{3B}{\isacharsemicolon}}\isanewline
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\ \ %
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\isaantiq
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thm\ rule{\isadigit{2}}{}%
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{\isaliteral{3B}{\isacharsemicolon}}\isanewline
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\ \ %
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\isaantiq
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thm\ rule{\isadigit{3}}{}%
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{\isaliteral{3B}{\isacharsemicolon}}\isanewline
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\ \ %
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\isaantiq
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thm\ rule{\isadigit{4}}{}%
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\endisaantiq
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{\isaliteral{3B}{\isacharsemicolon}}\isanewline
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{\isaliteral{2A7D}{\isacharverbatimclose}}%
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%
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\isamarkupsubsection{Apply Rules%
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}
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\isamarkuptrue%
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%
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\begin{isamarkuptext}%
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\noindent We try to apply the rules to a given expression.%
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\end{isamarkuptext}%
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\isamarkuptrue%
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%
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%
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%
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\isacommand{ML}\isamarkupfalse%
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\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
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\ \ val\ inverse{\isaliteral{5F}{\isacharunderscore}}Z\ {\isaliteral{3D}{\isacharequal}}\ append{\isaliteral{5F}{\isacharunderscore}}rls\ {\isaliteral{22}{\isachardoublequote}}inverse{\isaliteral{5F}{\isacharunderscore}}Z{\isaliteral{22}{\isachardoublequote}}\ e{\isaliteral{5F}{\isacharunderscore}}rls\isanewline
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\ \ \ \ {\isaliteral{5B}{\isacharbrackleft}}\ Thm\ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}rule{\isadigit{3}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}num{\isaliteral{5F}{\isacharunderscore}}str\ %
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\isaantiq
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thm\ rule{\isadigit{3}}{}%
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\endisaantiq
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{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\isanewline
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\ \ \ \ \ \ Thm\ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}rule{\isadigit{4}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}num{\isaliteral{5F}{\isacharunderscore}}str\ %
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\isaantiq
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thm\ rule{\isadigit{4}}{}%
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\endisaantiq
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{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\isanewline
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\ \ \ \ \ \ Thm\ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}rule{\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}num{\isaliteral{5F}{\isacharunderscore}}str\ %
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\isaantiq
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thm\ rule{\isadigit{1}}{}%
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\endisaantiq
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{\isaliteral{29}{\isacharparenright}}\ \ \ \isanewline
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\ \ \ \ {\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
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\isanewline
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\ \ val\ t\ {\isaliteral{3D}{\isacharequal}}\ str{\isadigit{2}}term\ {\isaliteral{22}{\isachardoublequote}}z\ {\isaliteral{2F}{\isacharslash}}\ {\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{1}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2B}{\isacharplus}}\ z\ {\isaliteral{2F}{\isacharslash}}\ {\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{2D}{\isacharminus}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2B}{\isacharplus}}\ {\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
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\ \ val\ SOME\ {\isaliteral{28}{\isacharparenleft}}t{\isaliteral{27}{\isacharprime}}{\isaliteral{2C}{\isacharcomma}}\ asm{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ rewrite{\isaliteral{5F}{\isacharunderscore}}set{\isaliteral{5F}{\isacharunderscore}}\ thy\ true\ inverse{\isaliteral{5F}{\isacharunderscore}}Z\ t{\isaliteral{3B}{\isacharsemicolon}}\isanewline
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\ \ term{\isadigit{2}}str\ t{\isaliteral{27}{\isacharprime}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{22}{\isachardoublequote}}z\ {\isaliteral{2F}{\isacharslash}}\ {\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{2D}{\isacharminus}}\ {\isaliteral{3F}{\isacharquery}}{\isaliteral{5C3C64656C74613E}{\isasymdelta}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{3F}{\isacharquery}}n{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2B}{\isacharplus}}\ z\ {\isaliteral{2F}{\isacharslash}}\ {\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{2D}{\isacharminus}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{3F}{\isacharquery}}{\isaliteral{5C3C64656C74613E}{\isasymdelta}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{3F}{\isacharquery}}n{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
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\ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}\isanewline
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\ \ \ {\isaliteral{2A}{\isacharasterisk}}\ Attention\ rule{\isadigit{1}}\ is\ applied\ before\ the\ expression\ is\ \isanewline
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\ \ \ {\isaliteral{2A}{\isacharasterisk}}\ checked\ for\ rule{\isadigit{4}}\ which\ would\ be\ correct{\isaliteral{21}{\isacharbang}}{\isaliteral{21}{\isacharbang}}{\isaliteral{21}{\isacharbang}}\isanewline
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\ \ \ {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
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{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline
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\isanewline
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\isacommand{ML}\isamarkupfalse%
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\ {\isaliteral{7B2A}{\isacharverbatimopen}}\ val\ {\isaliteral{28}{\isacharparenleft}}thy{\isaliteral{2C}{\isacharcomma}}\ ro{\isaliteral{2C}{\isacharcomma}}\ er{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}%
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\isaantiq
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theory\ Isac{}%
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\endisaantiq
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{\isaliteral{2C}{\isacharcomma}}\ tless{\isaliteral{5F}{\isacharunderscore}}true{\isaliteral{2C}{\isacharcomma}}\ eval{\isaliteral{5F}{\isacharunderscore}}rls{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline
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\isacommand{ML}\isamarkupfalse%
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\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
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\ \ val\ SOME\ {\isaliteral{28}{\isacharparenleft}}t{\isaliteral{2C}{\isacharcomma}}\ asm{\isadigit{1}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ \isanewline
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\ \ \ \ rewrite{\isaliteral{5F}{\isacharunderscore}}\ thy\ ro\ er\ true\ {\isaliteral{28}{\isacharparenleft}}num{\isaliteral{5F}{\isacharunderscore}}str\ %
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\isaantiq
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thm\ rule{\isadigit{3}}{}%
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\endisaantiq
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{\isaliteral{29}{\isacharparenright}}\ t{\isaliteral{3B}{\isacharsemicolon}}\isanewline
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\ \ term{\isadigit{2}}str\ t\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{2D}{\isacharminus}}\ {\isaliteral{3F}{\isacharquery}}u\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{2D}{\isacharminus}}\ {\isaliteral{3F}{\isacharquery}}n\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{1}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{2B}{\isacharplus}}\ z\ {\isaliteral{2F}{\isacharslash}}\ {\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{2D}{\isacharminus}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2B}{\isacharplus}}\ {\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
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\ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{2D}{\isacharminus}}\ real\ {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
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\ \ term{\isadigit{2}}str\ t{\isaliteral{3B}{\isacharsemicolon}}\isanewline
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\isanewline
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\ \ val\ SOME\ {\isaliteral{28}{\isacharparenleft}}t{\isaliteral{2C}{\isacharcomma}}\ asm{\isadigit{2}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ \isanewline
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\ \ \ \ rewrite{\isaliteral{5F}{\isacharunderscore}}\ thy\ ro\ er\ true\ {\isaliteral{28}{\isacharparenleft}}num{\isaliteral{5F}{\isacharunderscore}}str\ %
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\isaantiq
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thm\ rule{\isadigit{4}}{}%
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\endisaantiq
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{\isaliteral{29}{\isacharparenright}}\ t{\isaliteral{3B}{\isacharsemicolon}}\isanewline
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\ \ term{\isadigit{2}}str\ t\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{2D}{\isacharminus}}\ {\isaliteral{3F}{\isacharquery}}u\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{2D}{\isacharminus}}\ {\isaliteral{3F}{\isacharquery}}n\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{1}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ {\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}\ {\isaliteral{3F}{\isacharquery}}n\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{3F}{\isacharquery}}u\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{3F}{\isacharquery}}n{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{2B}{\isacharplus}}\ {\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
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\ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{2D}{\isacharminus}}\ real\ {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
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\ \ term{\isadigit{2}}str\ t{\isaliteral{3B}{\isacharsemicolon}}\isanewline
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\isanewline
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\ \ val\ SOME\ {\isaliteral{28}{\isacharparenleft}}t{\isaliteral{2C}{\isacharcomma}}\ asm{\isadigit{3}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ \isanewline
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\ \ \ \ rewrite{\isaliteral{5F}{\isacharunderscore}}\ thy\ ro\ er\ true\ {\isaliteral{28}{\isacharparenleft}}num{\isaliteral{5F}{\isacharunderscore}}str\ %
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\isaantiq
|
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|
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thm\ rule{\isadigit{1}}{}%
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|
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\endisaantiq
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|
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{\isaliteral{29}{\isacharparenright}}\ t{\isaliteral{3B}{\isacharsemicolon}}\isanewline
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\ \ term{\isadigit{2}}str\ t\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{2D}{\isacharminus}}\ {\isaliteral{3F}{\isacharquery}}u\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{2D}{\isacharminus}}\ {\isaliteral{3F}{\isacharquery}}n\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{1}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ {\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}\ {\isaliteral{3F}{\isacharquery}}n\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{3F}{\isacharquery}}u\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{3F}{\isacharquery}}n{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{3F}{\isacharquery}}{\isaliteral{5C3C64656C74613E}{\isasymdelta}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{3F}{\isacharquery}}n{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
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\ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{2D}{\isacharminus}}\ real\ {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
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\ \ term{\isadigit{2}}str\ t{\isaliteral{3B}{\isacharsemicolon}}\isanewline
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{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline
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\isacommand{ML}\isamarkupfalse%
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\ {\isaliteral{7B2A}{\isacharverbatimopen}}\ terms{\isadigit{2}}str\ {\isaliteral{28}{\isacharparenleft}}asm{\isadigit{1}}\ {\isaliteral{40}{\isacharat}}\ asm{\isadigit{2}}\ {\isaliteral{40}{\isacharat}}\ asm{\isadigit{3}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{2A7D}{\isacharverbatimclose}}%
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\endisatagML
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{\isafoldML}%
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%
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\isadelimML
|
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%
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\endisadelimML
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%
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\isamarkupsection{Prepare Steps for TP-based programming Language\label{sec:prepstep}%
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|
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}
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|
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\isamarkuptrue%
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%
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|
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\begin{isamarkuptext}%
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|
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\par \noindent The following sections are challenging with the CTP-based
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|
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possibilities of building the program. The goal is realized in
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Section~\ref{spec-meth} and Section~\ref{prog-steps}.
|
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|
317 |
\par The reader is advised to jump between the subsequent subsections and
|
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|
318 |
the respective steps in Section~\ref{prog-steps}. By comparing
|
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|
319 |
Section~\ref{sec:calc:ztrans} the calculation can be comprehended step
|
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|
320 |
by step.%
|
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|
321 |
\end{isamarkuptext}%
|
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|
322 |
\isamarkuptrue%
|
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|
323 |
%
|
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|
324 |
\isamarkupsubsection{Prepare Expression\label{prep-expr}%
|
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|
325 |
}
|
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|
326 |
\isamarkuptrue%
|
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|
327 |
%
|
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|
328 |
\begin{isamarkuptext}%
|
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|
329 |
\noindent We try two different notations and check which of them
|
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|
330 |
Isabelle can handle best.%
|
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|
331 |
\end{isamarkuptext}%
|
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|
332 |
\isamarkuptrue%
|
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|
333 |
%
|
neuper@42289
|
334 |
\isadelimML
|
neuper@42289
|
335 |
%
|
neuper@42289
|
336 |
\endisadelimML
|
neuper@42289
|
337 |
%
|
neuper@42289
|
338 |
\isatagML
|
neuper@42289
|
339 |
\isacommand{ML}\isamarkupfalse%
|
neuper@42289
|
340 |
\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
|
neuper@48761
|
341 |
\ \ val\ ctxt\ {\isaliteral{3D}{\isacharequal}}\ Proof_Context{\isaliteral{2E}{\isachardot}}init{\isaliteral{5F}{\isacharunderscore}}global\ %
|
neuper@42289
|
342 |
\isaantiq
|
neuper@42289
|
343 |
theory\ Isac{}%
|
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|
344 |
\endisaantiq
|
jan@42368
|
345 |
{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42368
|
346 |
\ \ val\ ctxt\ {\isaliteral{3D}{\isacharequal}}\ declare{\isaliteral{5F}{\isacharunderscore}}constraints{\isaliteral{27}{\isacharprime}}\ {\isaliteral{5B}{\isacharbrackleft}}%
|
neuper@42289
|
347 |
\isaantiq
|
jan@42368
|
348 |
term\ {\isaliteral{22}{\isachardoublequote}}z{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}real{\isaliteral{22}{\isachardoublequote}}{}%
|
neuper@42289
|
349 |
\endisaantiq
|
jan@42368
|
350 |
{\isaliteral{5D}{\isacharbrackright}}\ ctxt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
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|
351 |
\isanewline
|
jan@42368
|
352 |
\ \ val\ SOME\ fun{\isadigit{1}}\ {\isaliteral{3D}{\isacharequal}}\ \isanewline
|
jan@42368
|
353 |
\ \ \ \ parseNEW\ ctxt\ {\isaliteral{22}{\isachardoublequote}}X\ z\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{3}}\ {\isaliteral{2F}{\isacharslash}}\ {\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{1}}{\isaliteral{2F}{\isacharslash}}{\isadigit{4}}\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{1}}{\isaliteral{2F}{\isacharslash}}{\isadigit{8}}\ {\isaliteral{2A}{\isacharasterisk}}\ z\ {\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{1}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\ term{\isadigit{2}}str\ fun{\isadigit{1}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42368
|
354 |
\ \ val\ SOME\ fun{\isadigit{1}}{\isaliteral{27}{\isacharprime}}\ {\isaliteral{3D}{\isacharequal}}\ \isanewline
|
jan@42368
|
355 |
\ \ \ \ parseNEW\ ctxt\ {\isaliteral{22}{\isachardoublequote}}X\ z\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{3}}\ {\isaliteral{2F}{\isacharslash}}\ {\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{1}}{\isaliteral{2F}{\isacharslash}}{\isadigit{4}}\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{1}}{\isaliteral{2F}{\isacharslash}}{\isadigit{8}}\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{1}}{\isaliteral{2F}{\isacharslash}}z{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\ term{\isadigit{2}}str\ fun{\isadigit{1}}{\isaliteral{27}{\isacharprime}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
neuper@42289
|
356 |
{\isaliteral{2A7D}{\isacharverbatimclose}}%
|
neuper@42289
|
357 |
\endisatagML
|
neuper@42289
|
358 |
{\isafoldML}%
|
neuper@42289
|
359 |
%
|
neuper@42289
|
360 |
\isadelimML
|
neuper@42289
|
361 |
%
|
neuper@42289
|
362 |
\endisadelimML
|
neuper@42289
|
363 |
%
|
jan@42368
|
364 |
\isamarkupsubsubsection{Prepare Numerator and Denominator%
|
neuper@42289
|
365 |
}
|
neuper@42289
|
366 |
\isamarkuptrue%
|
neuper@42289
|
367 |
%
|
neuper@42289
|
368 |
\begin{isamarkuptext}%
|
jan@42381
|
369 |
\noindent The partial fraction decomposition is only possible if we
|
jan@42368
|
370 |
get the bound variable out of the numerator. Therefor we divide
|
jan@42368
|
371 |
the expression by $z$. Follow up the Calculation at
|
jan@42368
|
372 |
Section~\ref{sec:calc:ztrans} line number 02.%
|
neuper@42289
|
373 |
\end{isamarkuptext}%
|
neuper@42289
|
374 |
\isamarkuptrue%
|
neuper@42289
|
375 |
\isacommand{axiomatization}\isamarkupfalse%
|
neuper@42289
|
376 |
\ \isakeyword{where}\isanewline
|
neuper@42289
|
377 |
\ \ ruleZY{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}X\ z\ {\isaliteral{3D}{\isacharequal}}\ a\ {\isaliteral{2F}{\isacharslash}}\ b{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}X{\isaliteral{27}{\isacharprime}}\ z\ {\isaliteral{3D}{\isacharequal}}\ a\ {\isaliteral{2F}{\isacharslash}}\ {\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{2A}{\isacharasterisk}}\ b{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
|
neuper@42289
|
378 |
%
|
neuper@42289
|
379 |
\isadelimML
|
neuper@42289
|
380 |
\isanewline
|
neuper@42289
|
381 |
%
|
neuper@42289
|
382 |
\endisadelimML
|
neuper@42289
|
383 |
%
|
neuper@42289
|
384 |
\isatagML
|
neuper@42289
|
385 |
\isacommand{ML}\isamarkupfalse%
|
neuper@42289
|
386 |
\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
|
jan@42368
|
387 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}thy{\isaliteral{2C}{\isacharcomma}}\ ro{\isaliteral{2C}{\isacharcomma}}\ er{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}%
|
neuper@42289
|
388 |
\isaantiq
|
neuper@42289
|
389 |
theory\ Isac{}%
|
neuper@42289
|
390 |
\endisaantiq
|
neuper@42289
|
391 |
{\isaliteral{2C}{\isacharcomma}}\ tless{\isaliteral{5F}{\isacharunderscore}}true{\isaliteral{2C}{\isacharcomma}}\ eval{\isaliteral{5F}{\isacharunderscore}}rls{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42368
|
392 |
\ \ val\ SOME\ {\isaliteral{28}{\isacharparenleft}}fun{\isadigit{2}}{\isaliteral{2C}{\isacharcomma}}\ asm{\isadigit{1}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ \isanewline
|
jan@42368
|
393 |
\ \ \ \ rewrite{\isaliteral{5F}{\isacharunderscore}}\ thy\ ro\ er\ true\ \ %
|
neuper@42289
|
394 |
\isaantiq
|
neuper@42289
|
395 |
thm\ ruleZY{}%
|
neuper@42289
|
396 |
\endisaantiq
|
neuper@42289
|
397 |
\ fun{\isadigit{1}}{\isaliteral{3B}{\isacharsemicolon}}\ term{\isadigit{2}}str\ fun{\isadigit{2}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42368
|
398 |
\ \ val\ SOME\ {\isaliteral{28}{\isacharparenleft}}fun{\isadigit{2}}{\isaliteral{27}{\isacharprime}}{\isaliteral{2C}{\isacharcomma}}\ asm{\isadigit{1}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ \isanewline
|
jan@42368
|
399 |
\ \ \ \ rewrite{\isaliteral{5F}{\isacharunderscore}}\ thy\ ro\ er\ true\ \ %
|
neuper@42289
|
400 |
\isaantiq
|
neuper@42289
|
401 |
thm\ ruleZY{}%
|
neuper@42289
|
402 |
\endisaantiq
|
neuper@42289
|
403 |
\ fun{\isadigit{1}}{\isaliteral{27}{\isacharprime}}{\isaliteral{3B}{\isacharsemicolon}}\ term{\isadigit{2}}str\ fun{\isadigit{2}}{\isaliteral{27}{\isacharprime}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
neuper@42289
|
404 |
\isanewline
|
jan@42368
|
405 |
\ \ val\ SOME\ {\isaliteral{28}{\isacharparenleft}}fun{\isadigit{3}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ \isanewline
|
jan@42368
|
406 |
\ \ \ \ rewrite{\isaliteral{5F}{\isacharunderscore}}set{\isaliteral{5F}{\isacharunderscore}}\ %
|
neuper@42289
|
407 |
\isaantiq
|
neuper@42289
|
408 |
theory\ Isac{}%
|
neuper@42289
|
409 |
\endisaantiq
|
neuper@42289
|
410 |
\ false\ norm{\isaliteral{5F}{\isacharunderscore}}Rational\ fun{\isadigit{2}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42368
|
411 |
\ \ term{\isadigit{2}}str\ fun{\isadigit{3}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42368
|
412 |
\ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}\isanewline
|
jan@42368
|
413 |
\ \ \ {\isaliteral{2A}{\isacharasterisk}}\ Fails\ on\ x{\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{2D}{\isacharminus}}{\isadigit{1}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42368
|
414 |
\ \ \ {\isaliteral{2A}{\isacharasterisk}}\ We\ solve\ this\ problem\ by\ using\ {\isadigit{1}}{\isaliteral{2F}{\isacharslash}}x\ as\ a\ workaround{\isaliteral{2E}{\isachardot}}\isanewline
|
jan@42368
|
415 |
\ \ \ {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42368
|
416 |
\ \ val\ SOME\ {\isaliteral{28}{\isacharparenleft}}fun{\isadigit{3}}{\isaliteral{27}{\isacharprime}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ \isanewline
|
jan@42368
|
417 |
\ \ \ \ rewrite{\isaliteral{5F}{\isacharunderscore}}set{\isaliteral{5F}{\isacharunderscore}}\ %
|
neuper@42289
|
418 |
\isaantiq
|
neuper@42289
|
419 |
theory\ Isac{}%
|
neuper@42289
|
420 |
\endisaantiq
|
neuper@42289
|
421 |
\ false\ norm{\isaliteral{5F}{\isacharunderscore}}Rational\ fun{\isadigit{2}}{\isaliteral{27}{\isacharprime}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42368
|
422 |
\ \ term{\isadigit{2}}str\ fun{\isadigit{3}}{\isaliteral{27}{\isacharprime}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42368
|
423 |
\ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}\isanewline
|
jan@42368
|
424 |
\ \ \ {\isaliteral{2A}{\isacharasterisk}}\ OK\ {\isaliteral{2D}{\isacharminus}}\ workaround{\isaliteral{21}{\isacharbang}}\isanewline
|
jan@42368
|
425 |
\ \ \ {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42296
|
426 |
{\isaliteral{2A7D}{\isacharverbatimclose}}%
|
jan@42296
|
427 |
\endisatagML
|
jan@42296
|
428 |
{\isafoldML}%
|
jan@42296
|
429 |
%
|
jan@42296
|
430 |
\isadelimML
|
jan@42296
|
431 |
%
|
jan@42296
|
432 |
\endisadelimML
|
jan@42296
|
433 |
%
|
jan@42368
|
434 |
\isamarkupsubsubsection{Get the Argument of the Expression X'%
|
neuper@42304
|
435 |
}
|
neuper@42304
|
436 |
\isamarkuptrue%
|
neuper@42304
|
437 |
%
|
neuper@42304
|
438 |
\begin{isamarkuptext}%
|
jan@42368
|
439 |
\noindent We use \texttt{grep} for finding possibilities how we can
|
walther@59603
|
440 |
extract the bound variable in the expression. \ttfamily Prog_Expr.thy,
|
jan@42368
|
441 |
Tools.thy \normalfont contain general utilities: \ttfamily
|
jan@42368
|
442 |
eval\_argument\_in, eval\_rhs, eval\_lhs,\ldots \normalfont
|
jan@42368
|
443 |
\ttfamily grep -r "fun eva\_" * \normalfont shows all functions
|
jan@42368
|
444 |
witch can be used in a script. Lookup this files how to build
|
jan@42368
|
445 |
and handle such functions.
|
jan@42368
|
446 |
\par The next section shows how to introduce such a function.%
|
neuper@42304
|
447 |
\end{isamarkuptext}%
|
neuper@42304
|
448 |
\isamarkuptrue%
|
neuper@42304
|
449 |
%
|
jan@42370
|
450 |
\isamarkupsubsubsection{Decompose the Given Term Into lhs and rhs%
|
jan@42296
|
451 |
}
|
jan@42296
|
452 |
\isamarkuptrue%
|
jan@42296
|
453 |
%
|
jan@42296
|
454 |
\isadelimML
|
jan@42296
|
455 |
%
|
jan@42296
|
456 |
\endisadelimML
|
jan@42296
|
457 |
%
|
jan@42296
|
458 |
\isatagML
|
jan@42296
|
459 |
\isacommand{ML}\isamarkupfalse%
|
jan@42296
|
460 |
\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
|
neuper@42304
|
461 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}\ expr{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ HOLogic{\isaliteral{2E}{\isachardot}}dest{\isaliteral{5F}{\isacharunderscore}}eq\ fun{\isadigit{3}}{\isaliteral{27}{\isacharprime}}{\isaliteral{3B}{\isacharsemicolon}}\ term{\isadigit{2}}str\ expr{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42368
|
462 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}\ denom{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ \isanewline
|
jan@42368
|
463 |
\ \ \ \ HOLogic{\isaliteral{2E}{\isachardot}}dest{\isaliteral{5F}{\isacharunderscore}}bin\ {\isaliteral{22}{\isachardoublequote}}Rings{\isaliteral{2E}{\isachardot}}inverse{\isaliteral{5F}{\isacharunderscore}}class{\isaliteral{2E}{\isachardot}}divide{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{28}{\isacharparenleft}}type{\isaliteral{5F}{\isacharunderscore}}of\ expr{\isaliteral{29}{\isacharparenright}}\ expr{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
neuper@42304
|
464 |
\ \ term{\isadigit{2}}str\ denom\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{2D}{\isacharminus}}{\isadigit{1}}\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{2}}\ {\isaliteral{2A}{\isacharasterisk}}\ z\ {\isaliteral{2B}{\isacharplus}}\ {\isadigit{8}}\ {\isaliteral{2A}{\isacharasterisk}}\ z\ {\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}\ {\isadigit{2}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42296
|
465 |
{\isaliteral{2A7D}{\isacharverbatimclose}}%
|
jan@42296
|
466 |
\endisatagML
|
jan@42296
|
467 |
{\isafoldML}%
|
jan@42296
|
468 |
%
|
jan@42296
|
469 |
\isadelimML
|
jan@42296
|
470 |
%
|
jan@42296
|
471 |
\endisadelimML
|
jan@42296
|
472 |
%
|
jan@42296
|
473 |
\begin{isamarkuptext}%
|
jan@42370
|
474 |
\noindent We have rhs\footnote{Note: lhs means \em Left Hand Side
|
jan@42370
|
475 |
\normalfont and rhs means \em Right Hand Side \normalfont and indicates
|
wneuper@59585
|
476 |
the left or the right part of an equation.} in the Program language, but
|
jan@42370
|
477 |
we need a function which gets the denominator of a fraction.%
|
jan@42296
|
478 |
\end{isamarkuptext}%
|
jan@42296
|
479 |
\isamarkuptrue%
|
jan@42296
|
480 |
%
|
jan@42368
|
481 |
\isamarkupsubsubsection{Get the Denominator and Numerator out of a Fraction%
|
neuper@42304
|
482 |
}
|
neuper@42304
|
483 |
\isamarkuptrue%
|
neuper@42304
|
484 |
%
|
neuper@42304
|
485 |
\begin{isamarkuptext}%
|
jan@42381
|
486 |
\noindent The self written functions in e.g. \texttt{get\_denominator}
|
jan@42381
|
487 |
should become a constant for the Isabelle parser:%
|
neuper@42304
|
488 |
\end{isamarkuptext}%
|
neuper@42304
|
489 |
\isamarkuptrue%
|
neuper@42304
|
490 |
\isacommand{consts}\isamarkupfalse%
|
neuper@42304
|
491 |
\isanewline
|
jan@42365
|
492 |
\ \ get{\isaliteral{5F}{\isacharunderscore}}denominator\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}real\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\ real{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
|
jan@42365
|
493 |
\ \ get{\isaliteral{5F}{\isacharunderscore}}numerator\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}real\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\ real{\isaliteral{22}{\isachardoublequoteclose}}%
|
neuper@42304
|
494 |
\begin{isamarkuptext}%
|
jan@42368
|
495 |
\noindent With the above definition we run into problems when we parse
|
wneuper@59585
|
496 |
the Program \texttt{InverseZTransform}. This leads to \em ambiguous
|
jan@42368
|
497 |
parse trees. \normalfont We avoid this by moving the definition
|
jan@42369
|
498 |
to \ttfamily Rational.thy \normalfont and re-building {\sisac}.
|
jan@42368
|
499 |
\par \noindent ATTENTION: From now on \ttfamily
|
jan@42368
|
500 |
Build\_Inverse\_Z\_Transform \normalfont mimics a build from scratch;
|
jan@42369
|
501 |
it only works due to re-building {\sisac} several times (indicated
|
jan@42381
|
502 |
explicitly).%
|
neuper@42304
|
503 |
\end{isamarkuptext}%
|
neuper@42304
|
504 |
\isamarkuptrue%
|
neuper@42304
|
505 |
%
|
jan@42296
|
506 |
\isadelimML
|
jan@42296
|
507 |
%
|
jan@42296
|
508 |
\endisadelimML
|
jan@42296
|
509 |
%
|
jan@42296
|
510 |
\isatagML
|
jan@42296
|
511 |
\isacommand{ML}\isamarkupfalse%
|
jan@42296
|
512 |
\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
|
jan@42368
|
513 |
{\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}\isanewline
|
jan@42368
|
514 |
\ {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}get{\isaliteral{5F}{\isacharunderscore}}denominator{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\isanewline
|
jan@42368
|
515 |
\ {\isaliteral{2A}{\isacharasterisk}}\ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}Rational{\isaliteral{2E}{\isachardot}}get{\isaliteral{5F}{\isacharunderscore}}denominator{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ eval{\isaliteral{5F}{\isacharunderscore}}get{\isaliteral{5F}{\isacharunderscore}}denominator\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42368
|
516 |
\ {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
neuper@42304
|
517 |
fun\ eval{\isaliteral{5F}{\isacharunderscore}}get{\isaliteral{5F}{\isacharunderscore}}denominator\ {\isaliteral{28}{\isacharparenleft}}thmid{\isaliteral{3A}{\isacharcolon}}string{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5F}{\isacharunderscore}}\ \isanewline
|
neuper@42304
|
518 |
\ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}t\ as\ Const\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}Rational{\isaliteral{2E}{\isachardot}}get{\isaliteral{5F}{\isacharunderscore}}denominator{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5F}{\isacharunderscore}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{24}{\isachardollar}}\isanewline
|
jan@42369
|
519 |
\ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}Const\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}Rings{\isaliteral{2E}{\isachardot}}inverse{\isaliteral{5F}{\isacharunderscore}}class{\isaliteral{2E}{\isachardot}}divide{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5F}{\isacharunderscore}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{24}{\isachardollar}}num\ \isanewline
|
jan@42369
|
520 |
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{24}{\isachardollar}}denom{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ thy\ {\isaliteral{3D}{\isacharequal}}\ \isanewline
|
neuper@42304
|
521 |
\ \ \ \ \ \ \ \ SOME\ {\isaliteral{28}{\isacharparenleft}}mk{\isaliteral{5F}{\isacharunderscore}}thmid\ thmid\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{22}{\isachardoublequote}}\ \isanewline
|
jan@42368
|
522 |
\ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}Print{\isaliteral{5F}{\isacharunderscore}}Mode{\isaliteral{2E}{\isachardot}}setmp\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ \isanewline
|
jan@42368
|
523 |
\ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}Syntax{\isaliteral{2E}{\isachardot}}string{\isaliteral{5F}{\isacharunderscore}}of{\isaliteral{5F}{\isacharunderscore}}term\ {\isaliteral{28}{\isacharparenleft}}thy{\isadigit{2}}ctxt\ thy{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ denom{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ \isanewline
|
neuper@42304
|
524 |
\ \ \ \ \ \ \ \ \ \ Trueprop\ {\isaliteral{24}{\isachardollar}}\ {\isaliteral{28}{\isacharparenleft}}mk{\isaliteral{5F}{\isacharunderscore}}equality\ {\isaliteral{28}{\isacharparenleft}}t{\isaliteral{2C}{\isacharcomma}}\ denom{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
neuper@42304
|
525 |
\ \ {\isaliteral{7C}{\isacharbar}}\ eval{\isaliteral{5F}{\isacharunderscore}}get{\isaliteral{5F}{\isacharunderscore}}denominator\ {\isaliteral{5F}{\isacharunderscore}}\ {\isaliteral{5F}{\isacharunderscore}}\ {\isaliteral{5F}{\isacharunderscore}}\ {\isaliteral{5F}{\isacharunderscore}}\ {\isaliteral{3D}{\isacharequal}}\ NONE{\isaliteral{3B}{\isacharsemicolon}}\ \isanewline
|
neuper@42304
|
526 |
{\isaliteral{2A7D}{\isacharverbatimclose}}%
|
neuper@42289
|
527 |
\endisatagML
|
neuper@42289
|
528 |
{\isafoldML}%
|
neuper@42289
|
529 |
%
|
neuper@42289
|
530 |
\isadelimML
|
neuper@42289
|
531 |
%
|
neuper@42289
|
532 |
\endisadelimML
|
neuper@42289
|
533 |
%
|
neuper@42304
|
534 |
\begin{isamarkuptext}%
|
jan@42369
|
535 |
\noindent For the tests of \ttfamily eval\_get\_denominator \normalfont
|
jan@42369
|
536 |
see \ttfamily test/Knowledge/rational.sml\normalfont%
|
neuper@42304
|
537 |
\end{isamarkuptext}%
|
neuper@42304
|
538 |
\isamarkuptrue%
|
neuper@42304
|
539 |
%
|
neuper@42304
|
540 |
\begin{isamarkuptext}%
|
jan@42369
|
541 |
\noindent \ttfamily get\_numerator \normalfont should also become a
|
jan@42381
|
542 |
constant for the Isabelle parser, follow up the \texttt{const}
|
jan@42381
|
543 |
declaration above.%
|
neuper@42304
|
544 |
\end{isamarkuptext}%
|
neuper@42304
|
545 |
\isamarkuptrue%
|
neuper@42304
|
546 |
%
|
jan@42339
|
547 |
\isadelimML
|
jan@42339
|
548 |
%
|
jan@42339
|
549 |
\endisadelimML
|
jan@42339
|
550 |
%
|
jan@42339
|
551 |
\isatagML
|
jan@42339
|
552 |
\isacommand{ML}\isamarkupfalse%
|
jan@42339
|
553 |
\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
|
jan@42369
|
554 |
{\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}\isanewline
|
jan@42369
|
555 |
\ {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}get{\isaliteral{5F}{\isacharunderscore}}numerator{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\isanewline
|
jan@42369
|
556 |
\ {\isaliteral{2A}{\isacharasterisk}}\ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}Rational{\isaliteral{2E}{\isachardot}}get{\isaliteral{5F}{\isacharunderscore}}numerator{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ eval{\isaliteral{5F}{\isacharunderscore}}get{\isaliteral{5F}{\isacharunderscore}}numerator\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42369
|
557 |
\ {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42339
|
558 |
fun\ eval{\isaliteral{5F}{\isacharunderscore}}get{\isaliteral{5F}{\isacharunderscore}}numerator\ {\isaliteral{28}{\isacharparenleft}}thmid{\isaliteral{3A}{\isacharcolon}}string{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5F}{\isacharunderscore}}\ \isanewline
|
jan@42339
|
559 |
\ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}t\ as\ Const\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}Rational{\isaliteral{2E}{\isachardot}}get{\isaliteral{5F}{\isacharunderscore}}numerator{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5F}{\isacharunderscore}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{24}{\isachardollar}}\isanewline
|
jan@42339
|
560 |
\ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}Const\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}Rings{\isaliteral{2E}{\isachardot}}inverse{\isaliteral{5F}{\isacharunderscore}}class{\isaliteral{2E}{\isachardot}}divide{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5F}{\isacharunderscore}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{24}{\isachardollar}}num\isanewline
|
jan@42339
|
561 |
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{24}{\isachardollar}}denom\ {\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ thy\ {\isaliteral{3D}{\isacharequal}}\ \isanewline
|
jan@42339
|
562 |
\ \ \ \ \ \ \ \ SOME\ {\isaliteral{28}{\isacharparenleft}}mk{\isaliteral{5F}{\isacharunderscore}}thmid\ thmid\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{22}{\isachardoublequote}}\ \isanewline
|
jan@42369
|
563 |
\ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}Print{\isaliteral{5F}{\isacharunderscore}}Mode{\isaliteral{2E}{\isachardot}}setmp\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ \isanewline
|
jan@42369
|
564 |
\ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}Syntax{\isaliteral{2E}{\isachardot}}string{\isaliteral{5F}{\isacharunderscore}}of{\isaliteral{5F}{\isacharunderscore}}term\ {\isaliteral{28}{\isacharparenleft}}thy{\isadigit{2}}ctxt\ thy{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ num{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ \isanewline
|
jan@42339
|
565 |
\ \ \ \ \ \ \ \ \ \ Trueprop\ {\isaliteral{24}{\isachardollar}}\ {\isaliteral{28}{\isacharparenleft}}mk{\isaliteral{5F}{\isacharunderscore}}equality\ {\isaliteral{28}{\isacharparenleft}}t{\isaliteral{2C}{\isacharcomma}}\ num{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42339
|
566 |
\ \ {\isaliteral{7C}{\isacharbar}}\ eval{\isaliteral{5F}{\isacharunderscore}}get{\isaliteral{5F}{\isacharunderscore}}numerator\ {\isaliteral{5F}{\isacharunderscore}}\ {\isaliteral{5F}{\isacharunderscore}}\ {\isaliteral{5F}{\isacharunderscore}}\ {\isaliteral{5F}{\isacharunderscore}}\ {\isaliteral{3D}{\isacharequal}}\ NONE{\isaliteral{3B}{\isacharsemicolon}}\ \isanewline
|
jan@42339
|
567 |
{\isaliteral{2A7D}{\isacharverbatimclose}}%
|
jan@42339
|
568 |
\endisatagML
|
jan@42339
|
569 |
{\isafoldML}%
|
jan@42339
|
570 |
%
|
jan@42339
|
571 |
\isadelimML
|
jan@42339
|
572 |
%
|
jan@42339
|
573 |
\endisadelimML
|
jan@42339
|
574 |
%
|
jan@42365
|
575 |
\begin{isamarkuptext}%
|
jan@42381
|
576 |
\noindent We discovered several problems by implementing the
|
jan@42369
|
577 |
\ttfamily get\_numerator \normalfont function. Remember when
|
jan@42369
|
578 |
putting new functions to {\sisac}, put them in a thy file and rebuild
|
jan@42369
|
579 |
{\sisac}, also put them in the ruleset for the script!%
|
jan@42365
|
580 |
\end{isamarkuptext}%
|
jan@42365
|
581 |
\isamarkuptrue%
|
jan@42365
|
582 |
%
|
jan@42369
|
583 |
\isamarkupsubsection{Solve Equation\label{sec:solveq}%
|
neuper@42289
|
584 |
}
|
neuper@42289
|
585 |
\isamarkuptrue%
|
neuper@42289
|
586 |
%
|
neuper@42289
|
587 |
\begin{isamarkuptext}%
|
jan@42369
|
588 |
\noindent We have to find the zeros of the term, therefor we use our
|
jan@42369
|
589 |
\ttfamily get\_denominator \normalfont function from the step before
|
jan@42381
|
590 |
and try to solve the second order equation. (Follow up the Calculation
|
jan@42369
|
591 |
in Section~\ref{sec:calc:ztrans} Subproblem 2) Note: This type of
|
jan@42369
|
592 |
equation is too general for the present program.
|
jan@42369
|
593 |
\par We know that this equation can be categorized as \em univariate
|
jan@42369
|
594 |
equation \normalfont and solved with the functions {\sisac} provides
|
jan@42369
|
595 |
for this equation type. Later on {\sisac} should determine the type
|
jan@42369
|
596 |
of the given equation self.%
|
neuper@42289
|
597 |
\end{isamarkuptext}%
|
neuper@42289
|
598 |
\isamarkuptrue%
|
neuper@42289
|
599 |
%
|
neuper@42289
|
600 |
\isadelimML
|
neuper@42289
|
601 |
%
|
neuper@42289
|
602 |
\endisadelimML
|
neuper@42289
|
603 |
%
|
neuper@42289
|
604 |
\isatagML
|
neuper@42289
|
605 |
\isacommand{ML}\isamarkupfalse%
|
neuper@42289
|
606 |
\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
|
jan@42369
|
607 |
\ \ val\ denominator\ {\isaliteral{3D}{\isacharequal}}\ parseNEW\ ctxt\ {\isaliteral{22}{\isachardoublequote}}z{\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}{\isadigit{2}}\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{1}}{\isaliteral{2F}{\isacharslash}}{\isadigit{4}}{\isaliteral{2A}{\isacharasterisk}}z\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{1}}{\isaliteral{2F}{\isacharslash}}{\isadigit{8}}\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{0}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
608 |
\ \ val\ fmz\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}equality\ {\isaliteral{28}{\isacharparenleft}}z{\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}{\isadigit{2}}\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{1}}{\isaliteral{2F}{\isacharslash}}{\isadigit{4}}{\isaliteral{2A}{\isacharasterisk}}z\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{1}}{\isaliteral{2F}{\isacharslash}}{\isadigit{8}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{0}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}real{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\isanewline
|
jan@42369
|
609 |
\ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}solveFor\ z{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\isanewline
|
jan@42369
|
610 |
\ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}solutions\ L{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
611 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}dI{\isaliteral{27}{\isacharprime}}{\isaliteral{2C}{\isacharcomma}}pI{\isaliteral{27}{\isacharprime}}{\isaliteral{2C}{\isacharcomma}}mI{\isaliteral{27}{\isacharprime}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}Isac{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}univariate{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}equation{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}no{\isaliteral{5F}{\isacharunderscore}}met{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
neuper@42289
|
612 |
{\isaliteral{2A7D}{\isacharverbatimclose}}%
|
neuper@42289
|
613 |
\endisatagML
|
neuper@42289
|
614 |
{\isafoldML}%
|
neuper@42289
|
615 |
%
|
neuper@42289
|
616 |
\isadelimML
|
neuper@42289
|
617 |
%
|
neuper@42289
|
618 |
\endisadelimML
|
neuper@42289
|
619 |
%
|
neuper@42289
|
620 |
\begin{isamarkuptext}%
|
jan@42369
|
621 |
\noindent Check if the given equation matches the specification of this
|
jan@42381
|
622 |
equation type.%
|
neuper@42289
|
623 |
\end{isamarkuptext}%
|
neuper@42289
|
624 |
\isamarkuptrue%
|
neuper@42289
|
625 |
%
|
neuper@42289
|
626 |
\isadelimML
|
neuper@42289
|
627 |
%
|
neuper@42289
|
628 |
\endisadelimML
|
neuper@42289
|
629 |
%
|
neuper@42289
|
630 |
\isatagML
|
neuper@42289
|
631 |
\isacommand{ML}\isamarkupfalse%
|
neuper@42289
|
632 |
\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
|
jan@42369
|
633 |
\ \ match{\isaliteral{5F}{\isacharunderscore}}pbl\ fmz\ {\isaliteral{28}{\isacharparenleft}}get{\isaliteral{5F}{\isacharunderscore}}pbt\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}univariate{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}equation{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
neuper@42289
|
634 |
{\isaliteral{2A7D}{\isacharverbatimclose}}%
|
neuper@42289
|
635 |
\endisatagML
|
neuper@42289
|
636 |
{\isafoldML}%
|
neuper@42289
|
637 |
%
|
neuper@42289
|
638 |
\isadelimML
|
neuper@42289
|
639 |
%
|
neuper@42289
|
640 |
\endisadelimML
|
neuper@42289
|
641 |
%
|
neuper@42289
|
642 |
\begin{isamarkuptext}%
|
jan@42369
|
643 |
\noindent We switch up to the {\sisac} Context and try to solve the
|
jan@42369
|
644 |
equation with a more specific type definition.%
|
neuper@42289
|
645 |
\end{isamarkuptext}%
|
neuper@42289
|
646 |
\isamarkuptrue%
|
neuper@42289
|
647 |
%
|
neuper@42289
|
648 |
\isadelimML
|
neuper@42289
|
649 |
%
|
neuper@42289
|
650 |
\endisadelimML
|
neuper@42289
|
651 |
%
|
neuper@42289
|
652 |
\isatagML
|
neuper@42289
|
653 |
\isacommand{ML}\isamarkupfalse%
|
neuper@42289
|
654 |
\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
|
jan@42369
|
655 |
\ \ Context{\isaliteral{2E}{\isachardot}}theory{\isaliteral{5F}{\isacharunderscore}}name\ thy\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{22}{\isachardoublequote}}Isac{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
656 |
\ \ val\ denominator\ {\isaliteral{3D}{\isacharequal}}\ parseNEW\ ctxt\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{2D}{\isacharminus}}{\isadigit{1}}\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{2}}\ {\isaliteral{2A}{\isacharasterisk}}\ z\ {\isaliteral{2B}{\isacharplus}}\ {\isadigit{8}}\ {\isaliteral{2A}{\isacharasterisk}}\ z\ {\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}\ {\isadigit{2}}\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{0}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
657 |
\ \ val\ fmz\ {\isaliteral{3D}{\isacharequal}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}specification{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42369
|
658 |
\ \ \ \ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}equality\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2D}{\isacharminus}}{\isadigit{1}}\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{2}}\ {\isaliteral{2A}{\isacharasterisk}}\ z\ {\isaliteral{2B}{\isacharplus}}\ {\isadigit{8}}\ {\isaliteral{2A}{\isacharasterisk}}\ z\ {\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}\ {\isadigit{2}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{0}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}real{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}equality{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42369
|
659 |
\ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}solveFor\ z{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}bound\ variable{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42369
|
660 |
\ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}solutions\ L{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3B}{\isacharsemicolon}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}identifier\ for\isanewline
|
jan@42369
|
661 |
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ solution{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42369
|
662 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}dI{\isaliteral{27}{\isacharprime}}{\isaliteral{2C}{\isacharcomma}}pI{\isaliteral{27}{\isacharprime}}{\isaliteral{2C}{\isacharcomma}}mI{\isaliteral{27}{\isacharprime}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\isanewline
|
jan@42369
|
663 |
\ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}Isac{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ \isanewline
|
jan@42369
|
664 |
\ \ \ \ \ \ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}abcFormula{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}degree{\isaliteral{5F}{\isacharunderscore}}{\isadigit{2}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}polynomial{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}univariate{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}equation{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\isanewline
|
jan@42369
|
665 |
\ \ \ \ \ \ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}no{\isaliteral{5F}{\isacharunderscore}}met{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
neuper@42289
|
666 |
{\isaliteral{2A7D}{\isacharverbatimclose}}%
|
neuper@42289
|
667 |
\endisatagML
|
neuper@42289
|
668 |
{\isafoldML}%
|
neuper@42289
|
669 |
%
|
neuper@42289
|
670 |
\isadelimML
|
neuper@42289
|
671 |
%
|
neuper@42289
|
672 |
\endisadelimML
|
neuper@42289
|
673 |
%
|
neuper@42289
|
674 |
\begin{isamarkuptext}%
|
jan@42369
|
675 |
\noindent Check if the (other) given equation matches the
|
jan@42381
|
676 |
specification of this equation type.%
|
neuper@42289
|
677 |
\end{isamarkuptext}%
|
neuper@42289
|
678 |
\isamarkuptrue%
|
neuper@42289
|
679 |
%
|
neuper@42289
|
680 |
\isadelimML
|
neuper@42289
|
681 |
%
|
neuper@42289
|
682 |
\endisadelimML
|
neuper@42289
|
683 |
%
|
neuper@42289
|
684 |
\isatagML
|
neuper@42289
|
685 |
\isacommand{ML}\isamarkupfalse%
|
neuper@42289
|
686 |
\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
|
jan@42369
|
687 |
\ \ match{\isaliteral{5F}{\isacharunderscore}}pbl\ fmz\ {\isaliteral{28}{\isacharparenleft}}get{\isaliteral{5F}{\isacharunderscore}}pbt\ \isanewline
|
jan@42369
|
688 |
\ \ \ \ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}abcFormula{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}degree{\isaliteral{5F}{\isacharunderscore}}{\isadigit{2}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}polynomial{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}univariate{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}equation{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
neuper@42289
|
689 |
{\isaliteral{2A7D}{\isacharverbatimclose}}%
|
neuper@42289
|
690 |
\endisatagML
|
neuper@42289
|
691 |
{\isafoldML}%
|
neuper@42289
|
692 |
%
|
neuper@42289
|
693 |
\isadelimML
|
neuper@42289
|
694 |
%
|
neuper@42289
|
695 |
\endisadelimML
|
neuper@42289
|
696 |
%
|
neuper@42289
|
697 |
\begin{isamarkuptext}%
|
jan@42369
|
698 |
\noindent We stepwise solve the equation. This is done by the
|
jan@42369
|
699 |
use of a so called calc tree seen downwards.%
|
neuper@42289
|
700 |
\end{isamarkuptext}%
|
neuper@42289
|
701 |
\isamarkuptrue%
|
neuper@42289
|
702 |
%
|
neuper@42289
|
703 |
\isadelimML
|
neuper@42289
|
704 |
%
|
neuper@42289
|
705 |
\endisadelimML
|
neuper@42289
|
706 |
%
|
neuper@42289
|
707 |
\isatagML
|
neuper@42289
|
708 |
\isacommand{ML}\isamarkupfalse%
|
neuper@42289
|
709 |
\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
|
jan@42369
|
710 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ CalcTreeTEST\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{28}{\isacharparenleft}}fmz{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{28}{\isacharparenleft}}dI{\isaliteral{27}{\isacharprime}}{\isaliteral{2C}{\isacharcomma}}pI{\isaliteral{27}{\isacharprime}}{\isaliteral{2C}{\isacharcomma}}mI{\isaliteral{27}{\isacharprime}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
711 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
712 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
713 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
714 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
715 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
716 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
717 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
718 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
719 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
720 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
721 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\ \ \ \ \ \ \ \ \ \isanewline
|
jan@42369
|
722 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
723 |
\ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}\isanewline
|
jan@42369
|
724 |
\ \ \ {\isaliteral{2A}{\isacharasterisk}}\ nxt\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}{\isaliteral{2C}{\isacharcomma}}Check{\isaliteral{5F}{\isacharunderscore}}elementwise\ {\isaliteral{22}{\isachardoublequote}}Assumptions{\isaliteral{22}{\isachardoublequote}}{\isaliteral{29}{\isacharparenright}}\ \isanewline
|
jan@42369
|
725 |
\ \ \ {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42369
|
726 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\ \ \ \ \ \ \ \ \ \isanewline
|
jan@42369
|
727 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\ f{\isadigit{2}}str\ f{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
728 |
\ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}\isanewline
|
jan@42369
|
729 |
\ \ \ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{5B}{\isacharbrackleft}}z\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{1}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{2}}{\isaliteral{2C}{\isacharcomma}}\ z\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{1}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{4}}{\isaliteral{5D}{\isacharbrackright}}\isanewline
|
jan@42369
|
730 |
\ \ \ {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42369
|
731 |
\ \ show{\isaliteral{5F}{\isacharunderscore}}pt\ pt{\isaliteral{3B}{\isacharsemicolon}}\ \isanewline
|
jan@42369
|
732 |
\ \ val\ SOME\ f\ {\isaliteral{3D}{\isacharequal}}\ parseNEW\ ctxt\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5B}{\isacharbrackleft}}z{\isaliteral{3D}{\isacharequal}}{\isadigit{1}}{\isaliteral{2F}{\isacharslash}}{\isadigit{2}}{\isaliteral{2C}{\isacharcomma}}\ z{\isaliteral{3D}{\isacharequal}}{\isaliteral{2D}{\isacharminus}}{\isadigit{1}}{\isaliteral{2F}{\isacharslash}}{\isadigit{4}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
neuper@42289
|
733 |
{\isaliteral{2A7D}{\isacharverbatimclose}}%
|
neuper@42289
|
734 |
\endisatagML
|
neuper@42289
|
735 |
{\isafoldML}%
|
neuper@42289
|
736 |
%
|
neuper@42289
|
737 |
\isadelimML
|
neuper@42289
|
738 |
%
|
neuper@42289
|
739 |
\endisadelimML
|
neuper@42289
|
740 |
%
|
jan@42369
|
741 |
\isamarkupsubsection{Partial Fraction Decomposition\label{sec:pbz}%
|
jan@42369
|
742 |
}
|
jan@42369
|
743 |
\isamarkuptrue%
|
jan@42369
|
744 |
%
|
jan@42339
|
745 |
\begin{isamarkuptext}%
|
jan@42381
|
746 |
\noindent We go on with the decomposition of our expression. Follow up the
|
jan@42369
|
747 |
Calculation in Section~\ref{sec:calc:ztrans} Step~3 and later on
|
jan@42369
|
748 |
Subproblem~1.%
|
jan@42369
|
749 |
\end{isamarkuptext}%
|
jan@42369
|
750 |
\isamarkuptrue%
|
jan@42369
|
751 |
%
|
jan@42369
|
752 |
\isamarkupsubsubsection{Solutions of the Equation%
|
jan@42369
|
753 |
}
|
jan@42369
|
754 |
\isamarkuptrue%
|
jan@42369
|
755 |
%
|
jan@42369
|
756 |
\begin{isamarkuptext}%
|
jan@42369
|
757 |
\noindent We get the solutions of the before solved equation in a list.%
|
jan@42339
|
758 |
\end{isamarkuptext}%
|
jan@42339
|
759 |
\isamarkuptrue%
|
jan@42339
|
760 |
%
|
jan@42339
|
761 |
\isadelimML
|
jan@42339
|
762 |
%
|
jan@42339
|
763 |
\endisadelimML
|
jan@42339
|
764 |
%
|
jan@42339
|
765 |
\isatagML
|
jan@42339
|
766 |
\isacommand{ML}\isamarkupfalse%
|
jan@42339
|
767 |
\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
|
jan@42369
|
768 |
\ \ val\ SOME\ solutions\ {\isaliteral{3D}{\isacharequal}}\ parseNEW\ ctxt\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5B}{\isacharbrackleft}}z{\isaliteral{3D}{\isacharequal}}{\isadigit{1}}{\isaliteral{2F}{\isacharslash}}{\isadigit{2}}{\isaliteral{2C}{\isacharcomma}}\ z{\isaliteral{3D}{\isacharequal}}{\isaliteral{2D}{\isacharminus}}{\isadigit{1}}{\isaliteral{2F}{\isacharslash}}{\isadigit{4}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
769 |
\ \ term{\isadigit{2}}str\ solutions{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
770 |
\ \ atomty\ solutions{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42339
|
771 |
{\isaliteral{2A7D}{\isacharverbatimclose}}%
|
jan@42339
|
772 |
\endisatagML
|
jan@42339
|
773 |
{\isafoldML}%
|
jan@42339
|
774 |
%
|
jan@42339
|
775 |
\isadelimML
|
jan@42339
|
776 |
%
|
jan@42339
|
777 |
\endisadelimML
|
jan@42339
|
778 |
%
|
jan@42369
|
779 |
\isamarkupsubsubsection{Get Solutions out of a List%
|
jan@42369
|
780 |
}
|
jan@42369
|
781 |
\isamarkuptrue%
|
jan@42369
|
782 |
%
|
jan@42339
|
783 |
\begin{isamarkuptext}%
|
jan@42381
|
784 |
\noindent In {\sisac}'s TP-based programming language:
|
jan@42381
|
785 |
\begin{verbatim}
|
jan@42381
|
786 |
let $ $ s_1 = NTH 1 $ solutions; $ s_2 = NTH 2... $
|
jan@42381
|
787 |
\end{verbatim}
|
jan@42381
|
788 |
can be useful.%
|
jan@42339
|
789 |
\end{isamarkuptext}%
|
jan@42339
|
790 |
\isamarkuptrue%
|
jan@42339
|
791 |
%
|
jan@42339
|
792 |
\isadelimML
|
jan@42339
|
793 |
%
|
jan@42339
|
794 |
\endisadelimML
|
jan@42339
|
795 |
%
|
jan@42339
|
796 |
\isatagML
|
jan@42339
|
797 |
\isacommand{ML}\isamarkupfalse%
|
jan@42339
|
798 |
\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
|
jan@42369
|
799 |
\ \ val\ Const\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}List{\isaliteral{2E}{\isachardot}}list{\isaliteral{2E}{\isachardot}}Cons{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5F}{\isacharunderscore}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{24}{\isachardollar}}\ s{\isaliteral{5F}{\isacharunderscore}}{\isadigit{1}}\ {\isaliteral{24}{\isachardollar}}\ {\isaliteral{28}{\isacharparenleft}}Const\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}List{\isaliteral{2E}{\isachardot}}list{\isaliteral{2E}{\isachardot}}Cons{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5F}{\isacharunderscore}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42369
|
800 |
\ \ \ \ \ \ \ \ {\isaliteral{24}{\isachardollar}}\ s{\isaliteral{5F}{\isacharunderscore}}{\isadigit{2}}\ {\isaliteral{24}{\isachardollar}}\ Const\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}List{\isaliteral{2E}{\isachardot}}list{\isaliteral{2E}{\isachardot}}Nil{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5F}{\isacharunderscore}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ solutions{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
801 |
\ \ term{\isadigit{2}}str\ s{\isaliteral{5F}{\isacharunderscore}}{\isadigit{1}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
802 |
\ \ term{\isadigit{2}}str\ s{\isaliteral{5F}{\isacharunderscore}}{\isadigit{2}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42339
|
803 |
{\isaliteral{2A7D}{\isacharverbatimclose}}%
|
jan@42339
|
804 |
\endisatagML
|
jan@42339
|
805 |
{\isafoldML}%
|
jan@42339
|
806 |
%
|
jan@42339
|
807 |
\isadelimML
|
jan@42339
|
808 |
%
|
jan@42339
|
809 |
\endisadelimML
|
jan@42339
|
810 |
%
|
jan@42365
|
811 |
\begin{isamarkuptext}%
|
jan@42381
|
812 |
\noindent The ansatz for the \em Partial Fraction Decomposition \normalfont
|
jan@42369
|
813 |
requires to get the denominators of the partial fractions out of the
|
jan@42369
|
814 |
Solutions as:
|
jan@42369
|
815 |
\begin{itemize}
|
jan@42381
|
816 |
\item $Denominator_{1}=z-Zeropoint_{1}$
|
jan@42381
|
817 |
\item $Denominator_{2}=z-Zeropoint_{2}$
|
jan@42381
|
818 |
\item \ldots
|
jan@42369
|
819 |
\end{itemize}%
|
neuper@42289
|
820 |
\end{isamarkuptext}%
|
neuper@42289
|
821 |
\isamarkuptrue%
|
neuper@42289
|
822 |
%
|
neuper@42289
|
823 |
\isadelimML
|
neuper@42289
|
824 |
%
|
neuper@42289
|
825 |
\endisadelimML
|
neuper@42289
|
826 |
%
|
neuper@42289
|
827 |
\isatagML
|
neuper@42289
|
828 |
\isacommand{ML}\isamarkupfalse%
|
neuper@42289
|
829 |
\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
|
jan@42369
|
830 |
\ \ val\ xx\ {\isaliteral{3D}{\isacharequal}}\ HOLogic{\isaliteral{2E}{\isachardot}}dest{\isaliteral{5F}{\isacharunderscore}}eq\ s{\isaliteral{5F}{\isacharunderscore}}{\isadigit{1}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
831 |
\ \ val\ s{\isaliteral{5F}{\isacharunderscore}}{\isadigit{1}}{\isaliteral{27}{\isacharprime}}\ {\isaliteral{3D}{\isacharequal}}\ HOLogic{\isaliteral{2E}{\isachardot}}mk{\isaliteral{5F}{\isacharunderscore}}binop\ {\isaliteral{22}{\isachardoublequote}}Groups{\isaliteral{2E}{\isachardot}}minus{\isaliteral{5F}{\isacharunderscore}}class{\isaliteral{2E}{\isachardot}}minus{\isaliteral{22}{\isachardoublequote}}\ xx{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
832 |
\ \ val\ xx\ {\isaliteral{3D}{\isacharequal}}\ HOLogic{\isaliteral{2E}{\isachardot}}dest{\isaliteral{5F}{\isacharunderscore}}eq\ s{\isaliteral{5F}{\isacharunderscore}}{\isadigit{2}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
833 |
\ \ val\ s{\isaliteral{5F}{\isacharunderscore}}{\isadigit{2}}{\isaliteral{27}{\isacharprime}}\ {\isaliteral{3D}{\isacharequal}}\ HOLogic{\isaliteral{2E}{\isachardot}}mk{\isaliteral{5F}{\isacharunderscore}}binop\ {\isaliteral{22}{\isachardoublequote}}Groups{\isaliteral{2E}{\isachardot}}minus{\isaliteral{5F}{\isacharunderscore}}class{\isaliteral{2E}{\isachardot}}minus{\isaliteral{22}{\isachardoublequote}}\ xx{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
834 |
\ \ term{\isadigit{2}}str\ s{\isaliteral{5F}{\isacharunderscore}}{\isadigit{1}}{\isaliteral{27}{\isacharprime}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
835 |
\ \ term{\isadigit{2}}str\ s{\isaliteral{5F}{\isacharunderscore}}{\isadigit{2}}{\isaliteral{27}{\isacharprime}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
neuper@42289
|
836 |
{\isaliteral{2A7D}{\isacharverbatimclose}}%
|
neuper@42289
|
837 |
\endisatagML
|
neuper@42289
|
838 |
{\isafoldML}%
|
neuper@42289
|
839 |
%
|
neuper@42289
|
840 |
\isadelimML
|
neuper@42289
|
841 |
%
|
neuper@42289
|
842 |
\endisadelimML
|
neuper@42289
|
843 |
%
|
jan@42369
|
844 |
\begin{isamarkuptext}%
|
jan@42369
|
845 |
\noindent For the programming language a function collecting all the
|
jan@42369
|
846 |
above manipulations is helpful.%
|
jan@42369
|
847 |
\end{isamarkuptext}%
|
jan@42369
|
848 |
\isamarkuptrue%
|
jan@42369
|
849 |
%
|
jan@42369
|
850 |
\isadelimML
|
jan@42369
|
851 |
%
|
jan@42369
|
852 |
\endisadelimML
|
jan@42369
|
853 |
%
|
jan@42369
|
854 |
\isatagML
|
jan@42369
|
855 |
\isacommand{ML}\isamarkupfalse%
|
jan@42369
|
856 |
\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
|
jan@42369
|
857 |
\ \ fun\ fac{\isaliteral{5F}{\isacharunderscore}}from{\isaliteral{5F}{\isacharunderscore}}sol\ s\ {\isaliteral{3D}{\isacharequal}}\isanewline
|
jan@42369
|
858 |
\ \ \ \ let\ val\ {\isaliteral{28}{\isacharparenleft}}lhs{\isaliteral{2C}{\isacharcomma}}\ rhs{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ HOLogic{\isaliteral{2E}{\isachardot}}dest{\isaliteral{5F}{\isacharunderscore}}eq\ s\isanewline
|
jan@42369
|
859 |
\ \ \ \ in\ HOLogic{\isaliteral{2E}{\isachardot}}mk{\isaliteral{5F}{\isacharunderscore}}binop\ {\isaliteral{22}{\isachardoublequote}}Groups{\isaliteral{2E}{\isachardot}}minus{\isaliteral{5F}{\isacharunderscore}}class{\isaliteral{2E}{\isachardot}}minus{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{28}{\isacharparenleft}}lhs{\isaliteral{2C}{\isacharcomma}}\ rhs{\isaliteral{29}{\isacharparenright}}\ end{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
860 |
{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline
|
jan@42369
|
861 |
\isanewline
|
jan@42369
|
862 |
\isacommand{ML}\isamarkupfalse%
|
jan@42369
|
863 |
\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
|
jan@42369
|
864 |
\ \ fun\ mk{\isaliteral{5F}{\isacharunderscore}}prod\ prod\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{3D}{\isacharequal}}\isanewline
|
jan@42369
|
865 |
\ \ \ \ \ \ \ \ if\ prod\ {\isaliteral{3D}{\isacharequal}}\ e{\isaliteral{5F}{\isacharunderscore}}term\isanewline
|
jan@42369
|
866 |
\ \ \ \ \ \ \ \ then\ error\ {\isaliteral{22}{\isachardoublequote}}mk{\isaliteral{5F}{\isacharunderscore}}prod\ called\ with\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}\ \isanewline
|
jan@42369
|
867 |
\ \ \ \ \ \ \ \ else\ prod\isanewline
|
jan@42369
|
868 |
\ \ \ \ {\isaliteral{7C}{\isacharbar}}\ mk{\isaliteral{5F}{\isacharunderscore}}prod\ prod\ {\isaliteral{28}{\isacharparenleft}}t\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\isanewline
|
jan@42369
|
869 |
\ \ \ \ \ \ \ \ if\ prod\ {\isaliteral{3D}{\isacharequal}}\ e{\isaliteral{5F}{\isacharunderscore}}term\isanewline
|
jan@42369
|
870 |
\ \ \ \ \ \ \ \ then\ t\isanewline
|
jan@42369
|
871 |
\ \ \ \ \ \ \ \ else\ HOLogic{\isaliteral{2E}{\isachardot}}mk{\isaliteral{5F}{\isacharunderscore}}binop\ {\isaliteral{22}{\isachardoublequote}}Groups{\isaliteral{2E}{\isachardot}}times{\isaliteral{5F}{\isacharunderscore}}class{\isaliteral{2E}{\isachardot}}times{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{28}{\isacharparenleft}}prod{\isaliteral{2C}{\isacharcomma}}\ t{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42369
|
872 |
\ \ \ \ {\isaliteral{7C}{\isacharbar}}\ mk{\isaliteral{5F}{\isacharunderscore}}prod\ prod\ {\isaliteral{28}{\isacharparenleft}}t{\isadigit{1}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ t{\isadigit{2}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ ts{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\isanewline
|
jan@42369
|
873 |
\ \ \ \ \ \ \ \ \ \ if\ prod\ {\isaliteral{3D}{\isacharequal}}\ e{\isaliteral{5F}{\isacharunderscore}}term\ \isanewline
|
jan@42369
|
874 |
\ \ \ \ \ \ \ \ \ \ then\ \isanewline
|
jan@42369
|
875 |
\ \ \ \ \ \ \ \ \ \ \ \ \ let\ val\ p\ {\isaliteral{3D}{\isacharequal}}\ \isanewline
|
jan@42369
|
876 |
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ HOLogic{\isaliteral{2E}{\isachardot}}mk{\isaliteral{5F}{\isacharunderscore}}binop\ {\isaliteral{22}{\isachardoublequote}}Groups{\isaliteral{2E}{\isachardot}}times{\isaliteral{5F}{\isacharunderscore}}class{\isaliteral{2E}{\isachardot}}times{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{28}{\isacharparenleft}}t{\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ t{\isadigit{2}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42369
|
877 |
\ \ \ \ \ \ \ \ \ \ \ \ \ in\ mk{\isaliteral{5F}{\isacharunderscore}}prod\ p\ ts\ end\ \isanewline
|
jan@42369
|
878 |
\ \ \ \ \ \ \ \ \ \ else\ \isanewline
|
jan@42369
|
879 |
\ \ \ \ \ \ \ \ \ \ \ \ \ let\ val\ p\ {\isaliteral{3D}{\isacharequal}}\isanewline
|
jan@42369
|
880 |
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ HOLogic{\isaliteral{2E}{\isachardot}}mk{\isaliteral{5F}{\isacharunderscore}}binop\ {\isaliteral{22}{\isachardoublequote}}Groups{\isaliteral{2E}{\isachardot}}times{\isaliteral{5F}{\isacharunderscore}}class{\isaliteral{2E}{\isachardot}}times{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{28}{\isacharparenleft}}prod{\isaliteral{2C}{\isacharcomma}}\ t{\isadigit{1}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42369
|
881 |
\ \ \ \ \ \ \ \ \ \ \ \ \ in\ mk{\isaliteral{5F}{\isacharunderscore}}prod\ p\ {\isaliteral{28}{\isacharparenleft}}t{\isadigit{2}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ ts{\isaliteral{29}{\isacharparenright}}\ end\ \isanewline
|
jan@42369
|
882 |
{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline
|
jan@42369
|
883 |
\isanewline
|
jan@42369
|
884 |
\isacommand{ML}\isamarkupfalse%
|
jan@42369
|
885 |
\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
|
jan@42369
|
886 |
\ \ fun\ factors{\isaliteral{5F}{\isacharunderscore}}from{\isaliteral{5F}{\isacharunderscore}}solution\ sol\ {\isaliteral{3D}{\isacharequal}}\ \isanewline
|
jan@42369
|
887 |
\ \ \ \ let\ val\ ts\ {\isaliteral{3D}{\isacharequal}}\ HOLogic{\isaliteral{2E}{\isachardot}}dest{\isaliteral{5F}{\isacharunderscore}}list\ sol\isanewline
|
jan@42369
|
888 |
\ \ \ \ in\ mk{\isaliteral{5F}{\isacharunderscore}}prod\ e{\isaliteral{5F}{\isacharunderscore}}term\ {\isaliteral{28}{\isacharparenleft}}map\ fac{\isaliteral{5F}{\isacharunderscore}}from{\isaliteral{5F}{\isacharunderscore}}sol\ ts{\isaliteral{29}{\isacharparenright}}\ end{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
889 |
{\isaliteral{2A7D}{\isacharverbatimclose}}%
|
jan@42369
|
890 |
\endisatagML
|
jan@42369
|
891 |
{\isafoldML}%
|
jan@42369
|
892 |
%
|
jan@42369
|
893 |
\isadelimML
|
jan@42369
|
894 |
%
|
jan@42369
|
895 |
\endisadelimML
|
jan@42369
|
896 |
%
|
jan@42369
|
897 |
\begin{isamarkuptext}%
|
jan@42369
|
898 |
\noindent This function needs to be packed such that it can be evaluated
|
jan@42369
|
899 |
by the Lucas-Interpreter. Therefor we moved the function to the
|
jan@42369
|
900 |
corresponding \ttfamily Equation.thy \normalfont in our case
|
jan@42381
|
901 |
\ttfamily PartialFractions.thy \normalfont. The necessary steps
|
jan@42381
|
902 |
are quit the same as we have done with \ttfamily get\_denominator
|
jan@42369
|
903 |
\normalfont before.%
|
jan@42369
|
904 |
\end{isamarkuptext}%
|
jan@42369
|
905 |
\isamarkuptrue%
|
jan@42369
|
906 |
%
|
jan@42369
|
907 |
\isadelimML
|
jan@42369
|
908 |
%
|
jan@42369
|
909 |
\endisadelimML
|
jan@42369
|
910 |
%
|
jan@42369
|
911 |
\isatagML
|
jan@42369
|
912 |
\isacommand{ML}\isamarkupfalse%
|
jan@42369
|
913 |
\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
|
jan@42369
|
914 |
\ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}factors{\isaliteral{5F}{\isacharunderscore}}from{\isaliteral{5F}{\isacharunderscore}}solution{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\isanewline
|
jan@42369
|
915 |
\ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}Partial{\isaliteral{5F}{\isacharunderscore}}Fractions{\isaliteral{2E}{\isachardot}}factors{\isaliteral{5F}{\isacharunderscore}}from{\isaliteral{5F}{\isacharunderscore}}solution{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\isanewline
|
jan@42369
|
916 |
\ \ \ \ \ \ eval{\isaliteral{5F}{\isacharunderscore}}factors{\isaliteral{5F}{\isacharunderscore}}from{\isaliteral{5F}{\isacharunderscore}}solution\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42369
|
917 |
\ \ \ \ \ \ \isanewline
|
jan@42369
|
918 |
\ \ fun\ eval{\isaliteral{5F}{\isacharunderscore}}factors{\isaliteral{5F}{\isacharunderscore}}from{\isaliteral{5F}{\isacharunderscore}}solution\ {\isaliteral{28}{\isacharparenleft}}thmid{\isaliteral{3A}{\isacharcolon}}string{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5F}{\isacharunderscore}}\isanewline
|
jan@42369
|
919 |
\ \ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}t\ as\ Const\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}Partial{\isaliteral{5F}{\isacharunderscore}}Fractions{\isaliteral{2E}{\isachardot}}factors{\isaliteral{5F}{\isacharunderscore}}from{\isaliteral{5F}{\isacharunderscore}}solution{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5F}{\isacharunderscore}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{24}{\isachardollar}}\ sol{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42369
|
920 |
\ \ \ \ \ \ \ \ \ thy\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{28}{\isacharparenleft}}let\ val\ prod\ {\isaliteral{3D}{\isacharequal}}\ factors{\isaliteral{5F}{\isacharunderscore}}from{\isaliteral{5F}{\isacharunderscore}}solution\ sol\isanewline
|
jan@42369
|
921 |
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ in\ SOME\ {\isaliteral{28}{\isacharparenleft}}mk{\isaliteral{5F}{\isacharunderscore}}thmid\ thmid\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{22}{\isachardoublequote}}\isanewline
|
jan@42369
|
922 |
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}Print{\isaliteral{5F}{\isacharunderscore}}Mode{\isaliteral{2E}{\isachardot}}setmp\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\isanewline
|
jan@42369
|
923 |
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}Syntax{\isaliteral{2E}{\isachardot}}string{\isaliteral{5F}{\isacharunderscore}}of{\isaliteral{5F}{\isacharunderscore}}term\ {\isaliteral{28}{\isacharparenleft}}thy{\isadigit{2}}ctxt\ thy{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ prod{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\isanewline
|
jan@42369
|
924 |
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Trueprop\ {\isaliteral{24}{\isachardollar}}\ {\isaliteral{28}{\isacharparenleft}}mk{\isaliteral{5F}{\isacharunderscore}}equality\ {\isaliteral{28}{\isacharparenleft}}t{\isaliteral{2C}{\isacharcomma}}\ prod{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42369
|
925 |
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ end{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42369
|
926 |
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ handle\ {\isaliteral{5F}{\isacharunderscore}}\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\ NONE{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42369
|
927 |
\ \ \ {\isaliteral{7C}{\isacharbar}}\ eval{\isaliteral{5F}{\isacharunderscore}}factors{\isaliteral{5F}{\isacharunderscore}}from{\isaliteral{5F}{\isacharunderscore}}solution\ {\isaliteral{5F}{\isacharunderscore}}\ {\isaliteral{5F}{\isacharunderscore}}\ {\isaliteral{5F}{\isacharunderscore}}\ {\isaliteral{5F}{\isacharunderscore}}\ {\isaliteral{3D}{\isacharequal}}\ NONE{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
928 |
{\isaliteral{2A7D}{\isacharverbatimclose}}%
|
jan@42369
|
929 |
\endisatagML
|
jan@42369
|
930 |
{\isafoldML}%
|
jan@42369
|
931 |
%
|
jan@42369
|
932 |
\isadelimML
|
jan@42369
|
933 |
%
|
jan@42369
|
934 |
\endisadelimML
|
jan@42369
|
935 |
%
|
jan@42369
|
936 |
\begin{isamarkuptext}%
|
jan@42381
|
937 |
\noindent The tracing output of the calc tree after applying this
|
jan@42381
|
938 |
function was:
|
jan@42381
|
939 |
\begin{verbatim}
|
jan@42381
|
940 |
24 / factors_from_solution [z = 1/ 2, z = -1 / 4])]
|
jan@42381
|
941 |
\end{verbatim}
|
jan@42381
|
942 |
and the next step:
|
jan@42381
|
943 |
\begin{verbatim}
|
jan@42381
|
944 |
val nxt = ("Empty_Tac", ...): tac'_)
|
jan@42381
|
945 |
\end{verbatim}
|
jan@42381
|
946 |
These observations indicate, that the Lucas-Interpreter (LIP)
|
jan@42381
|
947 |
does not know how to evaluate \ttfamily factors\_from\_solution
|
jan@42381
|
948 |
\normalfont, so we knew that there is something wrong or missing.%
|
jan@42369
|
949 |
\end{isamarkuptext}%
|
jan@42369
|
950 |
\isamarkuptrue%
|
jan@42369
|
951 |
%
|
jan@42369
|
952 |
\begin{isamarkuptext}%
|
jan@42381
|
953 |
\noindent First we isolate the difficulty in the program as follows:
|
jan@42381
|
954 |
\begin{verbatim}
|
jan@42381
|
955 |
" (L_L::bool list) = (SubProblem (PolyEq', " ^
|
jan@42381
|
956 |
" [abcFormula, degree_2, polynomial, " ^
|
jan@42381
|
957 |
" univariate,equation], " ^
|
jan@42381
|
958 |
" [no_met]) " ^
|
jan@42381
|
959 |
" [BOOL equ, REAL zzz]); " ^
|
jan@42381
|
960 |
" (facs::real) = factors_from_solution L_L; " ^
|
jan@42381
|
961 |
" (foo::real) = Take facs " ^
|
jan@42381
|
962 |
\end{verbatim}
|
jan@42381
|
963 |
|
jan@42381
|
964 |
\par \noindent And see the tracing output:
|
jan@42381
|
965 |
|
jan@42381
|
966 |
\begin{verbatim}
|
jan@42381
|
967 |
[(([], Frm), Problem (Isac, [inverse,
|
jan@42381
|
968 |
Z_Transform,
|
jan@42381
|
969 |
SignalProcessing])),
|
jan@42381
|
970 |
(([1], Frm), X z = 3 / (z - 1 / 4 + -1 / 8 * (1 / z))),
|
jan@42381
|
971 |
(([1], Res), ?X' z = 3 / (z * (z - 1 / 4 + -1 / 8 * (1 / z)))),
|
jan@42381
|
972 |
(([2], Res), ?X' z = 24 / (-1 + -2 * z + 8 * z ^^^ 2)),
|
jan@42381
|
973 |
(([3], Pbl), solve (-1 + -2 * z + 8 * z ^^^ 2 = 0, z)),
|
jan@42381
|
974 |
(([3,1], Frm), -1 + -2 * z + 8 * z ^^^ 2 = 0),
|
jan@42381
|
975 |
(([3,1], Res), z = (- -2 + sqrt (-2 ^^^ 2 - 4 * 8 * -1)) / (2 * 8)|
|
jan@42381
|
976 |
z = (- -2 - sqrt (-2 ^^^ 2 - 4 * 8 * -1)) / (2 * 8)),
|
jan@42381
|
977 |
(([3,2], Res), z = 1 / 2 | z = -1 / 4),
|
jan@42381
|
978 |
(([3,3], Res), [ z = 1 / 2, z = -1 / 4]),
|
jan@42381
|
979 |
(([3,4], Res), [ z = 1 / 2, z = -1 / 4]),
|
jan@42381
|
980 |
(([3], Res), [ z = 1 / 2, z = -1 / 4]),
|
jan@42381
|
981 |
(([4], Frm), factors_from_solution [z = 1 / 2, z = -1 / 4])]
|
jan@42381
|
982 |
\end{verbatim}
|
jan@42381
|
983 |
|
jan@42381
|
984 |
\par \noindent In particular that:
|
jan@42381
|
985 |
|
jan@42381
|
986 |
\begin{verbatim}
|
jan@42381
|
987 |
(([3], Pbl), solve (-1 + -2 * z + 8 * z ^^^ 2 = 0, z)),
|
jan@42381
|
988 |
\end{verbatim}
|
jan@42381
|
989 |
\par \noindent Shows the equation which has been created in
|
jan@42381
|
990 |
the program by:
|
jan@42381
|
991 |
\begin{verbatim}
|
jan@42381
|
992 |
"(denom::real) = get_denominator funterm; " ^
|
jan@42381
|
993 |
(* get_denominator *)
|
jan@42381
|
994 |
"(equ::bool) = (denom = (0::real)); " ^
|
jan@42381
|
995 |
\end{verbatim}
|
jan@42369
|
996 |
|
jan@42381
|
997 |
\noindent \ttfamily get\_denominator \normalfont has been evaluated successfully,
|
jan@42369
|
998 |
but not\\ \ttfamily factors\_from\_solution.\normalfont
|
jan@42369
|
999 |
So we stepwise compare with an analogous case, \ttfamily get\_denominator
|
jan@42369
|
1000 |
\normalfont successfully done above: We know that LIP evaluates
|
jan@42369
|
1001 |
expressions in the program by use of the \emph{srls}, so we try to get
|
jan@42369
|
1002 |
the original \emph{srls}.\\
|
jan@42369
|
1003 |
|
jan@42381
|
1004 |
\begin{verbatim}
|
jan@42381
|
1005 |
val {srls,...} = get_met ["SignalProcessing",
|
jan@42381
|
1006 |
"Z_Transform",
|
neuper@42405
|
1007 |
"Inverse"];
|
jan@42381
|
1008 |
\end{verbatim}
|
jan@42369
|
1009 |
|
jan@42381
|
1010 |
\par \noindent Create 2 good example terms:
|
jan@42369
|
1011 |
|
jan@42381
|
1012 |
\begin{verbatim}
|
jan@42381
|
1013 |
val SOME t1 =
|
jan@42381
|
1014 |
parseNEW ctxt "get_denominator ((111::real) / 222)";
|
jan@42381
|
1015 |
val SOME t2 =
|
jan@42381
|
1016 |
parseNEW ctxt "factors_from_solution [(z::real)=1/2, z=-1/4]";
|
jan@42381
|
1017 |
\end{verbatim}
|
jan@42381
|
1018 |
|
jan@42381
|
1019 |
\par \noindent Rewrite the terms using srls:\\
|
jan@42369
|
1020 |
\ttfamily \par \noindent rewrite\_set\_ thy true srls t1;\\
|
jan@42369
|
1021 |
rewrite\_set\_ thy true srls t2;\\
|
jan@42369
|
1022 |
\par \noindent \normalfont Now we see a difference: \texttt{t1} gives
|
jan@42369
|
1023 |
\texttt{SOME} but \texttt{t2} gives \texttt{NONE}. We look at the
|
jan@42381
|
1024 |
\emph{srls}:
|
jan@42381
|
1025 |
\begin{verbatim}
|
jan@42381
|
1026 |
val srls =
|
walther@59851
|
1027 |
Rule_Set.Repeat{id = "srls_InverseZTransform",
|
walther@59773
|
1028 |
rules = [Num_Calc("Rational.get_numerator",
|
jan@42381
|
1029 |
eval_get_numerator "Rational.get_numerator"),
|
walther@59773
|
1030 |
Num_Calc("Partial_Fractions.factors_from_solution",
|
jan@42381
|
1031 |
eval_factors_from_solution
|
jan@42381
|
1032 |
"Partial_Fractions.factors_from_solution")]}
|
jan@42381
|
1033 |
\end{verbatim}
|
jan@42381
|
1034 |
\par \noindent Here everthing is perfect. So the error can
|
jan@42369
|
1035 |
only be in the SML code of \ttfamily eval\_factors\_from\_solution.
|
jan@42369
|
1036 |
\normalfont We try to check the code with an existing test; since the
|
jan@42369
|
1037 |
\emph{code} is in
|
jan@42369
|
1038 |
\begin{center}\ttfamily src/Tools/isac/Knowledge/Partial\_Fractions.thy
|
jan@42369
|
1039 |
\normalfont\end{center}
|
jan@42369
|
1040 |
the \emph{test} should be in
|
jan@42369
|
1041 |
\begin{center}\ttfamily test/Tools/isac/Knowledge/partial\_fractions.sml
|
jan@42369
|
1042 |
\normalfont\end{center}
|
jan@42369
|
1043 |
\par \noindent After updating the function \ttfamily
|
jan@42369
|
1044 |
factors\_from\_solution \normalfont to a new version and putting a
|
jan@42381
|
1045 |
test-case to \ttfamily Partial\_Fractions.sml \normalfont we tried again
|
jan@42369
|
1046 |
to evaluate the term with the same result.
|
jan@42369
|
1047 |
\par We opened the test \ttfamily Test\_Isac.thy \normalfont and saw that
|
jan@42369
|
1048 |
everything is working fine. Also we checked that the test \ttfamily
|
jan@42369
|
1049 |
partial\_fractions.sml \normalfont is used in \ttfamily Test\_Isac.thy
|
jan@42369
|
1050 |
\normalfont
|
jan@42369
|
1051 |
\begin{center}use \ttfamily "Knowledge/partial\_fractions.sml"
|
jan@42369
|
1052 |
\normalfont \end{center}
|
jan@42369
|
1053 |
and \ttfamily Partial\_Fractions.thy \normalfont is part is part of
|
jan@42381
|
1054 |
{\sisac} by evaluating
|
jan@42369
|
1055 |
|
jan@42381
|
1056 |
\begin{verbatim}
|
jan@42381
|
1057 |
val thy = \hyperlink{theory.Isac}{\mbox{\isa{Isac}}};
|
jan@42381
|
1058 |
\end{verbatim}
|
jan@42369
|
1059 |
|
jan@42381
|
1060 |
After rebuilding {\sisac} again it worked.%
|
jan@42369
|
1061 |
\end{isamarkuptext}%
|
jan@42369
|
1062 |
\isamarkuptrue%
|
jan@42369
|
1063 |
%
|
jan@42369
|
1064 |
\isamarkupsubsubsection{Build Expression%
|
neuper@42289
|
1065 |
}
|
neuper@42289
|
1066 |
\isamarkuptrue%
|
neuper@42289
|
1067 |
%
|
jan@42369
|
1068 |
\begin{isamarkuptext}%
|
jan@42381
|
1069 |
\noindent In {\sisac}'s TP-based programming language we can build
|
jan@42369
|
1070 |
expressions by:\\
|
jan@42369
|
1071 |
\ttfamily let s\_1 = Take numerator / (s\_1 * s\_2) \normalfont%
|
jan@42369
|
1072 |
\end{isamarkuptext}%
|
jan@42369
|
1073 |
\isamarkuptrue%
|
jan@42369
|
1074 |
%
|
jan@42369
|
1075 |
\isadelimML
|
jan@42369
|
1076 |
%
|
jan@42369
|
1077 |
\endisadelimML
|
jan@42369
|
1078 |
%
|
jan@42369
|
1079 |
\isatagML
|
jan@42369
|
1080 |
\isacommand{ML}\isamarkupfalse%
|
jan@42369
|
1081 |
\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
|
jan@42369
|
1082 |
\ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}\isanewline
|
jan@42381
|
1083 |
\ \ \ {\isaliteral{2A}{\isacharasterisk}}\ The\ main\ denominator\ is\ the\ multiplication\ of\ the\ denominators\ of\isanewline
|
jan@42369
|
1084 |
\ \ \ {\isaliteral{2A}{\isacharasterisk}}\ all\ partial\ fractions{\isaliteral{2E}{\isachardot}}\isanewline
|
jan@42369
|
1085 |
\ \ \ {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42369
|
1086 |
\ \ \ \isanewline
|
jan@42369
|
1087 |
\ \ val\ denominator{\isaliteral{27}{\isacharprime}}\ {\isaliteral{3D}{\isacharequal}}\ HOLogic{\isaliteral{2E}{\isachardot}}mk{\isaliteral{5F}{\isacharunderscore}}binop\ \isanewline
|
jan@42369
|
1088 |
\ \ \ \ {\isaliteral{22}{\isachardoublequote}}Groups{\isaliteral{2E}{\isachardot}}times{\isaliteral{5F}{\isacharunderscore}}class{\isaliteral{2E}{\isachardot}}times{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{28}{\isacharparenleft}}s{\isaliteral{5F}{\isacharunderscore}}{\isadigit{1}}{\isaliteral{27}{\isacharprime}}{\isaliteral{2C}{\isacharcomma}}\ s{\isaliteral{5F}{\isacharunderscore}}{\isadigit{2}}{\isaliteral{27}{\isacharprime}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1089 |
\ \ val\ SOME\ numerator\ {\isaliteral{3D}{\isacharequal}}\ parseNEW\ ctxt\ {\isaliteral{22}{\isachardoublequote}}{\isadigit{3}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}real{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1090 |
\isanewline
|
jan@42369
|
1091 |
\ \ val\ expr{\isaliteral{27}{\isacharprime}}\ {\isaliteral{3D}{\isacharequal}}\ HOLogic{\isaliteral{2E}{\isachardot}}mk{\isaliteral{5F}{\isacharunderscore}}binop\isanewline
|
jan@42369
|
1092 |
\ \ \ \ {\isaliteral{22}{\isachardoublequote}}Rings{\isaliteral{2E}{\isachardot}}inverse{\isaliteral{5F}{\isacharunderscore}}class{\isaliteral{2E}{\isachardot}}divide{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{28}{\isacharparenleft}}numerator{\isaliteral{2C}{\isacharcomma}}\ denominator{\isaliteral{27}{\isacharprime}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1093 |
\ \ term{\isadigit{2}}str\ expr{\isaliteral{27}{\isacharprime}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1094 |
{\isaliteral{2A7D}{\isacharverbatimclose}}%
|
jan@42369
|
1095 |
\endisatagML
|
jan@42369
|
1096 |
{\isafoldML}%
|
jan@42369
|
1097 |
%
|
jan@42369
|
1098 |
\isadelimML
|
jan@42369
|
1099 |
%
|
jan@42369
|
1100 |
\endisadelimML
|
jan@42369
|
1101 |
%
|
jan@42369
|
1102 |
\isamarkupsubsubsection{Apply the Partial Fraction Decomposion Ansatz%
|
jan@42369
|
1103 |
}
|
jan@42369
|
1104 |
\isamarkuptrue%
|
jan@42369
|
1105 |
%
|
jan@42369
|
1106 |
\begin{isamarkuptext}%
|
jan@42381
|
1107 |
\noindent We use the Ansatz of the Partial Fraction Decomposition for our
|
jan@42369
|
1108 |
expression 2nd order. Follow up the calculation in
|
jan@42369
|
1109 |
Section~\ref{sec:calc:ztrans} Step~03.%
|
jan@42369
|
1110 |
\end{isamarkuptext}%
|
jan@42369
|
1111 |
\isamarkuptrue%
|
jan@42369
|
1112 |
%
|
neuper@42289
|
1113 |
\isadelimML
|
neuper@42289
|
1114 |
%
|
neuper@42289
|
1115 |
\endisadelimML
|
neuper@42289
|
1116 |
%
|
neuper@42289
|
1117 |
\isatagML
|
neuper@42289
|
1118 |
\isacommand{ML}\isamarkupfalse%
|
neuper@42304
|
1119 |
\ {\isaliteral{7B2A}{\isacharverbatimopen}}Context{\isaliteral{2E}{\isachardot}}theory{\isaliteral{5F}{\isacharunderscore}}name\ thy\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{22}{\isachardoublequote}}Isac{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2A7D}{\isacharverbatimclose}}%
|
neuper@42289
|
1120 |
\endisatagML
|
neuper@42289
|
1121 |
{\isafoldML}%
|
neuper@42289
|
1122 |
%
|
neuper@42289
|
1123 |
\isadelimML
|
neuper@42289
|
1124 |
%
|
neuper@42289
|
1125 |
\endisadelimML
|
jan@42369
|
1126 |
%
|
jan@42369
|
1127 |
\begin{isamarkuptext}%
|
jan@42381
|
1128 |
\noindent We define two axiomatization, the first one is the main ansatz,
|
jan@42381
|
1129 |
the next one is just an equivalent transformation of the resulting
|
jan@42369
|
1130 |
equation. Both axiomatizations were moved to \ttfamily
|
jan@42369
|
1131 |
Partial\_Fractions.thy \normalfont and got their own rulesets. In later
|
jan@42381
|
1132 |
programs it is possible to use the rulesets and the machine will find
|
jan@42369
|
1133 |
the correct ansatz and equivalent transformation itself.%
|
jan@42369
|
1134 |
\end{isamarkuptext}%
|
jan@42369
|
1135 |
\isamarkuptrue%
|
neuper@42289
|
1136 |
\isacommand{axiomatization}\isamarkupfalse%
|
neuper@42289
|
1137 |
\ \isakeyword{where}\isanewline
|
jan@42369
|
1138 |
\ \ ansatz{\isaliteral{5F}{\isacharunderscore}}{\isadigit{2}}nd{\isaliteral{5F}{\isacharunderscore}}order{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}n\ {\isaliteral{2F}{\isacharslash}}\ {\isaliteral{28}{\isacharparenleft}}a{\isaliteral{2A}{\isacharasterisk}}b{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ A{\isaliteral{2F}{\isacharslash}}a\ {\isaliteral{2B}{\isacharplus}}\ B{\isaliteral{2F}{\isacharslash}}b{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{and}\isanewline
|
jan@42369
|
1139 |
\ \ equival{\isaliteral{5F}{\isacharunderscore}}trans{\isaliteral{5F}{\isacharunderscore}}{\isadigit{2}}nd{\isaliteral{5F}{\isacharunderscore}}order{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}n{\isaliteral{2F}{\isacharslash}}{\isaliteral{28}{\isacharparenleft}}a{\isaliteral{2A}{\isacharasterisk}}b{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ A{\isaliteral{2F}{\isacharslash}}a\ {\isaliteral{2B}{\isacharplus}}\ B{\isaliteral{2F}{\isacharslash}}b{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}n\ {\isaliteral{3D}{\isacharequal}}\ A{\isaliteral{2A}{\isacharasterisk}}b\ {\isaliteral{2B}{\isacharplus}}\ B{\isaliteral{2A}{\isacharasterisk}}a{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}%
|
jan@42365
|
1140 |
\begin{isamarkuptext}%
|
jan@42369
|
1141 |
\noindent We use our \ttfamily ansatz\_2nd\_order \normalfont to rewrite
|
jan@42381
|
1142 |
our expression and get an equation with our expression on the left
|
jan@42369
|
1143 |
and the partial fractions of it on the right hand side.%
|
jan@42365
|
1144 |
\end{isamarkuptext}%
|
jan@42365
|
1145 |
\isamarkuptrue%
|
jan@42365
|
1146 |
%
|
jan@42365
|
1147 |
\isadelimML
|
jan@42365
|
1148 |
%
|
jan@42365
|
1149 |
\endisadelimML
|
jan@42365
|
1150 |
%
|
jan@42365
|
1151 |
\isatagML
|
jan@42365
|
1152 |
\isacommand{ML}\isamarkupfalse%
|
jan@42365
|
1153 |
\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
|
jan@42369
|
1154 |
\ \ val\ SOME\ {\isaliteral{28}{\isacharparenleft}}t{\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ \isanewline
|
jan@42369
|
1155 |
\ \ \ \ rewrite{\isaliteral{5F}{\isacharunderscore}}\ %
|
jan@42365
|
1156 |
\isaantiq
|
jan@42365
|
1157 |
theory\ Isac{}%
|
jan@42365
|
1158 |
\endisaantiq
|
jan@42369
|
1159 |
\ e{\isaliteral{5F}{\isacharunderscore}}rew{\isaliteral{5F}{\isacharunderscore}}ord\ e{\isaliteral{5F}{\isacharunderscore}}rls\ false\ \isanewline
|
jan@42369
|
1160 |
\ \ \ \ \ \ \ \ \ \ \ \ \ %
|
jan@42369
|
1161 |
\isaantiq
|
jan@42369
|
1162 |
thm\ ansatz{\isaliteral{5F}{\isacharunderscore}}{\isadigit{2}}nd{\isaliteral{5F}{\isacharunderscore}}order{}%
|
jan@42369
|
1163 |
\endisaantiq
|
jan@42369
|
1164 |
\ expr{\isaliteral{27}{\isacharprime}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1165 |
\ \ term{\isadigit{2}}str\ t{\isadigit{1}}{\isaliteral{3B}{\isacharsemicolon}}\ atomty\ t{\isadigit{1}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1166 |
\ \ val\ eq{\isadigit{1}}\ {\isaliteral{3D}{\isacharequal}}\ HOLogic{\isaliteral{2E}{\isachardot}}mk{\isaliteral{5F}{\isacharunderscore}}eq\ {\isaliteral{28}{\isacharparenleft}}expr{\isaliteral{27}{\isacharprime}}{\isaliteral{2C}{\isacharcomma}}\ t{\isadigit{1}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1167 |
\ \ term{\isadigit{2}}str\ eq{\isadigit{1}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42365
|
1168 |
{\isaliteral{2A7D}{\isacharverbatimclose}}%
|
jan@42365
|
1169 |
\endisatagML
|
jan@42365
|
1170 |
{\isafoldML}%
|
jan@42365
|
1171 |
%
|
jan@42365
|
1172 |
\isadelimML
|
jan@42365
|
1173 |
%
|
jan@42365
|
1174 |
\endisadelimML
|
jan@42365
|
1175 |
%
|
jan@42369
|
1176 |
\begin{isamarkuptext}%
|
jan@42381
|
1177 |
\noindent Eliminate the denominators by multiplying the left and the
|
jan@42369
|
1178 |
right hand side of the equation with the main denominator. This is an
|
jan@42369
|
1179 |
simple equivalent transformation. Later on we use an own ruleset
|
jan@42369
|
1180 |
defined in \ttfamily Partial\_Fractions.thy \normalfont for doing this.
|
jan@42369
|
1181 |
Follow up the calculation in Section~\ref{sec:calc:ztrans} Step~04.%
|
jan@42369
|
1182 |
\end{isamarkuptext}%
|
neuper@42289
|
1183 |
\isamarkuptrue%
|
neuper@42289
|
1184 |
%
|
neuper@42289
|
1185 |
\isadelimML
|
neuper@42289
|
1186 |
%
|
neuper@42289
|
1187 |
\endisadelimML
|
neuper@42289
|
1188 |
%
|
neuper@42289
|
1189 |
\isatagML
|
neuper@42289
|
1190 |
\isacommand{ML}\isamarkupfalse%
|
neuper@42289
|
1191 |
\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
|
jan@42369
|
1192 |
\ \ val\ SOME\ {\isaliteral{28}{\isacharparenleft}}eq{\isadigit{2}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ \isanewline
|
jan@42369
|
1193 |
\ \ \ \ rewrite{\isaliteral{5F}{\isacharunderscore}}\ %
|
neuper@42289
|
1194 |
\isaantiq
|
neuper@42289
|
1195 |
theory\ Isac{}%
|
neuper@42289
|
1196 |
\endisaantiq
|
jan@42369
|
1197 |
\ e{\isaliteral{5F}{\isacharunderscore}}rew{\isaliteral{5F}{\isacharunderscore}}ord\ e{\isaliteral{5F}{\isacharunderscore}}rls\ false\ \isanewline
|
jan@42369
|
1198 |
\ \ \ \ \ \ \ \ \ \ \ \ \ %
|
neuper@42289
|
1199 |
\isaantiq
|
jan@42369
|
1200 |
thm\ equival{\isaliteral{5F}{\isacharunderscore}}trans{\isaliteral{5F}{\isacharunderscore}}{\isadigit{2}}nd{\isaliteral{5F}{\isacharunderscore}}order{}%
|
neuper@42289
|
1201 |
\endisaantiq
|
jan@42369
|
1202 |
\ eq{\isadigit{1}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1203 |
\ \ term{\isadigit{2}}str\ eq{\isadigit{2}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
neuper@42289
|
1204 |
{\isaliteral{2A7D}{\isacharverbatimclose}}%
|
neuper@42289
|
1205 |
\endisatagML
|
neuper@42289
|
1206 |
{\isafoldML}%
|
neuper@42289
|
1207 |
%
|
neuper@42289
|
1208 |
\isadelimML
|
neuper@42289
|
1209 |
%
|
neuper@42289
|
1210 |
\endisadelimML
|
neuper@42289
|
1211 |
%
|
jan@42369
|
1212 |
\begin{isamarkuptext}%
|
jan@42369
|
1213 |
\noindent We use the existing ruleset \ttfamily norm\_Rational \normalfont
|
jan@42369
|
1214 |
for simplifications on expressions.%
|
jan@42369
|
1215 |
\end{isamarkuptext}%
|
neuper@42289
|
1216 |
\isamarkuptrue%
|
neuper@42289
|
1217 |
%
|
neuper@42289
|
1218 |
\isadelimML
|
neuper@42289
|
1219 |
%
|
neuper@42289
|
1220 |
\endisadelimML
|
neuper@42289
|
1221 |
%
|
neuper@42289
|
1222 |
\isatagML
|
neuper@42289
|
1223 |
\isacommand{ML}\isamarkupfalse%
|
neuper@42289
|
1224 |
\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
|
jan@42369
|
1225 |
\ \ val\ SOME\ {\isaliteral{28}{\isacharparenleft}}eq{\isadigit{3}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ rewrite{\isaliteral{5F}{\isacharunderscore}}set{\isaliteral{5F}{\isacharunderscore}}\ %
|
jan@42369
|
1226 |
\isaantiq
|
jan@42369
|
1227 |
theory\ Isac{}%
|
jan@42369
|
1228 |
\endisaantiq
|
jan@42369
|
1229 |
\ false\ norm{\isaliteral{5F}{\isacharunderscore}}Rational\ eq{\isadigit{2}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1230 |
\ \ term{\isadigit{2}}str\ eq{\isadigit{3}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1231 |
\ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}\isanewline
|
jan@42369
|
1232 |
\ \ \ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{3F}{\isacharquery}}A\ {\isaliteral{3F}{\isacharquery}}B\ not\ simplified\isanewline
|
jan@42369
|
1233 |
\ \ \ {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42369
|
1234 |
{\isaliteral{2A7D}{\isacharverbatimclose}}%
|
jan@42369
|
1235 |
\endisatagML
|
jan@42369
|
1236 |
{\isafoldML}%
|
jan@42369
|
1237 |
%
|
jan@42369
|
1238 |
\isadelimML
|
jan@42369
|
1239 |
%
|
jan@42369
|
1240 |
\endisadelimML
|
jan@42369
|
1241 |
%
|
jan@42369
|
1242 |
\begin{isamarkuptext}%
|
jan@42381
|
1243 |
\noindent In Example~\ref{eg:gap} of my thesis I'm describing a problem about
|
jan@42369
|
1244 |
simplifications. The problem that we would like to have only a specific degree
|
jan@42381
|
1245 |
of simplification occurs right here, in the next step.%
|
jan@42369
|
1246 |
\end{isamarkuptext}%
|
jan@42369
|
1247 |
\isamarkuptrue%
|
jan@42369
|
1248 |
%
|
jan@42369
|
1249 |
\isadelimML
|
jan@42369
|
1250 |
%
|
jan@42369
|
1251 |
\endisadelimML
|
jan@42369
|
1252 |
%
|
jan@42369
|
1253 |
\isatagML
|
jan@42369
|
1254 |
\isacommand{ML}\isamarkupfalse%
|
jan@42369
|
1255 |
\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
|
jan@42369
|
1256 |
\ \ val\ SOME\ fract{\isadigit{1}}\ {\isaliteral{3D}{\isacharequal}}\isanewline
|
jan@42369
|
1257 |
\ \ \ \ parseNEW\ ctxt\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{1}}{\isaliteral{2F}{\isacharslash}}{\isadigit{2}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{2D}{\isacharminus}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{1}}{\isaliteral{2F}{\isacharslash}}{\isadigit{4}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}A{\isaliteral{2F}{\isacharslash}}{\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{1}}{\isaliteral{2F}{\isacharslash}}{\isadigit{2}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2B}{\isacharplus}}\ B{\isaliteral{2F}{\isacharslash}}{\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{2D}{\isacharminus}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{1}}{\isaliteral{2F}{\isacharslash}}{\isadigit{4}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1258 |
\ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}\isanewline
|
jan@42369
|
1259 |
\ \ \ {\isaliteral{2A}{\isacharasterisk}}\ A\ B\ {\isaliteral{21}{\isacharbang}}\isanewline
|
jan@42369
|
1260 |
\ \ \ {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42369
|
1261 |
\ \ val\ SOME\ {\isaliteral{28}{\isacharparenleft}}fract{\isadigit{2}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ \isanewline
|
jan@42369
|
1262 |
\ \ \ \ rewrite{\isaliteral{5F}{\isacharunderscore}}set{\isaliteral{5F}{\isacharunderscore}}\ %
|
jan@42369
|
1263 |
\isaantiq
|
jan@42369
|
1264 |
theory\ Isac{}%
|
jan@42369
|
1265 |
\endisaantiq
|
jan@42369
|
1266 |
\ false\ norm{\isaliteral{5F}{\isacharunderscore}}Rational\ fract{\isadigit{1}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1267 |
\ \ term{\isadigit{2}}str\ fract{\isadigit{2}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}A\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{2}}\ {\isaliteral{2A}{\isacharasterisk}}\ B\ {\isaliteral{2B}{\isacharplus}}\ {\isadigit{4}}\ {\isaliteral{2A}{\isacharasterisk}}\ A\ {\isaliteral{2A}{\isacharasterisk}}\ z\ {\isaliteral{2B}{\isacharplus}}\ {\isadigit{4}}\ {\isaliteral{2A}{\isacharasterisk}}\ B\ {\isaliteral{2A}{\isacharasterisk}}\ z{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{4}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1268 |
\ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}\isanewline
|
jan@42369
|
1269 |
\ \ \ {\isaliteral{2A}{\isacharasterisk}}\ term{\isadigit{2}}str\ fract{\isadigit{2}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{22}{\isachardoublequote}}A\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{1}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{4}}\ {\isaliteral{2B}{\isacharplus}}\ z{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2B}{\isacharplus}}\ B\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2D}{\isacharminus}}{\isadigit{1}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{2}}\ {\isaliteral{2B}{\isacharplus}}\ z{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}\ \isanewline
|
jan@42369
|
1270 |
\ \ \ {\isaliteral{2A}{\isacharasterisk}}\ would\ be\ more\ traditional{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}\isanewline
|
jan@42369
|
1271 |
\ \ \ {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42369
|
1272 |
{\isaliteral{2A7D}{\isacharverbatimclose}}%
|
jan@42369
|
1273 |
\endisatagML
|
jan@42369
|
1274 |
{\isafoldML}%
|
jan@42369
|
1275 |
%
|
jan@42369
|
1276 |
\isadelimML
|
jan@42369
|
1277 |
%
|
jan@42369
|
1278 |
\endisadelimML
|
jan@42369
|
1279 |
%
|
jan@42369
|
1280 |
\begin{isamarkuptext}%
|
jan@42369
|
1281 |
\noindent We walk around this problem by generating our new equation first.%
|
jan@42369
|
1282 |
\end{isamarkuptext}%
|
jan@42369
|
1283 |
\isamarkuptrue%
|
jan@42369
|
1284 |
%
|
jan@42369
|
1285 |
\isadelimML
|
jan@42369
|
1286 |
%
|
jan@42369
|
1287 |
\endisadelimML
|
jan@42369
|
1288 |
%
|
jan@42369
|
1289 |
\isatagML
|
jan@42369
|
1290 |
\isacommand{ML}\isamarkupfalse%
|
jan@42369
|
1291 |
\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
|
jan@42369
|
1292 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}numerator{\isaliteral{2C}{\isacharcomma}}\ denominator{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ HOLogic{\isaliteral{2E}{\isachardot}}dest{\isaliteral{5F}{\isacharunderscore}}eq\ eq{\isadigit{3}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1293 |
\ \ val\ eq{\isadigit{3}}{\isaliteral{27}{\isacharprime}}\ {\isaliteral{3D}{\isacharequal}}\ HOLogic{\isaliteral{2E}{\isachardot}}mk{\isaliteral{5F}{\isacharunderscore}}eq\ {\isaliteral{28}{\isacharparenleft}}numerator{\isaliteral{2C}{\isacharcomma}}\ fract{\isadigit{1}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1294 |
\ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}\isanewline
|
jan@42369
|
1295 |
\ \ \ {\isaliteral{2A}{\isacharasterisk}}\ A\ B\ {\isaliteral{21}{\isacharbang}}\isanewline
|
jan@42369
|
1296 |
\ \ \ {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42369
|
1297 |
\ \ term{\isadigit{2}}str\ eq{\isadigit{3}}{\isaliteral{27}{\isacharprime}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1298 |
\ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}\isanewline
|
jan@42369
|
1299 |
\ \ \ {\isaliteral{2A}{\isacharasterisk}}\ MANDATORY{\isaliteral{3A}{\isacharcolon}}\ simplify\ {\isaliteral{28}{\isacharparenleft}}and\ remove\ denominator{\isaliteral{29}{\isacharparenright}}\ otherwise\ {\isadigit{3}}\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{0}}\isanewline
|
jan@42369
|
1300 |
\ \ \ {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42369
|
1301 |
\ \ val\ SOME\ {\isaliteral{28}{\isacharparenleft}}eq{\isadigit{3}}{\isaliteral{27}{\isacharprime}}{\isaliteral{27}{\isacharprime}}\ {\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ \isanewline
|
jan@42369
|
1302 |
\ \ \ \ rewrite{\isaliteral{5F}{\isacharunderscore}}set{\isaliteral{5F}{\isacharunderscore}}\ %
|
jan@42369
|
1303 |
\isaantiq
|
jan@42369
|
1304 |
theory\ Isac{}%
|
jan@42369
|
1305 |
\endisaantiq
|
jan@42369
|
1306 |
\ false\ norm{\isaliteral{5F}{\isacharunderscore}}Rational\ eq{\isadigit{3}}{\isaliteral{27}{\isacharprime}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1307 |
\ \ term{\isadigit{2}}str\ eq{\isadigit{3}}{\isaliteral{27}{\isacharprime}}{\isaliteral{27}{\isacharprime}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1308 |
{\isaliteral{2A7D}{\isacharverbatimclose}}%
|
jan@42369
|
1309 |
\endisatagML
|
jan@42369
|
1310 |
{\isafoldML}%
|
jan@42369
|
1311 |
%
|
jan@42369
|
1312 |
\isadelimML
|
jan@42369
|
1313 |
%
|
jan@42369
|
1314 |
\endisadelimML
|
jan@42369
|
1315 |
%
|
jan@42369
|
1316 |
\begin{isamarkuptext}%
|
jan@42369
|
1317 |
\noindent Still working at {\sisac}\ldots%
|
jan@42369
|
1318 |
\end{isamarkuptext}%
|
jan@42369
|
1319 |
\isamarkuptrue%
|
jan@42369
|
1320 |
%
|
jan@42369
|
1321 |
\isadelimML
|
jan@42369
|
1322 |
%
|
jan@42369
|
1323 |
\endisadelimML
|
jan@42369
|
1324 |
%
|
jan@42369
|
1325 |
\isatagML
|
jan@42369
|
1326 |
\isacommand{ML}\isamarkupfalse%
|
jan@42369
|
1327 |
\ {\isaliteral{7B2A}{\isacharverbatimopen}}\ Context{\isaliteral{2E}{\isachardot}}theory{\isaliteral{5F}{\isacharunderscore}}name\ thy\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{22}{\isachardoublequote}}Isac{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{2A7D}{\isacharverbatimclose}}%
|
jan@42369
|
1328 |
\endisatagML
|
jan@42369
|
1329 |
{\isafoldML}%
|
jan@42369
|
1330 |
%
|
jan@42369
|
1331 |
\isadelimML
|
jan@42369
|
1332 |
%
|
jan@42369
|
1333 |
\endisadelimML
|
jan@42369
|
1334 |
%
|
jan@42369
|
1335 |
\isamarkupsubsubsection{Build a Rule-Set for the Ansatz%
|
jan@42369
|
1336 |
}
|
jan@42369
|
1337 |
\isamarkuptrue%
|
jan@42369
|
1338 |
%
|
jan@42369
|
1339 |
\begin{isamarkuptext}%
|
jan@42369
|
1340 |
\noindent The \emph{ansatz} rules violate the principle that each
|
jan@42369
|
1341 |
variable on the right-hand-side must also occur on the
|
jan@42369
|
1342 |
left-hand-side of the rule: A, B, etc. don't do that. Thus the
|
jan@42369
|
1343 |
rewriter marks these variables with question marks: ?A, ?B, etc.
|
jan@42369
|
1344 |
These question marks can be dropped by \ttfamily fun
|
jan@42369
|
1345 |
drop\_questionmarks\normalfont.%
|
jan@42369
|
1346 |
\end{isamarkuptext}%
|
jan@42369
|
1347 |
\isamarkuptrue%
|
jan@42369
|
1348 |
%
|
jan@42369
|
1349 |
\isadelimML
|
jan@42369
|
1350 |
%
|
jan@42369
|
1351 |
\endisadelimML
|
jan@42369
|
1352 |
%
|
jan@42369
|
1353 |
\isatagML
|
jan@42369
|
1354 |
\isacommand{ML}\isamarkupfalse%
|
jan@42369
|
1355 |
\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
|
jan@42369
|
1356 |
\ \ val\ ansatz{\isaliteral{5F}{\isacharunderscore}}rls\ {\isaliteral{3D}{\isacharequal}}\ prep{\isaliteral{5F}{\isacharunderscore}}rls{\isaliteral{28}{\isacharparenleft}}\isanewline
|
walther@59851
|
1357 |
\ \ \ \ Rule_Set.Repeat\ {\isaliteral{7B}{\isacharbraceleft}}id\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{22}{\isachardoublequote}}ansatz{\isaliteral{5F}{\isacharunderscore}}rls{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ preconds\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ rew{\isaliteral{5F}{\isacharunderscore}}ord\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}dummy{\isaliteral{5F}{\isacharunderscore}}ord{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}dummy{\isaliteral{5F}{\isacharunderscore}}ord{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\isanewline
|
walther@59851
|
1358 |
\ \ \ \ \ \ erls\ {\isaliteral{3D}{\isacharequal}}\ e{\isaliteral{5F}{\isacharunderscore}}rls{\isaliteral{2C}{\isacharcomma}}\ srls\ {\isaliteral{3D}{\isacharequal}}\ Rule_Set.Empty{\isaliteral{2C}{\isacharcomma}}\ calc\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\isanewline
|
jan@42369
|
1359 |
\ \ \ \ \ \ rules\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}\isanewline
|
jan@42369
|
1360 |
\ \ \ \ \ \ \ \ Thm\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}ansatz{\isaliteral{5F}{\isacharunderscore}}{\isadigit{2}}nd{\isaliteral{5F}{\isacharunderscore}}order{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}num{\isaliteral{5F}{\isacharunderscore}}str\ %
|
jan@42369
|
1361 |
\isaantiq
|
jan@42369
|
1362 |
thm\ ansatz{\isaliteral{5F}{\isacharunderscore}}{\isadigit{2}}nd{\isaliteral{5F}{\isacharunderscore}}order{}%
|
jan@42369
|
1363 |
\endisaantiq
|
jan@42369
|
1364 |
{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\isanewline
|
jan@42369
|
1365 |
\ \ \ \ \ \ \ \ Thm\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}equival{\isaliteral{5F}{\isacharunderscore}}trans{\isaliteral{5F}{\isacharunderscore}}{\isadigit{2}}nd{\isaliteral{5F}{\isacharunderscore}}order{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}num{\isaliteral{5F}{\isacharunderscore}}str\ %
|
jan@42369
|
1366 |
\isaantiq
|
jan@42369
|
1367 |
thm\ equival{\isaliteral{5F}{\isacharunderscore}}trans{\isaliteral{5F}{\isacharunderscore}}{\isadigit{2}}nd{\isaliteral{5F}{\isacharunderscore}}order{}%
|
jan@42369
|
1368 |
\endisaantiq
|
jan@42369
|
1369 |
{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42369
|
1370 |
\ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ \isanewline
|
jan@42369
|
1371 |
\ \ \ \ \ \ scr\ {\isaliteral{3D}{\isacharequal}}\ EmptyScr{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1372 |
{\isaliteral{2A7D}{\isacharverbatimclose}}%
|
jan@42369
|
1373 |
\endisatagML
|
jan@42369
|
1374 |
{\isafoldML}%
|
jan@42369
|
1375 |
%
|
jan@42369
|
1376 |
\isadelimML
|
jan@42369
|
1377 |
%
|
jan@42369
|
1378 |
\endisadelimML
|
jan@42369
|
1379 |
%
|
jan@42369
|
1380 |
\begin{isamarkuptext}%
|
jan@42381
|
1381 |
\noindent We apply the ruleset\ldots%
|
jan@42369
|
1382 |
\end{isamarkuptext}%
|
jan@42369
|
1383 |
\isamarkuptrue%
|
jan@42369
|
1384 |
%
|
jan@42369
|
1385 |
\isadelimML
|
jan@42369
|
1386 |
%
|
jan@42369
|
1387 |
\endisadelimML
|
jan@42369
|
1388 |
%
|
jan@42369
|
1389 |
\isatagML
|
jan@42369
|
1390 |
\isacommand{ML}\isamarkupfalse%
|
jan@42369
|
1391 |
\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
|
jan@42369
|
1392 |
\ \ val\ SOME\ {\isaliteral{28}{\isacharparenleft}}ttttt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ \isanewline
|
jan@42369
|
1393 |
\ \ \ \ rewrite{\isaliteral{5F}{\isacharunderscore}}set{\isaliteral{5F}{\isacharunderscore}}\ %
|
jan@42369
|
1394 |
\isaantiq
|
jan@42369
|
1395 |
theory\ Isac{}%
|
jan@42369
|
1396 |
\endisaantiq
|
jan@42369
|
1397 |
\ false\ ansatz{\isaliteral{5F}{\isacharunderscore}}rls\ expr{\isaliteral{27}{\isacharprime}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1398 |
{\isaliteral{2A7D}{\isacharverbatimclose}}%
|
jan@42369
|
1399 |
\endisatagML
|
jan@42369
|
1400 |
{\isafoldML}%
|
jan@42369
|
1401 |
%
|
jan@42369
|
1402 |
\isadelimML
|
jan@42369
|
1403 |
%
|
jan@42369
|
1404 |
\endisadelimML
|
jan@42369
|
1405 |
%
|
jan@42369
|
1406 |
\begin{isamarkuptext}%
|
jan@42369
|
1407 |
\noindent And check the output\ldots%
|
jan@42369
|
1408 |
\end{isamarkuptext}%
|
jan@42369
|
1409 |
\isamarkuptrue%
|
jan@42369
|
1410 |
%
|
jan@42369
|
1411 |
\isadelimML
|
jan@42369
|
1412 |
%
|
jan@42369
|
1413 |
\endisadelimML
|
jan@42369
|
1414 |
%
|
jan@42369
|
1415 |
\isatagML
|
jan@42369
|
1416 |
\isacommand{ML}\isamarkupfalse%
|
jan@42369
|
1417 |
\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
|
jan@42369
|
1418 |
\ \ term{\isadigit{2}}str\ expr{\isaliteral{27}{\isacharprime}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{22}{\isachardoublequote}}{\isadigit{3}}\ {\isaliteral{2F}{\isacharslash}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{1}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{2}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{2D}{\isacharminus}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{1}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{4}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1419 |
\ \ term{\isadigit{2}}str\ ttttt\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{3F}{\isacharquery}}A\ {\isaliteral{2F}{\isacharslash}}\ {\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{1}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{2}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{3F}{\isacharquery}}B\ {\isaliteral{2F}{\isacharslash}}\ {\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{2D}{\isacharminus}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{1}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{4}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1420 |
{\isaliteral{2A7D}{\isacharverbatimclose}}%
|
jan@42369
|
1421 |
\endisatagML
|
jan@42369
|
1422 |
{\isafoldML}%
|
jan@42369
|
1423 |
%
|
jan@42369
|
1424 |
\isadelimML
|
jan@42369
|
1425 |
%
|
jan@42369
|
1426 |
\endisadelimML
|
jan@42369
|
1427 |
%
|
jan@42381
|
1428 |
\isamarkupsubsubsection{Get the First Coefficient%
|
jan@42369
|
1429 |
}
|
jan@42369
|
1430 |
\isamarkuptrue%
|
jan@42369
|
1431 |
%
|
jan@42369
|
1432 |
\begin{isamarkuptext}%
|
jan@42381
|
1433 |
\noindent Now it's up to get the two coefficients A and B, which will be
|
jan@42381
|
1434 |
the numerators of our partial fractions. Continue following up the
|
jan@42369
|
1435 |
Calculation in Section~\ref{sec:calc:ztrans} Subproblem~1.%
|
jan@42369
|
1436 |
\end{isamarkuptext}%
|
jan@42369
|
1437 |
\isamarkuptrue%
|
jan@42369
|
1438 |
%
|
jan@42369
|
1439 |
\begin{isamarkuptext}%
|
jan@42381
|
1440 |
\noindent To get the first coefficient we substitute $z$ with the first
|
jan@42381
|
1441 |
zero-point we determined in Section~\ref{sec:solveq}.%
|
jan@42369
|
1442 |
\end{isamarkuptext}%
|
jan@42369
|
1443 |
\isamarkuptrue%
|
jan@42369
|
1444 |
%
|
jan@42369
|
1445 |
\isadelimML
|
jan@42369
|
1446 |
%
|
jan@42369
|
1447 |
\endisadelimML
|
jan@42369
|
1448 |
%
|
jan@42369
|
1449 |
\isatagML
|
jan@42369
|
1450 |
\isacommand{ML}\isamarkupfalse%
|
jan@42369
|
1451 |
\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
|
jan@42369
|
1452 |
\ \ val\ SOME\ {\isaliteral{28}{\isacharparenleft}}eq{\isadigit{4}}{\isaliteral{5F}{\isacharunderscore}}{\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\isanewline
|
jan@42369
|
1453 |
\ \ \ \ rewrite{\isaliteral{5F}{\isacharunderscore}}terms{\isaliteral{5F}{\isacharunderscore}}\ %
|
jan@42369
|
1454 |
\isaantiq
|
jan@42369
|
1455 |
theory\ Isac{}%
|
jan@42369
|
1456 |
\endisaantiq
|
jan@42369
|
1457 |
\ e{\isaliteral{5F}{\isacharunderscore}}rew{\isaliteral{5F}{\isacharunderscore}}ord\ e{\isaliteral{5F}{\isacharunderscore}}rls\ {\isaliteral{5B}{\isacharbrackleft}}s{\isaliteral{5F}{\isacharunderscore}}{\isadigit{1}}{\isaliteral{5D}{\isacharbrackright}}\ eq{\isadigit{3}}{\isaliteral{27}{\isacharprime}}{\isaliteral{27}{\isacharprime}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1458 |
\ \ term{\isadigit{2}}str\ eq{\isadigit{4}}{\isaliteral{5F}{\isacharunderscore}}{\isadigit{1}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1459 |
\ \ val\ SOME\ {\isaliteral{28}{\isacharparenleft}}eq{\isadigit{4}}{\isaliteral{5F}{\isacharunderscore}}{\isadigit{2}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\isanewline
|
jan@42369
|
1460 |
\ \ \ \ rewrite{\isaliteral{5F}{\isacharunderscore}}set{\isaliteral{5F}{\isacharunderscore}}\ %
|
jan@42369
|
1461 |
\isaantiq
|
jan@42369
|
1462 |
theory\ Isac{}%
|
jan@42369
|
1463 |
\endisaantiq
|
jan@42369
|
1464 |
\ false\ norm{\isaliteral{5F}{\isacharunderscore}}Rational\ eq{\isadigit{4}}{\isaliteral{5F}{\isacharunderscore}}{\isadigit{1}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1465 |
\ \ term{\isadigit{2}}str\ eq{\isadigit{4}}{\isaliteral{5F}{\isacharunderscore}}{\isadigit{2}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1466 |
\isanewline
|
jan@42369
|
1467 |
\ \ val\ fmz\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}equality\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{3}}{\isaliteral{3D}{\isacharequal}}{\isadigit{3}}{\isaliteral{2A}{\isacharasterisk}}A{\isaliteral{2F}{\isacharslash}}{\isaliteral{28}{\isacharparenleft}}{\isadigit{4}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}real{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}solveFor\ A{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}solutions\ L{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1468 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}dI{\isaliteral{27}{\isacharprime}}{\isaliteral{2C}{\isacharcomma}}pI{\isaliteral{27}{\isacharprime}}{\isaliteral{2C}{\isacharcomma}}mI{\isaliteral{27}{\isacharprime}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}Isac{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}univariate{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}equation{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}no{\isaliteral{5F}{\isacharunderscore}}met{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1469 |
\ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}\isanewline
|
jan@42381
|
1470 |
\ \ \ {\isaliteral{2A}{\isacharasterisk}}\ Solve\ the\ simple\ linear\ equation\ for\ A{\isaliteral{3A}{\isacharcolon}}\isanewline
|
jan@42369
|
1471 |
\ \ \ {\isaliteral{2A}{\isacharasterisk}}\ Return\ eq{\isaliteral{2C}{\isacharcomma}}\ not\ list\ of\ eq{\isaliteral{27}{\isacharprime}}s\isanewline
|
jan@42369
|
1472 |
\ \ \ {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42369
|
1473 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fa{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ CalcTreeTEST\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{28}{\isacharparenleft}}fmz{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{28}{\isacharparenleft}}dI{\isaliteral{27}{\isacharprime}}{\isaliteral{2C}{\isacharcomma}}pI{\isaliteral{27}{\isacharprime}}{\isaliteral{2C}{\isacharcomma}}mI{\isaliteral{27}{\isacharprime}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1474 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fa{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1475 |
\ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}Add{\isaliteral{5F}{\isacharunderscore}}Given\ {\isaliteral{22}{\isachardoublequote}}equality\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{3}}{\isaliteral{3D}{\isacharequal}}{\isadigit{3}}{\isaliteral{2A}{\isacharasterisk}}A{\isaliteral{2F}{\isacharslash}}{\isadigit{4}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42369
|
1476 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fa{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1477 |
\ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}Add{\isaliteral{5F}{\isacharunderscore}}Given\ {\isaliteral{22}{\isachardoublequote}}solveFor\ A{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42369
|
1478 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fa{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\ \isanewline
|
jan@42369
|
1479 |
\ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}Add{\isaliteral{5F}{\isacharunderscore}}Find\ {\isaliteral{22}{\isachardoublequote}}solutions\ L{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42369
|
1480 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fa{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1481 |
\ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}Specify{\isaliteral{5F}{\isacharunderscore}}Theory\ {\isaliteral{22}{\isachardoublequote}}Isac{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42369
|
1482 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fa{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
wneuper@59370
|
1483 |
\ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}Specify{\isaliteral{5F}{\isacharunderscore}}Problem\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}normalise{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}polynomial{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\isanewline
|
jan@42369
|
1484 |
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}univariate{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}equation{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42369
|
1485 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fa{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
wneuper@59370
|
1486 |
\ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}\ Specify{\isaliteral{5F}{\isacharunderscore}}Method{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}PolyEq{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}normalise{\isaliteral{5F}{\isacharunderscore}}poly{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42369
|
1487 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fa{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
wneuper@59370
|
1488 |
\ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}Apply{\isaliteral{5F}{\isacharunderscore}}Method{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}PolyEq{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}normalise{\isaliteral{5F}{\isacharunderscore}}poly{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42369
|
1489 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fa{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1490 |
\ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}Rewrite\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}all{\isaliteral{5F}{\isacharunderscore}}left{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}PolyEq{\isaliteral{2E}{\isachardot}}all{\isaliteral{5F}{\isacharunderscore}}left{\isaliteral{22}{\isachardoublequote}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42369
|
1491 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fa{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1492 |
\ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}Rewrite{\isaliteral{5F}{\isacharunderscore}}Set{\isaliteral{5F}{\isacharunderscore}}Inst{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}bdv{\isaliteral{2C}{\isacharcomma}}A{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}make{\isaliteral{5F}{\isacharunderscore}}ratpoly{\isaliteral{5F}{\isacharunderscore}}in{\isaliteral{22}{\isachardoublequote}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42369
|
1493 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fa{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1494 |
\ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}Rewrite{\isaliteral{5F}{\isacharunderscore}}Set\ {\isaliteral{22}{\isachardoublequote}}polyeq{\isaliteral{5F}{\isacharunderscore}}simplify{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42369
|
1495 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fa{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\ \isanewline
|
jan@42369
|
1496 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fa{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\ \isanewline
|
jan@42369
|
1497 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fa{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1498 |
\ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}Add{\isaliteral{5F}{\isacharunderscore}}Given\ {\isaliteral{22}{\isachardoublequote}}equality\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{3}}\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{3}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{4}}\ {\isaliteral{2A}{\isacharasterisk}}\ A\ {\isaliteral{3D}{\isacharequal}}{\isadigit{0}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42369
|
1499 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fa{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1500 |
\ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}Add{\isaliteral{5F}{\isacharunderscore}}Given\ {\isaliteral{22}{\isachardoublequote}}solveFor\ A{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42369
|
1501 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fa{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1502 |
\ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}Add{\isaliteral{5F}{\isacharunderscore}}Find\ {\isaliteral{22}{\isachardoublequote}}solutions\ A{\isaliteral{5F}{\isacharunderscore}}i{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42369
|
1503 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fa{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\ \isanewline
|
jan@42369
|
1504 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fa{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\ \isanewline
|
jan@42369
|
1505 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fa{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\ \isanewline
|
jan@42369
|
1506 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fa{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\ \isanewline
|
jan@42369
|
1507 |
\ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}Apply{\isaliteral{5F}{\isacharunderscore}}Method\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}PolyEq{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}solve{\isaliteral{5F}{\isacharunderscore}}d{\isadigit{1}}{\isaliteral{5F}{\isacharunderscore}}polyeq{\isaliteral{5F}{\isacharunderscore}}equation{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42369
|
1508 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fa{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1509 |
\ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}Rewrite{\isaliteral{5F}{\isacharunderscore}}Set{\isaliteral{5F}{\isacharunderscore}}Inst{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}bdv{\isaliteral{2C}{\isacharcomma}}A{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}d{\isadigit{1}}{\isaliteral{5F}{\isacharunderscore}}polyeq{\isaliteral{5F}{\isacharunderscore}}simplify{\isaliteral{22}{\isachardoublequote}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42369
|
1510 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fa{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1511 |
\ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}Rewrite{\isaliteral{5F}{\isacharunderscore}}Set\ {\isaliteral{22}{\isachardoublequote}}polyeq{\isaliteral{5F}{\isacharunderscore}}simplify{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42369
|
1512 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fa{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1513 |
\ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}Rewrite{\isaliteral{5F}{\isacharunderscore}}Set\ {\isaliteral{22}{\isachardoublequote}}norm{\isaliteral{5F}{\isacharunderscore}}Rational{\isaliteral{5F}{\isacharunderscore}}parenthesized{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42369
|
1514 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fa{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1515 |
\ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}Or{\isaliteral{5F}{\isacharunderscore}}to{\isaliteral{5F}{\isacharunderscore}}List{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42369
|
1516 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fa{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1517 |
\ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}Check{\isaliteral{5F}{\isacharunderscore}}elementwise\ {\isaliteral{22}{\isachardoublequote}}Assumptions{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42369
|
1518 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fa{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1519 |
\ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}Check{\isaliteral{5F}{\isacharunderscore}}Postcond\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}degree{\isaliteral{5F}{\isacharunderscore}}{\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}polynomial{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\isanewline
|
jan@42369
|
1520 |
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}univariate{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}equation{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42369
|
1521 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fa{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
wneuper@59370
|
1522 |
\ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}Check{\isaliteral{5F}{\isacharunderscore}}Postcond\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}normalise{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}polynomial{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\isanewline
|
jan@42369
|
1523 |
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}univariate{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}equation{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42369
|
1524 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fa{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1525 |
\ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}End{\isaliteral{5F}{\isacharunderscore}}Proof{\isaliteral{27}{\isacharprime}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42369
|
1526 |
\ \ f{\isadigit{2}}str\ fa{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1527 |
{\isaliteral{2A7D}{\isacharverbatimclose}}%
|
jan@42369
|
1528 |
\endisatagML
|
jan@42369
|
1529 |
{\isafoldML}%
|
jan@42369
|
1530 |
%
|
jan@42369
|
1531 |
\isadelimML
|
jan@42369
|
1532 |
%
|
jan@42369
|
1533 |
\endisadelimML
|
jan@42369
|
1534 |
%
|
jan@42381
|
1535 |
\isamarkupsubsubsection{Get Second Coefficient%
|
jan@42369
|
1536 |
}
|
jan@42369
|
1537 |
\isamarkuptrue%
|
jan@42369
|
1538 |
%
|
jan@42369
|
1539 |
\begin{isamarkuptext}%
|
jan@42369
|
1540 |
\noindent With the use of \texttt{thy} we check which theories the
|
jan@42369
|
1541 |
interpreter knows.%
|
jan@42369
|
1542 |
\end{isamarkuptext}%
|
jan@42369
|
1543 |
\isamarkuptrue%
|
jan@42369
|
1544 |
%
|
jan@42369
|
1545 |
\isadelimML
|
jan@42369
|
1546 |
%
|
jan@42369
|
1547 |
\endisadelimML
|
jan@42369
|
1548 |
%
|
jan@42369
|
1549 |
\isatagML
|
neuper@42289
|
1550 |
\isacommand{ML}\isamarkupfalse%
|
neuper@42289
|
1551 |
\ {\isaliteral{7B2A}{\isacharverbatimopen}}thy{\isaliteral{2A7D}{\isacharverbatimclose}}%
|
neuper@42289
|
1552 |
\endisatagML
|
neuper@42289
|
1553 |
{\isafoldML}%
|
neuper@42289
|
1554 |
%
|
neuper@42289
|
1555 |
\isadelimML
|
neuper@42289
|
1556 |
%
|
neuper@42289
|
1557 |
\endisadelimML
|
neuper@42289
|
1558 |
%
|
jan@42369
|
1559 |
\begin{isamarkuptext}%
|
jan@42381
|
1560 |
\noindent To get the second coefficient we substitute $z$ with the second
|
jan@42381
|
1561 |
zero-point we determined in Section~\ref{sec:solveq}.%
|
jan@42369
|
1562 |
\end{isamarkuptext}%
|
jan@42369
|
1563 |
\isamarkuptrue%
|
jan@42369
|
1564 |
%
|
jan@42369
|
1565 |
\isadelimML
|
jan@42369
|
1566 |
%
|
jan@42369
|
1567 |
\endisadelimML
|
jan@42369
|
1568 |
%
|
jan@42369
|
1569 |
\isatagML
|
jan@42369
|
1570 |
\isacommand{ML}\isamarkupfalse%
|
jan@42369
|
1571 |
\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
|
jan@42369
|
1572 |
\ \ val\ SOME\ {\isaliteral{28}{\isacharparenleft}}eq{\isadigit{4}}b{\isaliteral{5F}{\isacharunderscore}}{\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\isanewline
|
jan@42369
|
1573 |
\ \ \ \ rewrite{\isaliteral{5F}{\isacharunderscore}}terms{\isaliteral{5F}{\isacharunderscore}}\ %
|
jan@42369
|
1574 |
\isaantiq
|
jan@42369
|
1575 |
theory\ Isac{}%
|
jan@42369
|
1576 |
\endisaantiq
|
jan@42369
|
1577 |
\ e{\isaliteral{5F}{\isacharunderscore}}rew{\isaliteral{5F}{\isacharunderscore}}ord\ e{\isaliteral{5F}{\isacharunderscore}}rls\ {\isaliteral{5B}{\isacharbrackleft}}s{\isaliteral{5F}{\isacharunderscore}}{\isadigit{2}}{\isaliteral{5D}{\isacharbrackright}}\ eq{\isadigit{3}}{\isaliteral{27}{\isacharprime}}{\isaliteral{27}{\isacharprime}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1578 |
\ \ term{\isadigit{2}}str\ eq{\isadigit{4}}b{\isaliteral{5F}{\isacharunderscore}}{\isadigit{1}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1579 |
\ \ val\ SOME\ {\isaliteral{28}{\isacharparenleft}}eq{\isadigit{4}}b{\isaliteral{5F}{\isacharunderscore}}{\isadigit{2}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\isanewline
|
jan@42369
|
1580 |
\ \ \ \ rewrite{\isaliteral{5F}{\isacharunderscore}}set{\isaliteral{5F}{\isacharunderscore}}\ %
|
jan@42369
|
1581 |
\isaantiq
|
jan@42369
|
1582 |
theory\ Isac{}%
|
jan@42369
|
1583 |
\endisaantiq
|
jan@42369
|
1584 |
\ false\ norm{\isaliteral{5F}{\isacharunderscore}}Rational\ eq{\isadigit{4}}b{\isaliteral{5F}{\isacharunderscore}}{\isadigit{1}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1585 |
\ \ term{\isadigit{2}}str\ eq{\isadigit{4}}b{\isaliteral{5F}{\isacharunderscore}}{\isadigit{2}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1586 |
\isanewline
|
jan@42369
|
1587 |
\ \ val\ fmz\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}equality\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{3}}{\isaliteral{3D}{\isacharequal}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{3}}{\isaliteral{2A}{\isacharasterisk}}B{\isaliteral{2F}{\isacharslash}}{\isaliteral{28}{\isacharparenleft}}{\isadigit{4}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}real{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}solveFor\ B{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}solutions\ L{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1588 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}dI{\isaliteral{27}{\isacharprime}}{\isaliteral{2C}{\isacharcomma}}pI{\isaliteral{27}{\isacharprime}}{\isaliteral{2C}{\isacharcomma}}mI{\isaliteral{27}{\isacharprime}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}Isac{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}univariate{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}equation{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}no{\isaliteral{5F}{\isacharunderscore}}met{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1589 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fb{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ CalcTreeTEST\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{28}{\isacharparenleft}}fmz{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{28}{\isacharparenleft}}dI{\isaliteral{27}{\isacharprime}}{\isaliteral{2C}{\isacharcomma}}pI{\isaliteral{27}{\isacharprime}}{\isaliteral{2C}{\isacharcomma}}mI{\isaliteral{27}{\isacharprime}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1590 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fb{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1591 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fb{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1592 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fb{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1593 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fb{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1594 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fb{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1595 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fb{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1596 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fb{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1597 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fb{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1598 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fb{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1599 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fb{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1600 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fb{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1601 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fb{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1602 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fb{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1603 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fb{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1604 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fb{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1605 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fb{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1606 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fb{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1607 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fb{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1608 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fb{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1609 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fb{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1610 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fb{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1611 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fb{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1612 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fb{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1613 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fb{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1614 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fb{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1615 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fb{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1616 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fb{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\ \isanewline
|
jan@42369
|
1617 |
\ \ f{\isadigit{2}}str\ fb{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1618 |
{\isaliteral{2A7D}{\isacharverbatimclose}}%
|
jan@42369
|
1619 |
\endisatagML
|
jan@42369
|
1620 |
{\isafoldML}%
|
jan@42369
|
1621 |
%
|
jan@42369
|
1622 |
\isadelimML
|
jan@42369
|
1623 |
%
|
jan@42369
|
1624 |
\endisadelimML
|
jan@42369
|
1625 |
%
|
jan@42369
|
1626 |
\begin{isamarkuptext}%
|
jan@42369
|
1627 |
\noindent We compare our results with the pre calculated upshot.%
|
jan@42369
|
1628 |
\end{isamarkuptext}%
|
jan@42369
|
1629 |
\isamarkuptrue%
|
jan@42369
|
1630 |
%
|
jan@42369
|
1631 |
\isadelimML
|
jan@42369
|
1632 |
%
|
jan@42369
|
1633 |
\endisadelimML
|
jan@42369
|
1634 |
%
|
jan@42369
|
1635 |
\isatagML
|
jan@42369
|
1636 |
\isacommand{ML}\isamarkupfalse%
|
jan@42369
|
1637 |
\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
|
jan@42369
|
1638 |
\ \ if\ f{\isadigit{2}}str\ fa\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5B}{\isacharbrackleft}}A\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{4}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}\ then\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{29}{\isacharparenright}}\ else\ error\ {\isaliteral{22}{\isachardoublequote}}part{\isaliteral{2E}{\isachardot}}fract{\isaliteral{2E}{\isachardot}}\ eq{\isadigit{4}}{\isaliteral{5F}{\isacharunderscore}}{\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1639 |
\ \ if\ f{\isadigit{2}}str\ fb\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5B}{\isacharbrackleft}}B\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{4}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}\ then\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{29}{\isacharparenright}}\ else\ error\ {\isaliteral{22}{\isachardoublequote}}part{\isaliteral{2E}{\isachardot}}fract{\isaliteral{2E}{\isachardot}}\ eq{\isadigit{4}}{\isaliteral{5F}{\isacharunderscore}}{\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1640 |
{\isaliteral{2A7D}{\isacharverbatimclose}}%
|
jan@42369
|
1641 |
\endisatagML
|
jan@42369
|
1642 |
{\isafoldML}%
|
jan@42369
|
1643 |
%
|
jan@42369
|
1644 |
\isadelimML
|
jan@42369
|
1645 |
%
|
jan@42369
|
1646 |
\endisadelimML
|
jan@42369
|
1647 |
%
|
jan@42296
|
1648 |
\isamarkupsection{Implement the Specification and the Method \label{spec-meth}%
|
neuper@42289
|
1649 |
}
|
neuper@42289
|
1650 |
\isamarkuptrue%
|
neuper@42289
|
1651 |
%
|
neuper@42289
|
1652 |
\begin{isamarkuptext}%
|
jan@42369
|
1653 |
\noindent Now everything we need for solving the problem has been
|
jan@42369
|
1654 |
tested out. We now start by creating new nodes for our methods and
|
jan@42381
|
1655 |
further on our new program in the interpreter.%
|
neuper@42289
|
1656 |
\end{isamarkuptext}%
|
neuper@42289
|
1657 |
\isamarkuptrue%
|
neuper@42289
|
1658 |
%
|
jan@42370
|
1659 |
\isamarkupsubsection{Define the Field Descriptions for the
|
jan@42370
|
1660 |
Specification\label{sec:deffdes}%
|
neuper@42289
|
1661 |
}
|
neuper@42289
|
1662 |
\isamarkuptrue%
|
jan@42369
|
1663 |
%
|
jan@42369
|
1664 |
\begin{isamarkuptext}%
|
jan@42369
|
1665 |
\noindent We define the fields \em filterExpression \normalfont and
|
jan@42381
|
1666 |
\em stepResponse \normalfont both as equations, they represent the in- and
|
jan@42369
|
1667 |
output of the program.%
|
jan@42369
|
1668 |
\end{isamarkuptext}%
|
jan@42369
|
1669 |
\isamarkuptrue%
|
neuper@42289
|
1670 |
\isacommand{consts}\isamarkupfalse%
|
neuper@42289
|
1671 |
\isanewline
|
neuper@42289
|
1672 |
\ \ filterExpression\ \ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}bool\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\ una{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
|
neuper@42289
|
1673 |
\ \ stepResponse\ \ \ \ \ \ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}bool\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\ una{\isaliteral{22}{\isachardoublequoteclose}}%
|
neuper@42289
|
1674 |
\isamarkupsubsection{Define the Specification%
|
neuper@42289
|
1675 |
}
|
neuper@42289
|
1676 |
\isamarkuptrue%
|
neuper@42289
|
1677 |
%
|
jan@42369
|
1678 |
\begin{isamarkuptext}%
|
jan@42369
|
1679 |
\noindent The next step is defining the specifications as nodes in the
|
jan@42381
|
1680 |
designated part. We have to create the hierarchy node by node and start
|
jan@42369
|
1681 |
with \em SignalProcessing \normalfont and go on by creating the node
|
jan@42369
|
1682 |
\em Z\_Transform\normalfont.%
|
jan@42369
|
1683 |
\end{isamarkuptext}%
|
jan@42369
|
1684 |
\isamarkuptrue%
|
jan@42369
|
1685 |
%
|
neuper@42289
|
1686 |
\isadelimML
|
neuper@42289
|
1687 |
%
|
neuper@42289
|
1688 |
\endisadelimML
|
neuper@42289
|
1689 |
%
|
neuper@42289
|
1690 |
\isatagML
|
neuper@42289
|
1691 |
\isacommand{ML}\isamarkupfalse%
|
neuper@42289
|
1692 |
\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
|
jan@42369
|
1693 |
\ \ store{\isaliteral{5F}{\isacharunderscore}}pbt\isanewline
|
jan@42369
|
1694 |
\ \ \ {\isaliteral{28}{\isacharparenleft}}prep{\isaliteral{5F}{\isacharunderscore}}pbt\ thy\ {\isaliteral{22}{\isachardoublequote}}pbl{\isaliteral{5F}{\isacharunderscore}}SP{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ e{\isaliteral{5F}{\isacharunderscore}}pblID\isanewline
|
jan@42369
|
1695 |
\ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}SignalProcessing{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ e{\isaliteral{5F}{\isacharunderscore}}rls{\isaliteral{2C}{\isacharcomma}}\ NONE{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1696 |
\ \ store{\isaliteral{5F}{\isacharunderscore}}pbt\isanewline
|
jan@42369
|
1697 |
\ \ \ {\isaliteral{28}{\isacharparenleft}}prep{\isaliteral{5F}{\isacharunderscore}}pbt\ thy\ {\isaliteral{22}{\isachardoublequote}}pbl{\isaliteral{5F}{\isacharunderscore}}SP{\isaliteral{5F}{\isacharunderscore}}Ztrans{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ e{\isaliteral{5F}{\isacharunderscore}}pblID\isanewline
|
jan@42369
|
1698 |
\ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}Z{\isaliteral{5F}{\isacharunderscore}}Transform{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}SignalProcessing{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ e{\isaliteral{5F}{\isacharunderscore}}rls{\isaliteral{2C}{\isacharcomma}}\ NONE{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1699 |
{\isaliteral{2A7D}{\isacharverbatimclose}}%
|
jan@42369
|
1700 |
\endisatagML
|
jan@42369
|
1701 |
{\isafoldML}%
|
jan@42369
|
1702 |
%
|
jan@42369
|
1703 |
\isadelimML
|
jan@42369
|
1704 |
%
|
jan@42369
|
1705 |
\endisadelimML
|
jan@42369
|
1706 |
%
|
jan@42369
|
1707 |
\begin{isamarkuptext}%
|
jan@42369
|
1708 |
\noindent For the suddenly created node we have to define the input
|
jan@42381
|
1709 |
and output parameters. We already prepared their definition in
|
jan@42381
|
1710 |
Section~\ref{sec:deffdes}.%
|
jan@42369
|
1711 |
\end{isamarkuptext}%
|
jan@42369
|
1712 |
\isamarkuptrue%
|
jan@42369
|
1713 |
%
|
jan@42369
|
1714 |
\isadelimML
|
jan@42369
|
1715 |
%
|
jan@42369
|
1716 |
\endisadelimML
|
jan@42369
|
1717 |
%
|
jan@42369
|
1718 |
\isatagML
|
neuper@42289
|
1719 |
\isacommand{ML}\isamarkupfalse%
|
neuper@42289
|
1720 |
\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
|
jan@42369
|
1721 |
\ \ store{\isaliteral{5F}{\isacharunderscore}}pbt\isanewline
|
jan@42369
|
1722 |
\ \ \ {\isaliteral{28}{\isacharparenleft}}prep{\isaliteral{5F}{\isacharunderscore}}pbt\ thy\ {\isaliteral{22}{\isachardoublequote}}pbl{\isaliteral{5F}{\isacharunderscore}}SP{\isaliteral{5F}{\isacharunderscore}}Ztrans{\isaliteral{5F}{\isacharunderscore}}inv{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ e{\isaliteral{5F}{\isacharunderscore}}pblID\isanewline
|
jan@42369
|
1723 |
\ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}inverse{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}Z{\isaliteral{5F}{\isacharunderscore}}Transform{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}SignalProcessing{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\isanewline
|
jan@42369
|
1724 |
\ \ \ \ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{23}{\isacharhash}}Given{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{2C}{\isacharcomma}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}filterExpression\ X{\isaliteral{5F}{\isacharunderscore}}eq{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\isanewline
|
jan@42369
|
1725 |
\ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{23}{\isacharhash}}Find{\isaliteral{22}{\isachardoublequote}}\ \ {\isaliteral{2C}{\isacharcomma}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}stepResponse\ n{\isaliteral{5F}{\isacharunderscore}}eq{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42369
|
1726 |
\ \ \ \ {\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\isanewline
|
jan@42369
|
1727 |
\ \ \ \ append{\isaliteral{5F}{\isacharunderscore}}rls\ {\isaliteral{22}{\isachardoublequote}}e{\isaliteral{5F}{\isacharunderscore}}rls{\isaliteral{22}{\isachardoublequote}}\ e{\isaliteral{5F}{\isacharunderscore}}rls\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}for\ preds\ in\ where{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ NONE{\isaliteral{2C}{\isacharcomma}}\ \isanewline
|
jan@42369
|
1728 |
\ \ \ \ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}SignalProcessing{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}Z{\isaliteral{5F}{\isacharunderscore}}Transform{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}inverse{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
neuper@42289
|
1729 |
\isanewline
|
jan@42369
|
1730 |
\ \ show{\isaliteral{5F}{\isacharunderscore}}ptyps{\isaliteral{28}{\isacharparenleft}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1731 |
\ \ get{\isaliteral{5F}{\isacharunderscore}}pbt\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}inverse{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}Z{\isaliteral{5F}{\isacharunderscore}}Transform{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}SignalProcessing{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
neuper@42289
|
1732 |
{\isaliteral{2A7D}{\isacharverbatimclose}}%
|
neuper@42289
|
1733 |
\endisatagML
|
neuper@42289
|
1734 |
{\isafoldML}%
|
neuper@42289
|
1735 |
%
|
neuper@42289
|
1736 |
\isadelimML
|
neuper@42289
|
1737 |
%
|
neuper@42289
|
1738 |
\endisadelimML
|
neuper@42289
|
1739 |
%
|
neuper@42289
|
1740 |
\isamarkupsubsection{Define Name and Signature for the Method%
|
neuper@42289
|
1741 |
}
|
neuper@42289
|
1742 |
\isamarkuptrue%
|
jan@42369
|
1743 |
%
|
jan@42369
|
1744 |
\begin{isamarkuptext}%
|
jan@42369
|
1745 |
\noindent As a next step we store the definition of our new method as a
|
jan@42369
|
1746 |
constant for the interpreter.%
|
jan@42369
|
1747 |
\end{isamarkuptext}%
|
jan@42369
|
1748 |
\isamarkuptrue%
|
neuper@42289
|
1749 |
\isacommand{consts}\isamarkupfalse%
|
neuper@42289
|
1750 |
\isanewline
|
neuper@42289
|
1751 |
\ \ InverseZTransform\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5B}{\isacharbrackleft}}bool{\isaliteral{2C}{\isacharcomma}}\ bool{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\ bool{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
|
wneuper@59585
|
1752 |
\ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{28}{\isacharparenleft}}Program\ InverseZTransform\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5F}{\isacharunderscore}}\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2F}{\isacharslash}}{\isaliteral{2F}{\isacharslash}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isadigit{9}}{\isaliteral{29}{\isacharparenright}}%
|
jan@42370
|
1753 |
\isamarkupsubsection{Setup Parent Nodes in Hierarchy of Method\label{sec:cparentnode}%
|
neuper@42289
|
1754 |
}
|
neuper@42289
|
1755 |
\isamarkuptrue%
|
neuper@42289
|
1756 |
%
|
jan@42369
|
1757 |
\begin{isamarkuptext}%
|
jan@42369
|
1758 |
\noindent Again we have to generate the nodes step by step, first the
|
jan@42369
|
1759 |
parent node and then the originally \em Z\_Transformation
|
jan@42369
|
1760 |
\normalfont node. We have to define both nodes first with an empty script
|
jan@42369
|
1761 |
as content.%
|
jan@42369
|
1762 |
\end{isamarkuptext}%
|
jan@42369
|
1763 |
\isamarkuptrue%
|
jan@42369
|
1764 |
%
|
neuper@42289
|
1765 |
\isadelimML
|
neuper@42289
|
1766 |
%
|
neuper@42289
|
1767 |
\endisadelimML
|
neuper@42289
|
1768 |
%
|
neuper@42289
|
1769 |
\isatagML
|
neuper@42289
|
1770 |
\isacommand{ML}\isamarkupfalse%
|
neuper@42289
|
1771 |
\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
|
jan@42369
|
1772 |
\ \ store{\isaliteral{5F}{\isacharunderscore}}met\isanewline
|
jan@42369
|
1773 |
\ \ \ {\isaliteral{28}{\isacharparenleft}}prep{\isaliteral{5F}{\isacharunderscore}}met\ thy\ {\isaliteral{22}{\isachardoublequote}}met{\isaliteral{5F}{\isacharunderscore}}SP{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ e{\isaliteral{5F}{\isacharunderscore}}metID\isanewline
|
jan@42369
|
1774 |
\ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}SignalProcessing{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\isanewline
|
jan@42369
|
1775 |
\ \ \ \ \ {\isaliteral{7B}{\isacharbraceleft}}rew{\isaliteral{5F}{\isacharunderscore}}ord{\isaliteral{27}{\isacharprime}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{22}{\isachardoublequote}}tless{\isaliteral{5F}{\isacharunderscore}}true{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ rls{\isaliteral{27}{\isacharprime}}{\isaliteral{3D}{\isacharequal}}\ e{\isaliteral{5F}{\isacharunderscore}}rls{\isaliteral{2C}{\isacharcomma}}\ calc\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ \isanewline
|
jan@42369
|
1776 |
\ \ \ \ \ \ srls\ {\isaliteral{3D}{\isacharequal}}\ e{\isaliteral{5F}{\isacharunderscore}}rls{\isaliteral{2C}{\isacharcomma}}\ prls\ {\isaliteral{3D}{\isacharequal}}\ e{\isaliteral{5F}{\isacharunderscore}}rls{\isaliteral{2C}{\isacharcomma}}\isanewline
|
jan@42369
|
1777 |
\ \ \ \ \ \ crls\ {\isaliteral{3D}{\isacharequal}}\ e{\isaliteral{5F}{\isacharunderscore}}rls{\isaliteral{2C}{\isacharcomma}}\ nrls\ {\isaliteral{3D}{\isacharequal}}\ e{\isaliteral{5F}{\isacharunderscore}}rls{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}empty{\isaliteral{5F}{\isacharunderscore}}script{\isaliteral{22}{\isachardoublequote}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1778 |
\ \ store{\isaliteral{5F}{\isacharunderscore}}met\isanewline
|
jan@42369
|
1779 |
\ \ \ {\isaliteral{28}{\isacharparenleft}}prep{\isaliteral{5F}{\isacharunderscore}}met\ thy\ {\isaliteral{22}{\isachardoublequote}}met{\isaliteral{5F}{\isacharunderscore}}SP{\isaliteral{5F}{\isacharunderscore}}Ztrans{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ e{\isaliteral{5F}{\isacharunderscore}}metID\isanewline
|
jan@42369
|
1780 |
\ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}SignalProcessing{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}Z{\isaliteral{5F}{\isacharunderscore}}Transform{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\isanewline
|
jan@42369
|
1781 |
\ \ \ \ \ {\isaliteral{7B}{\isacharbraceleft}}rew{\isaliteral{5F}{\isacharunderscore}}ord{\isaliteral{27}{\isacharprime}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{22}{\isachardoublequote}}tless{\isaliteral{5F}{\isacharunderscore}}true{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ rls{\isaliteral{27}{\isacharprime}}{\isaliteral{3D}{\isacharequal}}\ e{\isaliteral{5F}{\isacharunderscore}}rls{\isaliteral{2C}{\isacharcomma}}\ calc\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ \isanewline
|
jan@42369
|
1782 |
\ \ \ \ \ \ srls\ {\isaliteral{3D}{\isacharequal}}\ e{\isaliteral{5F}{\isacharunderscore}}rls{\isaliteral{2C}{\isacharcomma}}\ prls\ {\isaliteral{3D}{\isacharequal}}\ e{\isaliteral{5F}{\isacharunderscore}}rls{\isaliteral{2C}{\isacharcomma}}\isanewline
|
jan@42369
|
1783 |
\ \ \ \ \ \ crls\ {\isaliteral{3D}{\isacharequal}}\ e{\isaliteral{5F}{\isacharunderscore}}rls{\isaliteral{2C}{\isacharcomma}}\ nrls\ {\isaliteral{3D}{\isacharequal}}\ e{\isaliteral{5F}{\isacharunderscore}}rls{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}empty{\isaliteral{5F}{\isacharunderscore}}script{\isaliteral{22}{\isachardoublequote}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1784 |
{\isaliteral{2A7D}{\isacharverbatimclose}}%
|
jan@42369
|
1785 |
\endisatagML
|
jan@42369
|
1786 |
{\isafoldML}%
|
jan@42369
|
1787 |
%
|
jan@42369
|
1788 |
\isadelimML
|
jan@42369
|
1789 |
%
|
jan@42369
|
1790 |
\endisadelimML
|
jan@42369
|
1791 |
%
|
jan@42369
|
1792 |
\begin{isamarkuptext}%
|
jan@42369
|
1793 |
\noindent After we generated both nodes, we can fill the containing
|
jan@42369
|
1794 |
script we want to implement later. First we define the specifications
|
jan@42369
|
1795 |
of the script in e.g. the in- and output.%
|
jan@42369
|
1796 |
\end{isamarkuptext}%
|
jan@42369
|
1797 |
\isamarkuptrue%
|
jan@42369
|
1798 |
%
|
jan@42369
|
1799 |
\isadelimML
|
jan@42369
|
1800 |
%
|
jan@42369
|
1801 |
\endisadelimML
|
jan@42369
|
1802 |
%
|
jan@42369
|
1803 |
\isatagML
|
neuper@42289
|
1804 |
\isacommand{ML}\isamarkupfalse%
|
neuper@42289
|
1805 |
\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
|
jan@42369
|
1806 |
\ \ store{\isaliteral{5F}{\isacharunderscore}}met\isanewline
|
jan@42369
|
1807 |
\ \ \ {\isaliteral{28}{\isacharparenleft}}prep{\isaliteral{5F}{\isacharunderscore}}met\ thy\ {\isaliteral{22}{\isachardoublequote}}met{\isaliteral{5F}{\isacharunderscore}}SP{\isaliteral{5F}{\isacharunderscore}}Ztrans{\isaliteral{5F}{\isacharunderscore}}inv{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ e{\isaliteral{5F}{\isacharunderscore}}metID\isanewline
|
jan@42369
|
1808 |
\ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}SignalProcessing{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}Z{\isaliteral{5F}{\isacharunderscore}}Transform{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}inverse{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ \isanewline
|
jan@42369
|
1809 |
\ \ \ \ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{23}{\isacharhash}}Given{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{2C}{\isacharcomma}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}filterExpression\ X{\isaliteral{5F}{\isacharunderscore}}eq{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\isanewline
|
jan@42369
|
1810 |
\ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{23}{\isacharhash}}Find{\isaliteral{22}{\isachardoublequote}}\ \ {\isaliteral{2C}{\isacharcomma}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}stepResponse\ n{\isaliteral{5F}{\isacharunderscore}}eq{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42369
|
1811 |
\ \ \ \ {\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\isanewline
|
jan@42369
|
1812 |
\ \ \ \ \ {\isaliteral{7B}{\isacharbraceleft}}rew{\isaliteral{5F}{\isacharunderscore}}ord{\isaliteral{27}{\isacharprime}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{22}{\isachardoublequote}}tless{\isaliteral{5F}{\isacharunderscore}}true{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ rls{\isaliteral{27}{\isacharprime}}{\isaliteral{3D}{\isacharequal}}\ e{\isaliteral{5F}{\isacharunderscore}}rls{\isaliteral{2C}{\isacharcomma}}\ calc\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ \isanewline
|
jan@42369
|
1813 |
\ \ \ \ \ \ srls\ {\isaliteral{3D}{\isacharequal}}\ e{\isaliteral{5F}{\isacharunderscore}}rls{\isaliteral{2C}{\isacharcomma}}\ prls\ {\isaliteral{3D}{\isacharequal}}\ e{\isaliteral{5F}{\isacharunderscore}}rls{\isaliteral{2C}{\isacharcomma}}\isanewline
|
jan@42369
|
1814 |
\ \ \ \ \ \ crls\ {\isaliteral{3D}{\isacharequal}}\ e{\isaliteral{5F}{\isacharunderscore}}rls{\isaliteral{2C}{\isacharcomma}}\ nrls\ {\isaliteral{3D}{\isacharequal}}\ e{\isaliteral{5F}{\isacharunderscore}}rls{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}empty{\isaliteral{5F}{\isacharunderscore}}script{\isaliteral{22}{\isachardoublequote}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1815 |
{\isaliteral{2A7D}{\isacharverbatimclose}}%
|
jan@42369
|
1816 |
\endisatagML
|
jan@42369
|
1817 |
{\isafoldML}%
|
jan@42369
|
1818 |
%
|
jan@42369
|
1819 |
\isadelimML
|
jan@42369
|
1820 |
%
|
jan@42369
|
1821 |
\endisadelimML
|
jan@42369
|
1822 |
%
|
jan@42369
|
1823 |
\begin{isamarkuptext}%
|
jan@42369
|
1824 |
\noindent After we stored the definition we can start implementing the
|
jan@42369
|
1825 |
script itself. As a first try we define only three rows containing one
|
jan@42369
|
1826 |
simple operation.%
|
jan@42369
|
1827 |
\end{isamarkuptext}%
|
jan@42369
|
1828 |
\isamarkuptrue%
|
jan@42369
|
1829 |
%
|
jan@42369
|
1830 |
\isadelimML
|
jan@42369
|
1831 |
%
|
jan@42369
|
1832 |
\endisadelimML
|
jan@42369
|
1833 |
%
|
jan@42369
|
1834 |
\isatagML
|
neuper@42289
|
1835 |
\isacommand{ML}\isamarkupfalse%
|
neuper@42289
|
1836 |
\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
|
jan@42369
|
1837 |
\ \ store{\isaliteral{5F}{\isacharunderscore}}met\isanewline
|
jan@42369
|
1838 |
\ \ \ {\isaliteral{28}{\isacharparenleft}}prep{\isaliteral{5F}{\isacharunderscore}}met\ thy\ {\isaliteral{22}{\isachardoublequote}}met{\isaliteral{5F}{\isacharunderscore}}SP{\isaliteral{5F}{\isacharunderscore}}Ztrans{\isaliteral{5F}{\isacharunderscore}}inv{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ e{\isaliteral{5F}{\isacharunderscore}}metID\isanewline
|
jan@42369
|
1839 |
\ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}SignalProcessing{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}Z{\isaliteral{5F}{\isacharunderscore}}Transform{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}inverse{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ \isanewline
|
jan@42369
|
1840 |
\ \ \ \ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{23}{\isacharhash}}Given{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{2C}{\isacharcomma}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}filterExpression\ X{\isaliteral{5F}{\isacharunderscore}}eq{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\isanewline
|
jan@42369
|
1841 |
\ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{23}{\isacharhash}}Find{\isaliteral{22}{\isachardoublequote}}\ \ {\isaliteral{2C}{\isacharcomma}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}stepResponse\ n{\isaliteral{5F}{\isacharunderscore}}eq{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42369
|
1842 |
\ \ \ \ {\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\isanewline
|
jan@42369
|
1843 |
\ \ \ \ \ {\isaliteral{7B}{\isacharbraceleft}}rew{\isaliteral{5F}{\isacharunderscore}}ord{\isaliteral{27}{\isacharprime}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{22}{\isachardoublequote}}tless{\isaliteral{5F}{\isacharunderscore}}true{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ rls{\isaliteral{27}{\isacharprime}}{\isaliteral{3D}{\isacharequal}}\ e{\isaliteral{5F}{\isacharunderscore}}rls{\isaliteral{2C}{\isacharcomma}}\ calc\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ \isanewline
|
jan@42369
|
1844 |
\ \ \ \ \ \ srls\ {\isaliteral{3D}{\isacharequal}}\ e{\isaliteral{5F}{\isacharunderscore}}rls{\isaliteral{2C}{\isacharcomma}}\ prls\ {\isaliteral{3D}{\isacharequal}}\ e{\isaliteral{5F}{\isacharunderscore}}rls{\isaliteral{2C}{\isacharcomma}}\isanewline
|
jan@42369
|
1845 |
\ \ \ \ \ \ crls\ {\isaliteral{3D}{\isacharequal}}\ e{\isaliteral{5F}{\isacharunderscore}}rls{\isaliteral{2C}{\isacharcomma}}\ nrls\ {\isaliteral{3D}{\isacharequal}}\ e{\isaliteral{5F}{\isacharunderscore}}rls{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{2C}{\isacharcomma}}\isanewline
|
wneuper@59585
|
1846 |
\ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}Program\ InverseZTransform\ {\isaliteral{28}{\isacharparenleft}}Xeq{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}bool{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5E}{\isacharcircum}}\isanewline
|
jan@42369
|
1847 |
\ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{28}{\isacharparenleft}}let\ X\ {\isaliteral{3D}{\isacharequal}}\ Take\ Xeq{\isaliteral{3B}{\isacharsemicolon}}{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5E}{\isacharcircum}}\isanewline
|
jan@42369
|
1848 |
\ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ X\ {\isaliteral{3D}{\isacharequal}}\ Rewrite\ ruleZY\ False\ X{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5E}{\isacharcircum}}\isanewline
|
jan@42369
|
1849 |
\ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ in\ X{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42369
|
1850 |
{\isaliteral{2A7D}{\isacharverbatimclose}}%
|
jan@42369
|
1851 |
\endisatagML
|
jan@42369
|
1852 |
{\isafoldML}%
|
jan@42369
|
1853 |
%
|
jan@42369
|
1854 |
\isadelimML
|
jan@42369
|
1855 |
%
|
jan@42369
|
1856 |
\endisadelimML
|
jan@42369
|
1857 |
%
|
jan@42369
|
1858 |
\begin{isamarkuptext}%
|
jan@42369
|
1859 |
\noindent Check if the method has been stored correctly\ldots%
|
jan@42369
|
1860 |
\end{isamarkuptext}%
|
jan@42369
|
1861 |
\isamarkuptrue%
|
jan@42369
|
1862 |
%
|
jan@42369
|
1863 |
\isadelimML
|
jan@42369
|
1864 |
%
|
jan@42369
|
1865 |
\endisadelimML
|
jan@42369
|
1866 |
%
|
jan@42369
|
1867 |
\isatagML
|
neuper@42304
|
1868 |
\isacommand{ML}\isamarkupfalse%
|
neuper@42304
|
1869 |
\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
|
jan@42369
|
1870 |
\ \ show{\isaliteral{5F}{\isacharunderscore}}mets{\isaliteral{28}{\isacharparenleft}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\ \isanewline
|
jan@42369
|
1871 |
{\isaliteral{2A7D}{\isacharverbatimclose}}%
|
jan@42369
|
1872 |
\endisatagML
|
jan@42369
|
1873 |
{\isafoldML}%
|
jan@42369
|
1874 |
%
|
jan@42369
|
1875 |
\isadelimML
|
jan@42369
|
1876 |
%
|
jan@42369
|
1877 |
\endisadelimML
|
jan@42369
|
1878 |
%
|
jan@42369
|
1879 |
\begin{isamarkuptext}%
|
jan@42381
|
1880 |
\noindent If yes we can get the method by stepping backwards through
|
jan@42381
|
1881 |
the hierarchy.%
|
jan@42369
|
1882 |
\end{isamarkuptext}%
|
jan@42369
|
1883 |
\isamarkuptrue%
|
jan@42369
|
1884 |
%
|
jan@42369
|
1885 |
\isadelimML
|
jan@42369
|
1886 |
%
|
jan@42369
|
1887 |
\endisadelimML
|
jan@42369
|
1888 |
%
|
jan@42369
|
1889 |
\isatagML
|
neuper@42304
|
1890 |
\isacommand{ML}\isamarkupfalse%
|
neuper@42304
|
1891 |
\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
|
jan@42369
|
1892 |
\ \ get{\isaliteral{5F}{\isacharunderscore}}met\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}SignalProcessing{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}Z{\isaliteral{5F}{\isacharunderscore}}Transform{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}inverse{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
neuper@42289
|
1893 |
{\isaliteral{2A7D}{\isacharverbatimclose}}%
|
neuper@42289
|
1894 |
\endisatagML
|
neuper@42289
|
1895 |
{\isafoldML}%
|
neuper@42289
|
1896 |
%
|
neuper@42289
|
1897 |
\isadelimML
|
neuper@42289
|
1898 |
%
|
neuper@42289
|
1899 |
\endisadelimML
|
neuper@42289
|
1900 |
%
|
jan@42381
|
1901 |
\isamarkupsection{Program in TP-based language \label{prog-steps}%
|
neuper@42289
|
1902 |
}
|
neuper@42289
|
1903 |
\isamarkuptrue%
|
neuper@42289
|
1904 |
%
|
neuper@42289
|
1905 |
\begin{isamarkuptext}%
|
jan@42381
|
1906 |
\noindent We start stepwise expanding our program. The script is a
|
jan@42381
|
1907 |
simple string containing several manipulation instructions.
|
jan@42370
|
1908 |
\par The first script we try contains no instruction, we only test if
|
jan@42370
|
1909 |
building scripts that way work.%
|
neuper@42289
|
1910 |
\end{isamarkuptext}%
|
neuper@42289
|
1911 |
\isamarkuptrue%
|
neuper@42289
|
1912 |
%
|
jan@42370
|
1913 |
\isamarkupsubsection{Stepwise Extend the Program%
|
neuper@42289
|
1914 |
}
|
neuper@42289
|
1915 |
\isamarkuptrue%
|
neuper@42289
|
1916 |
%
|
neuper@42289
|
1917 |
\isadelimML
|
neuper@42289
|
1918 |
%
|
neuper@42289
|
1919 |
\endisadelimML
|
neuper@42289
|
1920 |
%
|
neuper@42289
|
1921 |
\isatagML
|
neuper@42289
|
1922 |
\isacommand{ML}\isamarkupfalse%
|
neuper@42289
|
1923 |
\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
|
jan@42370
|
1924 |
\ \ val\ str\ {\isaliteral{3D}{\isacharequal}}\ \isanewline
|
wneuper@59585
|
1925 |
\ \ \ \ {\isaliteral{22}{\isachardoublequote}}Program\ InverseZTransform\ {\isaliteral{28}{\isacharparenleft}}Xeq{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}bool{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline
|
jan@42370
|
1926 |
\ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ Xeq{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
neuper@42304
|
1927 |
{\isaliteral{2A7D}{\isacharverbatimclose}}%
|
neuper@42304
|
1928 |
\endisatagML
|
neuper@42304
|
1929 |
{\isafoldML}%
|
neuper@42304
|
1930 |
%
|
neuper@42304
|
1931 |
\isadelimML
|
neuper@42304
|
1932 |
%
|
neuper@42304
|
1933 |
\endisadelimML
|
neuper@42304
|
1934 |
%
|
neuper@42304
|
1935 |
\begin{isamarkuptext}%
|
jan@42370
|
1936 |
\noindent Next we put some instructions in the script and try if we are
|
jan@42370
|
1937 |
able to solve our first equation.%
|
neuper@42304
|
1938 |
\end{isamarkuptext}%
|
neuper@42304
|
1939 |
\isamarkuptrue%
|
neuper@42304
|
1940 |
%
|
neuper@42304
|
1941 |
\isadelimML
|
neuper@42304
|
1942 |
%
|
neuper@42304
|
1943 |
\endisadelimML
|
neuper@42304
|
1944 |
%
|
neuper@42304
|
1945 |
\isatagML
|
neuper@42289
|
1946 |
\isacommand{ML}\isamarkupfalse%
|
neuper@42289
|
1947 |
\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
|
jan@42370
|
1948 |
\ \ val\ str\ {\isaliteral{3D}{\isacharequal}}\ \isanewline
|
wneuper@59585
|
1949 |
\ \ \ \ {\isaliteral{22}{\isachardoublequote}}Program\ InverseZTransform\ {\isaliteral{28}{\isacharparenleft}}Xeq{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}bool{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline
|
jan@42370
|
1950 |
\ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}\isanewline
|
jan@42370
|
1951 |
\ \ \ \ \ {\isaliteral{2A}{\isacharasterisk}}\ {\isadigit{1}}{\isaliteral{2F}{\isacharslash}}z{\isaliteral{29}{\isacharparenright}}\ instead\ of\ z\ {\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{1}}\isanewline
|
jan@42370
|
1952 |
\ \ \ \ \ {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42381
|
1953 |
\ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{28}{\isacharparenleft}}let\ X\ {\isaliteral{3D}{\isacharequal}}\ Take\ Xeq{\isaliteral{3B}{\isacharsemicolon}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline
|
jan@42381
|
1954 |
\ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ X{\isaliteral{27}{\isacharprime}}\ {\isaliteral{3D}{\isacharequal}}\ Rewrite\ ruleZY\ False\ X{\isaliteral{3B}{\isacharsemicolon}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline
|
jan@42370
|
1955 |
\ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}\isanewline
|
jan@42370
|
1956 |
\ \ \ \ \ {\isaliteral{2A}{\isacharasterisk}}\ z\ {\isaliteral{2A}{\isacharasterisk}}\ denominator\isanewline
|
jan@42370
|
1957 |
\ \ \ \ \ {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42381
|
1958 |
\ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ X{\isaliteral{27}{\isacharprime}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}Rewrite{\isaliteral{5F}{\isacharunderscore}}Set\ norm{\isaliteral{5F}{\isacharunderscore}}Rational\ False{\isaliteral{29}{\isacharparenright}}\ X{\isaliteral{27}{\isacharprime}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline
|
jan@42370
|
1959 |
\ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}\isanewline
|
jan@42370
|
1960 |
\ \ \ \ \ {\isaliteral{2A}{\isacharasterisk}}\ simplify\isanewline
|
jan@42370
|
1961 |
\ \ \ \ \ {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42370
|
1962 |
\ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ in\ X{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
1963 |
\ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}\isanewline
|
jan@42370
|
1964 |
\ \ \ \ \ {\isaliteral{2A}{\isacharasterisk}}\ NONE\isanewline
|
jan@42370
|
1965 |
\ \ \ \ \ {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
wneuper@59585
|
1966 |
\ \ \ \ {\isaliteral{22}{\isachardoublequote}}Program\ InverseZTransform\ {\isaliteral{28}{\isacharparenleft}}Xeq{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}bool{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline
|
jan@42370
|
1967 |
\ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}\isanewline
|
jan@42370
|
1968 |
\ \ \ \ \ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{1}}{\isaliteral{2F}{\isacharslash}}z{\isaliteral{29}{\isacharparenright}}\ instead\ of\ z\ {\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{1}}\isanewline
|
jan@42370
|
1969 |
\ \ \ \ \ {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42381
|
1970 |
\ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{28}{\isacharparenleft}}let\ X\ {\isaliteral{3D}{\isacharequal}}\ Take\ Xeq{\isaliteral{3B}{\isacharsemicolon}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline
|
jan@42381
|
1971 |
\ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ X{\isaliteral{27}{\isacharprime}}\ {\isaliteral{3D}{\isacharequal}}\ Rewrite\ ruleZY\ False\ X{\isaliteral{3B}{\isacharsemicolon}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline
|
jan@42370
|
1972 |
\ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}\isanewline
|
jan@42370
|
1973 |
\ \ \ \ \ {\isaliteral{2A}{\isacharasterisk}}\ z\ {\isaliteral{2A}{\isacharasterisk}}\ denominator\isanewline
|
jan@42370
|
1974 |
\ \ \ \ \ {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42381
|
1975 |
\ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ X{\isaliteral{27}{\isacharprime}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}Rewrite{\isaliteral{5F}{\isacharunderscore}}Set\ norm{\isaliteral{5F}{\isacharunderscore}}Rational\ False{\isaliteral{29}{\isacharparenright}}\ X{\isaliteral{27}{\isacharprime}}{\isaliteral{3B}{\isacharsemicolon}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline
|
jan@42370
|
1976 |
\ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}\isanewline
|
jan@42370
|
1977 |
\ \ \ \ \ {\isaliteral{2A}{\isacharasterisk}}\ simplify\isanewline
|
jan@42370
|
1978 |
\ \ \ \ \ {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42381
|
1979 |
\ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ X{\isaliteral{27}{\isacharprime}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}SubProblem\ {\isaliteral{28}{\isacharparenleft}}Isac{\isaliteral{27}{\isacharprime}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5B}{\isacharbrackleft}}pqFormula{\isaliteral{2C}{\isacharcomma}}degree{\isaliteral{5F}{\isacharunderscore}}{\isadigit{2}}{\isaliteral{2C}{\isacharcomma}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline
|
jan@42381
|
1980 |
\ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ polynomial{\isaliteral{2C}{\isacharcomma}}univariate{\isaliteral{2C}{\isacharcomma}}equation{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline
|
jan@42381
|
1981 |
\ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{5B}{\isacharbrackleft}}no{\isaliteral{5F}{\isacharunderscore}}met{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline
|
jan@42381
|
1982 |
\ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{5B}{\isacharbrackleft}}BOOL\ e{\isaliteral{5F}{\isacharunderscore}}e{\isaliteral{2C}{\isacharcomma}}\ REAL\ v{\isaliteral{5F}{\isacharunderscore}}v{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline
|
jan@42370
|
1983 |
\ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ \ \ \ \ \ \ in\ X{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
1984 |
{\isaliteral{2A7D}{\isacharverbatimclose}}%
|
jan@42370
|
1985 |
\endisatagML
|
jan@42370
|
1986 |
{\isafoldML}%
|
jan@42370
|
1987 |
%
|
jan@42370
|
1988 |
\isadelimML
|
jan@42370
|
1989 |
%
|
jan@42370
|
1990 |
\endisadelimML
|
jan@42370
|
1991 |
%
|
jan@42370
|
1992 |
\begin{isamarkuptext}%
|
jan@42381
|
1993 |
\noindent To solve the equation it is necessary to drop the left hand
|
jan@42370
|
1994 |
side, now we only need the denominator of the right hand side. The first
|
jan@42370
|
1995 |
equation solves the zeros of our expression.%
|
jan@42370
|
1996 |
\end{isamarkuptext}%
|
jan@42370
|
1997 |
\isamarkuptrue%
|
jan@42370
|
1998 |
%
|
jan@42370
|
1999 |
\isadelimML
|
jan@42370
|
2000 |
%
|
jan@42370
|
2001 |
\endisadelimML
|
jan@42370
|
2002 |
%
|
jan@42370
|
2003 |
\isatagML
|
jan@42370
|
2004 |
\isacommand{ML}\isamarkupfalse%
|
jan@42370
|
2005 |
\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
|
jan@42370
|
2006 |
\ \ val\ str\ {\isaliteral{3D}{\isacharequal}}\ \isanewline
|
wneuper@59585
|
2007 |
\ \ \ \ {\isaliteral{22}{\isachardoublequote}}Program\ InverseZTransform\ {\isaliteral{28}{\isacharparenleft}}Xeq{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}bool{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline
|
jan@42381
|
2008 |
\ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{28}{\isacharparenleft}}let\ X\ {\isaliteral{3D}{\isacharequal}}\ Take\ Xeq{\isaliteral{3B}{\isacharsemicolon}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline
|
jan@42381
|
2009 |
\ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ X{\isaliteral{27}{\isacharprime}}\ {\isaliteral{3D}{\isacharequal}}\ Rewrite\ ruleZY\ False\ X{\isaliteral{3B}{\isacharsemicolon}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline
|
jan@42381
|
2010 |
\ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ X{\isaliteral{27}{\isacharprime}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}Rewrite{\isaliteral{5F}{\isacharunderscore}}Set\ norm{\isaliteral{5F}{\isacharunderscore}}Rational\ False{\isaliteral{29}{\isacharparenright}}\ X{\isaliteral{27}{\isacharprime}}{\isaliteral{3B}{\isacharsemicolon}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline
|
jan@42381
|
2011 |
\ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ funterm\ {\isaliteral{3D}{\isacharequal}}\ rhs\ X{\isaliteral{27}{\isacharprime}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline
|
jan@42370
|
2012 |
\ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}\isanewline
|
jan@42370
|
2013 |
\ \ \ \ \ {\isaliteral{2A}{\isacharasterisk}}\ drop\ X{\isaliteral{27}{\isacharprime}}{\isaliteral{3D}{\isacharequal}}\ for\ equation\ solving\isanewline
|
jan@42370
|
2014 |
\ \ \ \ \ {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42370
|
2015 |
\ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ in\ X{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2016 |
{\isaliteral{2A7D}{\isacharverbatimclose}}%
|
jan@42370
|
2017 |
\endisatagML
|
jan@42370
|
2018 |
{\isafoldML}%
|
jan@42370
|
2019 |
%
|
jan@42370
|
2020 |
\isadelimML
|
jan@42370
|
2021 |
%
|
jan@42370
|
2022 |
\endisadelimML
|
jan@42370
|
2023 |
%
|
jan@42370
|
2024 |
\begin{isamarkuptext}%
|
jan@42370
|
2025 |
\noindent As mentioned above, we need the denominator of the right hand
|
jan@42370
|
2026 |
side. The equation itself consists of this denominator and tries to find
|
jan@42370
|
2027 |
a $z$ for this the denominator is equal to zero.%
|
jan@42370
|
2028 |
\end{isamarkuptext}%
|
jan@42370
|
2029 |
\isamarkuptrue%
|
jan@42370
|
2030 |
%
|
jan@42370
|
2031 |
\isadelimML
|
jan@42370
|
2032 |
%
|
jan@42370
|
2033 |
\endisadelimML
|
jan@42370
|
2034 |
%
|
jan@42370
|
2035 |
\isatagML
|
jan@42370
|
2036 |
\isacommand{ML}\isamarkupfalse%
|
jan@42370
|
2037 |
\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
|
jan@42370
|
2038 |
\ \ val\ str\ {\isaliteral{3D}{\isacharequal}}\ \isanewline
|
wneuper@59585
|
2039 |
\ \ \ \ {\isaliteral{22}{\isachardoublequote}}Program\ InverseZTransform\ {\isaliteral{28}{\isacharparenleft}}X{\isaliteral{5F}{\isacharunderscore}}eq{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}bool{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline
|
jan@42381
|
2040 |
\ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{28}{\isacharparenleft}}let\ X\ {\isaliteral{3D}{\isacharequal}}\ Take\ X{\isaliteral{5F}{\isacharunderscore}}eq{\isaliteral{3B}{\isacharsemicolon}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline
|
jan@42381
|
2041 |
\ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ X{\isaliteral{27}{\isacharprime}}\ {\isaliteral{3D}{\isacharequal}}\ Rewrite\ ruleZY\ False\ X{\isaliteral{3B}{\isacharsemicolon}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline
|
jan@42381
|
2042 |
\ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ X{\isaliteral{27}{\isacharprime}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}Rewrite{\isaliteral{5F}{\isacharunderscore}}Set\ norm{\isaliteral{5F}{\isacharunderscore}}Rational\ False{\isaliteral{29}{\isacharparenright}}\ X{\isaliteral{27}{\isacharprime}}{\isaliteral{3B}{\isacharsemicolon}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline
|
jan@42381
|
2043 |
\ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}X{\isaliteral{27}{\isacharprime}}{\isaliteral{5F}{\isacharunderscore}}z{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}real{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ lhs\ X{\isaliteral{27}{\isacharprime}}{\isaliteral{3B}{\isacharsemicolon}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline
|
jan@42381
|
2044 |
\ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}z{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}real{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ argument{\isaliteral{5F}{\isacharunderscore}}in\ X{\isaliteral{27}{\isacharprime}}{\isaliteral{5F}{\isacharunderscore}}z{\isaliteral{3B}{\isacharsemicolon}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline
|
jan@42381
|
2045 |
\ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}funterm{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}real{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ rhs\ X{\isaliteral{27}{\isacharprime}}{\isaliteral{3B}{\isacharsemicolon}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline
|
jan@42381
|
2046 |
\ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}denom{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}real{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ get{\isaliteral{5F}{\isacharunderscore}}denominator\ funterm{\isaliteral{3B}{\isacharsemicolon}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline
|
jan@42370
|
2047 |
\ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}\isanewline
|
jan@42370
|
2048 |
\ \ \ \ \ {\isaliteral{2A}{\isacharasterisk}}\ get{\isaliteral{5F}{\isacharunderscore}}denominator\isanewline
|
jan@42370
|
2049 |
\ \ \ \ \ {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42381
|
2050 |
\ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}equ{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}bool{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}denom\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{0}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}real{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline
|
jan@42381
|
2051 |
\ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}L{\isaliteral{5F}{\isacharunderscore}}L{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}bool\ list{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline
|
jan@42381
|
2052 |
\ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}SubProblem\ {\isaliteral{28}{\isacharparenleft}}Test{\isaliteral{27}{\isacharprime}}{\isaliteral{2C}{\isacharcomma}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline
|
jan@42381
|
2053 |
\ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{5B}{\isacharbrackleft}}linear{\isaliteral{2C}{\isacharcomma}}univariate{\isaliteral{2C}{\isacharcomma}}equation{\isaliteral{2C}{\isacharcomma}}test{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline
|
jan@42381
|
2054 |
\ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{5B}{\isacharbrackleft}}Test{\isaliteral{2C}{\isacharcomma}}solve{\isaliteral{5F}{\isacharunderscore}}linear{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline
|
jan@42381
|
2055 |
\ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{5B}{\isacharbrackleft}}BOOL\ equ{\isaliteral{2C}{\isacharcomma}}\ REAL\ z{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline
|
jan@42370
|
2056 |
\ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ in\ X{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2057 |
\isanewline
|
jan@42370
|
2058 |
\ \ parse\ thy\ str{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2059 |
\ \ val\ sc\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{28}{\isacharparenleft}}inst{\isaliteral{5F}{\isacharunderscore}}abs\ thy{\isaliteral{29}{\isacharparenright}}\ o\ term{\isaliteral{5F}{\isacharunderscore}}of\ o\ the\ o\ {\isaliteral{28}{\isacharparenleft}}parse\ thy{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ str{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2060 |
\ \ atomty\ sc{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2061 |
{\isaliteral{2A7D}{\isacharverbatimclose}}%
|
jan@42370
|
2062 |
\endisatagML
|
jan@42370
|
2063 |
{\isafoldML}%
|
jan@42370
|
2064 |
%
|
jan@42370
|
2065 |
\isadelimML
|
jan@42370
|
2066 |
%
|
jan@42370
|
2067 |
\endisadelimML
|
jan@42370
|
2068 |
%
|
jan@42370
|
2069 |
\begin{isamarkuptext}%
|
jan@42370
|
2070 |
\noindent This ruleset contains all functions that are in the script;
|
jan@42370
|
2071 |
The evaluation of the functions is done by rewriting using this ruleset.%
|
jan@42370
|
2072 |
\end{isamarkuptext}%
|
jan@42370
|
2073 |
\isamarkuptrue%
|
jan@42370
|
2074 |
%
|
jan@42370
|
2075 |
\isadelimML
|
jan@42370
|
2076 |
%
|
jan@42370
|
2077 |
\endisadelimML
|
jan@42370
|
2078 |
%
|
jan@42370
|
2079 |
\isatagML
|
jan@42370
|
2080 |
\isacommand{ML}\isamarkupfalse%
|
jan@42370
|
2081 |
\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
|
jan@42381
|
2082 |
\ \ val\ srls\ {\isaliteral{3D}{\isacharequal}}\ \isanewline
|
walther@59851
|
2083 |
\ \ \ \ Rule_Set.Repeat\ {\isaliteral{7B}{\isacharbraceleft}}id{\isaliteral{3D}{\isacharequal}}{\isaliteral{22}{\isachardoublequote}}srls{\isaliteral{5F}{\isacharunderscore}}InverseZTransform{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ \isanewline
|
jan@42381
|
2084 |
\ \ \ \ \ \ \ \ \ preconds\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\isanewline
|
jan@42381
|
2085 |
\ \ \ \ \ \ \ \ \ rew{\isaliteral{5F}{\isacharunderscore}}ord\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}termlessI{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}termlessI{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\isanewline
|
jan@42381
|
2086 |
\ \ \ \ \ \ \ \ \ erls\ {\isaliteral{3D}{\isacharequal}}\ append{\isaliteral{5F}{\isacharunderscore}}rls\ {\isaliteral{22}{\isachardoublequote}}erls{\isaliteral{5F}{\isacharunderscore}}in{\isaliteral{5F}{\isacharunderscore}}srls{\isaliteral{5F}{\isacharunderscore}}InverseZTransform{\isaliteral{22}{\isachardoublequote}}\ e{\isaliteral{5F}{\isacharunderscore}}rls\isanewline
|
jan@42381
|
2087 |
\ \ \ \ \ \ \ \ \ \ \ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}for\ asm\ in\ NTH{\isaliteral{5F}{\isacharunderscore}}CONS\ {\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
walther@59773
|
2088 |
\ \ \ \ \ \ \ \ \ \ \ \ Num_Calc\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}Orderings{\isaliteral{2E}{\isachardot}}ord{\isaliteral{5F}{\isacharunderscore}}class{\isaliteral{2E}{\isachardot}}less{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}eval{\isaliteral{5F}{\isacharunderscore}}equ\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{23}{\isacharhash}}less{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\isanewline
|
jan@42381
|
2089 |
\ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}{\isadigit{2}}nd\ NTH{\isaliteral{5F}{\isacharunderscore}}CONS\ pushes\ n{\isaliteral{2B}{\isacharplus}}{\isaliteral{2D}{\isacharminus}}{\isadigit{1}}\ into\ asms{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
walther@59773
|
2090 |
\ \ \ \ \ \ \ \ \ \ \ \ Num_Calc{\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}Groups{\isaliteral{2E}{\isachardot}}plus{\isaliteral{5F}{\isacharunderscore}}class{\isaliteral{2E}{\isachardot}}plus{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ eval{\isaliteral{5F}{\isacharunderscore}}binop\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{23}{\isacharhash}}add{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42381
|
2091 |
\ \ \ \ \ \ \ \ \ \ \ {\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ \isanewline
|
walther@59851
|
2092 |
\ \ \ \ \ \ \ \ \ srls\ {\isaliteral{3D}{\isacharequal}}\ Rule_Set.Empty{\isaliteral{2C}{\isacharcomma}}\ calc\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\isanewline
|
jan@42381
|
2093 |
\ \ \ \ \ \ \ \ \ rules\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}\isanewline
|
jan@42381
|
2094 |
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Thm\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}NTH{\isaliteral{5F}{\isacharunderscore}}CONS{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}num{\isaliteral{5F}{\isacharunderscore}}str\ %
|
jan@42296
|
2095 |
\isaantiq
|
jan@42296
|
2096 |
thm\ NTH{\isaliteral{5F}{\isacharunderscore}}CONS{}%
|
jan@42296
|
2097 |
\endisaantiq
|
jan@42296
|
2098 |
{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\isanewline
|
walther@59773
|
2099 |
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Num_Calc{\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}Groups{\isaliteral{2E}{\isachardot}}plus{\isaliteral{5F}{\isacharunderscore}}class{\isaliteral{2E}{\isachardot}}plus{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ \isanewline
|
jan@42381
|
2100 |
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ eval{\isaliteral{5F}{\isacharunderscore}}binop\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{23}{\isacharhash}}add{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\isanewline
|
jan@42381
|
2101 |
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Thm\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}NTH{\isaliteral{5F}{\isacharunderscore}}NIL{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}num{\isaliteral{5F}{\isacharunderscore}}str\ %
|
jan@42296
|
2102 |
\isaantiq
|
jan@42296
|
2103 |
thm\ NTH{\isaliteral{5F}{\isacharunderscore}}NIL{}%
|
jan@42296
|
2104 |
\endisaantiq
|
jan@42296
|
2105 |
{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\isanewline
|
walther@59773
|
2106 |
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Num_Calc{\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}Tools{\isaliteral{2E}{\isachardot}}lhs{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ eval{\isaliteral{5F}{\isacharunderscore}}lhs{\isaliteral{22}{\isachardoublequote}}eval{\isaliteral{5F}{\isacharunderscore}}lhs{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\isanewline
|
walther@59773
|
2107 |
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Num_Calc{\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}Tools{\isaliteral{2E}{\isachardot}}rhs{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ eval{\isaliteral{5F}{\isacharunderscore}}rhs{\isaliteral{22}{\isachardoublequote}}eval{\isaliteral{5F}{\isacharunderscore}}rhs{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\isanewline
|
walther@59773
|
2108 |
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Num_Calc{\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}Prog_Expr{\isaliteral{2E}{\isachardot}}argument{\isaliteral{27}{\isacharprime}}{\isaliteral{5F}{\isacharunderscore}}in{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\isanewline
|
walther@59603
|
2109 |
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ eval{\isaliteral{5F}{\isacharunderscore}}argument{\isaliteral{5F}{\isacharunderscore}}in\ {\isaliteral{22}{\isachardoublequote}}Prog_Expr{\isaliteral{2E}{\isachardot}}argument{\isaliteral{27}{\isacharprime}}{\isaliteral{5F}{\isacharunderscore}}in{\isaliteral{22}{\isachardoublequote}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\isanewline
|
walther@59773
|
2110 |
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Num_Calc{\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}Rational{\isaliteral{2E}{\isachardot}}get{\isaliteral{5F}{\isacharunderscore}}denominator{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\isanewline
|
jan@42381
|
2111 |
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ eval{\isaliteral{5F}{\isacharunderscore}}get{\isaliteral{5F}{\isacharunderscore}}denominator\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{23}{\isacharhash}}get{\isaliteral{5F}{\isacharunderscore}}denominator{\isaliteral{22}{\isachardoublequote}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\isanewline
|
walther@59773
|
2112 |
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Num_Calc{\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}Rational{\isaliteral{2E}{\isachardot}}get{\isaliteral{5F}{\isacharunderscore}}numerator{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\isanewline
|
jan@42381
|
2113 |
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ eval{\isaliteral{5F}{\isacharunderscore}}get{\isaliteral{5F}{\isacharunderscore}}numerator\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{23}{\isacharhash}}get{\isaliteral{5F}{\isacharunderscore}}numerator{\isaliteral{22}{\isachardoublequote}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\isanewline
|
walther@59773
|
2114 |
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Num_Calc{\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}Partial{\isaliteral{5F}{\isacharunderscore}}Fractions{\isaliteral{2E}{\isachardot}}factors{\isaliteral{5F}{\isacharunderscore}}from{\isaliteral{5F}{\isacharunderscore}}solution{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\isanewline
|
jan@42381
|
2115 |
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ eval{\isaliteral{5F}{\isacharunderscore}}factors{\isaliteral{5F}{\isacharunderscore}}from{\isaliteral{5F}{\isacharunderscore}}solution\ \isanewline
|
jan@42381
|
2116 |
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{23}{\isacharhash}}factors{\isaliteral{5F}{\isacharunderscore}}from{\isaliteral{5F}{\isacharunderscore}}solution{\isaliteral{22}{\isachardoublequote}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\isanewline
|
walther@59773
|
2117 |
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Num_Calc{\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}Partial{\isaliteral{5F}{\isacharunderscore}}Fractions{\isaliteral{2E}{\isachardot}}drop{\isaliteral{5F}{\isacharunderscore}}questionmarks{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\isanewline
|
jan@42381
|
2118 |
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ eval{\isaliteral{5F}{\isacharunderscore}}drop{\isaliteral{5F}{\isacharunderscore}}questionmarks\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{23}{\isacharhash}}drop{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{3F}{\isacharquery}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42381
|
2119 |
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\isanewline
|
jan@42381
|
2120 |
\ \ \ \ \ \ \ \ \ scr\ {\isaliteral{3D}{\isacharequal}}\ EmptyScr{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
neuper@42289
|
2121 |
{\isaliteral{2A7D}{\isacharverbatimclose}}%
|
neuper@42289
|
2122 |
\endisatagML
|
neuper@42289
|
2123 |
{\isafoldML}%
|
neuper@42289
|
2124 |
%
|
neuper@42289
|
2125 |
\isadelimML
|
neuper@42289
|
2126 |
%
|
neuper@42289
|
2127 |
\endisadelimML
|
neuper@42289
|
2128 |
%
|
neuper@42289
|
2129 |
\isamarkupsubsection{Store Final Version of Program for Execution%
|
neuper@42289
|
2130 |
}
|
neuper@42289
|
2131 |
\isamarkuptrue%
|
neuper@42289
|
2132 |
%
|
jan@42370
|
2133 |
\begin{isamarkuptext}%
|
jan@42370
|
2134 |
\noindent After we also tested how to write scripts and run them,
|
jan@42370
|
2135 |
we start creating the final version of our script and store it into
|
jan@42381
|
2136 |
the method for which we created a node in Section~\ref{sec:cparentnode}
|
jan@42370
|
2137 |
Note that we also did this stepwise, but we didn't kept every
|
jan@42370
|
2138 |
subversion.%
|
jan@42370
|
2139 |
\end{isamarkuptext}%
|
jan@42370
|
2140 |
\isamarkuptrue%
|
jan@42370
|
2141 |
%
|
neuper@42289
|
2142 |
\isadelimML
|
neuper@42289
|
2143 |
%
|
neuper@42289
|
2144 |
\endisadelimML
|
neuper@42289
|
2145 |
%
|
neuper@42289
|
2146 |
\isatagML
|
neuper@42289
|
2147 |
\isacommand{ML}\isamarkupfalse%
|
neuper@42289
|
2148 |
\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
|
jan@42370
|
2149 |
\ \ store{\isaliteral{5F}{\isacharunderscore}}met{\isaliteral{28}{\isacharparenleft}}\isanewline
|
jan@42370
|
2150 |
\ \ \ \ prep{\isaliteral{5F}{\isacharunderscore}}met\ thy\ {\isaliteral{22}{\isachardoublequote}}met{\isaliteral{5F}{\isacharunderscore}}SP{\isaliteral{5F}{\isacharunderscore}}Ztrans{\isaliteral{5F}{\isacharunderscore}}inv{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ e{\isaliteral{5F}{\isacharunderscore}}metID\isanewline
|
jan@42370
|
2151 |
\ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}SignalProcessing{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\isanewline
|
jan@42370
|
2152 |
\ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}Z{\isaliteral{5F}{\isacharunderscore}}Transform{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\isanewline
|
jan@42370
|
2153 |
\ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}inverse{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ \isanewline
|
jan@42370
|
2154 |
\ \ \ \ \ {\isaliteral{5B}{\isacharbrackleft}}\isanewline
|
jan@42370
|
2155 |
\ \ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{23}{\isacharhash}}Given{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{2C}{\isacharcomma}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}filterExpression\ X{\isaliteral{5F}{\isacharunderscore}}eq{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\isanewline
|
jan@42370
|
2156 |
\ \ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{23}{\isacharhash}}Find{\isaliteral{22}{\isachardoublequote}}\ \ {\isaliteral{2C}{\isacharcomma}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}stepResponse\ n{\isaliteral{5F}{\isacharunderscore}}eq{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42370
|
2157 |
\ \ \ \ \ {\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\isanewline
|
jan@42370
|
2158 |
\ \ \ \ \ {\isaliteral{7B}{\isacharbraceleft}}\isanewline
|
jan@42370
|
2159 |
\ \ \ \ \ \ \ rew{\isaliteral{5F}{\isacharunderscore}}ord{\isaliteral{27}{\isacharprime}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{22}{\isachardoublequote}}tless{\isaliteral{5F}{\isacharunderscore}}true{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\isanewline
|
jan@42370
|
2160 |
\ \ \ \ \ \ \ rls{\isaliteral{27}{\isacharprime}}{\isaliteral{3D}{\isacharequal}}\ e{\isaliteral{5F}{\isacharunderscore}}rls{\isaliteral{2C}{\isacharcomma}}\ calc\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\isanewline
|
jan@42370
|
2161 |
\ \ \ \ \ \ \ srls\ {\isaliteral{3D}{\isacharequal}}\ srls{\isaliteral{2C}{\isacharcomma}}\ \isanewline
|
jan@42370
|
2162 |
\ \ \ \ \ \ \ prls\ {\isaliteral{3D}{\isacharequal}}\ e{\isaliteral{5F}{\isacharunderscore}}rls{\isaliteral{2C}{\isacharcomma}}\isanewline
|
jan@42370
|
2163 |
\ \ \ \ \ \ \ crls\ {\isaliteral{3D}{\isacharequal}}\ e{\isaliteral{5F}{\isacharunderscore}}rls{\isaliteral{2C}{\isacharcomma}}\ nrls\ {\isaliteral{3D}{\isacharequal}}\ e{\isaliteral{5F}{\isacharunderscore}}rls\isanewline
|
jan@42370
|
2164 |
\ \ \ \ \ {\isaliteral{7D}{\isacharbraceright}}{\isaliteral{2C}{\isacharcomma}}\isanewline
|
wneuper@59585
|
2165 |
\ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}Program\ InverseZTransform\ {\isaliteral{28}{\isacharparenleft}}X{\isaliteral{5F}{\isacharunderscore}}eq{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}bool{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline
|
jan@42370
|
2166 |
\ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{28}{\isacharparenleft}}{\isadigit{1}}{\isaliteral{2F}{\isacharslash}}z{\isaliteral{29}{\isacharparenright}}\ instead\ of\ z\ {\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{1}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42370
|
2167 |
\ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}let\ X\ {\isaliteral{3D}{\isacharequal}}\ Take\ X{\isaliteral{5F}{\isacharunderscore}}eq{\isaliteral{3B}{\isacharsemicolon}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline
|
jan@42370
|
2168 |
\ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ X{\isaliteral{27}{\isacharprime}}\ {\isaliteral{3D}{\isacharequal}}\ Rewrite\ ruleZY\ False\ X{\isaliteral{3B}{\isacharsemicolon}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline
|
jan@42370
|
2169 |
\ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}z\ {\isaliteral{2A}{\isacharasterisk}}\ denominator{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42370
|
2170 |
\ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}num{\isaliteral{5F}{\isacharunderscore}}orig{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}real{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ get{\isaliteral{5F}{\isacharunderscore}}numerator\ {\isaliteral{28}{\isacharparenleft}}rhs\ X{\isaliteral{27}{\isacharprime}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline
|
jan@42370
|
2171 |
\ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ X{\isaliteral{27}{\isacharprime}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}Rewrite{\isaliteral{5F}{\isacharunderscore}}Set\ norm{\isaliteral{5F}{\isacharunderscore}}Rational\ False{\isaliteral{29}{\isacharparenright}}\ X{\isaliteral{27}{\isacharprime}}{\isaliteral{3B}{\isacharsemicolon}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline
|
jan@42370
|
2172 |
\ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}simplify{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42370
|
2173 |
\ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}X{\isaliteral{27}{\isacharprime}}{\isaliteral{5F}{\isacharunderscore}}z{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}real{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ lhs\ X{\isaliteral{27}{\isacharprime}}{\isaliteral{3B}{\isacharsemicolon}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline
|
jan@42370
|
2174 |
\ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}zzz{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}real{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ argument{\isaliteral{5F}{\isacharunderscore}}in\ X{\isaliteral{27}{\isacharprime}}{\isaliteral{5F}{\isacharunderscore}}z{\isaliteral{3B}{\isacharsemicolon}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline
|
jan@42370
|
2175 |
\ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}funterm{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}real{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ rhs\ X{\isaliteral{27}{\isacharprime}}{\isaliteral{3B}{\isacharsemicolon}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline
|
jan@42370
|
2176 |
\ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}drop\ X{\isaliteral{27}{\isacharprime}}\ z\ {\isaliteral{3D}{\isacharequal}}\ for\ equation\ solving{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42370
|
2177 |
\ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}denom{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}real{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ get{\isaliteral{5F}{\isacharunderscore}}denominator\ funterm{\isaliteral{3B}{\isacharsemicolon}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline
|
jan@42370
|
2178 |
\ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}get{\isaliteral{5F}{\isacharunderscore}}denominator{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42370
|
2179 |
\ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}num{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}real{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ get{\isaliteral{5F}{\isacharunderscore}}numerator\ funterm{\isaliteral{3B}{\isacharsemicolon}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline
|
jan@42370
|
2180 |
\ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}get{\isaliteral{5F}{\isacharunderscore}}numerator{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42370
|
2181 |
\ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}equ{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}bool{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}denom\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{0}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}real{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline
|
jan@42370
|
2182 |
\ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}L{\isaliteral{5F}{\isacharunderscore}}L{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}bool\ list{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}SubProblem\ {\isaliteral{28}{\isacharparenleft}}PolyEq{\isaliteral{27}{\isacharprime}}{\isaliteral{2C}{\isacharcomma}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline
|
jan@42370
|
2183 |
\ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ \ \ \ {\isaliteral{5B}{\isacharbrackleft}}abcFormula{\isaliteral{2C}{\isacharcomma}}degree{\isaliteral{5F}{\isacharunderscore}}{\isadigit{2}}{\isaliteral{2C}{\isacharcomma}}polynomial{\isaliteral{2C}{\isacharcomma}}univariate{\isaliteral{2C}{\isacharcomma}}equation{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline
|
jan@42370
|
2184 |
\ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ \ \ \ {\isaliteral{5B}{\isacharbrackleft}}no{\isaliteral{5F}{\isacharunderscore}}met{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline
|
jan@42370
|
2185 |
\ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ \ \ \ {\isaliteral{5B}{\isacharbrackleft}}BOOL\ equ{\isaliteral{2C}{\isacharcomma}}\ REAL\ zzz{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline
|
jan@42370
|
2186 |
\ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}facs{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}real{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ factors{\isaliteral{5F}{\isacharunderscore}}from{\isaliteral{5F}{\isacharunderscore}}solution\ L{\isaliteral{5F}{\isacharunderscore}}L{\isaliteral{3B}{\isacharsemicolon}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline
|
jan@42370
|
2187 |
\ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}eql{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}real{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ Take\ {\isaliteral{28}{\isacharparenleft}}num{\isaliteral{5F}{\isacharunderscore}}orig\ {\isaliteral{2F}{\isacharslash}}\ facs{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\ \isanewline
|
neuper@42304
|
2188 |
\isanewline
|
jan@42370
|
2189 |
\ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}eqr{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}real{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}Try\ {\isaliteral{28}{\isacharparenleft}}Rewrite{\isaliteral{5F}{\isacharunderscore}}Set\ ansatz{\isaliteral{5F}{\isacharunderscore}}rls\ False{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ eql{\isaliteral{3B}{\isacharsemicolon}}\ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline
|
jan@42339
|
2190 |
\isanewline
|
jan@42370
|
2191 |
\ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}eq{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}bool{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ Take\ {\isaliteral{28}{\isacharparenleft}}eql\ {\isaliteral{3D}{\isacharequal}}\ eqr{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline
|
jan@42370
|
2192 |
\ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}Maybe\ possible\ to\ use\ HOLogic{\isaliteral{2E}{\isachardot}}mk{\isaliteral{5F}{\isacharunderscore}}eq\ {\isaliteral{3F}{\isacharquery}}{\isaliteral{3F}{\isacharquery}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42370
|
2193 |
\ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ eq\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}Try\ {\isaliteral{28}{\isacharparenleft}}Rewrite{\isaliteral{5F}{\isacharunderscore}}Set\ equival{\isaliteral{5F}{\isacharunderscore}}trans\ False{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ eq{\isaliteral{3B}{\isacharsemicolon}}\ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\ \isanewline
|
jan@42339
|
2194 |
\isanewline
|
jan@42370
|
2195 |
\ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ eq\ {\isaliteral{3D}{\isacharequal}}\ drop{\isaliteral{5F}{\isacharunderscore}}questionmarks\ eq{\isaliteral{3B}{\isacharsemicolon}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline
|
jan@42370
|
2196 |
\ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}z{\isadigit{1}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}real{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}rhs\ {\isaliteral{28}{\isacharparenleft}}NTH\ {\isadigit{1}}\ L{\isaliteral{5F}{\isacharunderscore}}L{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline
|
jan@42370
|
2197 |
\ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}\ \isanewline
|
jan@42381
|
2198 |
\ \ \ \ \ \ {\isaliteral{2A}{\isacharasterisk}}\ prepare\ equation\ for\ a\ {\isaliteral{2D}{\isacharminus}}\ eq{\isaliteral{5F}{\isacharunderscore}}a\isanewline
|
jan@42381
|
2199 |
\ \ \ \ \ \ {\isaliteral{2A}{\isacharasterisk}}\ therefor\ substitute\ z\ with\ solution\ {\isadigit{1}}\ {\isaliteral{2D}{\isacharminus}}\ z{\isadigit{1}}\isanewline
|
jan@42370
|
2200 |
\ \ \ \ \ \ {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42370
|
2201 |
\ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}z{\isadigit{2}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}real{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}rhs\ {\isaliteral{28}{\isacharparenleft}}NTH\ {\isadigit{2}}\ L{\isaliteral{5F}{\isacharunderscore}}L{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline
|
jan@42370
|
2202 |
\ \isanewline
|
jan@42370
|
2203 |
\ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}eq{\isaliteral{5F}{\isacharunderscore}}a{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}bool{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ Take\ eq{\isaliteral{3B}{\isacharsemicolon}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline
|
jan@42370
|
2204 |
\ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ eq{\isaliteral{5F}{\isacharunderscore}}a\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}Substitute\ {\isaliteral{5B}{\isacharbrackleft}}zzz{\isaliteral{3D}{\isacharequal}}z{\isadigit{1}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\ eq{\isaliteral{3B}{\isacharsemicolon}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline
|
jan@42370
|
2205 |
\ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ eq{\isaliteral{5F}{\isacharunderscore}}a\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}Rewrite{\isaliteral{5F}{\isacharunderscore}}Set\ norm{\isaliteral{5F}{\isacharunderscore}}Rational\ False{\isaliteral{29}{\isacharparenright}}\ eq{\isaliteral{5F}{\isacharunderscore}}a{\isaliteral{3B}{\isacharsemicolon}}\ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline
|
jan@42370
|
2206 |
\ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}sol{\isaliteral{5F}{\isacharunderscore}}a{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}bool\ list{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline
|
jan@42370
|
2207 |
\ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}SubProblem\ {\isaliteral{28}{\isacharparenleft}}Isac{\isaliteral{27}{\isacharprime}}{\isaliteral{2C}{\isacharcomma}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline
|
jan@42370
|
2208 |
\ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{5B}{\isacharbrackleft}}univariate{\isaliteral{2C}{\isacharcomma}}equation{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5B}{\isacharbrackleft}}no{\isaliteral{5F}{\isacharunderscore}}met{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline
|
jan@42370
|
2209 |
\ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{5B}{\isacharbrackleft}}BOOL\ eq{\isaliteral{5F}{\isacharunderscore}}a{\isaliteral{2C}{\isacharcomma}}\ REAL\ {\isaliteral{28}{\isacharparenleft}}A{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}real{\isaliteral{29}{\isacharparenright}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline
|
jan@42370
|
2210 |
\ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}a{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}real{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}rhs{\isaliteral{28}{\isacharparenleft}}NTH\ {\isadigit{1}}\ sol{\isaliteral{5F}{\isacharunderscore}}a{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline
|
jan@42339
|
2211 |
\isanewline
|
jan@42370
|
2212 |
\ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}eq{\isaliteral{5F}{\isacharunderscore}}b{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}bool{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ Take\ eq{\isaliteral{3B}{\isacharsemicolon}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline
|
jan@42370
|
2213 |
\ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ eq{\isaliteral{5F}{\isacharunderscore}}b\ {\isaliteral{3D}{\isacharequal}}\ \ {\isaliteral{28}{\isacharparenleft}}Substitute\ {\isaliteral{5B}{\isacharbrackleft}}zzz{\isaliteral{3D}{\isacharequal}}z{\isadigit{2}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\ eq{\isaliteral{5F}{\isacharunderscore}}b{\isaliteral{3B}{\isacharsemicolon}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline
|
jan@42370
|
2214 |
\ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ eq{\isaliteral{5F}{\isacharunderscore}}b\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}Rewrite{\isaliteral{5F}{\isacharunderscore}}Set\ norm{\isaliteral{5F}{\isacharunderscore}}Rational\ False{\isaliteral{29}{\isacharparenright}}\ eq{\isaliteral{5F}{\isacharunderscore}}b{\isaliteral{3B}{\isacharsemicolon}}\ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline
|
jan@42370
|
2215 |
\ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}sol{\isaliteral{5F}{\isacharunderscore}}b{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}bool\ list{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline
|
jan@42370
|
2216 |
\ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}SubProblem\ {\isaliteral{28}{\isacharparenleft}}Isac{\isaliteral{27}{\isacharprime}}{\isaliteral{2C}{\isacharcomma}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline
|
jan@42370
|
2217 |
\ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{5B}{\isacharbrackleft}}univariate{\isaliteral{2C}{\isacharcomma}}equation{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5B}{\isacharbrackleft}}no{\isaliteral{5F}{\isacharunderscore}}met{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline
|
jan@42370
|
2218 |
\ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{5B}{\isacharbrackleft}}BOOL\ eq{\isaliteral{5F}{\isacharunderscore}}b{\isaliteral{2C}{\isacharcomma}}\ REAL\ {\isaliteral{28}{\isacharparenleft}}B{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}real{\isaliteral{29}{\isacharparenright}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline
|
jan@42370
|
2219 |
\ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}b{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}real{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}rhs{\isaliteral{28}{\isacharparenleft}}NTH\ {\isadigit{1}}\ sol{\isaliteral{5F}{\isacharunderscore}}b{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline
|
jan@42365
|
2220 |
\isanewline
|
jan@42370
|
2221 |
\ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ eqr\ {\isaliteral{3D}{\isacharequal}}\ drop{\isaliteral{5F}{\isacharunderscore}}questionmarks\ eqr{\isaliteral{3B}{\isacharsemicolon}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline
|
jan@42370
|
2222 |
\ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}pbz{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}real{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ Take\ eqr{\isaliteral{3B}{\isacharsemicolon}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline
|
jan@42381
|
2223 |
\ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ pbz\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{28}{\isacharparenleft}}Substitute\ {\isaliteral{5B}{\isacharbrackleft}}A{\isaliteral{3D}{\isacharequal}}a{\isaliteral{2C}{\isacharcomma}}\ B{\isaliteral{3D}{\isacharequal}}b{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\ pbz{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline
|
jan@42365
|
2224 |
\isanewline
|
jan@42370
|
2225 |
\ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ pbz\ {\isaliteral{3D}{\isacharequal}}\ Rewrite\ ruleYZ\ False\ pbz{\isaliteral{3B}{\isacharsemicolon}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline
|
jan@42370
|
2226 |
\ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ pbz\ {\isaliteral{3D}{\isacharequal}}\ drop{\isaliteral{5F}{\isacharunderscore}}questionmarks\ pbz{\isaliteral{3B}{\isacharsemicolon}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline
|
jan@42365
|
2227 |
\isanewline
|
jan@42381
|
2228 |
\ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}X{\isaliteral{5F}{\isacharunderscore}}z{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}bool{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ Take\ {\isaliteral{28}{\isacharparenleft}}X{\isaliteral{5F}{\isacharunderscore}}z\ {\isaliteral{3D}{\isacharequal}}\ pbz{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline
|
jan@42381
|
2229 |
\ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}n{\isaliteral{5F}{\isacharunderscore}}eq{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}bool{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}Rewrite{\isaliteral{5F}{\isacharunderscore}}Set\ inverse{\isaliteral{5F}{\isacharunderscore}}z\ False{\isaliteral{29}{\isacharparenright}}\ X{\isaliteral{5F}{\isacharunderscore}}z{\isaliteral{3B}{\isacharsemicolon}}\ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline
|
jan@42381
|
2230 |
\ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ n{\isaliteral{5F}{\isacharunderscore}}eq\ {\isaliteral{3D}{\isacharequal}}\ drop{\isaliteral{5F}{\isacharunderscore}}questionmarks\ n{\isaliteral{5F}{\isacharunderscore}}eq\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline
|
jan@42370
|
2231 |
\ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}in\ n{\isaliteral{5F}{\isacharunderscore}}eq{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}\ \isanewline
|
jan@42370
|
2232 |
\ \ \ \ {\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42370
|
2233 |
\ \ \ \ \ \ \ \ \ \ \ {\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
neuper@42289
|
2234 |
{\isaliteral{2A7D}{\isacharverbatimclose}}%
|
neuper@42289
|
2235 |
\endisatagML
|
neuper@42289
|
2236 |
{\isafoldML}%
|
neuper@42289
|
2237 |
%
|
neuper@42289
|
2238 |
\isadelimML
|
neuper@42289
|
2239 |
%
|
neuper@42289
|
2240 |
\endisadelimML
|
neuper@42289
|
2241 |
%
|
neuper@42289
|
2242 |
\isamarkupsubsection{Check the Program%
|
neuper@42289
|
2243 |
}
|
neuper@42289
|
2244 |
\isamarkuptrue%
|
neuper@42289
|
2245 |
%
|
jan@42370
|
2246 |
\begin{isamarkuptext}%
|
jan@42370
|
2247 |
\noindent When the script is ready we can start checking our work.%
|
jan@42370
|
2248 |
\end{isamarkuptext}%
|
jan@42370
|
2249 |
\isamarkuptrue%
|
jan@42370
|
2250 |
%
|
jan@42370
|
2251 |
\isamarkupsubsubsection{Check the Formalization%
|
neuper@42289
|
2252 |
}
|
neuper@42289
|
2253 |
\isamarkuptrue%
|
neuper@42289
|
2254 |
%
|
neuper@42304
|
2255 |
\begin{isamarkuptext}%
|
jan@42370
|
2256 |
\noindent First we want to check the formalization of the in and
|
jan@42381
|
2257 |
output of our program.%
|
neuper@42304
|
2258 |
\end{isamarkuptext}%
|
neuper@42304
|
2259 |
\isamarkuptrue%
|
neuper@42304
|
2260 |
%
|
neuper@42304
|
2261 |
\isadelimML
|
neuper@42304
|
2262 |
%
|
neuper@42304
|
2263 |
\endisadelimML
|
neuper@42304
|
2264 |
%
|
neuper@42304
|
2265 |
\isatagML
|
neuper@42304
|
2266 |
\isacommand{ML}\isamarkupfalse%
|
neuper@42304
|
2267 |
\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
|
jan@42370
|
2268 |
\ \ val\ fmz\ {\isaliteral{3D}{\isacharequal}}\ \isanewline
|
jan@42370
|
2269 |
\ \ \ \ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}filterExpression\ {\isaliteral{28}{\isacharparenleft}}X\ \ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{3}}\ {\isaliteral{2F}{\isacharslash}}\ {\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{1}}{\isaliteral{2F}{\isacharslash}}{\isadigit{4}}\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{1}}{\isaliteral{2F}{\isacharslash}}{\isadigit{8}}\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{1}}{\isaliteral{2F}{\isacharslash}}{\isaliteral{28}{\isacharparenleft}}z{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}real{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\isanewline
|
jan@42370
|
2270 |
\ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}stepResponse\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{5B}{\isacharbrackleft}}n{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}real{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}bool{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2271 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}dI{\isaliteral{2C}{\isacharcomma}}pI{\isaliteral{2C}{\isacharcomma}}mI{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ \isanewline
|
jan@42370
|
2272 |
\ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}Isac{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}inverse{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}Z{\isaliteral{5F}{\isacharunderscore}}Transform{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}SignalProcessing{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ \isanewline
|
jan@42370
|
2273 |
\ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}SignalProcessing{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}Z{\isaliteral{5F}{\isacharunderscore}}Transform{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}inverse{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2274 |
\isanewline
|
jan@42370
|
2275 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5B}{\isacharbrackleft}}\isanewline
|
jan@42370
|
2276 |
\ \ \ \ \ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}\isanewline
|
jan@42370
|
2277 |
\ \ \ \ \ \ \ \ \ \ \ \ {\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\isanewline
|
jan@42370
|
2278 |
\ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{5B}{\isacharbrackleft}}{\isadigit{1}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\isanewline
|
jan@42370
|
2279 |
\ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{23}{\isacharhash}}Given{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\isanewline
|
jan@42370
|
2280 |
\ \ \ \ \ \ \ \ \ \ \ \ Const\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}Inverse{\isaliteral{5F}{\isacharunderscore}}Z{\isaliteral{5F}{\isacharunderscore}}Transform{\isaliteral{2E}{\isachardot}}filterExpression{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5F}{\isacharunderscore}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\isanewline
|
jan@42370
|
2281 |
\ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{5B}{\isacharbrackleft}}Const\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}HOL{\isaliteral{2E}{\isachardot}}eq{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5F}{\isacharunderscore}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{24}{\isachardollar}}\ {\isaliteral{5F}{\isacharunderscore}}\ {\isaliteral{24}{\isachardollar}}\ {\isaliteral{5F}{\isacharunderscore}}{\isaliteral{5D}{\isacharbrackright}}\isanewline
|
jan@42370
|
2282 |
\ \ \ \ \ \ \ \ \ \ {\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\isanewline
|
jan@42370
|
2283 |
\ \ \ \ \ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}\isanewline
|
jan@42370
|
2284 |
\ \ \ \ \ \ \ \ \ \ \ \ {\isadigit{2}}{\isaliteral{2C}{\isacharcomma}}\isanewline
|
jan@42370
|
2285 |
\ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{5B}{\isacharbrackleft}}{\isadigit{1}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\isanewline
|
jan@42370
|
2286 |
\ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{23}{\isacharhash}}Find{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\isanewline
|
jan@42370
|
2287 |
\ \ \ \ \ \ \ \ \ \ \ \ Const\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}Inverse{\isaliteral{5F}{\isacharunderscore}}Z{\isaliteral{5F}{\isacharunderscore}}Transform{\isaliteral{2E}{\isachardot}}stepResponse{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5F}{\isacharunderscore}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\isanewline
|
jan@42370
|
2288 |
\ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{5B}{\isacharbrackleft}}Free\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}x{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5F}{\isacharunderscore}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{24}{\isachardollar}}\ {\isaliteral{5F}{\isacharunderscore}}{\isaliteral{5D}{\isacharbrackright}}\isanewline
|
jan@42370
|
2289 |
\ \ \ \ \ \ \ \ \ \ {\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42370
|
2290 |
\ \ \ \ \ \ \ {\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}\isanewline
|
jan@42370
|
2291 |
\ \ \ \ \ \ {\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ prep{\isaliteral{5F}{\isacharunderscore}}ori\ fmz\ thy\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{23}{\isacharhash}}ppc\ o\ get{\isaliteral{5F}{\isacharunderscore}}pbt{\isaliteral{29}{\isacharparenright}}\ pI{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2292 |
\isanewline
|
wneuper@59585
|
2293 |
\ \ val\ Program\ sc\ \isanewline
|
jan@42370
|
2294 |
\ \ \ \ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{23}{\isacharhash}}scr\ o\ get{\isaliteral{5F}{\isacharunderscore}}met{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}SignalProcessing{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\isanewline
|
jan@42370
|
2295 |
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}Z{\isaliteral{5F}{\isacharunderscore}}Transform{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\isanewline
|
jan@42370
|
2296 |
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}inverse{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2297 |
\ \ atomty\ sc{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42316
|
2298 |
{\isaliteral{2A7D}{\isacharverbatimclose}}%
|
jan@42316
|
2299 |
\endisatagML
|
jan@42316
|
2300 |
{\isafoldML}%
|
jan@42316
|
2301 |
%
|
jan@42316
|
2302 |
\isadelimML
|
jan@42316
|
2303 |
%
|
jan@42316
|
2304 |
\endisadelimML
|
jan@42316
|
2305 |
%
|
jan@42370
|
2306 |
\isamarkupsubsubsection{Stepwise Check the Program\label{sec:stepcheck}%
|
jan@42370
|
2307 |
}
|
jan@42370
|
2308 |
\isamarkuptrue%
|
jan@42370
|
2309 |
%
|
jan@42316
|
2310 |
\begin{isamarkuptext}%
|
jan@42381
|
2311 |
\noindent We start to stepwise execute our new program in a calculation
|
jan@42370
|
2312 |
tree and check if every node implements that what we have wanted.%
|
jan@42316
|
2313 |
\end{isamarkuptext}%
|
jan@42316
|
2314 |
\isamarkuptrue%
|
jan@42316
|
2315 |
%
|
jan@42316
|
2316 |
\isadelimML
|
jan@42316
|
2317 |
%
|
jan@42316
|
2318 |
\endisadelimML
|
jan@42316
|
2319 |
%
|
jan@42316
|
2320 |
\isatagML
|
jan@42316
|
2321 |
\isacommand{ML}\isamarkupfalse%
|
jan@42316
|
2322 |
\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
|
jan@42370
|
2323 |
\ \ trace{\isaliteral{5F}{\isacharunderscore}}rewrite\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ false{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2324 |
\ \ trace{\isaliteral{5F}{\isacharunderscore}}script\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ false{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2325 |
\ \ print{\isaliteral{5F}{\isacharunderscore}}depth\ {\isadigit{9}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2326 |
\ \ \isanewline
|
jan@42370
|
2327 |
\ \ val\ fmz\ {\isaliteral{3D}{\isacharequal}}\isanewline
|
jan@42370
|
2328 |
\ \ \ \ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}filterExpression\ {\isaliteral{28}{\isacharparenleft}}X\ z\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{3}}\ {\isaliteral{2F}{\isacharslash}}\ {\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{1}}{\isaliteral{2F}{\isacharslash}}{\isadigit{4}}\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{1}}{\isaliteral{2F}{\isacharslash}}{\isadigit{8}}\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{1}}{\isaliteral{2F}{\isacharslash}}{\isaliteral{28}{\isacharparenleft}}z{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}real{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\isanewline
|
jan@42370
|
2329 |
\ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}stepResponse\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{5B}{\isacharbrackleft}}n{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}real{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}bool{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2330 |
\ \ \ \ \ \isanewline
|
jan@42370
|
2331 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}dI{\isaliteral{2C}{\isacharcomma}}pI{\isaliteral{2C}{\isacharcomma}}mI{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\isanewline
|
jan@42370
|
2332 |
\ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}Isac{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}inverse{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}Z{\isaliteral{5F}{\isacharunderscore}}Transform{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}SignalProcessing{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ \isanewline
|
jan@42370
|
2333 |
\ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}SignalProcessing{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}Z{\isaliteral{5F}{\isacharunderscore}}Transform{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}inverse{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2334 |
\ \ \ \ \ \ \ \ \ \ \ \ \ \isanewline
|
jan@42370
|
2335 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ \ {\isaliteral{3D}{\isacharequal}}\ CalcTreeTEST\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{28}{\isacharparenleft}}fmz{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{28}{\isacharparenleft}}dI{\isaliteral{2C}{\isacharcomma}}pI{\isaliteral{2C}{\isacharcomma}}mI{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2336 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\ \isanewline
|
jan@42370
|
2337 |
\ \ \ \ {\isaliteral{22}{\isachardoublequote}}Add{\isaliteral{5F}{\isacharunderscore}}Given{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2338 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2339 |
\ \ \ \ {\isaliteral{22}{\isachardoublequote}}Add{\isaliteral{5F}{\isacharunderscore}}Find{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2340 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2341 |
\ \ \ \ {\isaliteral{22}{\isachardoublequote}}Specify{\isaliteral{5F}{\isacharunderscore}}Theory{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2342 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2343 |
\ \ \ \ {\isaliteral{22}{\isachardoublequote}}Specify{\isaliteral{5F}{\isacharunderscore}}Problem{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2344 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2345 |
\ \ \ \ {\isaliteral{22}{\isachardoublequote}}Specify{\isaliteral{5F}{\isacharunderscore}}Method{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2346 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2347 |
\ \ \ \ {\isaliteral{22}{\isachardoublequote}}Apply{\isaliteral{5F}{\isacharunderscore}}Method{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2348 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2349 |
\ \ \ \ {\isaliteral{22}{\isachardoublequote}}Rewrite\ {\isaliteral{28}{\isacharparenleft}}ruleZY{\isaliteral{2C}{\isacharcomma}}\ Inverse{\isaliteral{5F}{\isacharunderscore}}Z{\isaliteral{5F}{\isacharunderscore}}Transform{\isaliteral{2E}{\isachardot}}ruleZY{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2350 |
\ \ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{2D}{\isacharminus}}{\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ X\ z\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{3}}\ {\isaliteral{2F}{\isacharslash}}\ {\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{1}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{4}}\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{1}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{8}}\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{1}}\ {\isaliteral{2F}{\isacharslash}}\ z{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2351 |
\ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}\isanewline
|
jan@42370
|
2352 |
\ \ \ {\isaliteral{2A}{\isacharasterisk}}\ TODO\ naming{\isaliteral{21}{\isacharbang}}\isanewline
|
jan@42370
|
2353 |
\ \ \ {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42370
|
2354 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2355 |
\ \ \ \ {\isaliteral{22}{\isachardoublequote}}Rewrite{\isaliteral{5F}{\isacharunderscore}}Set\ norm{\isaliteral{5F}{\isacharunderscore}}Rational{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2356 |
\ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ X{\isaliteral{27}{\isacharprime}}\ z\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{3}}\ {\isaliteral{2F}{\isacharslash}}\ {\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{1}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{4}}\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{1}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{8}}\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{1}}\ {\isaliteral{2F}{\isacharslash}}\ z{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2357 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\ \isanewline
|
jan@42370
|
2358 |
\ \ \ \ {\isaliteral{22}{\isachardoublequote}}SubProblem{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
neuper@42304
|
2359 |
{\isaliteral{2A7D}{\isacharverbatimclose}}%
|
neuper@42304
|
2360 |
\endisatagML
|
neuper@42304
|
2361 |
{\isafoldML}%
|
neuper@42304
|
2362 |
%
|
neuper@42304
|
2363 |
\isadelimML
|
neuper@42304
|
2364 |
%
|
neuper@42304
|
2365 |
\endisadelimML
|
neuper@42304
|
2366 |
%
|
neuper@42304
|
2367 |
\begin{isamarkuptext}%
|
jan@42370
|
2368 |
\noindent Instead of \ttfamily nxt = Subproblem \normalfont above we had
|
jan@42370
|
2369 |
\ttfamily Empty\_Tac; \normalfont the search for the reason considered
|
jan@42370
|
2370 |
the following points:\begin{itemize}
|
jan@42381
|
2371 |
\item What shows \ttfamily show\_pt pt;\normalfont\ldots?
|
jan@42381
|
2372 |
\begin{verbatim}(([2], Res), ?X' z = 24 / (-1 + -2 * z + 8 * z ^^^ 2))]\end{verbatim}
|
jan@42370
|
2373 |
The calculation is ok but no \ttfamily next \normalfont step found:
|
jan@42370
|
2374 |
Should be\\ \ttfamily nxt = Subproblem\normalfont!
|
jan@42370
|
2375 |
\item What shows \ttfamily trace\_script := true; \normalfont we read
|
jan@42381
|
2376 |
bottom up\ldots
|
jan@42381
|
2377 |
\begin{verbatim}
|
jan@42381
|
2378 |
@@@next leaf 'SubProblem
|
jan@42381
|
2379 |
(PolyEq',[abcFormula, degree_2, polynomial,
|
jan@42381
|
2380 |
univariate, equation], no_meth)
|
jan@42381
|
2381 |
[BOOL equ, REAL z]'
|
walther@59717
|
2382 |
---> Program.Tac 'SubProblem (PolyEq',
|
jan@42381
|
2383 |
[abcFormula, degree_2, polynomial,
|
jan@42381
|
2384 |
univariate, equation], no_meth)
|
jan@42381
|
2385 |
[BOOL (-1 + -2 * z + 8 * z \^\^\^ ~2 = 0), REAL z]'
|
jan@42381
|
2386 |
\end{verbatim}
|
jan@42370
|
2387 |
We see the SubProblem with correct arguments from searching next
|
walther@59717
|
2388 |
step (program text !!!--->!!! Program.Tac (script tactic) with arguments
|
jan@42370
|
2389 |
evaluated.)
|
wneuper@59585
|
2390 |
\item Do we have the right Program \ldots difference in the
|
jan@42381
|
2391 |
arguments in the arguments\ldots
|
jan@42381
|
2392 |
\begin{verbatim}
|
neuper@48790
|
2393 |
val Prog s =
|
jan@42381
|
2394 |
(#scr o get_met) ["SignalProcessing",
|
jan@42381
|
2395 |
"Z_Transform",
|
neuper@42405
|
2396 |
"Inverse"];
|
walther@59868
|
2397 |
writeln (UnparseC.term s);
|
jan@42381
|
2398 |
\end{verbatim}
|
jan@42370
|
2399 |
\ldots shows the right script. Difference in the arguments.
|
jan@42370
|
2400 |
\item Test --- Why helpless here ? --- shows: \ttfamily replace
|
wneuper@59585
|
2401 |
no\_meth by [no\_meth] \normalfont in Program
|
jan@42370
|
2402 |
\end{itemize}%
|
neuper@42304
|
2403 |
\end{isamarkuptext}%
|
neuper@42304
|
2404 |
\isamarkuptrue%
|
neuper@42304
|
2405 |
%
|
neuper@42304
|
2406 |
\isadelimML
|
neuper@42304
|
2407 |
%
|
neuper@42304
|
2408 |
\endisadelimML
|
neuper@42304
|
2409 |
%
|
neuper@42304
|
2410 |
\isatagML
|
neuper@42304
|
2411 |
\isacommand{ML}\isamarkupfalse%
|
neuper@42304
|
2412 |
\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
|
jan@42370
|
2413 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\ \isanewline
|
jan@42370
|
2414 |
\ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}Model{\isaliteral{5F}{\isacharunderscore}}Problem{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
neuper@42289
|
2415 |
{\isaliteral{2A7D}{\isacharverbatimclose}}%
|
neuper@42289
|
2416 |
\endisatagML
|
neuper@42289
|
2417 |
{\isafoldML}%
|
neuper@42289
|
2418 |
%
|
neuper@42289
|
2419 |
\isadelimML
|
neuper@42289
|
2420 |
%
|
neuper@42289
|
2421 |
\endisadelimML
|
neuper@42289
|
2422 |
%
|
neuper@42289
|
2423 |
\begin{isamarkuptext}%
|
jan@42370
|
2424 |
\noindent Instead of \ttfamily nxt = Model\_Problem \normalfont above
|
jan@42370
|
2425 |
we had \ttfamily Empty\_Tac; \normalfont the search for the reason
|
jan@42370
|
2426 |
considered the following points:\begin{itemize}
|
jan@42370
|
2427 |
\item Difference in the arguments
|
jan@42381
|
2428 |
\item Comparison with Subsection~\ref{sec:solveq}: There solving this
|
jan@42370
|
2429 |
equation works, so there must be some difference in the arguments
|
jan@42370
|
2430 |
of the Subproblem: RIGHT: we had \ttfamily [no\_meth] \normalfont
|
jan@42370
|
2431 |
instead of \ttfamily [no\_met] \normalfont ;-)
|
jan@42370
|
2432 |
\end{itemize}%
|
neuper@42289
|
2433 |
\end{isamarkuptext}%
|
neuper@42289
|
2434 |
\isamarkuptrue%
|
neuper@42289
|
2435 |
%
|
neuper@42289
|
2436 |
\isadelimML
|
neuper@42289
|
2437 |
%
|
neuper@42289
|
2438 |
\endisadelimML
|
neuper@42289
|
2439 |
%
|
neuper@42289
|
2440 |
\isatagML
|
neuper@42289
|
2441 |
\isacommand{ML}\isamarkupfalse%
|
neuper@42289
|
2442 |
\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
|
jan@42370
|
2443 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2444 |
\ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}Add{\isaliteral{5F}{\isacharunderscore}}Given\ equality\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2D}{\isacharminus}}{\isadigit{1}}\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{2}}\ {\isaliteral{2A}{\isacharasterisk}}\ z\ {\isaliteral{2B}{\isacharplus}}\ {\isadigit{8}}\ {\isaliteral{2A}{\isacharasterisk}}\ z\ {\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}\ {\isadigit{2}}\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{0}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42370
|
2445 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2446 |
\ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}Add{\isaliteral{5F}{\isacharunderscore}}Given\ solveFor\ z{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42370
|
2447 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2448 |
\ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}Add{\isaliteral{5F}{\isacharunderscore}}Find\ solutions\ z{\isaliteral{5F}{\isacharunderscore}}i{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42370
|
2449 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2450 |
\ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}Specify{\isaliteral{5F}{\isacharunderscore}}Theory\ Isac{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
neuper@42289
|
2451 |
{\isaliteral{2A7D}{\isacharverbatimclose}}%
|
neuper@42289
|
2452 |
\endisatagML
|
neuper@42289
|
2453 |
{\isafoldML}%
|
neuper@42289
|
2454 |
%
|
neuper@42289
|
2455 |
\isadelimML
|
neuper@42289
|
2456 |
%
|
neuper@42289
|
2457 |
\endisadelimML
|
neuper@42289
|
2458 |
%
|
jan@42370
|
2459 |
\begin{isamarkuptext}%
|
jan@42370
|
2460 |
\noindent We had \ttfamily nxt = Empty\_Tac instead Specify\_Theory;
|
jan@42370
|
2461 |
\normalfont The search for the reason considered the following points:
|
jan@42370
|
2462 |
\begin{itemize}
|
jan@42370
|
2463 |
\item Was there an error message? NO -- ok
|
jan@42370
|
2464 |
\item Has \ttfamily nxt = Add\_Find \normalfont been inserted in pt:\\
|
jan@42370
|
2465 |
\ttfamily get\_obj g\_pbl pt (fst p);\normalfont? YES -- ok
|
jan@42381
|
2466 |
\item What is the returned formula:
|
jan@42381
|
2467 |
\begin{verbatim}
|
neuper@52101
|
2468 |
print_depth 999; f; print_depth 3;
|
jan@42381
|
2469 |
{ Find = [ Correct "solutions z_i"],
|
jan@42381
|
2470 |
With = [],
|
jan@42381
|
2471 |
Given = [Correct "equality (-1 + -2*z + 8*z ^^^ 2 = 0)",
|
jan@42381
|
2472 |
Correct "solveFor z"],
|
jan@42381
|
2473 |
Where = [...],
|
jan@42381
|
2474 |
Relate = [] }
|
jan@42381
|
2475 |
\end{verbatim}
|
jan@42370
|
2476 |
\normalfont The only False is the reason: the Where (the precondition) is
|
jan@42370
|
2477 |
False for good reasons: The precondition seems to check for linear
|
jan@42370
|
2478 |
equations, not for the one we want to solve! Removed this error by
|
wneuper@59585
|
2479 |
correcting the Program from \ttfamily SubProblem (PolyEq',
|
jan@42370
|
2480 |
\lbrack linear,univariate,equation,
|
jan@42370
|
2481 |
test\rbrack, \lbrack Test,solve\_linear\rbrack \normalfont to
|
jan@42370
|
2482 |
\ttfamily SubProblem (PolyEq',\\ \lbrack abcFormula,degree\_2,
|
jan@42370
|
2483 |
polynomial,univariate,equation\rbrack,\\
|
jan@42370
|
2484 |
\lbrack PolyEq,solve\_d2\_polyeq\_abc\_equation
|
jan@42370
|
2485 |
\rbrack\normalfont
|
jan@42370
|
2486 |
You find the appropriate type of equation at the
|
jan@42370
|
2487 |
{\sisac}-WEB-Page\footnote{
|
jan@42370
|
2488 |
\href{http://www.ist.tugraz.at/projects/isac/www/kbase/pbl/index\_pbl.html}
|
jan@42370
|
2489 |
{http://www.ist.tugraz.at/projects/isac/www/kbase/pbl/index\_pbl.html}
|
jan@42370
|
2490 |
}
|
jan@42370
|
2491 |
And the respective method in \ttfamily Knowledge/PolyEq.thy \normalfont
|
jan@42370
|
2492 |
at the respective \ttfamily store\_pbt. \normalfont Or you leave the
|
wneuper@59585
|
2493 |
selection of the appropriate type to isac as done in the final Program ;-))
|
jan@42370
|
2494 |
\end{itemize}%
|
jan@42370
|
2495 |
\end{isamarkuptext}%
|
neuper@42289
|
2496 |
\isamarkuptrue%
|
neuper@42289
|
2497 |
%
|
neuper@42289
|
2498 |
\isadelimML
|
neuper@42289
|
2499 |
%
|
neuper@42289
|
2500 |
\endisadelimML
|
neuper@42289
|
2501 |
%
|
neuper@42289
|
2502 |
\isatagML
|
neuper@42289
|
2503 |
\isacommand{ML}\isamarkupfalse%
|
neuper@42289
|
2504 |
\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
|
jan@42370
|
2505 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\ \isanewline
|
jan@42370
|
2506 |
\ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}Specify{\isaliteral{5F}{\isacharunderscore}}Problem\ {\isaliteral{5B}{\isacharbrackleft}}abcFormula{\isaliteral{2C}{\isacharcomma}}{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42370
|
2507 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2508 |
\ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}Specify{\isaliteral{5F}{\isacharunderscore}}Method\ {\isaliteral{5B}{\isacharbrackleft}}PolyEq{\isaliteral{2C}{\isacharcomma}}solve{\isaliteral{5F}{\isacharunderscore}}d{\isadigit{2}}{\isaliteral{5F}{\isacharunderscore}}polyeq{\isaliteral{5F}{\isacharunderscore}}abc{\isaliteral{5F}{\isacharunderscore}}equation{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42370
|
2509 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\ \isanewline
|
jan@42370
|
2510 |
\ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}Apply{\isaliteral{5F}{\isacharunderscore}}Method\ {\isaliteral{5B}{\isacharbrackleft}}PolyEq{\isaliteral{2C}{\isacharcomma}}solve{\isaliteral{5F}{\isacharunderscore}}d{\isadigit{2}}{\isaliteral{5F}{\isacharunderscore}}polyeq{\isaliteral{5F}{\isacharunderscore}}abc{\isaliteral{5F}{\isacharunderscore}}equation{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42370
|
2511 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2512 |
\ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}Rewrite{\isaliteral{5F}{\isacharunderscore}}Set{\isaliteral{5F}{\isacharunderscore}}Inst\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{28}{\isacharparenleft}}bdv{\isaliteral{2C}{\isacharcomma}}\ z{\isaliteral{29}{\isacharparenright}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ d{\isadigit{2}}{\isaliteral{5F}{\isacharunderscore}}polyeq{\isaliteral{5F}{\isacharunderscore}}abcFormula{\isaliteral{5F}{\isacharunderscore}}simplify{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42370
|
2513 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2514 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2515 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2516 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2517 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2518 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2519 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2520 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2521 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2522 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2523 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2524 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2525 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2526 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2527 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2528 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2529 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
wneuper@59370
|
2530 |
\ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}Specify{\isaliteral{5F}{\isacharunderscore}}Problem\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}normalise{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}polynomial{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}univariate{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}equation{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42370
|
2531 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
wneuper@59370
|
2532 |
\ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}Specify{\isaliteral{5F}{\isacharunderscore}}Method\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}PolyEq{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}normalise{\isaliteral{5F}{\isacharunderscore}}poly{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42370
|
2533 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
wneuper@59370
|
2534 |
\ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}Apply{\isaliteral{5F}{\isacharunderscore}}Method\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}PolyEq{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}normalise{\isaliteral{5F}{\isacharunderscore}}poly{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42370
|
2535 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2536 |
\ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}Rewrite\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}all{\isaliteral{5F}{\isacharunderscore}}left{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}PolyEq{\isaliteral{2E}{\isachardot}}all{\isaliteral{5F}{\isacharunderscore}}left{\isaliteral{22}{\isachardoublequote}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42370
|
2537 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2538 |
\ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}Rewrite{\isaliteral{5F}{\isacharunderscore}}Set{\isaliteral{5F}{\isacharunderscore}}Inst\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}bdv{\isaliteral{2C}{\isacharcomma}}\ A{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}make{\isaliteral{5F}{\isacharunderscore}}ratpoly{\isaliteral{5F}{\isacharunderscore}}in{\isaliteral{22}{\isachardoublequote}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42370
|
2539 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\ \isanewline
|
jan@42370
|
2540 |
\ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}Rewrite{\isaliteral{5F}{\isacharunderscore}}Set\ {\isaliteral{22}{\isachardoublequote}}polyeq{\isaliteral{5F}{\isacharunderscore}}simplify{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42370
|
2541 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\ \isanewline
|
jan@42370
|
2542 |
\ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}Subproblem{\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}Isac{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}degree{\isaliteral{5F}{\isacharunderscore}}{\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}polynomial{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}univariate{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}equation{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
|
jan@42370
|
2543 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2544 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2545 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2546 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2547 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2548 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2549 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2550 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2551 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2552 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2553 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2554 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2555 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2556 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2557 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2558 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2559 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2560 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2561 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2562 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2563 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2564 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2565 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2566 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2567 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2568 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2569 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2570 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2571 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2572 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2573 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2574 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2575 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2576 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2577 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2578 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2579 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2580 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2581 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2582 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2583 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2584 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2585 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2586 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2587 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2588 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2589 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2590 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2591 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2592 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2593 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2594 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2595 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2596 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2597 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2598 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2599 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2600 |
\ \ val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
|
jan@42370
|
2601 |
{\isaliteral{2A7D}{\isacharverbatimclose}}%
|
jan@42370
|
2602 |
\endisatagML
|
jan@42370
|
2603 |
{\isafoldML}%
|
jan@42370
|
2604 |
%
|
jan@42370
|
2605 |
\isadelimML
|
jan@42370
|
2606 |
%
|
jan@42370
|
2607 |
\endisadelimML
|
jan@42370
|
2608 |
%
|
jan@42370
|
2609 |
\begin{isamarkuptext}%
|
jan@42370
|
2610 |
\noindent As a last step we check the tracing output of the last calc
|
jan@42370
|
2611 |
tree instruction and compare it with the pre-calculated result.%
|
jan@42370
|
2612 |
\end{isamarkuptext}%
|
jan@42370
|
2613 |
\isamarkuptrue%
|
jan@42370
|
2614 |
%
|
jan@42381
|
2615 |
\isamarkupsection{Improve and Transfer into Knowledge%
|
jan@42381
|
2616 |
}
|
jan@42381
|
2617 |
\isamarkuptrue%
|
jan@42381
|
2618 |
%
|
jan@42381
|
2619 |
\begin{isamarkuptext}%
|
jan@42381
|
2620 |
We want to improve the very long program \ttfamily InverseZTransform
|
jan@42381
|
2621 |
\normalfont by modularisation: partial fraction decomposition shall
|
jan@42381
|
2622 |
become a sub-problem.
|
jan@42381
|
2623 |
|
jan@42381
|
2624 |
We could transfer all knowledge in \ttfamily Build\_Inverse\_Z\_Transform.thy
|
jan@42381
|
2625 |
\normalfont first to the \ttfamily Knowledge/Inverse\_Z\_Transform.thy
|
jan@42381
|
2626 |
\normalfont and then modularise. In this case TODO problems?!?
|
jan@42381
|
2627 |
|
jan@42381
|
2628 |
We chose another way and go bottom up: first we build the sub-problem in
|
jan@42381
|
2629 |
\ttfamily Partial\_Fractions.thy \normalfont with the term:
|
jan@42381
|
2630 |
|
jan@42381
|
2631 |
$$\frac{3}{x\cdot(z - \frac{1}{4} + \frac{-1}{8}\cdot\frac{1}{z})}$$
|
jan@42381
|
2632 |
|
jan@42381
|
2633 |
\noindent (how this still can be improved see \ttfamily Partial\_Fractions.thy\normalfont),
|
jan@42381
|
2634 |
and re-use all stuff prepared in \ttfamily Build\_Inverse\_Z\_Transform.thy:
|
jan@42381
|
2635 |
\normalfont The knowledge will be transferred to \ttfamily src/../Partial\_Fractions.thy
|
jan@42381
|
2636 |
\normalfont and the respective tests to:
|
jan@42381
|
2637 |
\begin{center}\ttfamily test/../sartial\_fractions.sml\normalfont\end{center}%
|
jan@42381
|
2638 |
\end{isamarkuptext}%
|
jan@42381
|
2639 |
\isamarkuptrue%
|
jan@42381
|
2640 |
%
|
jan@42381
|
2641 |
\isamarkupsubsection{Transfer to Partial\_Fractions.thy%
|
jan@42381
|
2642 |
}
|
jan@42381
|
2643 |
\isamarkuptrue%
|
jan@42381
|
2644 |
%
|
jan@42381
|
2645 |
\begin{isamarkuptext}%
|
jan@42381
|
2646 |
First we transfer both, knowledge and tests into:
|
jan@42381
|
2647 |
\begin{center}\ttfamily src/../Partial\_Fractions.thy\normalfont\end{center}
|
jan@42381
|
2648 |
in order to immediately have the test results.
|
jan@42381
|
2649 |
|
jan@42381
|
2650 |
We copy \ttfamily factors\_from\_solution, drop\_questionmarks,\\
|
jan@42381
|
2651 |
ansatz\_2nd\_order \normalfont and rule-sets --- no problem.
|
jan@42381
|
2652 |
|
jan@42381
|
2653 |
Also \ttfamily store\_pbt ..\\ "pbl\_simp\_rat\_partfrac"
|
jan@42381
|
2654 |
\normalfont is easy.
|
jan@42381
|
2655 |
|
jan@42381
|
2656 |
But then we copy from:\\
|
jan@42381
|
2657 |
(1) \ttfamily Build\_Inverse\_Z\_Transform.thy store\_met\ldots "met\_SP\_Ztrans\_inv"
|
jan@42381
|
2658 |
\normalfont\\ to\\
|
jan@42381
|
2659 |
(2) \ttfamily Partial\_Fractions.thy store\_met\ldots "met\_SP\_Ztrans\_inv"
|
jan@42381
|
2660 |
\normalfont\\ and cut out the respective part from the program. First we ensure that
|
jan@42381
|
2661 |
the string is correct. When we insert the string into (2)
|
jan@42381
|
2662 |
\ttfamily store\_met .. "met\_partial\_fraction" \normalfont --- and get an error.%
|
jan@42381
|
2663 |
\end{isamarkuptext}%
|
jan@42381
|
2664 |
\isamarkuptrue%
|
jan@42381
|
2665 |
%
|
jan@42381
|
2666 |
\isamarkupsubsubsection{'Programming' in ISAC's TP-based Language%
|
jan@42381
|
2667 |
}
|
jan@42381
|
2668 |
\isamarkuptrue%
|
jan@42381
|
2669 |
%
|
jan@42381
|
2670 |
\begin{isamarkuptext}%
|
jan@42381
|
2671 |
At the present state writing programs in {\sisac} is particularly cumbersome.
|
jan@42381
|
2672 |
So we give hints how to cope with the many obstacles. Below we describe the
|
jan@42381
|
2673 |
steps we did in making (2) run.
|
jan@42381
|
2674 |
|
jan@42381
|
2675 |
\begin{enumerate}
|
jan@42381
|
2676 |
\item We check if the \textbf{string} containing the program is correct.
|
jan@42381
|
2677 |
\item We check if the \textbf{types in the program} are correct.
|
jan@42381
|
2678 |
For this purpose we start start with the first and last lines
|
jan@42381
|
2679 |
\begin{verbatim}
|
jan@42381
|
2680 |
"PartFracScript (f_f::real) (v_v::real) = " ^
|
jan@42381
|
2681 |
" (let X = Take f_f; " ^
|
jan@42381
|
2682 |
" pbz = ((Substitute []) X) " ^
|
jan@42381
|
2683 |
" in pbz)"
|
jan@42381
|
2684 |
\end{verbatim}
|
jan@42381
|
2685 |
The last but one line helps not to bother with ';'.
|
jan@42381
|
2686 |
\item Then we add line by line. Already the first line causes the error.
|
jan@42381
|
2687 |
So we investigate it by
|
jan@42381
|
2688 |
\begin{verbatim}
|
neuper@48761
|
2689 |
val ctxt = Proof_Context.init_global @ { theory } ;
|
jan@42381
|
2690 |
val SOME t =
|
jan@42381
|
2691 |
parseNEW ctxt "(num_orig::real) =
|
jan@42381
|
2692 |
get_numerator(rhs f_f)";
|
jan@42381
|
2693 |
\end{verbatim}
|
jan@42381
|
2694 |
and see a type clash: \ttfamily rhs \normalfont from (1) requires type
|
jan@42381
|
2695 |
\ttfamily bool \normalfont while (2) wants to have \ttfamily (f\_f::real).
|
jan@42381
|
2696 |
\normalfont Of course, we don't need \ttfamily rhs \normalfont anymore.
|
jan@42381
|
2697 |
\item Type-checking can be very tedious. One might even inspect the
|
jan@42381
|
2698 |
parse-tree of the program with {\sisac}'s specific debug tools:
|
jan@42381
|
2699 |
\begin{verbatim}
|
neuper@48790
|
2700 |
val {scr = Prog t,...} =
|
jan@42381
|
2701 |
get_met ["simplification",
|
jan@42381
|
2702 |
"of_rationals",
|
jan@42381
|
2703 |
"to_partial_fraction"];
|
jan@42381
|
2704 |
atomty_thy @ { theory } t ;
|
jan@42381
|
2705 |
\end{verbatim}
|
jan@42381
|
2706 |
\item We check if the \textbf{semantics of the program} by stepwise evaluation
|
jan@42381
|
2707 |
of the program. Evaluation is done by the Lucas-Interpreter, which works
|
wneuper@59592
|
2708 |
using the knowledge in theory Isac_Knowledge; so we have to re-build Isac. And the
|
jan@42381
|
2709 |
test are performed simplest in a file which is loaded with Isac.
|
jan@42381
|
2710 |
See \ttfamily tests/../partial\_fractions.sml \normalfont.
|
jan@42381
|
2711 |
\end{enumerate}%
|
jan@42381
|
2712 |
\end{isamarkuptext}%
|
jan@42381
|
2713 |
\isamarkuptrue%
|
jan@42381
|
2714 |
%
|
jan@42381
|
2715 |
\isamarkupsubsection{Transfer to Inverse\_Z\_Transform.thy%
|
jan@42381
|
2716 |
}
|
jan@42381
|
2717 |
\isamarkuptrue%
|
jan@42381
|
2718 |
%
|
jan@42381
|
2719 |
\begin{isamarkuptext}%
|
jan@42381
|
2720 |
Unfortunately it was not possible to complete this task. Because we ran out of time\ldots%
|
jan@42381
|
2721 |
\end{isamarkuptext}%
|
jan@42381
|
2722 |
\isamarkuptrue%
|
neuper@42289
|
2723 |
%
|
neuper@42289
|
2724 |
\isadelimtheory
|
neuper@42289
|
2725 |
%
|
neuper@42289
|
2726 |
\endisadelimtheory
|
neuper@42289
|
2727 |
%
|
neuper@42289
|
2728 |
\isatagtheory
|
neuper@42289
|
2729 |
\isacommand{end}\isamarkupfalse%
|
neuper@42289
|
2730 |
%
|
neuper@42289
|
2731 |
\endisatagtheory
|
neuper@42289
|
2732 |
{\isafoldtheory}%
|
neuper@42289
|
2733 |
%
|
neuper@42289
|
2734 |
\isadelimtheory
|
neuper@42289
|
2735 |
%
|
neuper@42289
|
2736 |
\endisadelimtheory
|
neuper@42289
|
2737 |
\isanewline
|
neuper@42289
|
2738 |
\isanewline
|
neuper@42289
|
2739 |
\end{isabellebody}%
|
neuper@42289
|
2740 |
%%% Local Variables:
|
neuper@42289
|
2741 |
%%% mode: latex
|
neuper@42289
|
2742 |
%%% TeX-master: "root"
|
neuper@42289
|
2743 |
%%% End:
|