1.1 --- a/test/Tools/isac/ADDTESTS/course/SignalProcess/document/Build_Inverse_Z_Transform.tex	Fri Oct 07 16:23:56 2011 +0200
     1.2 +++ b/test/Tools/isac/ADDTESTS/course/SignalProcess/document/Build_Inverse_Z_Transform.tex	Fri Oct 07 16:54:31 2011 +0200
     1.3 @@ -10,8 +10,7 @@
     1.4  %
     1.5  \isatagtheory
     1.6  \isacommand{theory}\isamarkupfalse%
     1.7 -\ Build{\isaliteral{5F}{\isacharunderscore}}Inverse{\isaliteral{5F}{\isacharunderscore}}Z{\isaliteral{5F}{\isacharunderscore}}Transform\ \isakeyword{imports}\ \isanewline
     1.8 -\ \ Isac\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}{\isaliteral{2F}{\isacharslash}}{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}{\isaliteral{2F}{\isacharslash}}{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}{\isaliteral{2F}{\isacharslash}}{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}{\isaliteral{2F}{\isacharslash}}{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}{\isaliteral{2F}{\isacharslash}}{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}{\isaliteral{2F}{\isacharslash}}src{\isaliteral{2F}{\isacharslash}}Tools{\isaliteral{2F}{\isacharslash}}isac{\isaliteral{2F}{\isacharslash}}Knowledge{\isaliteral{2F}{\isacharslash}}Partial{\isaliteral{5F}{\isacharunderscore}}Fractions{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
     1.9 +\ Build{\isaliteral{5F}{\isacharunderscore}}Inverse{\isaliteral{5F}{\isacharunderscore}}Z{\isaliteral{5F}{\isacharunderscore}}Transform\ \isakeyword{imports}\ Isac\isanewline
    1.10  \ \ \isanewline
    1.11  \isakeyword{begin}%
    1.12  \endisatagtheory
    1.13 @@ -23,9 +22,9 @@
    1.14  %
    1.15  \begin{isamarkuptext}%
    1.16  We stepwise build Inverse_Z_Transform.thy as an exercise.
    1.17 -  Because subsection "Stepwise Check the Program" requires Inverse_Z_Transform.thy 
    1.18 -  as a subtheory of Isac.thy, the setup has been changed from
    1.19 -  "theory Inverse_Z_Transform imports Isac begin.." to the above.
    1.20 +  Because subsection "Stepwise Check the Program" requires 
    1.21 +  Inverse_Z_Transform.thy as a subtheory of Isac.thy, the setup has been changed 
    1.22 +  from "theory Inverse_Z_Transform imports Isac begin.." to the above.
    1.23  
    1.24    ATTENTION WITH NAMES OF IDENTIFIERS WHEN GOING INTO INTERNALS:
    1.25    Here in this theory there are the internal names twice, for instance we have
    1.26 @@ -240,8 +239,7 @@
    1.27  \endisaantiq
    1.28  {\isaliteral{29}{\isacharparenright}}\ t{\isaliteral{3B}{\isacharsemicolon}}\isanewline
    1.29  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}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{2D}{\isacharminus}}\ real\ {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
    1.30 -term{\isadigit{2}}str\ t{\isaliteral{3B}{\isacharsemicolon}}\isanewline
    1.31 -{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline
    1.32 +term{\isadigit{2}}str\ t{\isaliteral{3B}{\isacharsemicolon}}{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline
    1.33  \isacommand{ML}\isamarkupfalse%
    1.34  \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
    1.35  val\ SOME\ {\isaliteral{28}{\isacharparenleft}}t{\isaliteral{2C}{\isacharcomma}}\ asm{\isadigit{2}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ rewrite{\isaliteral{5F}{\isacharunderscore}}\ thy\ ro\ er\ true\ {\isaliteral{28}{\isacharparenleft}}num{\isaliteral{5F}{\isacharunderscore}}str\ %
    1.36 @@ -317,8 +315,10 @@
    1.37  \isadelimML
    1.38  %
    1.39  \endisadelimML
    1.40 -\isanewline
    1.41 -\isanewline
    1.42 +%
    1.43 +\isamarkupsubsubsection{multply with z%
    1.44 +}
    1.45 +\isamarkuptrue%
    1.46  \isacommand{axiomatization}\isamarkupfalse%
    1.47  \ \isakeyword{where}\isanewline
    1.48  \ \ 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
    1.49 @@ -367,7 +367,21 @@
    1.50  %
    1.51  \endisadelimML
    1.52  %
    1.53 -\isamarkupsubsection{build equation from given term%
    1.54 +\isamarkupsubsubsection{get argument of X': z is the variable the equation is solved for%
    1.55 +}
    1.56 +\isamarkuptrue%
    1.57 +%
    1.58 +\begin{isamarkuptext}%
    1.59 +grep... Atools.thy, Tools.thy contain general utilities: eval_argument_in, eval_rhs, eval_lhs,...
    1.60 +
    1.61 +grep -r "fun eva_" ... shows all functions witch can be used in a script.
    1.62 +lookup this files how to build and handle such functions.
    1.63 +
    1.64 +the next section shows how to introduce such a function.%
    1.65 +\end{isamarkuptext}%
    1.66 +\isamarkuptrue%
    1.67 +%
    1.68 +\isamarkupsubsubsection{Decompose given term into lhs = rhs%
    1.69  }
    1.70  \isamarkuptrue%
    1.71  %
    1.72 @@ -378,9 +392,9 @@
    1.73  \isatagML
    1.74  \isacommand{ML}\isamarkupfalse%
    1.75  \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
    1.76 -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
    1.77 -val\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}\ denom{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ 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
    1.78 -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
    1.79 +\ \ 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
    1.80 +\ \ val\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}\ denom{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ 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
    1.81 +\ \ 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
    1.82  {\isaliteral{2A7D}{\isacharverbatimclose}}%
    1.83  \endisatagML
    1.84  {\isafoldML}%
    1.85 @@ -390,11 +404,36 @@
    1.86  \endisadelimML
    1.87  %
    1.88  \begin{isamarkuptext}%
    1.89 -we have rhs in the language, but we need a function 
    1.90 +we have rhs in the Script language, but we need a function 
    1.91    which gets the denominator of a fraction%
    1.92  \end{isamarkuptext}%
    1.93  \isamarkuptrue%
    1.94  %
    1.95 +\begin{isamarkuptext}%
    1.96 +---------------------------begin partial fractions snip--------------------------%
    1.97 +\end{isamarkuptext}%
    1.98 +\isamarkuptrue%
    1.99 +%
   1.100 +\isamarkupsubsubsection{get the denominator out of a fraction%
   1.101 +}
   1.102 +\isamarkuptrue%
   1.103 +%
   1.104 +\begin{isamarkuptext}%
   1.105 +get denominator should become a constant for the isabelle parser:%
   1.106 +\end{isamarkuptext}%
   1.107 +\isamarkuptrue%
   1.108 +\isacommand{consts}\isamarkupfalse%
   1.109 +\isanewline
   1.110 +\ \ 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}}%
   1.111 +\begin{isamarkuptext}%
   1.112 +With the above definition we run into problems with parsing the Script InverseZTransform:
   1.113 +  This leads to "ambiguous parse trees" and we avoid this by shifting the definition
   1.114 +  to Rationa.thy and re-building Isac.
   1.115 +  ATTENTION: from now on Build_Inverse_Z_Transform mimics a build from scratch;
   1.116 +  it only works due to re-building Isac several times (indicated explicityl).%
   1.117 +\end{isamarkuptext}%
   1.118 +\isamarkuptrue%
   1.119 +%
   1.120  \isadelimML
   1.121  %
   1.122  \endisadelimML
   1.123 @@ -402,14 +441,17 @@
   1.124  \isatagML
   1.125  \isacommand{ML}\isamarkupfalse%
   1.126  \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
   1.127 -{\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}GOON\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
   1.128 +{\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}get{\isaliteral{5F}{\isacharunderscore}}denominator{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\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}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
   1.129 +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
   1.130 +		\ \ \ \ \ \ {\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
   1.131 +\ \ \ \ \ \ \ \ \ \ \ \ \ \ {\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\ {\isaliteral{24}{\isachardollar}}\isanewline
   1.132 +\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ denom{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ thy\ {\isaliteral{3D}{\isacharequal}}\ \isanewline
   1.133 +\ \ \ \ \ \ \ \ SOME\ {\isaliteral{28}{\isacharparenleft}}mk{\isaliteral{5F}{\isacharunderscore}}thmid\ thmid\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{22}{\isachardoublequote}}\ \isanewline
   1.134 +\ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}Print{\isaliteral{5F}{\isacharunderscore}}Mode{\isaliteral{2E}{\isachardot}}setmp\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\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
   1.135 +	\ \ \ \ \ \ \ \ \ \ 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
   1.136 +\ \ {\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
   1.137  \isanewline
   1.138 -{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline
   1.139 -\isacommand{ML}\isamarkupfalse%
   1.140 -\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
   1.141 -{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline
   1.142 -\isacommand{ML}\isamarkupfalse%
   1.143 -\ {\isaliteral{7B2A}{\isacharverbatimopen}}{\isaliteral{2A7D}{\isacharverbatimclose}}%
   1.144 +{\isaliteral{2A7D}{\isacharverbatimclose}}%
   1.145  \endisatagML
   1.146  {\isafoldML}%
   1.147  %
   1.148 @@ -417,6 +459,16 @@
   1.149  %
   1.150  \endisadelimML
   1.151  %
   1.152 +\begin{isamarkuptext}%
   1.153 +tests of eval_get_denominator see test/Knowledge/rational.sml%
   1.154 +\end{isamarkuptext}%
   1.155 +\isamarkuptrue%
   1.156 +%
   1.157 +\begin{isamarkuptext}%
   1.158 +---------------------------end partial fractions snip--------------------------%
   1.159 +\end{isamarkuptext}%
   1.160 +\isamarkuptrue%
   1.161 +%
   1.162  \isamarkupsubsection{solve equation%
   1.163  }
   1.164  \isamarkuptrue%
   1.165 @@ -465,14 +517,14 @@
   1.166  \isanewline
   1.167  \isacommand{ML}\isamarkupfalse%
   1.168  \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
   1.169 -val\ denominator\ {\isaliteral{3D}{\isacharequal}}\ parseNEW\ ctxt\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{2D}{\isacharminus}}{\isadigit{1}}{\isaliteral{2F}{\isacharslash}}{\isadigit{8}}\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{1}}{\isaliteral{2F}{\isacharslash}}{\isadigit{4}}{\isaliteral{2A}{\isacharasterisk}}z\ {\isaliteral{2B}{\isacharplus}}\ z{\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}{\isadigit{2}}\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{0}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
   1.170 +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
   1.171  val\ fmz\ {\isaliteral{3D}{\isacharequal}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}specification{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
   1.172 -\ \ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}equality\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2D}{\isacharminus}}{\isadigit{1}}{\isaliteral{2F}{\isacharslash}}{\isadigit{8}}\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2D}{\isacharminus}}{\isadigit{1}}{\isaliteral{2F}{\isacharslash}}{\isadigit{4}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2A}{\isacharasterisk}}z\ {\isaliteral{2B}{\isacharplus}}\ 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
   1.173 +\ \ {\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
   1.174  \ \ \ {\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
   1.175  \ \ \ {\isaliteral{22}{\isachardoublequote}}solutions\ L{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3B}{\isacharsemicolon}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}identifier\ for\ solution{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
   1.176 -{\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}liste\ der\ theoreme\ die\ zum\ lösen\ benötigt\ werden{\isaliteral{2C}{\isacharcomma}}\ aus\ isac{\isaliteral{2C}{\isacharcomma}}\ keine\ spezielle\ methode\ {\isaliteral{28}{\isacharparenleft}}no\ met{\isaliteral{29}{\isacharparenright}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
   1.177 +\isanewline
   1.178  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
   1.179 -\ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}Isac{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}pqFormula{\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}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}no{\isaliteral{5F}{\isacharunderscore}}met{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
   1.180 +\ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}Isac{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\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}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}no{\isaliteral{5F}{\isacharunderscore}}met{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
   1.181  {\isaliteral{2A7D}{\isacharverbatimclose}}%
   1.182  \endisatagML
   1.183  {\isafoldML}%
   1.184 @@ -493,7 +545,7 @@
   1.185  \isatagML
   1.186  \isacommand{ML}\isamarkupfalse%
   1.187  \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
   1.188 -match{\isaliteral{5F}{\isacharunderscore}}pbl\ fmz\ {\isaliteral{28}{\isacharparenleft}}get{\isaliteral{5F}{\isacharunderscore}}pbt\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}pqFormula{\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
   1.189 +match{\isaliteral{5F}{\isacharunderscore}}pbl\ fmz\ {\isaliteral{28}{\isacharparenleft}}get{\isaliteral{5F}{\isacharunderscore}}pbt\ {\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
   1.190  {\isaliteral{2A7D}{\isacharverbatimclose}}%
   1.191  \endisatagML
   1.192  {\isafoldML}%
   1.193 @@ -514,6 +566,9 @@
   1.194  \isatagML
   1.195  \isacommand{ML}\isamarkupfalse%
   1.196  \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
   1.197 +{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline
   1.198 +\isacommand{ML}\isamarkupfalse%
   1.199 +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
   1.200  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
   1.201  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
   1.202  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
   1.203 @@ -529,7 +584,7 @@
   1.204  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}}\ {\isaliteral{28}{\isacharparenleft}}{\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}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
   1.205  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
   1.206  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
   1.207 -{\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{5B}{\isacharbrackleft}}z\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{1}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{8}}\ {\isaliteral{2B}{\isacharplus}}\ sqrt\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{9}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{1}}{\isadigit{6}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{2}}{\isaliteral{2C}{\isacharcomma}}\ z\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{1}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{8}}\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{1}}\ {\isaliteral{2A}{\isacharasterisk}}\ sqrt\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{9}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{1}}{\isadigit{6}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{2}}{\isaliteral{5D}{\isacharbrackright}}\ TODO\ sqrt{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
   1.208 +{\isaliteral{28}{\isacharparenleft}}{\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}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
   1.209  show{\isaliteral{5F}{\isacharunderscore}}pt\ pt{\isaliteral{3B}{\isacharsemicolon}}\ \isanewline
   1.210  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
   1.211  {\isaliteral{2A7D}{\isacharverbatimclose}}%
   1.212 @@ -644,7 +699,7 @@
   1.213  %
   1.214  \isatagML
   1.215  \isacommand{ML}\isamarkupfalse%
   1.216 -\ {\isaliteral{7B2A}{\isacharverbatimopen}}Context{\isaliteral{2E}{\isachardot}}theory{\isaliteral{5F}{\isacharunderscore}}name\ thy\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{22}{\isachardoublequote}}Isac{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2A7D}{\isacharverbatimclose}}%
   1.217 +\ {\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}}%
   1.218  \endisatagML
   1.219  {\isafoldML}%
   1.220  %
   1.221 @@ -1016,8 +1071,13 @@
   1.222  \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ X\ {\isaliteral{3D}{\isacharequal}}\ Rewrite\ ruleZY\ False\ X{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5E}{\isacharcircum}}\isanewline
   1.223  \ \ {\isaliteral{22}{\isachardoublequote}}\ \ in\ X{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}\isanewline
   1.224  \ {\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
   1.225 -\isanewline
   1.226 +{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline
   1.227 +\isacommand{ML}\isamarkupfalse%
   1.228 +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
   1.229  show{\isaliteral{5F}{\isacharunderscore}}mets{\isaliteral{28}{\isacharparenleft}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
   1.230 +{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline
   1.231 +\isacommand{ML}\isamarkupfalse%
   1.232 +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
   1.233  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
   1.234  {\isaliteral{2A7D}{\isacharverbatimclose}}%
   1.235  \endisatagML
   1.236 @@ -1085,11 +1145,11 @@
   1.237  {\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
   1.238  {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ X{\isaliteral{27}{\isacharprime}}\ {\isaliteral{3D}{\isacharequal}}\ Rewrite\ ruleZY\ False\ X{\isaliteral{3B}{\isacharsemicolon}}{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5E}{\isacharcircum}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}z\ {\isaliteral{2A}{\isacharasterisk}}\ denominator{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
   1.239  {\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}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}simplify{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
   1.240 -{\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ funterm\ {\isaliteral{3D}{\isacharequal}}\ Take\ {\isaliteral{28}{\isacharparenleft}}rhs\ X{\isaliteral{27}{\isacharprime}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5E}{\isacharcircum}}\ {\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
   1.241 -{\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ denom\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}Rewrite{\isaliteral{5F}{\isacharunderscore}}Set\ partial{\isaliteral{5F}{\isacharunderscore}}fraction\ False{\isaliteral{29}{\isacharparenright}}\ funterm{\isaliteral{3B}{\isacharsemicolon}}{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5E}{\isacharcircum}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}get{\isaliteral{5F}{\isacharunderscore}}denominator{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
   1.242 -{\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ equ\ {\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
   1.243 -{\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ fun{\isaliteral{5F}{\isacharunderscore}}arg\ {\isaliteral{3D}{\isacharequal}}\ Take\ {\isaliteral{28}{\isacharparenleft}}lhs\ X{\isaliteral{27}{\isacharprime}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5E}{\isacharcircum}}\isanewline
   1.244 -{\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ arg\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}Rewrite{\isaliteral{5F}{\isacharunderscore}}Set\ partial{\isaliteral{5F}{\isacharunderscore}}fraction\ False{\isaliteral{29}{\isacharparenright}}\ X{\isaliteral{27}{\isacharprime}}{\isaliteral{3B}{\isacharsemicolon}}{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5E}{\isacharcircum}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}get{\isaliteral{5F}{\isacharunderscore}}argument\ TODO{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
   1.245 +{\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
   1.246 +{\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
   1.247 +{\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}}\ {\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
   1.248 +{\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}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}get{\isaliteral{5F}{\isacharunderscore}}denominator{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
   1.249 +{\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
   1.250  {\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
   1.251  {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}SubProblem\ {\isaliteral{28}{\isacharparenleft}}Test{\isaliteral{27}{\isacharprime}}{\isaliteral{2C}{\isacharcomma}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5E}{\isacharcircum}}\isanewline
   1.252  {\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
   1.253 @@ -1102,7 +1162,25 @@
   1.254  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
   1.255  atomty\ sc{\isaliteral{3B}{\isacharsemicolon}}\isanewline
   1.256  \isanewline
   1.257 -{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline
   1.258 +{\isaliteral{2A7D}{\isacharverbatimclose}}%
   1.259 +\endisatagML
   1.260 +{\isafoldML}%
   1.261 +%
   1.262 +\isadelimML
   1.263 +%
   1.264 +\endisadelimML
   1.265 +%
   1.266 +\begin{isamarkuptext}%
   1.267 +This ruleset contains all functions that are in the script; 
   1.268 +The evaluation of the functions is done by rewriting using this ruleset.%
   1.269 +\end{isamarkuptext}%
   1.270 +\isamarkuptrue%
   1.271 +%
   1.272 +\isadelimML
   1.273 +%
   1.274 +\endisadelimML
   1.275 +%
   1.276 +\isatagML
   1.277  \isacommand{ML}\isamarkupfalse%
   1.278  \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
   1.279  val\ srls\ {\isaliteral{3D}{\isacharequal}}\ Rls\ {\isaliteral{7B}{\isacharbraceleft}}id{\isaliteral{3D}{\isacharequal}}{\isaliteral{22}{\isachardoublequote}}srls{\isaliteral{5F}{\isacharunderscore}}InverseZTransform{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ \isanewline
   1.280 @@ -1126,7 +1204,9 @@
   1.281  {\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\isanewline
   1.282  			\ \ \ \ \ 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}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{3C}{\isacharless}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}\ ONLY\ USED{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
   1.283  			\ \ \ \ \ 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}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{3C}{\isacharless}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}\ ONLY\ USED{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
   1.284 -			\ \ \ \ \ Calc{\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}Atools{\isaliteral{2E}{\isachardot}}argument{\isaliteral{27}{\isacharprime}}{\isaliteral{5F}{\isacharunderscore}}in{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ eval{\isaliteral{5F}{\isacharunderscore}}argument{\isaliteral{5F}{\isacharunderscore}}in\ {\isaliteral{22}{\isachardoublequote}}Atools{\isaliteral{2E}{\isachardot}}argument{\isaliteral{27}{\isacharprime}}{\isaliteral{5F}{\isacharunderscore}}in{\isaliteral{22}{\isachardoublequote}}{\isaliteral{29}{\isacharparenright}}\isanewline
   1.285 +			\ \ \ \ \ Calc{\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}Atools{\isaliteral{2E}{\isachardot}}argument{\isaliteral{27}{\isacharprime}}{\isaliteral{5F}{\isacharunderscore}}in{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ eval{\isaliteral{5F}{\isacharunderscore}}argument{\isaliteral{5F}{\isacharunderscore}}in\ {\isaliteral{22}{\isachardoublequote}}Atools{\isaliteral{2E}{\isachardot}}argument{\isaliteral{27}{\isacharprime}}{\isaliteral{5F}{\isacharunderscore}}in{\isaliteral{22}{\isachardoublequote}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\isanewline
   1.286 +\ \ \ \ \ Calc{\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}Rational{\isaliteral{2E}{\isachardot}}get{\isaliteral{5F}{\isacharunderscore}}denominator{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\isanewline
   1.287 +\ \ \ \ \ \ \ eval{\isaliteral{5F}{\isacharunderscore}}get{\isaliteral{5F}{\isacharunderscore}}denominator\ {\isaliteral{22}{\isachardoublequote}}Rational{\isaliteral{2E}{\isachardot}}get{\isaliteral{5F}{\isacharunderscore}}denominator{\isaliteral{22}{\isachardoublequote}}{\isaliteral{29}{\isacharparenright}}\isanewline
   1.288  			\ \ \ \ {\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\isanewline
   1.289  		\ \ scr\ {\isaliteral{3D}{\isacharequal}}\ EmptyScr{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
   1.290  {\isaliteral{2A7D}{\isacharverbatimclose}}%
   1.291 @@ -1161,28 +1241,17 @@
   1.292  {\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
   1.293  {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ X{\isaliteral{27}{\isacharprime}}\ {\isaliteral{3D}{\isacharequal}}\ Rewrite\ ruleZY\ False\ X{\isaliteral{3B}{\isacharsemicolon}}{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5E}{\isacharcircum}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}z\ {\isaliteral{2A}{\isacharasterisk}}\ denominator{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
   1.294  {\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}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}simplify{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
   1.295 -{\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ funterm\ {\isaliteral{3D}{\isacharequal}}\ Take\ {\isaliteral{28}{\isacharparenleft}}rhs\ X{\isaliteral{27}{\isacharprime}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5E}{\isacharcircum}}\ {\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
   1.296 -{\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ denom\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}Rewrite{\isaliteral{5F}{\isacharunderscore}}Set\ partial{\isaliteral{5F}{\isacharunderscore}}fraction\ False{\isaliteral{29}{\isacharparenright}}\ funterm{\isaliteral{3B}{\isacharsemicolon}}{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5E}{\isacharcircum}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}get{\isaliteral{5F}{\isacharunderscore}}denominator{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
   1.297 -{\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ equ\ {\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
   1.298 -{\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ fun{\isaliteral{5F}{\isacharunderscore}}arg\ {\isaliteral{3D}{\isacharequal}}\ Take\ {\isaliteral{28}{\isacharparenleft}}lhs\ X{\isaliteral{27}{\isacharprime}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5E}{\isacharcircum}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{3D}{\isacharequal}}\ get{\isaliteral{5F}{\isacharunderscore}}argument\ {\isaliteral{28}{\isacharparenleft}}lhs\ X{\isaliteral{27}{\isacharprime}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
   1.299 -{\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ arg\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}Rewrite{\isaliteral{5F}{\isacharunderscore}}Set\ partial{\isaliteral{5F}{\isacharunderscore}}fraction\ False{\isaliteral{29}{\isacharparenright}}\ X{\isaliteral{27}{\isacharprime}}{\isaliteral{3B}{\isacharsemicolon}}{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5E}{\isacharcircum}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}get{\isaliteral{5F}{\isacharunderscore}}argument\ TODO{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
   1.300 -{\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
   1.301 -{\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}SubProblem\ {\isaliteral{28}{\isacharparenleft}}Test{\isaliteral{27}{\isacharprime}}{\isaliteral{2C}{\isacharcomma}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5E}{\isacharcircum}}\isanewline
   1.302 -{\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
   1.303 -{\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
   1.304 -{\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
   1.305 +{\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}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
   1.306 +{\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}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
   1.307 +{\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}}\ {\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
   1.308 +{\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}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}get{\isaliteral{5F}{\isacharunderscore}}denominator{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
   1.309 +{\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
   1.310 +\isanewline
   1.311 +{\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
   1.312 +{\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}}no{\isaliteral{5F}{\isacharunderscore}}meth{\isaliteral{29}{\isacharparenright}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5E}{\isacharcircum}}\isanewline
   1.313 +{\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ \ \ {\isaliteral{5B}{\isacharbrackleft}}BOOL\ equ{\isaliteral{2C}{\isacharcomma}}\ REAL\ zzz{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5E}{\isacharcircum}}\isanewline
   1.314  {\isaliteral{22}{\isachardoublequote}}\ \ in\ X{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}\isanewline
   1.315  \ {\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
   1.316 -{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline
   1.317 -\isacommand{ML}\isamarkupfalse%
   1.318 -\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
   1.319 -{\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}GOON\ tip\ for\ eval{\isaliteral{5F}{\isacharunderscore}}get{\isaliteral{5F}{\isacharunderscore}}argument{\isaliteral{3A}{\isacharcolon}}\ compare\ eval{\isaliteral{5F}{\isacharunderscore}}get{\isaliteral{5F}{\isacharunderscore}}denominator{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
   1.320 -val\ funId\ {\isaliteral{24}{\isachardollar}}\ arg\ {\isaliteral{3D}{\isacharequal}}\ %
   1.321 -\isaantiq
   1.322 -term\ {\isaliteral{22}{\isachardoublequote}}X\ {\isaliteral{28}{\isacharparenleft}}z{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}real{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}{}%
   1.323 -\endisaantiq
   1.324 -{\isaliteral{3B}{\isacharsemicolon}}\isanewline
   1.325 -\isanewline
   1.326  {\isaliteral{2A7D}{\isacharverbatimclose}}%
   1.327  \endisatagML
   1.328  {\isafoldML}%
   1.329 @@ -1240,22 +1309,137 @@
   1.330  \isatagML
   1.331  \isacommand{ML}\isamarkupfalse%
   1.332  \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
   1.333 -trace{\isaliteral{5F}{\isacharunderscore}}script\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ false{\isaliteral{3B}{\isacharsemicolon}}\ print{\isaliteral{5F}{\isacharunderscore}}depth\ {\isadigit{9}}{\isadigit{9}}{\isadigit{9}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
   1.334 +trace{\isaliteral{5F}{\isacharunderscore}}rewrite\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ false{\isaliteral{3B}{\isacharsemicolon}}\isanewline
   1.335 +trace{\isaliteral{5F}{\isacharunderscore}}script\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ true{\isaliteral{3B}{\isacharsemicolon}}\ print{\isaliteral{5F}{\isacharunderscore}}depth\ {\isadigit{9}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
   1.336  val\ fmz\ {\isaliteral{3D}{\isacharequal}}\ {\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
   1.337  \ \ {\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
   1.338  val\ {\isaliteral{28}{\isacharparenleft}}dI{\isaliteral{2C}{\isacharcomma}}pI{\isaliteral{2C}{\isacharcomma}}mI{\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}}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
   1.339  \ \ {\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
   1.340  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
   1.341 +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}}\ {\isaliteral{22}{\isachardoublequote}}Add{\isaliteral{5F}{\isacharunderscore}}Given{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
   1.342 +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}}\ {\isaliteral{22}{\isachardoublequote}}Add{\isaliteral{5F}{\isacharunderscore}}Find{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
   1.343 +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}}\ {\isaliteral{22}{\isachardoublequote}}Specify{\isaliteral{5F}{\isacharunderscore}}Theory{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
   1.344 +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}}\ {\isaliteral{22}{\isachardoublequote}}Specify{\isaliteral{5F}{\isacharunderscore}}Problem{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
   1.345 +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}}\ {\isaliteral{22}{\isachardoublequote}}Specify{\isaliteral{5F}{\isacharunderscore}}Method{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
   1.346 +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}}\ {\isaliteral{22}{\isachardoublequote}}nxt\ {\isaliteral{3D}{\isacharequal}}\ Apply{\isaliteral{5F}{\isacharunderscore}}Method{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
   1.347 +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}}\ {\isaliteral{22}{\isachardoublequote}}nxt\ {\isaliteral{3D}{\isacharequal}}\ 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{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}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}TODO\ naming{\isaliteral{21}{\isacharbang}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
   1.348 +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}}\ {\isaliteral{22}{\isachardoublequote}}nxt\ {\isaliteral{3D}{\isacharequal}}\ Rewrite{\isaliteral{5F}{\isacharunderscore}}Set\ norm{\isaliteral{5F}{\isacharunderscore}}Rational\ {\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
   1.349 +{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline
   1.350 +\isacommand{ML}\isamarkupfalse%
   1.351 +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
   1.352 +{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline
   1.353 +\isacommand{ML}\isamarkupfalse%
   1.354 +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
   1.355 +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}}\ {\isaliteral{22}{\isachardoublequote}}Empty{\isaliteral{5F}{\isacharunderscore}}Tac\ instead\ SubProblem{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
   1.356 +{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline
   1.357 +\isacommand{ML}\isamarkupfalse%
   1.358 +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
   1.359 +show{\isaliteral{5F}{\isacharunderscore}}pt\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
   1.360 +{\isaliteral{2A7D}{\isacharverbatimclose}}%
   1.361 +\endisatagML
   1.362 +{\isafoldML}%
   1.363 +%
   1.364 +\isadelimML
   1.365 +%
   1.366 +\endisadelimML
   1.367 +%
   1.368 +\begin{isamarkuptext}%
   1.369 +Instead of nxt = Subproblem above we had Empty_Tac; search for errors:
   1.370 +  # what shows show_pt pt; ...
   1.371 +    (([2], Res), ?X' z = 24 / (-1 + -2 * z + 8 * z ^^^ 2))] ..calculation ok,
   1.372 +    but no "next" step found: should be "nxt = Subproblem" ?!?
   1.373 +  # what shows trace_script := true; we read bottom up ...
   1.374 +    @@@ next   leaf 'SubProbfrom
   1.375 +     (PolyEq', [abcFormula, degree_2, polynomial, univariate, equation],
   1.376 +      no_meth)
   1.377 +     [BOOL equ, REAL z]' ---> STac 'SubProblem
   1.378 +     (PolyEq', [abcFormula, degree_2, polynomial, univariate, equation],
   1.379 +      no_meth)
   1.380 +     [BOOL (-1 + -2 * z + 8 * z ^^^ 2 = 0), REAL z]'
   1.381 +    ... and see the SubProblem with correct arguments 
   1.382 +    (program text ---> STac (script tactic) with arguments evaluated.)
   1.383 +  # do we have the right Script ...
   1.384 +    val Script s = (#scr o get_met) ["SignalProcessing","Z_Transform","inverse"];
   1.385 +    writeln (term2str s);
   1.386 +    ... shows the right script.
   1.387 +  #%
   1.388 +\end{isamarkuptext}%
   1.389 +\isamarkuptrue%
   1.390 +%
   1.391 +\isadelimML
   1.392 +%
   1.393 +\endisadelimML
   1.394 +%
   1.395 +\isatagML
   1.396 +\isacommand{ML}\isamarkupfalse%
   1.397 +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
   1.398 +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}}\ {\isaliteral{22}{\isachardoublequote}}nxt\ {\isaliteral{3D}{\isacharequal}}\ Model{\isaliteral{5F}{\isacharunderscore}}Problem{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
   1.399 +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}}\ {\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}}\ {\isadigit{0}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
   1.400 +{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline
   1.401 +\isacommand{ML}\isamarkupfalse%
   1.402 +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
   1.403 +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}}\ {\isaliteral{22}{\isachardoublequote}}solveFor\ z{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
   1.404 +{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline
   1.405 +\isacommand{ML}\isamarkupfalse%
   1.406 +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
   1.407 +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}}\ {\isaliteral{22}{\isachardoublequote}}nxt\ {\isaliteral{3D}{\isacharequal}}\ Add{\isaliteral{5F}{\isacharunderscore}}Find{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
   1.408 +{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline
   1.409 +\isacommand{ML}\isamarkupfalse%
   1.410 +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
   1.411 +show{\isaliteral{5F}{\isacharunderscore}}pt\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
   1.412 +{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline
   1.413 +\isacommand{ML}\isamarkupfalse%
   1.414 +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
   1.415 +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}}\ {\isaliteral{22}{\isachardoublequote}}nxt\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}Empty{\isaliteral{5F}{\isacharunderscore}}Tac{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
   1.416 +{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline
   1.417 +\isacommand{ML}\isamarkupfalse%
   1.418 +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
   1.419 +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}}\ {\isaliteral{22}{\isachardoublequote}}nxt\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}Empty{\isaliteral{5F}{\isacharunderscore}}Tac\ instead\ Specify{\isaliteral{5F}{\isacharunderscore}}Theory{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
   1.420 +{\isaliteral{2A7D}{\isacharverbatimclose}}%
   1.421 +\endisatagML
   1.422 +{\isafoldML}%
   1.423 +%
   1.424 +\isadelimML
   1.425 +%
   1.426 +\endisadelimML
   1.427 +%
   1.428 +\begin{isamarkuptext}%
   1.429 +We had "nxt = (Empty_Tac"; the search for the reason considered the following points:
   1.430 +  # was there an error message ? NO --ok
   1.431 +  # has "nxt = Add_Find" been inserted in pt: get_obj g_pbl pt (fst p); YES --ok
   1.432 +  # what is the returned "formula": print_depth 999; f; print_depth 999; --
   1.433 +    {Find = [Correct "solutions z_i"], With = [], 
   1.434 +     Given = [Correct "equality (-1 + -2 * z + 8 * z ^^^ 2 = 0)", Correct "solveFor z"],
   1.435 +     Where = [False "matches (z = 0) (-1 + -2 * z + 8 * z ^^^ 2 = 0) |\n
   1.436 +                     matches (?b * z = 0) (-1 + -2 * z + 8 * z ^^^ 2 = 0) |\n
   1.437 +                     matches (?a + z = 0) (-1 + -2 * z + 8 * z ^^^ 2 = 0) |\n
   1.438 +                     matches (?a + ?b * z = 0) (-1 + -2 * z + 8 * z ^^^ 2 = 0)"],
   1.439 +     Relate = []}
   1.440 +     -- the only False is the reason: the Where (the precondition) is False for good reasons:
   1.441 +     the precondition seems to check for linear equations, not for the one we want to solve!
   1.442 +  Removed this error by correcting the Script
   1.443 +  from SubProblem (PolyEq', [linear,univariate,equation,test], [Test,solve_linear]
   1.444 +  to   SubProblem (PolyEq', [abcFormula,degree_2,polynomial,univariate,equation],
   1.445 +                   [PolyEq,solve_d2_polyeq_abc_equation]
   1.446 +  You find the appropriate type of equation at
   1.447 +    http://www.ist.tugraz.at/projects/isac/www/kbase/pbl/index_pbl.html
   1.448 +  and the respective method in Knowledge/PolyEq.thy at the respective store_pbt.
   1.449 +  Or you leave the selection of the appropriate type to isac as done in the final Script ;-))%
   1.450 +\end{isamarkuptext}%
   1.451 +\isamarkuptrue%
   1.452 +%
   1.453 +\isadelimML
   1.454 +%
   1.455 +\endisadelimML
   1.456 +%
   1.457 +\isatagML
   1.458 +\isacommand{ML}\isamarkupfalse%
   1.459 +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
   1.460  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
   1.461 -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
   1.462 -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
   1.463 -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
   1.464 -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
   1.465 -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}}\ {\isaliteral{22}{\isachardoublequote}}nxt\ {\isaliteral{3D}{\isacharequal}}\ Apply{\isaliteral{5F}{\isacharunderscore}}Method{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
   1.466 -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}}\ {\isaliteral{22}{\isachardoublequote}}nxt\ {\isaliteral{3D}{\isacharequal}}\ 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{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
   1.467 -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}}\ {\isaliteral{22}{\isachardoublequote}}nxt\ {\isaliteral{3D}{\isacharequal}}\ Rewrite{\isaliteral{5F}{\isacharunderscore}}Set\ norm{\isaliteral{5F}{\isacharunderscore}}Rational\ {\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
   1.468 -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}}\ {\isaliteral{22}{\isachardoublequote}}nxt\ {\isaliteral{3D}{\isacharequal}}\ Take\ {\isadigit{2}}{\isadigit{4}}\ {\isaliteral{2F}{\isacharslash}}\ {\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{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
   1.469 -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}}\ {\isaliteral{22}{\isachardoublequote}}\ \ \ Empty{\isaliteral{5F}{\isacharunderscore}}Tac{\isaliteral{21}{\isacharbang}}\ \ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
   1.470 +{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline
   1.471 +\isacommand{ML}\isamarkupfalse%
   1.472 +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
   1.473 +\isanewline
   1.474  {\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline
   1.475  \isacommand{ML}\isamarkupfalse%
   1.476  \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline