wneuper/isa: test/Tools/isac/ADDTESTS/course/SignalProcess/document/Build_Inverse_Z

1 %

     2 \begin{isabellebody}%

     3 \def\isabellecontext{Build{\isaliteral{5F}{\isacharunderscore}}Inverse{\isaliteral{5F}{\isacharunderscore}}Z{\isaliteral{5F}{\isacharunderscore}}Transform}%

4 %

     5 \isadelimtheory

     6 \isanewline

     7 \isanewline

8 %

     9 \endisadelimtheory

    10 %

    11 \isatagtheory

    12 \isacommand{theory}\isamarkupfalse%

    13 \ Build{\isaliteral{5F}{\isacharunderscore}}Inverse{\isaliteral{5F}{\isacharunderscore}}Z{\isaliteral{5F}{\isacharunderscore}}Transform\ \isakeyword{imports}\ Isac\isanewline

    14 \ \ \isanewline

    15 \isakeyword{begin}%

    16 \endisatagtheory

    17 {\isafoldtheory}%

    18 %

    19 \isadelimtheory

    20 %

    21 \endisadelimtheory

    22 %

    23 \begin{isamarkuptext}%

    24 We stepwise build \texttt{Inverse\_Z\_Transform.thy} as an exercise.

    25   Because subsection "Stepwise Check the Program" requires

    26   \texttt{Inverse\_Z\_Transform.thy} as a subtheory of Isac.thy, the setup has been changed

    27   from "theory Inverse_Z_Transform imports Isac begin.." to the above.

    29   ATTENTION WITH NAMES OF IDENTIFIERS WHEN GOING INTO INTERNALS:

    30   Here in this theory there are the internal names twice, for instance we have

    31   (Thm.derivation_name \isa{rule{\isadigit{1}}} = "Build_Inverse_Z_Transform.rule1") = true;

    32   but actually in us will be "Inverse_Z_Transform.rule1"%

    33 \end{isamarkuptext}%

    34 \isamarkuptrue%

    35 %

    36 \isadelimML

    37 %

    38 \endisadelimML

    39 %

    40 \isatagML

    41 \isacommand{ML}\isamarkupfalse%

    42 \ {\isaliteral{7B2A}{\isacharverbatimopen}}val\ thy\ {\isaliteral{3D}{\isacharequal}}\ %

    43 \isaantiq

    44 theory\ Isac{}%

    45 \endisaantiq

    46 {\isaliteral{3B}{\isacharsemicolon}}{\isaliteral{2A7D}{\isacharverbatimclose}}%

    47 \endisatagML

    48 {\isafoldML}%

    49 %

    50 \isadelimML

    51 %

    52 \endisadelimML

    53 %

    54 \isamarkupsection{trials towards Z transform%

    55 }

    56 \isamarkuptrue%

    57 %

    58 \begin{isamarkuptext}%

    59 ===============================%

    60 \end{isamarkuptext}%

    61 \isamarkuptrue%

    62 %

    63 \isamarkupsubsection{terms%

    64 }

    65 \isamarkuptrue%

    66 %

    67 \isadelimML

    68 %

    69 \endisadelimML

    70 %

    71 \isatagML

    72 \isacommand{ML}\isamarkupfalse%

    73 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

    74 %

    75 \isaantiq

    76 term\ {\isaliteral{22}{\isachardoublequote}}{\isadigit{1}}\ {\isaliteral{3C}{\isacharless}}\ {\isaliteral{7C}{\isacharbar}}{\isaliteral{7C}{\isacharbar}}\ z\ {\isaliteral{7C}{\isacharbar}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{22}{\isachardoublequote}}{}%

    77 \endisaantiq

    78 {\isaliteral{3B}{\isacharsemicolon}}\isanewline

    79 %

    80 \isaantiq

    81 term\ {\isaliteral{22}{\isachardoublequote}}z\ {\isaliteral{2F}{\isacharslash}}\ {\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{1}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}{}%

    82 \endisaantiq

    83 {\isaliteral{3B}{\isacharsemicolon}}\isanewline

    84 %

    85 \isaantiq

    86 term\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{2D}{\isacharminus}}u\ {\isaliteral{2D}{\isacharminus}}n\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}{}%

    87 \endisaantiq

    88 {\isaliteral{3B}{\isacharsemicolon}}\isanewline

    89 %

    90 \isaantiq

    91 term\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{2D}{\isacharminus}}u\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{2D}{\isacharminus}}n\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{1}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}{}%

    92 \endisaantiq

    93 {\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{5B}{\isacharbrackleft}}\ {\isaliteral{5D}{\isacharbrackright}}\ denotes\ lists\ {\isaliteral{21}{\isacharbang}}{\isaliteral{21}{\isacharbang}}{\isaliteral{21}{\isacharbang}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

    94 %

    95 \isaantiq

    96 term\ {\isaliteral{22}{\isachardoublequote}}z\ {\isaliteral{2F}{\isacharslash}}{\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{1}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{2D}{\isacharminus}}u\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{2D}{\isacharminus}}n\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{1}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}{}%

    97 \endisaantiq

    98 {\isaliteral{3B}{\isacharsemicolon}}Isac\isanewline

    99 %

   100 \isaantiq

   101 term\ {\isaliteral{22}{\isachardoublequote}}{\isadigit{1}}\ {\isaliteral{3C}{\isacharless}}\ {\isaliteral{7C}{\isacharbar}}{\isaliteral{7C}{\isacharbar}}\ z\ {\isaliteral{7C}{\isacharbar}}{\isaliteral{7C}{\isacharbar}}\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\ z\ {\isaliteral{2F}{\isacharslash}}\ {\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{1}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{2D}{\isacharminus}}u\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{2D}{\isacharminus}}n\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{1}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}{}%

   102 \endisaantiq

   103 {\isaliteral{3B}{\isacharsemicolon}}\isanewline

   104 term{\isadigit{2}}str\ %

   105 \isaantiq

   106 term\ {\isaliteral{22}{\isachardoublequote}}{\isadigit{1}}\ {\isaliteral{3C}{\isacharless}}\ {\isaliteral{7C}{\isacharbar}}{\isaliteral{7C}{\isacharbar}}\ z\ {\isaliteral{7C}{\isacharbar}}{\isaliteral{7C}{\isacharbar}}\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\ z\ {\isaliteral{2F}{\isacharslash}}\ {\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{1}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{2D}{\isacharminus}}u\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{2D}{\isacharminus}}n\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{1}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}{}%

   107 \endisaantiq

   108 {\isaliteral{3B}{\isacharsemicolon}}\isanewline

   109 {\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline

   110 \isacommand{ML}\isamarkupfalse%

   111 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

   112 {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}alpha\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ \ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{3C}{\isacharless}}{\isaliteral{2F}{\isacharslash}}alpha{\isaliteral{3E}{\isachargreater}}{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

   113 %

   114 \isaantiq

   115 term\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ {\isaliteral{22}{\isachardoublequote}}{}%

   116 \endisaantiq

   117 {\isaliteral{3B}{\isacharsemicolon}}\isanewline

   118 %

   119 \isaantiq

   120 term\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C64656C74613E}{\isasymdelta}}\ {\isaliteral{22}{\isachardoublequote}}{}%

   121 \endisaantiq

   122 {\isaliteral{3B}{\isacharsemicolon}}\isanewline

   123 %

   124 \isaantiq

   125 term\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C7068693E}{\isasymphi}}\ {\isaliteral{22}{\isachardoublequote}}{}%

   126 \endisaantiq

   127 {\isaliteral{3B}{\isacharsemicolon}}\isanewline

   128 %

   129 \isaantiq

   130 term\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C72686F3E}{\isasymrho}}\ {\isaliteral{22}{\isachardoublequote}}{}%

   131 \endisaantiq

   132 {\isaliteral{3B}{\isacharsemicolon}}\isanewline

   133 term{\isadigit{2}}str\ %

   134 \isaantiq

   135 term\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C72686F3E}{\isasymrho}}\ {\isaliteral{22}{\isachardoublequote}}{}%

   136 \endisaantiq

   137 {\isaliteral{3B}{\isacharsemicolon}}\isanewline

   138 {\isaliteral{2A7D}{\isacharverbatimclose}}%

   139 \endisatagML

   140 {\isafoldML}%

   141 %

   142 \isadelimML

   143 %

   144 \endisadelimML

   145 %

   146 \isamarkupsubsection{rules%

   147 }

   148 \isamarkuptrue%

   149 \isacommand{axiomatization}\isamarkupfalse%

   150 \ \isakeyword{where}\ \isanewline

   151 \ \ rule{\isadigit{1}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isadigit{1}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5C3C64656C74613E}{\isasymdelta}}{\isaliteral{5B}{\isacharbrackleft}}n{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{and}\isanewline

   152 \ \ rule{\isadigit{2}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{7C}{\isacharbar}}\ z\ {\isaliteral{7C}{\isacharbar}}{\isaliteral{7C}{\isacharbar}}\ {\isaliteral{3E}{\isachargreater}}\ {\isadigit{1}}\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\ z\ {\isaliteral{2F}{\isacharslash}}\ {\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{1}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ u\ {\isaliteral{5B}{\isacharbrackleft}}n{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{and}\isanewline

   153 \ \ rule{\isadigit{3}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{7C}{\isacharbar}}\ z\ {\isaliteral{7C}{\isacharbar}}{\isaliteral{7C}{\isacharbar}}\ {\isaliteral{3C}{\isacharless}}\ {\isadigit{1}}\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\ z\ {\isaliteral{2F}{\isacharslash}}\ {\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{1}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{2D}{\isacharminus}}u\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{2D}{\isacharminus}}n\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{1}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{and}\ \isanewline

   154 \ \ rule{\isadigit{4}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{7C}{\isacharbar}}\ z\ {\isaliteral{7C}{\isacharbar}}{\isaliteral{7C}{\isacharbar}}\ {\isaliteral{3E}{\isachargreater}}\ {\isaliteral{7C}{\isacharbar}}{\isaliteral{7C}{\isacharbar}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ {\isaliteral{7C}{\isacharbar}}{\isaliteral{7C}{\isacharbar}}\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\ z\ {\isaliteral{2F}{\isacharslash}}\ {\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{2D}{\isacharminus}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}n\ {\isaliteral{2A}{\isacharasterisk}}\ u\ {\isaliteral{5B}{\isacharbrackleft}}n{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{and}\isanewline

   155 \ \ rule{\isadigit{5}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{7C}{\isacharbar}}\ z\ {\isaliteral{7C}{\isacharbar}}{\isaliteral{7C}{\isacharbar}}\ {\isaliteral{3C}{\isacharless}}\ {\isaliteral{7C}{\isacharbar}}{\isaliteral{7C}{\isacharbar}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ {\isaliteral{7C}{\isacharbar}}{\isaliteral{7C}{\isacharbar}}\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\ z\ {\isaliteral{2F}{\isacharslash}}\ {\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{2D}{\isacharminus}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}n{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2A}{\isacharasterisk}}\ u\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{2D}{\isacharminus}}n\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{1}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{and}\isanewline

   156 \ \ rule{\isadigit{6}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{7C}{\isacharbar}}{\isaliteral{7C}{\isacharbar}}\ z\ {\isaliteral{7C}{\isacharbar}}{\isaliteral{7C}{\isacharbar}}\ {\isaliteral{3E}{\isachargreater}}\ {\isadigit{1}}\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\ z{\isaliteral{2F}{\isacharslash}}{\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{1}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}{\isadigit{2}}\ {\isaliteral{3D}{\isacharequal}}\ n\ {\isaliteral{2A}{\isacharasterisk}}\ u\ {\isaliteral{5B}{\isacharbrackleft}}n{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline

   157 %

   158 \isadelimML

   159 %

   160 \endisadelimML

   161 %

   162 \isatagML

   163 \isacommand{ML}\isamarkupfalse%

   164 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

   165 %

   166 \isaantiq

   167 thm\ rule{\isadigit{1}}{}%

   168 \endisaantiq

   169 {\isaliteral{3B}{\isacharsemicolon}}\isanewline

   170 %

   171 \isaantiq

   172 thm\ rule{\isadigit{2}}{}%

   173 \endisaantiq

   174 {\isaliteral{3B}{\isacharsemicolon}}\isanewline

   175 %

   176 \isaantiq

   177 thm\ rule{\isadigit{3}}{}%

   178 \endisaantiq

   179 {\isaliteral{3B}{\isacharsemicolon}}\isanewline

   180 %

   181 \isaantiq

   182 thm\ rule{\isadigit{4}}{}%

   183 \endisaantiq

   184 {\isaliteral{3B}{\isacharsemicolon}}\isanewline

   185 {\isaliteral{2A7D}{\isacharverbatimclose}}%

   186 \endisatagML

   187 {\isafoldML}%

   188 %

   189 \isadelimML

   190 %

   191 \endisadelimML

   192 %

   193 \isamarkupsubsection{apply rules%

   194 }

   195 \isamarkuptrue%

   196 %

   197 \isadelimML

   198 %

   199 \endisadelimML

   200 %

   201 \isatagML

   202 \isacommand{ML}\isamarkupfalse%

   203 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

   204 val\ inverse{\isaliteral{5F}{\isacharunderscore}}Z\ {\isaliteral{3D}{\isacharequal}}\ append{\isaliteral{5F}{\isacharunderscore}}rls\ {\isaliteral{22}{\isachardoublequote}}inverse{\isaliteral{5F}{\isacharunderscore}}Z{\isaliteral{22}{\isachardoublequote}}\ e{\isaliteral{5F}{\isacharunderscore}}rls\isanewline

   205 \ \ {\isaliteral{5B}{\isacharbrackleft}}\ Thm\ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}rule{\isadigit{3}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}num{\isaliteral{5F}{\isacharunderscore}}str\ %

   206 \isaantiq

   207 thm\ rule{\isadigit{3}}{}%

   208 \endisaantiq

   209 {\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\isanewline

   210 \ \ \ \ Thm\ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}rule{\isadigit{4}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}num{\isaliteral{5F}{\isacharunderscore}}str\ %

   211 \isaantiq

   212 thm\ rule{\isadigit{4}}{}%

   213 \endisaantiq

   214 {\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\isanewline

   215 \ \ \ \ Thm\ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}rule{\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}num{\isaliteral{5F}{\isacharunderscore}}str\ %

   216 \isaantiq

   217 thm\ rule{\isadigit{1}}{}%

   218 \endisaantiq

   219 {\isaliteral{29}{\isacharparenright}}\ \ \ \isanewline

   220 \ \ {\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

   221 \isanewline

   222 val\ t\ {\isaliteral{3D}{\isacharequal}}\ str{\isadigit{2}}term\ {\isaliteral{22}{\isachardoublequote}}z\ {\isaliteral{2F}{\isacharslash}}\ {\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{1}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2B}{\isacharplus}}\ z\ {\isaliteral{2F}{\isacharslash}}\ {\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{2D}{\isacharminus}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2B}{\isacharplus}}\ {\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

   223 val\ SOME\ {\isaliteral{28}{\isacharparenleft}}t{\isaliteral{27}{\isacharprime}}{\isaliteral{2C}{\isacharcomma}}\ asm{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ rewrite{\isaliteral{5F}{\isacharunderscore}}set{\isaliteral{5F}{\isacharunderscore}}\ thy\ true\ inverse{\isaliteral{5F}{\isacharunderscore}}Z\ t{\isaliteral{3B}{\isacharsemicolon}}\isanewline

   224 term{\isadigit{2}}str\ t{\isaliteral{27}{\isacharprime}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{22}{\isachardoublequote}}z\ {\isaliteral{2F}{\isacharslash}}\ {\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{2D}{\isacharminus}}\ {\isaliteral{3F}{\isacharquery}}{\isaliteral{5C3C64656C74613E}{\isasymdelta}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{3F}{\isacharquery}}n{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2B}{\isacharplus}}\ z\ {\isaliteral{2F}{\isacharslash}}\ {\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{2D}{\isacharminus}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{3F}{\isacharquery}}{\isaliteral{5C3C64656C74613E}{\isasymdelta}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{3F}{\isacharquery}}n{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}attention\ rule{\isadigit{1}}\ {\isaliteral{21}{\isacharbang}}{\isaliteral{21}{\isacharbang}}{\isaliteral{21}{\isacharbang}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

   225 {\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline

   226 \isacommand{ML}\isamarkupfalse%

   227 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

   228 val\ {\isaliteral{28}{\isacharparenleft}}thy{\isaliteral{2C}{\isacharcomma}}\ ro{\isaliteral{2C}{\isacharcomma}}\ er{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}%

   229 \isaantiq

   230 theory\ Isac{}%

   231 \endisaantiq

   232 {\isaliteral{2C}{\isacharcomma}}\ tless{\isaliteral{5F}{\isacharunderscore}}true{\isaliteral{2C}{\isacharcomma}}\ eval{\isaliteral{5F}{\isacharunderscore}}rls{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

   233 {\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline

   234 \isacommand{ML}\isamarkupfalse%

   235 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

   236 val\ SOME\ {\isaliteral{28}{\isacharparenleft}}t{\isaliteral{2C}{\isacharcomma}}\ asm{\isadigit{1}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ rewrite{\isaliteral{5F}{\isacharunderscore}}\ thy\ ro\ er\ true\ {\isaliteral{28}{\isacharparenleft}}num{\isaliteral{5F}{\isacharunderscore}}str\ %

   237 \isaantiq

   238 thm\ rule{\isadigit{3}}{}%

   239 \endisaantiq

   240 {\isaliteral{29}{\isacharparenright}}\ t{\isaliteral{3B}{\isacharsemicolon}}\isanewline

   241 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

   242 term{\isadigit{2}}str\ t{\isaliteral{3B}{\isacharsemicolon}}{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline

   243 \isacommand{ML}\isamarkupfalse%

   244 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

   245 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\ %

   246 \isaantiq

   247 thm\ rule{\isadigit{4}}{}%

   248 \endisaantiq

   249 {\isaliteral{29}{\isacharparenright}}\ t{\isaliteral{3B}{\isacharsemicolon}}\isanewline

   250 term{\isadigit{2}}str\ t\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{2D}{\isacharminus}}\ {\isaliteral{3F}{\isacharquery}}u\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{2D}{\isacharminus}}\ {\isaliteral{3F}{\isacharquery}}n\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{1}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ {\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}\ {\isaliteral{3F}{\isacharquery}}n\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{3F}{\isacharquery}}u\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{3F}{\isacharquery}}n{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{2B}{\isacharplus}}\ {\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{2D}{\isacharminus}}\ real\ {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

   251 term{\isadigit{2}}str\ t{\isaliteral{3B}{\isacharsemicolon}}\isanewline

   252 {\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline

   253 \isacommand{ML}\isamarkupfalse%

   254 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

   255 val\ SOME\ {\isaliteral{28}{\isacharparenleft}}t{\isaliteral{2C}{\isacharcomma}}\ asm{\isadigit{3}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ rewrite{\isaliteral{5F}{\isacharunderscore}}\ thy\ ro\ er\ true\ {\isaliteral{28}{\isacharparenleft}}num{\isaliteral{5F}{\isacharunderscore}}str\ %

   256 \isaantiq

   257 thm\ rule{\isadigit{1}}{}%

   258 \endisaantiq

   259 {\isaliteral{29}{\isacharparenright}}\ t{\isaliteral{3B}{\isacharsemicolon}}\isanewline

   260 term{\isadigit{2}}str\ t\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{2D}{\isacharminus}}\ {\isaliteral{3F}{\isacharquery}}u\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{2D}{\isacharminus}}\ {\isaliteral{3F}{\isacharquery}}n\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{1}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ {\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}\ {\isaliteral{3F}{\isacharquery}}n\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{3F}{\isacharquery}}u\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{3F}{\isacharquery}}n{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{3F}{\isacharquery}}{\isaliteral{5C3C64656C74613E}{\isasymdelta}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{3F}{\isacharquery}}n{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{2D}{\isacharminus}}\ real\ {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

   261 term{\isadigit{2}}str\ t{\isaliteral{3B}{\isacharsemicolon}}\isanewline

   262 {\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline

   263 \isacommand{ML}\isamarkupfalse%

   264 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

   265 terms{\isadigit{2}}str\ {\isaliteral{28}{\isacharparenleft}}asm{\isadigit{1}}\ {\isaliteral{40}{\isacharat}}\ asm{\isadigit{2}}\ {\isaliteral{40}{\isacharat}}\ asm{\isadigit{3}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

   266 {\isaliteral{2A7D}{\isacharverbatimclose}}%

   267 \endisatagML

   268 {\isafoldML}%

   269 %

   270 \isadelimML

   271 %

   272 \endisadelimML

   273 %

   274 \isamarkupsection{Prepare steps for CTP-based programming language%

   275 }

   276 \isamarkuptrue%

   277 %

   278 \begin{isamarkuptext}%

   279 TODO insert Calculation (Referenz?!)

   281 The goal... realized in sections below, in Sect.\ref{spec-meth} and Sect.\ref{prog-steps}

   283 the reader is advised to jump between the subsequent subsections and the respective steps in Sect.\ref{prog-steps}%

   284 \end{isamarkuptext}%

   285 \isamarkuptrue%

   286 %

   287 \isamarkupsubsection{prepare expression \label{prep-expr}%

   288 }

   289 \isamarkuptrue%

   290 %

   291 \isadelimML

   292 %

   293 \endisadelimML

   294 %

   295 \isatagML

   296 \isacommand{ML}\isamarkupfalse%

   297 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

   298 val\ ctxt\ {\isaliteral{3D}{\isacharequal}}\ ProofContext{\isaliteral{2E}{\isachardot}}init{\isaliteral{5F}{\isacharunderscore}}global\ %

   299 \isaantiq

   300 theory\ Isac{}%

   301 \endisaantiq

   302 {\isaliteral{3B}{\isacharsemicolon}}\isanewline

   303 val\ ctxt\ {\isaliteral{3D}{\isacharequal}}\ declare{\isaliteral{5F}{\isacharunderscore}}constraints{\isaliteral{27}{\isacharprime}}\ {\isaliteral{5B}{\isacharbrackleft}}%

   304 \isaantiq

   305 term\ {\isaliteral{22}{\isachardoublequote}}z{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}real{\isaliteral{22}{\isachardoublequote}}{}%

   306 \endisaantiq

   307 {\isaliteral{5D}{\isacharbrackright}}\ ctxt{\isaliteral{3B}{\isacharsemicolon}}\isanewline

   308 \isanewline

   309 val\ SOME\ fun{\isadigit{1}}\ {\isaliteral{3D}{\isacharequal}}\ parseNEW\ ctxt\ {\isaliteral{22}{\isachardoublequote}}X\ z\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{3}}\ {\isaliteral{2F}{\isacharslash}}\ {\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{1}}{\isaliteral{2F}{\isacharslash}}{\isadigit{4}}\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{1}}{\isaliteral{2F}{\isacharslash}}{\isadigit{8}}\ {\isaliteral{2A}{\isacharasterisk}}\ z\ {\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{1}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\ term{\isadigit{2}}str\ fun{\isadigit{1}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

   310 val\ SOME\ fun{\isadigit{1}}{\isaliteral{27}{\isacharprime}}\ {\isaliteral{3D}{\isacharequal}}\ parseNEW\ ctxt\ {\isaliteral{22}{\isachardoublequote}}X\ z\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{3}}\ {\isaliteral{2F}{\isacharslash}}\ {\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{1}}{\isaliteral{2F}{\isacharslash}}{\isadigit{4}}\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{1}}{\isaliteral{2F}{\isacharslash}}{\isadigit{8}}\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{1}}{\isaliteral{2F}{\isacharslash}}z{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\ term{\isadigit{2}}str\ fun{\isadigit{1}}{\isaliteral{27}{\isacharprime}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

   311 {\isaliteral{2A7D}{\isacharverbatimclose}}%

   312 \endisatagML

   313 {\isafoldML}%

   314 %

   315 \isadelimML

   316 %

   317 \endisadelimML

   318 %

   319 \isamarkupsubsubsection{multply with z%

   320 }

   321 \isamarkuptrue%

   322 \isacommand{axiomatization}\isamarkupfalse%

   323 \ \isakeyword{where}\isanewline

   324 \ \ 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

   325 %

   326 \isadelimML

   327 \isanewline

   328 %

   329 \endisadelimML

   330 %

   331 \isatagML

   332 \isacommand{ML}\isamarkupfalse%

   333 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

   334 val\ {\isaliteral{28}{\isacharparenleft}}thy{\isaliteral{2C}{\isacharcomma}}\ ro{\isaliteral{2C}{\isacharcomma}}\ er{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}%

   335 \isaantiq

   336 theory\ Isac{}%

   337 \endisaantiq

   338 {\isaliteral{2C}{\isacharcomma}}\ tless{\isaliteral{5F}{\isacharunderscore}}true{\isaliteral{2C}{\isacharcomma}}\ eval{\isaliteral{5F}{\isacharunderscore}}rls{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

   339 val\ SOME\ {\isaliteral{28}{\isacharparenleft}}fun{\isadigit{2}}{\isaliteral{2C}{\isacharcomma}}\ asm{\isadigit{1}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ rewrite{\isaliteral{5F}{\isacharunderscore}}\ thy\ ro\ er\ true\ \ %

   340 \isaantiq

   341 thm\ ruleZY{}%

   342 \endisaantiq

   343 \ fun{\isadigit{1}}{\isaliteral{3B}{\isacharsemicolon}}\ term{\isadigit{2}}str\ fun{\isadigit{2}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

   344 val\ SOME\ {\isaliteral{28}{\isacharparenleft}}fun{\isadigit{2}}{\isaliteral{27}{\isacharprime}}{\isaliteral{2C}{\isacharcomma}}\ asm{\isadigit{1}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ rewrite{\isaliteral{5F}{\isacharunderscore}}\ thy\ ro\ er\ true\ \ %

   345 \isaantiq

   346 thm\ ruleZY{}%

   347 \endisaantiq

   348 \ fun{\isadigit{1}}{\isaliteral{27}{\isacharprime}}{\isaliteral{3B}{\isacharsemicolon}}\ term{\isadigit{2}}str\ fun{\isadigit{2}}{\isaliteral{27}{\isacharprime}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

   349 \isanewline

   350 val\ SOME\ {\isaliteral{28}{\isacharparenleft}}fun{\isadigit{3}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ rewrite{\isaliteral{5F}{\isacharunderscore}}set{\isaliteral{5F}{\isacharunderscore}}\ %

   351 \isaantiq

   352 theory\ Isac{}%

   353 \endisaantiq

   354 \ false\ norm{\isaliteral{5F}{\isacharunderscore}}Rational\ fun{\isadigit{2}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

   355 term{\isadigit{2}}str\ fun{\isadigit{3}}{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}fails\ on\ x{\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{2D}{\isacharminus}}{\isadigit{1}}{\isaliteral{29}{\isacharparenright}}\ TODO{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

   356 val\ SOME\ {\isaliteral{28}{\isacharparenleft}}fun{\isadigit{3}}{\isaliteral{27}{\isacharprime}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ rewrite{\isaliteral{5F}{\isacharunderscore}}set{\isaliteral{5F}{\isacharunderscore}}\ %

   357 \isaantiq

   358 theory\ Isac{}%

   359 \endisaantiq

   360 \ false\ norm{\isaliteral{5F}{\isacharunderscore}}Rational\ fun{\isadigit{2}}{\isaliteral{27}{\isacharprime}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

   361 term{\isadigit{2}}str\ fun{\isadigit{3}}{\isaliteral{27}{\isacharprime}}{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}OK{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

   362 {\isaliteral{2A7D}{\isacharverbatimclose}}%

   363 \endisatagML

   364 {\isafoldML}%

   365 %

   366 \isadelimML

   367 %

   368 \endisadelimML

   369 %

   370 \isamarkupsubsubsection{get argument of X': z is the variable the equation is solved for%

   371 }

   372 \isamarkuptrue%

   373 %

   374 \begin{isamarkuptext}%

   375 grep... Atools.thy, Tools.thy contain general utilities: eval_argument_in, eval_rhs, eval_lhs,...

   377 grep -r "fun eva_" ... shows all functions witch can be used in a script.

   378 lookup this files how to build and handle such functions.

   380 the next section shows how to introduce such a function.%

   381 \end{isamarkuptext}%

   382 \isamarkuptrue%

   383 %

   384 \isamarkupsubsubsection{Decompose given term into lhs = rhs%

   385 }

   386 \isamarkuptrue%

   387 %

   388 \isadelimML

   389 %

   390 \endisadelimML

   391 %

   392 \isatagML

   393 \isacommand{ML}\isamarkupfalse%

   394 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

   395 \ \ 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

   396 \ \ 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

   397 \ \ 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

   398 {\isaliteral{2A7D}{\isacharverbatimclose}}%

   399 \endisatagML

   400 {\isafoldML}%

   401 %

   402 \isadelimML

   403 %

   404 \endisadelimML

   405 %

   406 \begin{isamarkuptext}%

   407 we have rhs in the Script language, but we need a function

   408   which gets the denominator of a fraction%

   409 \end{isamarkuptext}%

   410 \isamarkuptrue%

   411 %

   412 \isamarkupsubsubsection{get the denominator and numerator out of a fraction%

   413 }

   414 \isamarkuptrue%

   415 %

   416 \begin{isamarkuptext}%

   417 get denominator should become a constant for the isabelle parser:%

   418 \end{isamarkuptext}%

   419 \isamarkuptrue%

   420 \isacommand{consts}\isamarkupfalse%

   421 \isanewline

   422 \ \ get{\isaliteral{5F}{\isacharunderscore}}denominator\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}real\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\ real{\isaliteral{22}{\isachardoublequoteclose}}\isanewline

   423 \ \ get{\isaliteral{5F}{\isacharunderscore}}numerator\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}real\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\ real{\isaliteral{22}{\isachardoublequoteclose}}%

   424 \begin{isamarkuptext}%

   425 With the above definition we run into problems with parsing the Script InverseZTransform:

   426   This leads to "ambiguous parse trees" and we avoid this by shifting the definition

   427   to Rational.thy and re-building Isac.

   428   ATTENTION: from now on Build_Inverse_Z_Transform mimics a build from scratch;

   429   it only works due to re-building Isac several times (indicated explicityl).%

   430 \end{isamarkuptext}%

   431 \isamarkuptrue%

   432 %

   433 \isadelimML

   434 %

   435 \endisadelimML

   436 %

   437 \isatagML

   438 \isacommand{ML}\isamarkupfalse%

   439 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

   440 {\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

   441 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

   442 		\ \ \ \ \ \ {\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

   443 \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\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

   444 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ denom{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ thy\ {\isaliteral{3D}{\isacharequal}}\ \isanewline

   445 \ \ \ \ \ \ \ \ SOME\ {\isaliteral{28}{\isacharparenleft}}mk{\isaliteral{5F}{\isacharunderscore}}thmid\ thmid\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{22}{\isachardoublequote}}\ \isanewline

   446 \ \ \ \ \ \ \ \ \ \ \ \ {\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

   447 	\ \ \ \ \ \ \ \ \ \ 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

   448 \ \ {\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

   449 \isanewline

   450 {\isaliteral{2A7D}{\isacharverbatimclose}}%

   451 \endisatagML

   452 {\isafoldML}%

   453 %

   454 \isadelimML

   455 %

   456 \endisadelimML

   457 %

   458 \begin{isamarkuptext}%

   459 tests of eval_get_denominator see test/Knowledge/rational.sml%

   460 \end{isamarkuptext}%

   461 \isamarkuptrue%

   462 %

   463 \begin{isamarkuptext}%

   464 get numerator should also become a constant for the isabelle parser:%

   465 \end{isamarkuptext}%

   466 \isamarkuptrue%

   467 %

   468 \isadelimML

   469 %

   470 \endisadelimML

   471 %

   472 \isatagML

   473 \isacommand{ML}\isamarkupfalse%

   474 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

   475 fun\ eval{\isaliteral{5F}{\isacharunderscore}}get{\isaliteral{5F}{\isacharunderscore}}numerator\ {\isaliteral{28}{\isacharparenleft}}thmid{\isaliteral{3A}{\isacharcolon}}string{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5F}{\isacharunderscore}}\ \isanewline

   476 		\ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}t\ as\ Const\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}Rational{\isaliteral{2E}{\isachardot}}get{\isaliteral{5F}{\isacharunderscore}}numerator{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5F}{\isacharunderscore}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{24}{\isachardollar}}\isanewline

   477 \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}Const\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}Rings{\isaliteral{2E}{\isachardot}}inverse{\isaliteral{5F}{\isacharunderscore}}class{\isaliteral{2E}{\isachardot}}divide{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5F}{\isacharunderscore}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{24}{\isachardollar}}num\isanewline

   478 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{24}{\isachardollar}}denom\ {\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ thy\ {\isaliteral{3D}{\isacharequal}}\ \isanewline

   479 \ \ \ \ \ \ \ \ SOME\ {\isaliteral{28}{\isacharparenleft}}mk{\isaliteral{5F}{\isacharunderscore}}thmid\ thmid\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{22}{\isachardoublequote}}\ \isanewline

   480 \ \ \ \ \ \ \ \ \ \ \ \ {\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}}\ num{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ \isanewline

   481 	\ \ \ \ \ \ \ \ \ \ Trueprop\ {\isaliteral{24}{\isachardollar}}\ {\isaliteral{28}{\isacharparenleft}}mk{\isaliteral{5F}{\isacharunderscore}}equality\ {\isaliteral{28}{\isacharparenleft}}t{\isaliteral{2C}{\isacharcomma}}\ num{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\isanewline

   482 \ \ {\isaliteral{7C}{\isacharbar}}\ eval{\isaliteral{5F}{\isacharunderscore}}get{\isaliteral{5F}{\isacharunderscore}}numerator\ {\isaliteral{5F}{\isacharunderscore}}\ {\isaliteral{5F}{\isacharunderscore}}\ {\isaliteral{5F}{\isacharunderscore}}\ {\isaliteral{5F}{\isacharunderscore}}\ {\isaliteral{3D}{\isacharequal}}\ NONE{\isaliteral{3B}{\isacharsemicolon}}\ \isanewline

   483 {\isaliteral{2A7D}{\isacharverbatimclose}}%

   484 \endisatagML

   485 {\isafoldML}%

   486 %

   487 \isadelimML

   488 %

   489 \endisadelimML

   490 %

   491 \begin{isamarkuptext}%

   492 We discovered severell problems by implementing the get_numerator function.

   493 Remember when putting new functions to Isac, put them in a thy file and rebuild

   494 isac, also put them in the ruleset for the script!%

   495 \end{isamarkuptext}%

   496 \isamarkuptrue%

   497 %

   498 \isamarkupsubsection{solve equation%

   499 }

   500 \isamarkuptrue%

   501 %

   502 \begin{isamarkuptext}%

   503 this type of equation if too general for the present program%

   504 \end{isamarkuptext}%

   505 \isamarkuptrue%

   506 %

   507 \isadelimML

   508 %

   509 \endisadelimML

   510 %

   511 \isatagML

   512 \isacommand{ML}\isamarkupfalse%

   513 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

   514 {\isaliteral{22}{\isachardoublequote}}{\isaliteral{2D}{\isacharminus}}{\isaliteral{2D}{\isacharminus}}{\isaliteral{2D}{\isacharminus}}{\isaliteral{2D}{\isacharminus}}{\isaliteral{2D}{\isacharminus}}{\isaliteral{2D}{\isacharminus}}{\isaliteral{2D}{\isacharminus}}{\isaliteral{2D}{\isacharminus}}{\isaliteral{2D}{\isacharminus}}{\isaliteral{2D}{\isacharminus}}{\isaliteral{2D}{\isacharminus}}\ Minisubplb{\isaliteral{2F}{\isacharslash}}{\isadigit{1}}{\isadigit{0}}{\isadigit{0}}{\isaliteral{2D}{\isacharminus}}init{\isaliteral{2D}{\isacharminus}}rootp\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}OK{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}bl{\isaliteral{2E}{\isachardot}}sml\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{2D}{\isacharminus}}{\isaliteral{2D}{\isacharminus}}{\isaliteral{2D}{\isacharminus}}{\isaliteral{2D}{\isacharminus}}{\isaliteral{2D}{\isacharminus}}{\isaliteral{2D}{\isacharminus}}{\isaliteral{2D}{\isacharminus}}{\isaliteral{2D}{\isacharminus}}{\isaliteral{2D}{\isacharminus}}{\isaliteral{2D}{\isacharminus}}{\isaliteral{2D}{\isacharminus}}{\isaliteral{2D}{\isacharminus}}{\isaliteral{2D}{\isacharminus}}{\isaliteral{2D}{\isacharminus}}{\isaliteral{2D}{\isacharminus}}{\isaliteral{2D}{\isacharminus}}{\isaliteral{2D}{\isacharminus}}{\isaliteral{2D}{\isacharminus}}{\isaliteral{2D}{\isacharminus}}{\isaliteral{2D}{\isacharminus}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

   515 val\ denominator\ {\isaliteral{3D}{\isacharequal}}\ parseNEW\ ctxt\ {\isaliteral{22}{\isachardoublequote}}z{\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}{\isadigit{2}}\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{1}}{\isaliteral{2F}{\isacharslash}}{\isadigit{4}}{\isaliteral{2A}{\isacharasterisk}}z\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{1}}{\isaliteral{2F}{\isacharslash}}{\isadigit{8}}\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{0}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

   516 val\ fmz\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}equality\ {\isaliteral{28}{\isacharparenleft}}z{\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}{\isadigit{2}}\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{1}}{\isaliteral{2F}{\isacharslash}}{\isadigit{4}}{\isaliteral{2A}{\isacharasterisk}}z\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{1}}{\isaliteral{2F}{\isacharslash}}{\isadigit{8}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{0}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}real{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}solveFor\ z{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}solutions\ L{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

   517 val\ {\isaliteral{28}{\isacharparenleft}}dI{\isaliteral{27}{\isacharprime}}{\isaliteral{2C}{\isacharcomma}}pI{\isaliteral{27}{\isacharprime}}{\isaliteral{2C}{\isacharcomma}}mI{\isaliteral{27}{\isacharprime}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}Isac{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}univariate{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}equation{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}no{\isaliteral{5F}{\isacharunderscore}}met{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

   518 {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}\ TODO{\isaliteral{3A}{\isacharcolon}}\ ISAC\ determines\ type\ of\ eq{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

   519 {\isaliteral{2A7D}{\isacharverbatimclose}}%

   520 \endisatagML

   521 {\isafoldML}%

   522 %

   523 \isadelimML

   524 %

   525 \endisadelimML

   526 %

   527 \begin{isamarkuptext}%

   528 Does the Equation Match the Specification ?%

   529 \end{isamarkuptext}%

   530 \isamarkuptrue%

   531 %

   532 \isadelimML

   533 %

   534 \endisadelimML

   535 %

   536 \isatagML

   537 \isacommand{ML}\isamarkupfalse%

   538 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

   539 match{\isaliteral{5F}{\isacharunderscore}}pbl\ fmz\ {\isaliteral{28}{\isacharparenleft}}get{\isaliteral{5F}{\isacharunderscore}}pbt\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}univariate{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}equation{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

   540 {\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline

   541 \isacommand{ML}\isamarkupfalse%

   542 \ {\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}}\isanewline

   543 \isanewline

   544 \isacommand{ML}\isamarkupfalse%

   545 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

   546 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

   547 val\ fmz\ {\isaliteral{3D}{\isacharequal}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}specification{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

   548 \ \ {\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

   549 \ \ \ {\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

   550 \ \ \ {\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

   551 \isanewline

   552 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

   553 \ \ {\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

   554 {\isaliteral{2A7D}{\isacharverbatimclose}}%

   555 \endisatagML

   556 {\isafoldML}%

   557 %

   558 \isadelimML

   559 %

   560 \endisadelimML

   561 %

   562 \begin{isamarkuptext}%

   563 Does the Other Equation Match the Specification ?%

   564 \end{isamarkuptext}%

   565 \isamarkuptrue%

   566 %

   567 \isadelimML

   568 %

   569 \endisadelimML

   570 %

   571 \isatagML

   572 \isacommand{ML}\isamarkupfalse%

   573 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

   574 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

   575 {\isaliteral{2A7D}{\isacharverbatimclose}}%

   576 \endisatagML

   577 {\isafoldML}%

   578 %

   579 \isadelimML

   580 %

   581 \endisadelimML

   582 %

   583 \begin{isamarkuptext}%

   584 Solve Equation Stepwise%

   585 \end{isamarkuptext}%

   586 \isamarkuptrue%

   587 %

   588 \isadelimML

   589 %

   590 \endisadelimML

   591 %

   592 \isatagML

   593 \isacommand{ML}\isamarkupfalse%

   594 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

   595 {\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline

   596 \isacommand{ML}\isamarkupfalse%

   597 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

   598 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

   599 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

   600 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

   601 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

   602 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

   603 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

   604 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

   605 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

   606 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

   607 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

   608 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

   609 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

   610 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

   611 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

   612 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

   613 {\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

   614 show{\isaliteral{5F}{\isacharunderscore}}pt\ pt{\isaliteral{3B}{\isacharsemicolon}}\ \isanewline

   615 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

   616 {\isaliteral{2A7D}{\isacharverbatimclose}}%

   617 \endisatagML

   618 {\isafoldML}%

   619 %

   620 \isadelimML

   621 %

   622 \endisadelimML

   623 %

   624 \isamarkupsubsection{partial fraction decomposition%

   625 }

   626 \isamarkuptrue%

   627 %

   628 \isamarkupsubsubsection{solution of the equation%

   629 }

   630 \isamarkuptrue%

   631 %

   632 \isadelimML

   633 %

   634 \endisadelimML

   635 %

   636 \isatagML

   637 \isacommand{ML}\isamarkupfalse%

   638 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

   639 val\ SOME\ solutions\ {\isaliteral{3D}{\isacharequal}}\ parseNEW\ ctxt\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5B}{\isacharbrackleft}}z{\isaliteral{3D}{\isacharequal}}{\isadigit{1}}{\isaliteral{2F}{\isacharslash}}{\isadigit{2}}{\isaliteral{2C}{\isacharcomma}}\ z{\isaliteral{3D}{\isacharequal}}{\isaliteral{2D}{\isacharminus}}{\isadigit{1}}{\isaliteral{2F}{\isacharslash}}{\isadigit{4}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

   640 term{\isadigit{2}}str\ solutions{\isaliteral{3B}{\isacharsemicolon}}\isanewline

   641 atomty\ solutions{\isaliteral{3B}{\isacharsemicolon}}\isanewline

   642 {\isaliteral{2A7D}{\isacharverbatimclose}}%

   643 \endisatagML

   644 {\isafoldML}%

   645 %

   646 \isadelimML

   647 %

   648 \endisadelimML

   649 %

   650 \isamarkupsubsubsection{get solutions out of list%

   651 }

   652 \isamarkuptrue%

   653 %

   654 \begin{isamarkuptext}%

   655 in isac's CTP-based programming language: let$ $s_1 = NTH 1$ solutions; $s_2 = NTH 2...$%

   656 \end{isamarkuptext}%

   657 \isamarkuptrue%

   658 %

   659 \isadelimML

   660 %

   661 \endisadelimML

   662 %

   663 \isatagML

   664 \isacommand{ML}\isamarkupfalse%

   665 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

   666 val\ Const\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}List{\isaliteral{2E}{\isachardot}}list{\isaliteral{2E}{\isachardot}}Cons{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5F}{\isacharunderscore}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{24}{\isachardollar}}\ s{\isaliteral{5F}{\isacharunderscore}}{\isadigit{1}}\ {\isaliteral{24}{\isachardollar}}\ {\isaliteral{28}{\isacharparenleft}}Const\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}List{\isaliteral{2E}{\isachardot}}list{\isaliteral{2E}{\isachardot}}Cons{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5F}{\isacharunderscore}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{24}{\isachardollar}}\isanewline

   667 \ \ \ \ \ \ s{\isaliteral{5F}{\isacharunderscore}}{\isadigit{2}}\ {\isaliteral{24}{\isachardollar}}\ Const\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}List{\isaliteral{2E}{\isachardot}}list{\isaliteral{2E}{\isachardot}}Nil{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5F}{\isacharunderscore}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ solutions{\isaliteral{3B}{\isacharsemicolon}}\isanewline

   668 term{\isadigit{2}}str\ s{\isaliteral{5F}{\isacharunderscore}}{\isadigit{1}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

   669 term{\isadigit{2}}str\ s{\isaliteral{5F}{\isacharunderscore}}{\isadigit{2}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

   670 {\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline

   671 \isanewline

   672 \isacommand{ML}\isamarkupfalse%

   673 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}Solutions\ as\ Denominator\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{2D}{\isacharminus}}{\isaliteral{3E}{\isachargreater}}\ Denominator{\isadigit{1}}\ {\isaliteral{3D}{\isacharequal}}\ z\ {\isaliteral{2D}{\isacharminus}}\ Zeropoint{\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ Denominator{\isadigit{2}}\ {\isaliteral{3D}{\isacharequal}}\ z{\isaliteral{2D}{\isacharminus}}Zeropoint{\isadigit{2}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

   674 val\ xx\ {\isaliteral{3D}{\isacharequal}}\ HOLogic{\isaliteral{2E}{\isachardot}}dest{\isaliteral{5F}{\isacharunderscore}}eq\ s{\isaliteral{5F}{\isacharunderscore}}{\isadigit{1}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

   675 val\ s{\isaliteral{5F}{\isacharunderscore}}{\isadigit{1}}{\isaliteral{27}{\isacharprime}}\ {\isaliteral{3D}{\isacharequal}}\ HOLogic{\isaliteral{2E}{\isachardot}}mk{\isaliteral{5F}{\isacharunderscore}}binop\ {\isaliteral{22}{\isachardoublequote}}Groups{\isaliteral{2E}{\isachardot}}minus{\isaliteral{5F}{\isacharunderscore}}class{\isaliteral{2E}{\isachardot}}minus{\isaliteral{22}{\isachardoublequote}}\ xx{\isaliteral{3B}{\isacharsemicolon}}\isanewline

   676 val\ xx\ {\isaliteral{3D}{\isacharequal}}\ HOLogic{\isaliteral{2E}{\isachardot}}dest{\isaliteral{5F}{\isacharunderscore}}eq\ s{\isaliteral{5F}{\isacharunderscore}}{\isadigit{2}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

   677 val\ s{\isaliteral{5F}{\isacharunderscore}}{\isadigit{2}}{\isaliteral{27}{\isacharprime}}\ {\isaliteral{3D}{\isacharequal}}\ HOLogic{\isaliteral{2E}{\isachardot}}mk{\isaliteral{5F}{\isacharunderscore}}binop\ {\isaliteral{22}{\isachardoublequote}}Groups{\isaliteral{2E}{\isachardot}}minus{\isaliteral{5F}{\isacharunderscore}}class{\isaliteral{2E}{\isachardot}}minus{\isaliteral{22}{\isachardoublequote}}\ xx{\isaliteral{3B}{\isacharsemicolon}}\isanewline

   678 term{\isadigit{2}}str\ s{\isaliteral{5F}{\isacharunderscore}}{\isadigit{1}}{\isaliteral{27}{\isacharprime}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

   679 term{\isadigit{2}}str\ s{\isaliteral{5F}{\isacharunderscore}}{\isadigit{2}}{\isaliteral{27}{\isacharprime}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

   680 {\isaliteral{2A7D}{\isacharverbatimclose}}%

   681 \endisatagML

   682 {\isafoldML}%

   683 %

   684 \isadelimML

   685 %

   686 \endisadelimML

   687 %

   688 \begin{isamarkuptext}%

   689 for the programming language a function

   690   collecting all the above manipulations is helpful%

   691 \end{isamarkuptext}%

   692 \isamarkuptrue%

   693 %

   694 \isadelimML

   695 %

   696 \endisadelimML

   697 %

   698 \isatagML

   699 \isacommand{ML}\isamarkupfalse%

   700 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

   701 fun\ mk{\isaliteral{5F}{\isacharunderscore}}minus{\isaliteral{5F}{\isacharunderscore}}{\isadigit{1}}\ T\ {\isaliteral{3D}{\isacharequal}}\ Free{\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2D}{\isacharminus}}{\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ T{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}TODO\ DELETE\ WITH\ numbers{\isaliteral{5F}{\isacharunderscore}}to{\isaliteral{5F}{\isacharunderscore}}string{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

   702 fun\ flip{\isaliteral{5F}{\isacharunderscore}}sign\ t\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}TODO\ improve\ for\ use\ in\ factors{\isaliteral{5F}{\isacharunderscore}}from{\isaliteral{5F}{\isacharunderscore}}solution{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{2D}{\isacharminus}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{2D}{\isacharminus}}{\isadigit{1}}{\isaliteral{29}{\isacharparenright}}\ etc{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

   703 \ \ let\ val\ minus{\isaliteral{5F}{\isacharunderscore}}{\isadigit{1}}\ {\isaliteral{3D}{\isacharequal}}\ t\ {\isaliteral{7C}{\isacharbar}}{\isaliteral{3E}{\isachargreater}}\ type{\isaliteral{5F}{\isacharunderscore}}of\ {\isaliteral{7C}{\isacharbar}}{\isaliteral{3E}{\isachargreater}}\ mk{\isaliteral{5F}{\isacharunderscore}}minus{\isaliteral{5F}{\isacharunderscore}}{\isadigit{1}}\isanewline

   704 \ \ in\ HOLogic{\isaliteral{2E}{\isachardot}}mk{\isaliteral{5F}{\isacharunderscore}}binop\ {\isaliteral{22}{\isachardoublequote}}Groups{\isaliteral{2E}{\isachardot}}times{\isaliteral{5F}{\isacharunderscore}}class{\isaliteral{2E}{\isachardot}}times{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{28}{\isacharparenleft}}minus{\isaliteral{5F}{\isacharunderscore}}{\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ t{\isaliteral{29}{\isacharparenright}}\ end{\isaliteral{3B}{\isacharsemicolon}}\isanewline

   705 fun\ fac{\isaliteral{5F}{\isacharunderscore}}from{\isaliteral{5F}{\isacharunderscore}}sol\ s\ {\isaliteral{3D}{\isacharequal}}\isanewline

   706 \ \ let\ val\ {\isaliteral{28}{\isacharparenleft}}lhs{\isaliteral{2C}{\isacharcomma}}\ rhs{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ HOLogic{\isaliteral{2E}{\isachardot}}dest{\isaliteral{5F}{\isacharunderscore}}eq\ s\isanewline

   707 \ \ in\ HOLogic{\isaliteral{2E}{\isachardot}}mk{\isaliteral{5F}{\isacharunderscore}}binop\ {\isaliteral{22}{\isachardoublequote}}Groups{\isaliteral{2E}{\isachardot}}plus{\isaliteral{5F}{\isacharunderscore}}class{\isaliteral{2E}{\isachardot}}plus{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{28}{\isacharparenleft}}lhs{\isaliteral{2C}{\isacharcomma}}\ flip{\isaliteral{5F}{\isacharunderscore}}sign\ rhs{\isaliteral{29}{\isacharparenright}}\ end{\isaliteral{3B}{\isacharsemicolon}}\isanewline

   708 {\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline

   709 \isacommand{ML}\isamarkupfalse%

   710 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

   711 e{\isaliteral{5F}{\isacharunderscore}}term\isanewline

   712 {\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline

   713 \isacommand{ML}\isamarkupfalse%

   714 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

   715 fun\ mk{\isaliteral{5F}{\isacharunderscore}}prod\ prod\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{3D}{\isacharequal}}\isanewline

   716 \ \ \ \ \ \ if\ prod\ {\isaliteral{3D}{\isacharequal}}\ e{\isaliteral{5F}{\isacharunderscore}}term\ then\ error\ {\isaliteral{22}{\isachardoublequote}}mk{\isaliteral{5F}{\isacharunderscore}}prod\ called\ with\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}\ else\ prod\isanewline

   717 \ \ {\isaliteral{7C}{\isacharbar}}\ mk{\isaliteral{5F}{\isacharunderscore}}prod\ prod\ {\isaliteral{28}{\isacharparenleft}}t\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\isanewline

   718 \ \ \ \ \ \ if\ prod\ {\isaliteral{3D}{\isacharequal}}\ e{\isaliteral{5F}{\isacharunderscore}}term\ then\ t\ else\ HOLogic{\isaliteral{2E}{\isachardot}}mk{\isaliteral{5F}{\isacharunderscore}}binop\ {\isaliteral{22}{\isachardoublequote}}Groups{\isaliteral{2E}{\isachardot}}times{\isaliteral{5F}{\isacharunderscore}}class{\isaliteral{2E}{\isachardot}}times{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{28}{\isacharparenleft}}prod{\isaliteral{2C}{\isacharcomma}}\ t{\isaliteral{29}{\isacharparenright}}\isanewline

   719 \ \ {\isaliteral{7C}{\isacharbar}}\ mk{\isaliteral{5F}{\isacharunderscore}}prod\ prod\ {\isaliteral{28}{\isacharparenleft}}t{\isadigit{1}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ t{\isadigit{2}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ ts{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\isanewline

   720 \ \ \ \ \ \ \ \ if\ prod\ {\isaliteral{3D}{\isacharequal}}\ e{\isaliteral{5F}{\isacharunderscore}}term\ \isanewline

   721 \ \ \ \ \ \ \ \ then\ \isanewline

   722 \ \ \ \ \ \ \ \ \ \ \ let\ val\ p\ {\isaliteral{3D}{\isacharequal}}\ HOLogic{\isaliteral{2E}{\isachardot}}mk{\isaliteral{5F}{\isacharunderscore}}binop\ {\isaliteral{22}{\isachardoublequote}}Groups{\isaliteral{2E}{\isachardot}}times{\isaliteral{5F}{\isacharunderscore}}class{\isaliteral{2E}{\isachardot}}times{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{28}{\isacharparenleft}}t{\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ t{\isadigit{2}}{\isaliteral{29}{\isacharparenright}}\isanewline

   723 \ \ \ \ \ \ \ \ \ \ \ in\ mk{\isaliteral{5F}{\isacharunderscore}}prod\ p\ ts\ end\ \isanewline

   724 \ \ \ \ \ \ \ \ else\ \isanewline

   725 \ \ \ \ \ \ \ \ \ \ \ let\ val\ p\ {\isaliteral{3D}{\isacharequal}}\ HOLogic{\isaliteral{2E}{\isachardot}}mk{\isaliteral{5F}{\isacharunderscore}}binop\ {\isaliteral{22}{\isachardoublequote}}Groups{\isaliteral{2E}{\isachardot}}times{\isaliteral{5F}{\isacharunderscore}}class{\isaliteral{2E}{\isachardot}}times{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{28}{\isacharparenleft}}prod{\isaliteral{2C}{\isacharcomma}}\ t{\isadigit{1}}{\isaliteral{29}{\isacharparenright}}\isanewline

   726 \ \ \ \ \ \ \ \ \ \ \ in\ mk{\isaliteral{5F}{\isacharunderscore}}prod\ p\ {\isaliteral{28}{\isacharparenleft}}t{\isadigit{2}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ ts{\isaliteral{29}{\isacharparenright}}\ end\ \isanewline

   727 {\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline

   728 \isacommand{ML}\isamarkupfalse%

   729 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

   730 {\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline

   731 \isacommand{ML}\isamarkupfalse%

   732 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

   733 {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}probably\ keept\ these\ test\ in\ test{\isaliteral{2F}{\isacharslash}}Tools{\isaliteral{2F}{\isacharslash}}isac{\isaliteral{2F}{\isacharslash}}{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}\isanewline

   734 {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}mk{\isaliteral{5F}{\isacharunderscore}}prod\ e{\isaliteral{5F}{\isacharunderscore}}term\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3B}{\isacharsemicolon}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

   735 \isanewline

   736 val\ prod\ {\isaliteral{3D}{\isacharequal}}\ mk{\isaliteral{5F}{\isacharunderscore}}prod\ e{\isaliteral{5F}{\isacharunderscore}}term\ {\isaliteral{5B}{\isacharbrackleft}}str{\isadigit{2}}term\ {\isaliteral{22}{\isachardoublequote}}x\ {\isaliteral{2B}{\isacharplus}}\ {\isadigit{1}}{\isadigit{2}}{\isadigit{3}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3B}{\isacharsemicolon}}\ \isanewline

   737 term{\isadigit{2}}str\ prod\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{22}{\isachardoublequote}}x\ {\isaliteral{2B}{\isacharplus}}\ {\isadigit{1}}{\isadigit{2}}{\isadigit{3}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

   738 \isanewline

   739 val\ sol\ {\isaliteral{3D}{\isacharequal}}\ str{\isadigit{2}}term\ {\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

   740 val\ sols\ {\isaliteral{3D}{\isacharequal}}\ HOLogic{\isaliteral{2E}{\isachardot}}dest{\isaliteral{5F}{\isacharunderscore}}list\ sol{\isaliteral{3B}{\isacharsemicolon}}\isanewline

   741 val\ facs\ {\isaliteral{3D}{\isacharequal}}\ map\ fac{\isaliteral{5F}{\isacharunderscore}}from{\isaliteral{5F}{\isacharunderscore}}sol\ sols{\isaliteral{3B}{\isacharsemicolon}}\isanewline

   742 val\ prod\ {\isaliteral{3D}{\isacharequal}}\ mk{\isaliteral{5F}{\isacharunderscore}}prod\ e{\isaliteral{5F}{\isacharunderscore}}term\ facs{\isaliteral{3B}{\isacharsemicolon}}\ \isanewline

   743 term{\isadigit{2}}str\ prod\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{1}}\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{1}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{2}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{1}}\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2D}{\isacharminus}}{\isadigit{1}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{4}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

   744 \isanewline

   745 val\ prod\ {\isaliteral{3D}{\isacharequal}}\ mk{\isaliteral{5F}{\isacharunderscore}}prod\ e{\isaliteral{5F}{\isacharunderscore}}term\ {\isaliteral{5B}{\isacharbrackleft}}str{\isadigit{2}}term\ {\isaliteral{22}{\isachardoublequote}}x\ {\isaliteral{2B}{\isacharplus}}\ {\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ str{\isadigit{2}}term\ {\isaliteral{22}{\isachardoublequote}}x\ {\isaliteral{2B}{\isacharplus}}\ {\isadigit{2}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ str{\isadigit{2}}term\ {\isaliteral{22}{\isachardoublequote}}x\ {\isaliteral{2B}{\isacharplus}}\ {\isadigit{3}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3B}{\isacharsemicolon}}\ \isanewline

   746 term{\isadigit{2}}str\ prod\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{2B}{\isacharplus}}\ {\isadigit{1}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{2B}{\isacharplus}}\ {\isadigit{2}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{2B}{\isacharplus}}\ {\isadigit{3}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

   747 {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

   748 \isanewline

   749 fun\ factors{\isaliteral{5F}{\isacharunderscore}}from{\isaliteral{5F}{\isacharunderscore}}solution\ sol\ {\isaliteral{3D}{\isacharequal}}\ \isanewline

   750 \ \ let\ val\ ts\ {\isaliteral{3D}{\isacharequal}}\ HOLogic{\isaliteral{2E}{\isachardot}}dest{\isaliteral{5F}{\isacharunderscore}}list\ sol\isanewline

   751 \ \ in\ mk{\isaliteral{5F}{\isacharunderscore}}prod\ e{\isaliteral{5F}{\isacharunderscore}}term\ {\isaliteral{28}{\isacharparenleft}}map\ fac{\isaliteral{5F}{\isacharunderscore}}from{\isaliteral{5F}{\isacharunderscore}}sol\ ts{\isaliteral{29}{\isacharparenright}}\ end{\isaliteral{3B}{\isacharsemicolon}}\isanewline

   752 {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}\isanewline

   753 val\ sol\ {\isaliteral{3D}{\isacharequal}}\ str{\isadigit{2}}term\ {\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

   754 val\ fs\ {\isaliteral{3D}{\isacharequal}}\ factors{\isaliteral{5F}{\isacharunderscore}}from{\isaliteral{5F}{\isacharunderscore}}solution\ sol{\isaliteral{3B}{\isacharsemicolon}}\isanewline

   755 term{\isadigit{2}}str\ fs\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{1}}\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{1}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{2}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{1}}\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2D}{\isacharminus}}{\isadigit{1}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{4}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}\isanewline

   756 {\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

   757 {\isaliteral{2A7D}{\isacharverbatimclose}}%

   758 \endisatagML

   759 {\isafoldML}%

   760 %

   761 \isadelimML

   762 %

   763 \endisadelimML

   764 %

   765 \begin{isamarkuptext}%

   766 This function needs to be packed such that it can be evaluated by the Lucas-Interpreter:

   767   # shift these functions into the related Equation.thy

   768   #  -- compare steps done with get_denominator above

   769   # done 02.12.2011 moved to PartialFractions.thy%

   770 \end{isamarkuptext}%

   771 \isamarkuptrue%

   772 %

   773 \isadelimML

   774 %

   775 \endisadelimML

   776 %

   777 \isatagML

   778 \isacommand{ML}\isamarkupfalse%

   779 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

   780 {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}factors{\isaliteral{5F}{\isacharunderscore}}from{\isaliteral{5F}{\isacharunderscore}}solution{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}Partial{\isaliteral{5F}{\isacharunderscore}}Fractions{\isaliteral{2E}{\isachardot}}factors{\isaliteral{5F}{\isacharunderscore}}from{\isaliteral{5F}{\isacharunderscore}}solution{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ eval{\isaliteral{5F}{\isacharunderscore}}factors{\isaliteral{5F}{\isacharunderscore}}from{\isaliteral{5F}{\isacharunderscore}}solution\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

   781 fun\ eval{\isaliteral{5F}{\isacharunderscore}}factors{\isaliteral{5F}{\isacharunderscore}}from{\isaliteral{5F}{\isacharunderscore}}solution\ {\isaliteral{28}{\isacharparenleft}}thmid{\isaliteral{3A}{\isacharcolon}}string{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5F}{\isacharunderscore}}\isanewline

   782 \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}t\ as\ Const\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}Partial{\isaliteral{5F}{\isacharunderscore}}Fractions{\isaliteral{2E}{\isachardot}}factors{\isaliteral{5F}{\isacharunderscore}}from{\isaliteral{5F}{\isacharunderscore}}solution{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5F}{\isacharunderscore}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{24}{\isachardollar}}\ sol{\isaliteral{29}{\isacharparenright}}\ thy\ {\isaliteral{3D}{\isacharequal}}\isanewline

   783 \ \ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{28}{\isacharparenleft}}let\ val\ prod\ {\isaliteral{3D}{\isacharequal}}\ factors{\isaliteral{5F}{\isacharunderscore}}from{\isaliteral{5F}{\isacharunderscore}}solution\ sol\isanewline

   784 \ \ \ \ \ \ \ \ \ in\ SOME\ {\isaliteral{28}{\isacharparenleft}}mk{\isaliteral{5F}{\isacharunderscore}}thmid\ thmid\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{22}{\isachardoublequote}}\isanewline

   785 \ \ \ \ \ \ \ \ \ \ \ {\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}}\ prod{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\isanewline

   786 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Trueprop\ {\isaliteral{24}{\isachardollar}}\ {\isaliteral{28}{\isacharparenleft}}mk{\isaliteral{5F}{\isacharunderscore}}equality\ {\isaliteral{28}{\isacharparenleft}}t{\isaliteral{2C}{\isacharcomma}}\ prod{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\isanewline

   787 \ \ \ \ \ \ \ \ \ end{\isaliteral{29}{\isacharparenright}}\isanewline

   788 \ \ \ \ \ \ \ handle\ {\isaliteral{5F}{\isacharunderscore}}\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\ NONE{\isaliteral{29}{\isacharparenright}}\isanewline

   789 \ {\isaliteral{7C}{\isacharbar}}\ eval{\isaliteral{5F}{\isacharunderscore}}factors{\isaliteral{5F}{\isacharunderscore}}from{\isaliteral{5F}{\isacharunderscore}}solution\ {\isaliteral{5F}{\isacharunderscore}}\ {\isaliteral{5F}{\isacharunderscore}}\ {\isaliteral{5F}{\isacharunderscore}}\ {\isaliteral{5F}{\isacharunderscore}}\ {\isaliteral{3D}{\isacharequal}}\ NONE{\isaliteral{3B}{\isacharsemicolon}}\isanewline

   790 {\isaliteral{2A7D}{\isacharverbatimclose}}%

   791 \endisatagML

   792 {\isafoldML}%

   793 %

   794 \isadelimML

   795 %

   796 \endisadelimML

   797 %

   798 \begin{isamarkuptext}%

   799 The tracing output of the calc tree after apllying this function was

   800 24 / factors_from_solution [z = 1/ 2, z = -1 / 4])]  and the next step

   801  val nxt = ("Empty_Tac", ...): tac'_).

   802 These observations indicate, that the Lucas-Interpreter (LIP) does

   803 not know how to evaluate factors_from_solution, so there is something

   804 wrong or missing.

   806 # First we isolate the difficulty in the program as follows:

   807   :

   808   "      (L_L::bool list) = (SubProblem (PolyEq'," ^

   809   "          [abcFormula,degree_2,polynomial,univariate,equation],[no_met])" ^

   810   "        [BOOL equ, REAL zzz]);              " ^

   811   "      (facs::real) = factors_from_solution L_L;" ^

   812   "      (foo::real) = Take facs" ^

   813   :

   814 and see

   815   [

   816   (([], Frm), Problem (Isac, [inverse, Z_Transform, SignalProcessing])),

   817   (([1], Frm), X z = 3 / (z - 1 / 4 + -1 / 8 * (1 / z))),

   818   (([1], Res), ?X' z = 3 / (z * (z - 1 / 4 + -1 / 8 * (1 / z)))),

   819   (([2], Res), ?X' z = 24 / (-1 + -2 * z + 8 * z ^^^ 2)),

   820   (([3], Pbl), solve (-1 + -2 * z + 8 * z ^^^ 2 = 0, z)),

   821   (([3,1], Frm), -1 + -2 * z + 8 * z ^^^ 2 = 0),

   822   (([3,1], Res), z = (- -2 + sqrt (-2 ^^^ 2 - 4 * 8 * -1)) / (2 * 8) |

   823                  z = (- -2 - sqrt (-2 ^^^ 2 - 4 * 8 * -1)) / (2 * 8)),

   824   (([3,2], Res), z = 1 / 2 | z = -1 / 4),

   825   (([3,3], Res), [z = 1 / 2, z = -1 / 4]),

   826   (([3,4], Res), [z = 1 / 2, z = -1 / 4]),

   827   (([3], Res), [z = 1 / 2, z = -1 / 4]),

   828   (([4], Frm), factors_from_solution [z = 1 / 2, z = -1 / 4])]

   829 in particular that

   830   (([3], Pbl), solve (-1 + -2 * z + 8 * z ^^^ 2 = 0, z)),

   831 shows the equation which has been created in the program by

   832   "      (denom::real) = get_denominator funterm;" ^ (*get_denominator*)

   833   "      (equ::bool) = (denom = (0::real));" ^

   834 # 'get_denominator' has been evaluated successfully, but not factors_from_solution.

   835 So we stepwise compare with an analogous case, get_denominator

   836 successfully done above: We know that LIP evaluates expressions in the

   837 program by use of the "srls", so we

   838 # try to get the original srls

   840   val {srls, ...} = get_met ["SignalProcessing","Z_Transform","inverse"];

   842 # create 2 good example terms

   843   val SOME t1 = parseNEW ctxt "get_denominator ((111::real) / 222)";

   844   val SOME t2 = parseNEW ctxt "factors_from_solution [(z::real) = 1 / 2, z = -1 / 4]";

   846 # rewrite the terms using srls

   847   rewrite_set_ thy true srls t1;

   848   rewrite_set_ thy true srls t2;

   850 and we see a difference: t1 gives SOME, t2 gives NONE.

   851 Now we look at the srls:

   852   val srls = Rls {id="srls_InverseZTransform",

   853     :

   854     rules =

   855       [

   856         :

   857         Calc("Rational.get_numerator",

   858           eval_get_numerator "Rational.get_numerator"),

   859         Calc("Partial_Fractions.factors_from_solution",

   860           eval_factors_from_solution "Partial_Fractions.factors_from_solution")

   861       ],

   862     :

   864 Here everthing is perfect. So the error can only be in the SML code of eval_factors_from_solution.

   865 We try to check the code with an existing test; since the code is in

   867   src/Tools/isac/Knowledge/Partial_Fractions.thy

   869 the test should be in

   871   test/Tools/isac/Knowledge/partial_fractions.sml

   873 -------------------------------------------------------------------------------

   874 After updating the function get_factors_from solution to a new version and

   875 putting a testcase to Partial_Fractions.sml we tried again to evaluate the

   876 term with the same result.

   877 We opened the test Test_Isac.thy and saw that everything is working fine.

   878 Also we checked that the test partial_fractions.sml is used in Test_Isac.thy

   880 -->  use "Knowledge/partial_fractions.sml"

   882 and Partial_Fractions.thy is part is part of isac by evaluating

   884 val thy = \hyperlink{theory.Isac}{\mbox{\isa{Isac}}};

   886 after rebuilding isac again it worked%

   887 \end{isamarkuptext}%

   888 \isamarkuptrue%

   889 %

   890 \isamarkupsubsubsection{build expression%

   891 }

   892 \isamarkuptrue%

   893 %

   894 \begin{isamarkuptext}%

   895 in isac's CTP-based programming language: let s_1 = Take numerator / (s_1 * s_2)%

   896 \end{isamarkuptext}%

   897 \isamarkuptrue%

   898 %

   899 \isadelimML

   900 %

   901 \endisadelimML

   902 %

   903 \isatagML

   904 \isacommand{ML}\isamarkupfalse%

   905 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

   906 {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}The\ Main\ Denominator\ is\ the\ multiplikation\ of\ the\ partial\ fraction\ denominators{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

   907 val\ denominator{\isaliteral{27}{\isacharprime}}\ {\isaliteral{3D}{\isacharequal}}\ HOLogic{\isaliteral{2E}{\isachardot}}mk{\isaliteral{5F}{\isacharunderscore}}binop\ {\isaliteral{22}{\isachardoublequote}}Groups{\isaliteral{2E}{\isachardot}}times{\isaliteral{5F}{\isacharunderscore}}class{\isaliteral{2E}{\isachardot}}times{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{28}{\isacharparenleft}}s{\isaliteral{5F}{\isacharunderscore}}{\isadigit{1}}{\isaliteral{27}{\isacharprime}}{\isaliteral{2C}{\isacharcomma}}\ s{\isaliteral{5F}{\isacharunderscore}}{\isadigit{2}}{\isaliteral{27}{\isacharprime}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3B}{\isacharsemicolon}}\isanewline

   908 val\ SOME\ numerator\ {\isaliteral{3D}{\isacharequal}}\ parseNEW\ ctxt\ {\isaliteral{22}{\isachardoublequote}}{\isadigit{3}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}real{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

   909 \isanewline

   910 val\ expr{\isaliteral{27}{\isacharprime}}\ {\isaliteral{3D}{\isacharequal}}\ HOLogic{\isaliteral{2E}{\isachardot}}mk{\isaliteral{5F}{\isacharunderscore}}binop\ {\isaliteral{22}{\isachardoublequote}}Rings{\isaliteral{2E}{\isachardot}}inverse{\isaliteral{5F}{\isacharunderscore}}class{\isaliteral{2E}{\isachardot}}divide{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{28}{\isacharparenleft}}numerator{\isaliteral{2C}{\isacharcomma}}\ denominator{\isaliteral{27}{\isacharprime}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

   911 term{\isadigit{2}}str\ expr{\isaliteral{27}{\isacharprime}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

   912 {\isaliteral{2A7D}{\isacharverbatimclose}}%

   913 \endisatagML

   914 {\isafoldML}%

   915 %

   916 \isadelimML

   917 %

   918 \endisadelimML

   919 %

   920 \isamarkupsubsubsection{Ansatz - create partial fractions out of our expression%

   921 }

   922 \isamarkuptrue%

   923 %

   924 \isadelimML

   925 %

   926 \endisadelimML

   927 %

   928 \isatagML

   929 \isacommand{ML}\isamarkupfalse%

   930 \ {\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}}%

   931 \endisatagML

   932 {\isafoldML}%

   933 %

   934 \isadelimML

   935 %

   936 \endisadelimML

   937 \isanewline

   938 \isanewline

   939 \isacommand{axiomatization}\isamarkupfalse%

   940 \ \isakeyword{where}\isanewline

   941 \ \ ansatz{\isadigit{2}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}n\ {\isaliteral{2F}{\isacharslash}}\ {\isaliteral{28}{\isacharparenleft}}a{\isaliteral{2A}{\isacharasterisk}}b{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ A{\isaliteral{2F}{\isacharslash}}a\ {\isaliteral{2B}{\isacharplus}}\ B{\isaliteral{2F}{\isacharslash}}{\isaliteral{28}{\isacharparenleft}}b{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}real{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{and}\isanewline

   942 \ \ multiply{\isaliteral{5F}{\isacharunderscore}}eq{\isadigit{2}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{28}{\isacharparenleft}}n{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}real{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2F}{\isacharslash}}\ {\isaliteral{28}{\isacharparenleft}}a{\isaliteral{2A}{\isacharasterisk}}b{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ A{\isaliteral{2F}{\isacharslash}}a\ {\isaliteral{2B}{\isacharplus}}\ B{\isaliteral{2F}{\isacharslash}}b{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}a{\isaliteral{2A}{\isacharasterisk}}b{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{28}{\isacharparenleft}}n\ \ {\isaliteral{2F}{\isacharslash}}\ {\isaliteral{28}{\isacharparenleft}}a{\isaliteral{2A}{\isacharasterisk}}b{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ a{\isaliteral{2A}{\isacharasterisk}}b{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{28}{\isacharparenleft}}A{\isaliteral{2F}{\isacharslash}}a\ {\isaliteral{2B}{\isacharplus}}\ B{\isaliteral{2F}{\isacharslash}}b{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}real{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\ \ \isanewline

   943 %

   944 \isadelimML

   945 \isanewline

   946 %

   947 \endisadelimML

   948 %

   949 \isatagML

   950 \isacommand{ML}\isamarkupfalse%

   951 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

   952 {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}we\ use\ our\ ansatz{\isadigit{2}}\ to\ rewrite\ our\ expression\ and\ get\ an\ equilation\ with\ our\ expression\ on\ the\ left\ and\ the\ partial\ fractions\ of\ it\ on\ the\ right\ side{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

   953 val\ SOME\ {\isaliteral{28}{\isacharparenleft}}t{\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ rewrite{\isaliteral{5F}{\isacharunderscore}}\ %

   954 \isaantiq

   955 theory\ Isac{}%

   956 \endisaantiq

   957 \ e{\isaliteral{5F}{\isacharunderscore}}rew{\isaliteral{5F}{\isacharunderscore}}ord\ e{\isaliteral{5F}{\isacharunderscore}}rls\ false\ %

   958 \isaantiq

   959 thm\ ansatz{\isadigit{2}}{}%

   960 \endisaantiq

   961 \ expr{\isaliteral{27}{\isacharprime}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

   962 term{\isadigit{2}}str\ t{\isadigit{1}}{\isaliteral{3B}{\isacharsemicolon}}\ atomty\ t{\isadigit{1}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

   963 val\ eq{\isadigit{1}}\ {\isaliteral{3D}{\isacharequal}}\ HOLogic{\isaliteral{2E}{\isachardot}}mk{\isaliteral{5F}{\isacharunderscore}}eq\ {\isaliteral{28}{\isacharparenleft}}expr{\isaliteral{27}{\isacharprime}}{\isaliteral{2C}{\isacharcomma}}\ t{\isadigit{1}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

   964 term{\isadigit{2}}str\ eq{\isadigit{1}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

   965 {\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline

   966 \isacommand{ML}\isamarkupfalse%

   967 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

   968 {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}eliminate\ the\ demoninators\ by\ multiplying\ the\ left\ and\ the\ right\ side\ with\ the\ main\ denominator{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

   969 val\ SOME\ {\isaliteral{28}{\isacharparenleft}}eq{\isadigit{2}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ rewrite{\isaliteral{5F}{\isacharunderscore}}\ %

   970 \isaantiq

   971 theory\ Isac{}%

   972 \endisaantiq

   973 \ e{\isaliteral{5F}{\isacharunderscore}}rew{\isaliteral{5F}{\isacharunderscore}}ord\ e{\isaliteral{5F}{\isacharunderscore}}rls\ false\ %

   974 \isaantiq

   975 thm\ multiply{\isaliteral{5F}{\isacharunderscore}}eq{\isadigit{2}}{}%

   976 \endisaantiq

   977 \ eq{\isadigit{1}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

   978 term{\isadigit{2}}str\ eq{\isadigit{2}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

   979 {\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline

   980 \isacommand{ML}\isamarkupfalse%

   981 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

   982 {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}simplificatoin{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

   983 val\ SOME\ {\isaliteral{28}{\isacharparenleft}}eq{\isadigit{3}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ rewrite{\isaliteral{5F}{\isacharunderscore}}set{\isaliteral{5F}{\isacharunderscore}}\ %

   984 \isaantiq

   985 theory\ Isac{}%

   986 \endisaantiq

   987 \ false\ norm{\isaliteral{5F}{\isacharunderscore}}Rational\ eq{\isadigit{2}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

   988 term{\isadigit{2}}str\ eq{\isadigit{3}}{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{3F}{\isacharquery}}A\ {\isaliteral{3F}{\isacharquery}}B\ not\ simplified{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

   989 {\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline

   990 \isacommand{ML}\isamarkupfalse%

   991 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

   992 val\ SOME\ fract{\isadigit{1}}\ {\isaliteral{3D}{\isacharequal}}\isanewline

   993 \ \ parseNEW\ ctxt\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{1}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{2}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{2D}{\isacharminus}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{1}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{4}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}A\ {\isaliteral{2F}{\isacharslash}}\ {\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{1}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{2}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2B}{\isacharplus}}\ B\ {\isaliteral{2F}{\isacharslash}}\ {\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{2D}{\isacharminus}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{1}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{4}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}A\ B\ {\isaliteral{21}{\isacharbang}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

   994 val\ SOME\ {\isaliteral{28}{\isacharparenleft}}fract{\isadigit{2}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ rewrite{\isaliteral{5F}{\isacharunderscore}}set{\isaliteral{5F}{\isacharunderscore}}\ %

   995 \isaantiq

   996 theory\ Isac{}%

   997 \endisaantiq

   998 \ false\ norm{\isaliteral{5F}{\isacharunderscore}}Rational\ fract{\isadigit{1}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

   999 term{\isadigit{2}}str\ fract{\isadigit{2}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}A\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{2}}\ {\isaliteral{2A}{\isacharasterisk}}\ B\ {\isaliteral{2B}{\isacharplus}}\ {\isadigit{4}}\ {\isaliteral{2A}{\isacharasterisk}}\ A\ {\isaliteral{2A}{\isacharasterisk}}\ z\ {\isaliteral{2B}{\isacharplus}}\ {\isadigit{4}}\ {\isaliteral{2A}{\isacharasterisk}}\ B\ {\isaliteral{2A}{\isacharasterisk}}\ z{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{4}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1000 {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}term{\isadigit{2}}str\ fract{\isadigit{2}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{22}{\isachardoublequote}}A\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{1}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{4}}\ {\isaliteral{2B}{\isacharplus}}\ z{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2B}{\isacharplus}}\ B\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2D}{\isacharminus}}{\isadigit{1}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{2}}\ {\isaliteral{2B}{\isacharplus}}\ z{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}\ would\ be\ more\ traditional{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1001 {\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline

  1002 \isacommand{ML}\isamarkupfalse%

  1003 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

  1004 val\ {\isaliteral{28}{\isacharparenleft}}numerator{\isaliteral{2C}{\isacharcomma}}\ denominator{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ HOLogic{\isaliteral{2E}{\isachardot}}dest{\isaliteral{5F}{\isacharunderscore}}eq\ eq{\isadigit{3}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1005 val\ eq{\isadigit{3}}{\isaliteral{27}{\isacharprime}}\ {\isaliteral{3D}{\isacharequal}}\ HOLogic{\isaliteral{2E}{\isachardot}}mk{\isaliteral{5F}{\isacharunderscore}}eq\ {\isaliteral{28}{\isacharparenleft}}numerator{\isaliteral{2C}{\isacharcomma}}\ fract{\isadigit{1}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}A\ B\ {\isaliteral{21}{\isacharbang}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1006 term{\isadigit{2}}str\ eq{\isadigit{3}}{\isaliteral{27}{\isacharprime}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1007 {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}MANDATORY{\isaliteral{3A}{\isacharcolon}}\ simplify\ {\isaliteral{28}{\isacharparenleft}}and\ remove\ denominator{\isaliteral{29}{\isacharparenright}}\ otherwise\ {\isadigit{3}}\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{0}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1008 val\ SOME\ {\isaliteral{28}{\isacharparenleft}}eq{\isadigit{3}}{\isaliteral{27}{\isacharprime}}{\isaliteral{27}{\isacharprime}}\ {\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ rewrite{\isaliteral{5F}{\isacharunderscore}}set{\isaliteral{5F}{\isacharunderscore}}\ %

  1009 \isaantiq

  1010 theory\ Isac{}%

  1011 \endisaantiq

  1012 \ false\ norm{\isaliteral{5F}{\isacharunderscore}}Rational\ eq{\isadigit{3}}{\isaliteral{27}{\isacharprime}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1013 term{\isadigit{2}}str\ eq{\isadigit{3}}{\isaliteral{27}{\isacharprime}}{\isaliteral{27}{\isacharprime}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1014 {\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline

  1015 \isacommand{ML}\isamarkupfalse%

  1016 \ {\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}}%

  1017 \endisatagML

  1018 {\isafoldML}%

  1019 %

  1020 \isadelimML

  1021 %

  1022 \endisadelimML

  1023 %

  1024 \isamarkupsubsubsection{Build a rule-set for ansatz%

  1025 }

  1026 \isamarkuptrue%

  1027 %

  1028 \begin{isamarkuptext}%

  1029 the "ansatz" rules violate the principle that each variable on

  1030   the right-hand-side must also occur on the left-hand-side of the rule:

  1031   A, B, etc don't.

  1032   Thus the rewriter marks these variables with question marks: ?A, ?B, etc.

  1033   These question marks can be dropped by "fun drop_questionmarks".%

  1034 \end{isamarkuptext}%

  1035 \isamarkuptrue%

  1036 %

  1037 \isadelimML

  1038 %

  1039 \endisadelimML

  1040 %

  1041 \isatagML

  1042 \isacommand{ML}\isamarkupfalse%

  1043 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

  1044 val\ ansatz{\isaliteral{5F}{\isacharunderscore}}rls\ {\isaliteral{3D}{\isacharequal}}\ prep{\isaliteral{5F}{\isacharunderscore}}rls{\isaliteral{28}{\isacharparenleft}}\isanewline

  1045 \ \ Rls\ {\isaliteral{7B}{\isacharbraceleft}}id\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{22}{\isachardoublequote}}ansatz{\isaliteral{5F}{\isacharunderscore}}rls{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ preconds\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ rew{\isaliteral{5F}{\isacharunderscore}}ord\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}dummy{\isaliteral{5F}{\isacharunderscore}}ord{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}dummy{\isaliteral{5F}{\isacharunderscore}}ord{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\ \isanewline

  1046 	\ \ erls\ {\isaliteral{3D}{\isacharequal}}\ e{\isaliteral{5F}{\isacharunderscore}}rls{\isaliteral{2C}{\isacharcomma}}\ srls\ {\isaliteral{3D}{\isacharequal}}\ Erls{\isaliteral{2C}{\isacharcomma}}\ calc\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\isanewline

  1047 	\ \ rules\ {\isaliteral{3D}{\isacharequal}}\ \isanewline

  1048 	\ \ \ {\isaliteral{5B}{\isacharbrackleft}}Thm\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}ansatz{\isadigit{2}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}num{\isaliteral{5F}{\isacharunderscore}}str\ %

  1049 \isaantiq

  1050 thm\ ansatz{\isadigit{2}}{}%

  1051 \endisaantiq

  1052 {\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\isanewline

  1053 	\ \ \ \ Thm\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}multiply{\isaliteral{5F}{\isacharunderscore}}eq{\isadigit{2}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}num{\isaliteral{5F}{\isacharunderscore}}str\ %

  1054 \isaantiq

  1055 thm\ multiply{\isaliteral{5F}{\isacharunderscore}}eq{\isadigit{2}}{}%

  1056 \endisaantiq

  1057 {\isaliteral{29}{\isacharparenright}}\isanewline

  1058 	\ \ \ {\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ \isanewline

  1059 	\ scr\ {\isaliteral{3D}{\isacharequal}}\ EmptyScr{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1060 {\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline

  1061 \isacommand{ML}\isamarkupfalse%

  1062 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

  1063 val\ SOME\ {\isaliteral{28}{\isacharparenleft}}ttttt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ rewrite{\isaliteral{5F}{\isacharunderscore}}set{\isaliteral{5F}{\isacharunderscore}}\ %

  1064 \isaantiq

  1065 theory\ Isac{}%

  1066 \endisaantiq

  1067 \ false\ ansatz{\isaliteral{5F}{\isacharunderscore}}rls\ expr{\isaliteral{27}{\isacharprime}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1068 {\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline

  1069 \isacommand{ML}\isamarkupfalse%

  1070 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

  1071 term{\isadigit{2}}str\ expr{\isaliteral{27}{\isacharprime}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{22}{\isachardoublequote}}{\isadigit{3}}\ {\isaliteral{2F}{\isacharslash}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{1}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{2}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{2D}{\isacharminus}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{1}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{4}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1072 term{\isadigit{2}}str\ ttttt\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{3F}{\isacharquery}}A\ {\isaliteral{2F}{\isacharslash}}\ {\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{1}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{2}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{3F}{\isacharquery}}B\ {\isaliteral{2F}{\isacharslash}}\ {\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{2D}{\isacharminus}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{1}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{4}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1073 {\isaliteral{2A7D}{\isacharverbatimclose}}%

  1074 \endisatagML

  1075 {\isafoldML}%

  1076 %

  1077 \isadelimML

  1078 %

  1079 \endisadelimML

  1080 %

  1081 \isamarkupsubsubsection{get first koeffizient%

  1082 }

  1083 \isamarkuptrue%

  1084 %

  1085 \isadelimML

  1086 %

  1087 \endisadelimML

  1088 %

  1089 \isatagML

  1090 \isacommand{ML}\isamarkupfalse%

  1091 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

  1092 {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}substitude\ z\ with\ the\ first\ zeropoint\ to\ get\ A{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1093 val\ SOME\ {\isaliteral{28}{\isacharparenleft}}eq{\isadigit{4}}{\isaliteral{5F}{\isacharunderscore}}{\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ rewrite{\isaliteral{5F}{\isacharunderscore}}terms{\isaliteral{5F}{\isacharunderscore}}\ %

  1094 \isaantiq

  1095 theory\ Isac{}%

  1096 \endisaantiq

  1097 \ e{\isaliteral{5F}{\isacharunderscore}}rew{\isaliteral{5F}{\isacharunderscore}}ord\ e{\isaliteral{5F}{\isacharunderscore}}rls\ {\isaliteral{5B}{\isacharbrackleft}}s{\isaliteral{5F}{\isacharunderscore}}{\isadigit{1}}{\isaliteral{5D}{\isacharbrackright}}\ eq{\isadigit{3}}{\isaliteral{27}{\isacharprime}}{\isaliteral{27}{\isacharprime}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1098 term{\isadigit{2}}str\ eq{\isadigit{4}}{\isaliteral{5F}{\isacharunderscore}}{\isadigit{1}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1099 \isanewline

  1100 val\ SOME\ {\isaliteral{28}{\isacharparenleft}}eq{\isadigit{4}}{\isaliteral{5F}{\isacharunderscore}}{\isadigit{2}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ rewrite{\isaliteral{5F}{\isacharunderscore}}set{\isaliteral{5F}{\isacharunderscore}}\ %

  1101 \isaantiq

  1102 theory\ Isac{}%

  1103 \endisaantiq

  1104 \ false\ norm{\isaliteral{5F}{\isacharunderscore}}Rational\ eq{\isadigit{4}}{\isaliteral{5F}{\isacharunderscore}}{\isadigit{1}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1105 term{\isadigit{2}}str\ eq{\isadigit{4}}{\isaliteral{5F}{\isacharunderscore}}{\isadigit{2}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1106 \isanewline

  1107 val\ fmz\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}equality\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{3}}\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{3}}\ {\isaliteral{2A}{\isacharasterisk}}\ A\ {\isaliteral{2F}{\isacharslash}}\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{4}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}real{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}solveFor\ A{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}solutions\ L{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1108 val\ {\isaliteral{28}{\isacharparenleft}}dI{\isaliteral{27}{\isacharprime}}{\isaliteral{2C}{\isacharcomma}}pI{\isaliteral{27}{\isacharprime}}{\isaliteral{2C}{\isacharcomma}}mI{\isaliteral{27}{\isacharprime}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}Isac{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}univariate{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}equation{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}no{\isaliteral{5F}{\isacharunderscore}}met{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1109 {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}solve\ the\ simple\ linear\ equilation\ for\ A\ TODO{\isaliteral{3A}{\isacharcolon}}\ return\ eq{\isaliteral{2C}{\isacharcomma}}\ not\ list\ of\ eq{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1110 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fa{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ CalcTreeTEST\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{28}{\isacharparenleft}}fmz{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{28}{\isacharparenleft}}dI{\isaliteral{27}{\isacharprime}}{\isaliteral{2C}{\isacharcomma}}pI{\isaliteral{27}{\isacharprime}}{\isaliteral{2C}{\isacharcomma}}mI{\isaliteral{27}{\isacharprime}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1111 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fa{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}Add{\isaliteral{5F}{\isacharunderscore}}Given\ {\isaliteral{22}{\isachardoublequote}}equality\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{3}}\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{3}}\ {\isaliteral{2A}{\isacharasterisk}}\ A\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{4}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1112 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fa{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}\ Add{\isaliteral{5F}{\isacharunderscore}}Given\ {\isaliteral{22}{\isachardoublequote}}solveFor\ A{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1113 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fa{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}Add{\isaliteral{5F}{\isacharunderscore}}Find\ {\isaliteral{22}{\isachardoublequote}}solutions\ L{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1114 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fa{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}Specify{\isaliteral{5F}{\isacharunderscore}}Theory\ {\isaliteral{22}{\isachardoublequote}}Isac{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1115 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fa{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}Specify{\isaliteral{5F}{\isacharunderscore}}Problem\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}normalize{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}polynomial{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ \isanewline

  1116 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}univariate{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}equation{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1117 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fa{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}\ Specify{\isaliteral{5F}{\isacharunderscore}}Method\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}PolyEq{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}normalize{\isaliteral{5F}{\isacharunderscore}}poly{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1118 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fa{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}Apply{\isaliteral{5F}{\isacharunderscore}}Method\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}PolyEq{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}normalize{\isaliteral{5F}{\isacharunderscore}}poly{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1119 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fa{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}Rewrite\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}all{\isaliteral{5F}{\isacharunderscore}}left{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}PolyEq{\isaliteral{2E}{\isachardot}}all{\isaliteral{5F}{\isacharunderscore}}left{\isaliteral{22}{\isachardoublequote}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1120 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fa{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}Rewrite{\isaliteral{5F}{\isacharunderscore}}Set{\isaliteral{5F}{\isacharunderscore}}Inst\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}bdv{\isaliteral{2C}{\isacharcomma}}\ A{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}make{\isaliteral{5F}{\isacharunderscore}}ratpoly{\isaliteral{5F}{\isacharunderscore}}in{\isaliteral{22}{\isachardoublequote}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1121 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fa{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}Rewrite{\isaliteral{5F}{\isacharunderscore}}Set\ {\isaliteral{22}{\isachardoublequote}}polyeq{\isaliteral{5F}{\isacharunderscore}}simplify{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1122 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fa{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1123 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fa{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1124 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fa{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}Add{\isaliteral{5F}{\isacharunderscore}}Given\ {\isaliteral{22}{\isachardoublequote}}equality\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{3}}\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{3}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{4}}\ {\isaliteral{2A}{\isacharasterisk}}\ A\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{0}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1125 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fa{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}Add{\isaliteral{5F}{\isacharunderscore}}Given\ {\isaliteral{22}{\isachardoublequote}}solveFor\ A{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1126 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fa{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}Add{\isaliteral{5F}{\isacharunderscore}}Find\ {\isaliteral{22}{\isachardoublequote}}solutions\ A{\isaliteral{5F}{\isacharunderscore}}i{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1127 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fa{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1128 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fa{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1129 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fa{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1130 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fa{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}Apply{\isaliteral{5F}{\isacharunderscore}}Method\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}PolyEq{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}solve{\isaliteral{5F}{\isacharunderscore}}d{\isadigit{1}}{\isaliteral{5F}{\isacharunderscore}}polyeq{\isaliteral{5F}{\isacharunderscore}}equation{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1131 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fa{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}Rewrite{\isaliteral{5F}{\isacharunderscore}}Set{\isaliteral{5F}{\isacharunderscore}}Inst\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}bdv{\isaliteral{2C}{\isacharcomma}}\ A{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}d{\isadigit{1}}{\isaliteral{5F}{\isacharunderscore}}polyeq{\isaliteral{5F}{\isacharunderscore}}simplify{\isaliteral{22}{\isachardoublequote}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1132 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fa{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}Rewrite{\isaliteral{5F}{\isacharunderscore}}Set\ {\isaliteral{22}{\isachardoublequote}}polyeq{\isaliteral{5F}{\isacharunderscore}}simplify{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1133 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fa{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}Rewrite{\isaliteral{5F}{\isacharunderscore}}Set\ {\isaliteral{22}{\isachardoublequote}}norm{\isaliteral{5F}{\isacharunderscore}}Rational{\isaliteral{5F}{\isacharunderscore}}parenthesized{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1134 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fa{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}Or{\isaliteral{5F}{\isacharunderscore}}to{\isaliteral{5F}{\isacharunderscore}}List{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1135 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fa{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}Check{\isaliteral{5F}{\isacharunderscore}}elementwise\ {\isaliteral{22}{\isachardoublequote}}Assumptions{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1136 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fa{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}Check{\isaliteral{5F}{\isacharunderscore}}Postcond\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}degree{\isaliteral{5F}{\isacharunderscore}}{\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}polynomial{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ \isanewline

  1137 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}univariate{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}equation{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1138 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fa{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}Check{\isaliteral{5F}{\isacharunderscore}}Postcond\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}normalize{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}polynomial{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ \isanewline

  1139 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}univariate{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}equation{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1140 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fa{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}End{\isaliteral{5F}{\isacharunderscore}}Proof{\isaliteral{27}{\isacharprime}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1141 f{\isadigit{2}}str\ fa{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1142 {\isaliteral{2A7D}{\isacharverbatimclose}}%

  1143 \endisatagML

  1144 {\isafoldML}%

  1145 %

  1146 \isadelimML

  1147 %

  1148 \endisadelimML

  1149 %

  1150 \isamarkupsubsubsection{get second koeffizient%

  1151 }

  1152 \isamarkuptrue%

  1153 %

  1154 \isadelimML

  1155 %

  1156 \endisadelimML

  1157 %

  1158 \isatagML

  1159 \isacommand{ML}\isamarkupfalse%

  1160 \ {\isaliteral{7B2A}{\isacharverbatimopen}}thy{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline

  1161 \isanewline

  1162 \isacommand{ML}\isamarkupfalse%

  1163 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

  1164 {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}substitude\ z\ with\ the\ second\ zeropoint\ to\ get\ B{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1165 val\ SOME\ {\isaliteral{28}{\isacharparenleft}}eq{\isadigit{4}}b{\isaliteral{5F}{\isacharunderscore}}{\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ rewrite{\isaliteral{5F}{\isacharunderscore}}terms{\isaliteral{5F}{\isacharunderscore}}\ %

  1166 \isaantiq

  1167 theory\ Isac{}%

  1168 \endisaantiq

  1169 \ e{\isaliteral{5F}{\isacharunderscore}}rew{\isaliteral{5F}{\isacharunderscore}}ord\ e{\isaliteral{5F}{\isacharunderscore}}rls\ {\isaliteral{5B}{\isacharbrackleft}}s{\isaliteral{5F}{\isacharunderscore}}{\isadigit{2}}{\isaliteral{5D}{\isacharbrackright}}\ eq{\isadigit{3}}{\isaliteral{27}{\isacharprime}}{\isaliteral{27}{\isacharprime}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1170 term{\isadigit{2}}str\ eq{\isadigit{4}}b{\isaliteral{5F}{\isacharunderscore}}{\isadigit{1}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1171 \isanewline

  1172 val\ SOME\ {\isaliteral{28}{\isacharparenleft}}eq{\isadigit{4}}b{\isaliteral{5F}{\isacharunderscore}}{\isadigit{2}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ rewrite{\isaliteral{5F}{\isacharunderscore}}set{\isaliteral{5F}{\isacharunderscore}}\ %

  1173 \isaantiq

  1174 theory\ Isac{}%

  1175 \endisaantiq

  1176 \ false\ norm{\isaliteral{5F}{\isacharunderscore}}Rational\ eq{\isadigit{4}}b{\isaliteral{5F}{\isacharunderscore}}{\isadigit{1}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1177 term{\isadigit{2}}str\ eq{\isadigit{4}}b{\isaliteral{5F}{\isacharunderscore}}{\isadigit{2}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1178 {\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline

  1179 \isacommand{ML}\isamarkupfalse%

  1180 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

  1181 {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}solve\ the\ simple\ linear\ equilation\ for\ B\ TODO{\isaliteral{3A}{\isacharcolon}}\ return\ eq{\isaliteral{2C}{\isacharcomma}}\ not\ list\ of\ eq{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1182 val\ fmz\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}equality\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{3}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{3}}\ {\isaliteral{2A}{\isacharasterisk}}\ B\ {\isaliteral{2F}{\isacharslash}}\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{4}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}real{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}solveFor\ B{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}solutions\ L{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1183 val\ {\isaliteral{28}{\isacharparenleft}}dI{\isaliteral{27}{\isacharprime}}{\isaliteral{2C}{\isacharcomma}}pI{\isaliteral{27}{\isacharprime}}{\isaliteral{2C}{\isacharcomma}}mI{\isaliteral{27}{\isacharprime}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}Isac{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}univariate{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}equation{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}no{\isaliteral{5F}{\isacharunderscore}}met{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1184 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fb{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ CalcTreeTEST\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{28}{\isacharparenleft}}fmz{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{28}{\isacharparenleft}}dI{\isaliteral{27}{\isacharprime}}{\isaliteral{2C}{\isacharcomma}}pI{\isaliteral{27}{\isacharprime}}{\isaliteral{2C}{\isacharcomma}}mI{\isaliteral{27}{\isacharprime}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1185 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fb{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1186 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fb{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1187 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fb{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1188 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fb{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1189 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fb{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1190 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fb{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1191 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fb{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1192 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fb{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1193 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fb{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1194 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fb{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1195 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fb{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1196 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fb{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1197 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fb{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1198 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fb{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1199 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fb{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1200 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fb{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1201 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fb{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1202 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fb{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1203 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fb{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1204 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fb{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1205 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fb{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1206 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fb{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1207 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fb{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1208 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fb{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1209 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fb{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1210 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fb{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1211 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}fb{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\ \isanewline

  1212 f{\isadigit{2}}str\ fb{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1213 {\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline

  1214 \isanewline

  1215 \isacommand{ML}\isamarkupfalse%

  1216 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}check\ koeffizients{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1217 if\ f{\isadigit{2}}str\ fa\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5B}{\isacharbrackleft}}A\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{4}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}\ then\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{29}{\isacharparenright}}\ else\ error\ {\isaliteral{22}{\isachardoublequote}}part{\isaliteral{2E}{\isachardot}}fract{\isaliteral{2E}{\isachardot}}\ eq{\isadigit{4}}{\isaliteral{5F}{\isacharunderscore}}{\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1218 if\ f{\isadigit{2}}str\ fb\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5B}{\isacharbrackleft}}B\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{4}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequote}}\ then\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{29}{\isacharparenright}}\ else\ error\ {\isaliteral{22}{\isachardoublequote}}part{\isaliteral{2E}{\isachardot}}fract{\isaliteral{2E}{\isachardot}}\ eq{\isadigit{4}}{\isaliteral{5F}{\isacharunderscore}}{\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1219 {\isaliteral{2A7D}{\isacharverbatimclose}}%

  1220 \endisatagML

  1221 {\isafoldML}%

  1222 %

  1223 \isadelimML

  1224 %

  1225 \endisadelimML

  1226 %

  1227 \isamarkupsubsubsection{substitute expression with solutions%

  1228 }

  1229 \isamarkuptrue%

  1230 %

  1231 \isadelimML

  1232 %

  1233 \endisadelimML

  1234 %

  1235 \isatagML

  1236 \isacommand{ML}\isamarkupfalse%

  1237 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

  1238 {\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline

  1239 \isacommand{ML}\isamarkupfalse%

  1240 \ {\isaliteral{7B2A}{\isacharverbatimopen}}thy{\isaliteral{2A7D}{\isacharverbatimclose}}%

  1241 \endisatagML

  1242 {\isafoldML}%

  1243 %

  1244 \isadelimML

  1245 %

  1246 \endisadelimML

  1247 %

  1248 \isamarkupsection{Implement the Specification and the Method \label{spec-meth}%

  1249 }

  1250 \isamarkuptrue%

  1251 %

  1252 \begin{isamarkuptext}%

  1253 ==============================================%

  1254 \end{isamarkuptext}%

  1255 \isamarkuptrue%

  1256 %

  1257 \isamarkupsubsection{Define the Field Descriptions for the specification%

  1258 }

  1259 \isamarkuptrue%

  1260 \isacommand{consts}\isamarkupfalse%

  1261 \isanewline

  1262 \ \ filterExpression\ \ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}bool\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\ una{\isaliteral{22}{\isachardoublequoteclose}}\isanewline

  1263 \ \ stepResponse\ \ \ \ \ \ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}bool\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\ una{\isaliteral{22}{\isachardoublequoteclose}}%

  1264 \isamarkupsubsection{Define the Specification%

  1265 }

  1266 \isamarkuptrue%

  1267 %

  1268 \isadelimML

  1269 %

  1270 \endisadelimML

  1271 %

  1272 \isatagML

  1273 \isacommand{ML}\isamarkupfalse%

  1274 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

  1275 store{\isaliteral{5F}{\isacharunderscore}}pbt\isanewline

  1276 \ {\isaliteral{28}{\isacharparenleft}}prep{\isaliteral{5F}{\isacharunderscore}}pbt\ thy\ {\isaliteral{22}{\isachardoublequote}}pbl{\isaliteral{5F}{\isacharunderscore}}SP{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ e{\isaliteral{5F}{\isacharunderscore}}pblID\isanewline

  1277 \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}SignalProcessing{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ e{\isaliteral{5F}{\isacharunderscore}}rls{\isaliteral{2C}{\isacharcomma}}\ NONE{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1278 store{\isaliteral{5F}{\isacharunderscore}}pbt\isanewline

  1279 \ {\isaliteral{28}{\isacharparenleft}}prep{\isaliteral{5F}{\isacharunderscore}}pbt\ thy\ {\isaliteral{22}{\isachardoublequote}}pbl{\isaliteral{5F}{\isacharunderscore}}SP{\isaliteral{5F}{\isacharunderscore}}Ztrans{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ e{\isaliteral{5F}{\isacharunderscore}}pblID\isanewline

  1280 \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}Z{\isaliteral{5F}{\isacharunderscore}}Transform{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}SignalProcessing{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ e{\isaliteral{5F}{\isacharunderscore}}rls{\isaliteral{2C}{\isacharcomma}}\ NONE{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1281 {\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline

  1282 \isacommand{ML}\isamarkupfalse%

  1283 \ {\isaliteral{7B2A}{\isacharverbatimopen}}thy{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline

  1284 \isacommand{ML}\isamarkupfalse%

  1285 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

  1286 store{\isaliteral{5F}{\isacharunderscore}}pbt\isanewline

  1287 \ {\isaliteral{28}{\isacharparenleft}}prep{\isaliteral{5F}{\isacharunderscore}}pbt\ thy\ {\isaliteral{22}{\isachardoublequote}}pbl{\isaliteral{5F}{\isacharunderscore}}SP{\isaliteral{5F}{\isacharunderscore}}Ztrans{\isaliteral{5F}{\isacharunderscore}}inv{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ e{\isaliteral{5F}{\isacharunderscore}}pblID\isanewline

  1288 \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}inverse{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}Z{\isaliteral{5F}{\isacharunderscore}}Transform{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}SignalProcessing{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\isanewline

  1289 \ \ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{23}{\isacharhash}}Given{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{2C}{\isacharcomma}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}filterExpression\ X{\isaliteral{5F}{\isacharunderscore}}eq{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\isanewline

  1290 \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{23}{\isacharhash}}Find{\isaliteral{22}{\isachardoublequote}}\ \ {\isaliteral{2C}{\isacharcomma}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}stepResponse\ n{\isaliteral{5F}{\isacharunderscore}}eq{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1291 \ \ {\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\isanewline

  1292 \ \ append{\isaliteral{5F}{\isacharunderscore}}rls\ {\isaliteral{22}{\isachardoublequote}}e{\isaliteral{5F}{\isacharunderscore}}rls{\isaliteral{22}{\isachardoublequote}}\ e{\isaliteral{5F}{\isacharunderscore}}rls\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}for\ preds\ in\ where{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ NONE{\isaliteral{2C}{\isacharcomma}}\ \isanewline

  1293 \ \ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}SignalProcessing{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}Z{\isaliteral{5F}{\isacharunderscore}}Transform{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}inverse{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1294 \isanewline

  1295 show{\isaliteral{5F}{\isacharunderscore}}ptyps{\isaliteral{28}{\isacharparenleft}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1296 get{\isaliteral{5F}{\isacharunderscore}}pbt\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}inverse{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}Z{\isaliteral{5F}{\isacharunderscore}}Transform{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}SignalProcessing{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1297 {\isaliteral{2A7D}{\isacharverbatimclose}}%

  1298 \endisatagML

  1299 {\isafoldML}%

  1300 %

  1301 \isadelimML

  1302 %

  1303 \endisadelimML

  1304 %

  1305 \isamarkupsubsection{Define Name and Signature for the Method%

  1306 }

  1307 \isamarkuptrue%

  1308 \isacommand{consts}\isamarkupfalse%

  1309 \isanewline

  1310 \ \ InverseZTransform\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{5B}{\isacharbrackleft}}bool{\isaliteral{2C}{\isacharcomma}}\ bool{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{3E}{\isachargreater}}\ bool{\isaliteral{22}{\isachardoublequoteclose}}\isanewline

  1311 \ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequoteopen}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{28}{\isacharparenleft}}Script\ InverseZTransform\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5F}{\isacharunderscore}}\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2F}{\isacharslash}}{\isaliteral{2F}{\isacharslash}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\ {\isadigit{9}}{\isaliteral{29}{\isacharparenright}}%

  1312 \isamarkupsubsection{Setup Parent Nodes in Hierarchy of Method%

  1313 }

  1314 \isamarkuptrue%

  1315 %

  1316 \isadelimML

  1317 %

  1318 \endisadelimML

  1319 %

  1320 \isatagML

  1321 \isacommand{ML}\isamarkupfalse%

  1322 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

  1323 store{\isaliteral{5F}{\isacharunderscore}}met\isanewline

  1324 \ {\isaliteral{28}{\isacharparenleft}}prep{\isaliteral{5F}{\isacharunderscore}}met\ thy\ {\isaliteral{22}{\isachardoublequote}}met{\isaliteral{5F}{\isacharunderscore}}SP{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ e{\isaliteral{5F}{\isacharunderscore}}metID\isanewline

  1325 \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}SignalProcessing{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\isanewline

  1326 \ \ \ {\isaliteral{7B}{\isacharbraceleft}}rew{\isaliteral{5F}{\isacharunderscore}}ord{\isaliteral{27}{\isacharprime}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{22}{\isachardoublequote}}tless{\isaliteral{5F}{\isacharunderscore}}true{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ rls{\isaliteral{27}{\isacharprime}}{\isaliteral{3D}{\isacharequal}}\ e{\isaliteral{5F}{\isacharunderscore}}rls{\isaliteral{2C}{\isacharcomma}}\ calc\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ srls\ {\isaliteral{3D}{\isacharequal}}\ e{\isaliteral{5F}{\isacharunderscore}}rls{\isaliteral{2C}{\isacharcomma}}\ prls\ {\isaliteral{3D}{\isacharequal}}\ e{\isaliteral{5F}{\isacharunderscore}}rls{\isaliteral{2C}{\isacharcomma}}\isanewline

  1327 \ \ \ \ crls\ {\isaliteral{3D}{\isacharequal}}\ e{\isaliteral{5F}{\isacharunderscore}}rls{\isaliteral{2C}{\isacharcomma}}\ nrls\ {\isaliteral{3D}{\isacharequal}}\ e{\isaliteral{5F}{\isacharunderscore}}rls{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}empty{\isaliteral{5F}{\isacharunderscore}}script{\isaliteral{22}{\isachardoublequote}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1328 store{\isaliteral{5F}{\isacharunderscore}}met\isanewline

  1329 \ {\isaliteral{28}{\isacharparenleft}}prep{\isaliteral{5F}{\isacharunderscore}}met\ thy\ {\isaliteral{22}{\isachardoublequote}}met{\isaliteral{5F}{\isacharunderscore}}SP{\isaliteral{5F}{\isacharunderscore}}Ztrans{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ e{\isaliteral{5F}{\isacharunderscore}}metID\isanewline

  1330 \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}SignalProcessing{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}Z{\isaliteral{5F}{\isacharunderscore}}Transform{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\isanewline

  1331 \ \ \ {\isaliteral{7B}{\isacharbraceleft}}rew{\isaliteral{5F}{\isacharunderscore}}ord{\isaliteral{27}{\isacharprime}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{22}{\isachardoublequote}}tless{\isaliteral{5F}{\isacharunderscore}}true{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ rls{\isaliteral{27}{\isacharprime}}{\isaliteral{3D}{\isacharequal}}\ e{\isaliteral{5F}{\isacharunderscore}}rls{\isaliteral{2C}{\isacharcomma}}\ calc\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ srls\ {\isaliteral{3D}{\isacharequal}}\ e{\isaliteral{5F}{\isacharunderscore}}rls{\isaliteral{2C}{\isacharcomma}}\ prls\ {\isaliteral{3D}{\isacharequal}}\ e{\isaliteral{5F}{\isacharunderscore}}rls{\isaliteral{2C}{\isacharcomma}}\isanewline

  1332 \ \ \ \ crls\ {\isaliteral{3D}{\isacharequal}}\ e{\isaliteral{5F}{\isacharunderscore}}rls{\isaliteral{2C}{\isacharcomma}}\ nrls\ {\isaliteral{3D}{\isacharequal}}\ e{\isaliteral{5F}{\isacharunderscore}}rls{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}empty{\isaliteral{5F}{\isacharunderscore}}script{\isaliteral{22}{\isachardoublequote}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1333 {\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline

  1334 \isacommand{ML}\isamarkupfalse%

  1335 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

  1336 store{\isaliteral{5F}{\isacharunderscore}}met\isanewline

  1337 \ {\isaliteral{28}{\isacharparenleft}}prep{\isaliteral{5F}{\isacharunderscore}}met\ thy\ {\isaliteral{22}{\isachardoublequote}}met{\isaliteral{5F}{\isacharunderscore}}SP{\isaliteral{5F}{\isacharunderscore}}Ztrans{\isaliteral{5F}{\isacharunderscore}}inv{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ e{\isaliteral{5F}{\isacharunderscore}}metID\isanewline

  1338 \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}SignalProcessing{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}Z{\isaliteral{5F}{\isacharunderscore}}Transform{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}inverse{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ \isanewline

  1339 \ \ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{23}{\isacharhash}}Given{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{2C}{\isacharcomma}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}filterExpression\ X{\isaliteral{5F}{\isacharunderscore}}eq{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\isanewline

  1340 \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{23}{\isacharhash}}Find{\isaliteral{22}{\isachardoublequote}}\ \ {\isaliteral{2C}{\isacharcomma}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}stepResponse\ n{\isaliteral{5F}{\isacharunderscore}}eq{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1341 \ \ {\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\isanewline

  1342 \ \ \ {\isaliteral{7B}{\isacharbraceleft}}rew{\isaliteral{5F}{\isacharunderscore}}ord{\isaliteral{27}{\isacharprime}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{22}{\isachardoublequote}}tless{\isaliteral{5F}{\isacharunderscore}}true{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ rls{\isaliteral{27}{\isacharprime}}{\isaliteral{3D}{\isacharequal}}\ e{\isaliteral{5F}{\isacharunderscore}}rls{\isaliteral{2C}{\isacharcomma}}\ calc\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ srls\ {\isaliteral{3D}{\isacharequal}}\ e{\isaliteral{5F}{\isacharunderscore}}rls{\isaliteral{2C}{\isacharcomma}}\ prls\ {\isaliteral{3D}{\isacharequal}}\ e{\isaliteral{5F}{\isacharunderscore}}rls{\isaliteral{2C}{\isacharcomma}}\isanewline

  1343 \ \ \ \ crls\ {\isaliteral{3D}{\isacharequal}}\ e{\isaliteral{5F}{\isacharunderscore}}rls{\isaliteral{2C}{\isacharcomma}}\ nrls\ {\isaliteral{3D}{\isacharequal}}\ e{\isaliteral{5F}{\isacharunderscore}}rls{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{2C}{\isacharcomma}}\isanewline

  1344 \ \ {\isaliteral{22}{\isachardoublequote}}empty{\isaliteral{5F}{\isacharunderscore}}script{\isaliteral{22}{\isachardoublequote}}\isanewline

  1345 \ {\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1346 {\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline

  1347 \isacommand{ML}\isamarkupfalse%

  1348 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

  1349 store{\isaliteral{5F}{\isacharunderscore}}met\isanewline

  1350 \ {\isaliteral{28}{\isacharparenleft}}prep{\isaliteral{5F}{\isacharunderscore}}met\ thy\ {\isaliteral{22}{\isachardoublequote}}met{\isaliteral{5F}{\isacharunderscore}}SP{\isaliteral{5F}{\isacharunderscore}}Ztrans{\isaliteral{5F}{\isacharunderscore}}inv{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ e{\isaliteral{5F}{\isacharunderscore}}metID\isanewline

  1351 \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}SignalProcessing{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}Z{\isaliteral{5F}{\isacharunderscore}}Transform{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}inverse{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ \isanewline

  1352 \ \ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{23}{\isacharhash}}Given{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{2C}{\isacharcomma}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}filterExpression\ X{\isaliteral{5F}{\isacharunderscore}}eq{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\isanewline

  1353 \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{23}{\isacharhash}}Find{\isaliteral{22}{\isachardoublequote}}\ \ {\isaliteral{2C}{\isacharcomma}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}stepResponse\ n{\isaliteral{5F}{\isacharunderscore}}eq{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1354 \ \ {\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\isanewline

  1355 \ \ \ {\isaliteral{7B}{\isacharbraceleft}}rew{\isaliteral{5F}{\isacharunderscore}}ord{\isaliteral{27}{\isacharprime}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{22}{\isachardoublequote}}tless{\isaliteral{5F}{\isacharunderscore}}true{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ rls{\isaliteral{27}{\isacharprime}}{\isaliteral{3D}{\isacharequal}}\ e{\isaliteral{5F}{\isacharunderscore}}rls{\isaliteral{2C}{\isacharcomma}}\ calc\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ srls\ {\isaliteral{3D}{\isacharequal}}\ e{\isaliteral{5F}{\isacharunderscore}}rls{\isaliteral{2C}{\isacharcomma}}\ prls\ {\isaliteral{3D}{\isacharequal}}\ e{\isaliteral{5F}{\isacharunderscore}}rls{\isaliteral{2C}{\isacharcomma}}\isanewline

  1356 \ \ \ \ crls\ {\isaliteral{3D}{\isacharequal}}\ e{\isaliteral{5F}{\isacharunderscore}}rls{\isaliteral{2C}{\isacharcomma}}\ nrls\ {\isaliteral{3D}{\isacharequal}}\ e{\isaliteral{5F}{\isacharunderscore}}rls{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{2C}{\isacharcomma}}\isanewline

  1357 \ \ {\isaliteral{22}{\isachardoublequote}}Script\ InverseZTransform\ {\isaliteral{28}{\isacharparenleft}}Xeq{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}bool{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5E}{\isacharcircum}}\isanewline

  1358 \ \ {\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{28}{\isacharparenleft}}let\ X\ {\isaliteral{3D}{\isacharequal}}\ Take\ Xeq{\isaliteral{3B}{\isacharsemicolon}}{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5E}{\isacharcircum}}\isanewline

  1359 \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ X\ {\isaliteral{3D}{\isacharequal}}\ Rewrite\ ruleZY\ False\ X{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5E}{\isacharcircum}}\isanewline

  1360 \ \ {\isaliteral{22}{\isachardoublequote}}\ \ in\ X{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}\isanewline

  1361 \ {\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1362 {\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline

  1363 \isacommand{ML}\isamarkupfalse%

  1364 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

  1365 show{\isaliteral{5F}{\isacharunderscore}}mets{\isaliteral{28}{\isacharparenleft}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1366 {\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline

  1367 \isacommand{ML}\isamarkupfalse%

  1368 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

  1369 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

  1370 {\isaliteral{2A7D}{\isacharverbatimclose}}%

  1371 \endisatagML

  1372 {\isafoldML}%

  1373 %

  1374 \isadelimML

  1375 %

  1376 \endisadelimML

  1377 %

  1378 \isamarkupsection{Program in CTP-based language \label{prog-steps}%

  1379 }

  1380 \isamarkuptrue%

  1381 %

  1382 \begin{isamarkuptext}%

  1383 =================================%

  1384 \end{isamarkuptext}%

  1385 \isamarkuptrue%

  1386 %

  1387 \isamarkupsubsection{Stepwise extend Program%

  1388 }

  1389 \isamarkuptrue%

  1390 %

  1391 \isadelimML

  1392 %

  1393 \endisadelimML

  1394 %

  1395 \isatagML

  1396 \isacommand{ML}\isamarkupfalse%

  1397 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

  1398 val\ str\ {\isaliteral{3D}{\isacharequal}}\ \isanewline

  1399 {\isaliteral{22}{\isachardoublequote}}Script\ InverseZTransform\ {\isaliteral{28}{\isacharparenleft}}Xeq{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}bool{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5E}{\isacharcircum}}\isanewline

  1400 {\isaliteral{22}{\isachardoublequote}}\ Xeq{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1401 {\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline

  1402 \isacommand{ML}\isamarkupfalse%

  1403 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

  1404 val\ str\ {\isaliteral{3D}{\isacharequal}}\ \isanewline

  1405 {\isaliteral{22}{\isachardoublequote}}Script\ InverseZTransform\ {\isaliteral{28}{\isacharparenleft}}Xeq{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}bool{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5E}{\isacharcircum}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{28}{\isacharparenleft}}{\isadigit{1}}{\isaliteral{2F}{\isacharslash}}z{\isaliteral{29}{\isacharparenright}}\ instead\ of\ z\ {\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{1}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1406 {\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{28}{\isacharparenleft}}let\ X\ {\isaliteral{3D}{\isacharequal}}\ Take\ Xeq{\isaliteral{3B}{\isacharsemicolon}}{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5E}{\isacharcircum}}\isanewline

  1407 {\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

  1408 {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ X{\isaliteral{27}{\isacharprime}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}Rewrite{\isaliteral{5F}{\isacharunderscore}}Set\ norm{\isaliteral{5F}{\isacharunderscore}}Rational\ False{\isaliteral{29}{\isacharparenright}}\ X{\isaliteral{27}{\isacharprime}}{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5E}{\isacharcircum}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}simplify{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1409 {\isaliteral{22}{\isachardoublequote}}\ \ in\ X{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1410 {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}NONE{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1411 {\isaliteral{22}{\isachardoublequote}}Script\ InverseZTransform\ {\isaliteral{28}{\isacharparenleft}}Xeq{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}bool{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5E}{\isacharcircum}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{28}{\isacharparenleft}}{\isadigit{1}}{\isaliteral{2F}{\isacharslash}}z{\isaliteral{29}{\isacharparenright}}\ instead\ of\ z\ {\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{1}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1412 {\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{28}{\isacharparenleft}}let\ X\ {\isaliteral{3D}{\isacharequal}}\ Take\ Xeq{\isaliteral{3B}{\isacharsemicolon}}{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5E}{\isacharcircum}}\isanewline

  1413 {\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

  1414 {\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

  1415 {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ X{\isaliteral{27}{\isacharprime}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}SubProblem\ {\isaliteral{28}{\isacharparenleft}}Isac{\isaliteral{27}{\isacharprime}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5B}{\isacharbrackleft}}pqFormula{\isaliteral{2C}{\isacharcomma}}degree{\isaliteral{5F}{\isacharunderscore}}{\isadigit{2}}{\isaliteral{2C}{\isacharcomma}}polynomial{\isaliteral{2C}{\isacharcomma}}univariate{\isaliteral{2C}{\isacharcomma}}equation{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5B}{\isacharbrackleft}}no{\isaliteral{5F}{\isacharunderscore}}met{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\ \ \ {\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5E}{\isacharcircum}}\isanewline

  1416 \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{5B}{\isacharbrackleft}}BOOL\ e{\isaliteral{5F}{\isacharunderscore}}e{\isaliteral{2C}{\isacharcomma}}\ REAL\ v{\isaliteral{5F}{\isacharunderscore}}v{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5E}{\isacharcircum}}\isanewline

  1417 {\isaliteral{22}{\isachardoublequote}}\ \ in\ X{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1418 {\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline

  1419 \isacommand{ML}\isamarkupfalse%

  1420 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

  1421 val\ str\ {\isaliteral{3D}{\isacharequal}}\ \isanewline

  1422 {\isaliteral{22}{\isachardoublequote}}Script\ InverseZTransform\ {\isaliteral{28}{\isacharparenleft}}Xeq{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}bool{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5E}{\isacharcircum}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{28}{\isacharparenleft}}{\isadigit{1}}{\isaliteral{2F}{\isacharslash}}z{\isaliteral{29}{\isacharparenright}}\ instead\ of\ z\ {\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{1}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1423 {\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{28}{\isacharparenleft}}let\ X\ {\isaliteral{3D}{\isacharequal}}\ Take\ Xeq{\isaliteral{3B}{\isacharsemicolon}}{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5E}{\isacharcircum}}\isanewline

  1424 {\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

  1425 {\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

  1426 {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ funterm\ {\isaliteral{3D}{\isacharequal}}\ rhs\ X{\isaliteral{27}{\isacharprime}}{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5E}{\isacharcircum}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}drop\ X{\isaliteral{27}{\isacharprime}}{\isaliteral{3D}{\isacharequal}}\ for\ equation\ solving{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1427 {\isaliteral{22}{\isachardoublequote}}\ \ in\ X{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1428 {\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline

  1429 \isacommand{ML}\isamarkupfalse%

  1430 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

  1431 val\ str\ {\isaliteral{3D}{\isacharequal}}\ \isanewline

  1432 {\isaliteral{22}{\isachardoublequote}}Script\ InverseZTransform\ {\isaliteral{28}{\isacharparenleft}}X{\isaliteral{5F}{\isacharunderscore}}eq{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}bool{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5E}{\isacharcircum}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{28}{\isacharparenleft}}{\isadigit{1}}{\isaliteral{2F}{\isacharslash}}z{\isaliteral{29}{\isacharparenright}}\ instead\ of\ z\ {\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{1}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1433 {\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

  1434 {\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

  1435 {\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

  1436 {\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

  1437 {\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

  1438 {\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

  1439 {\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

  1440 {\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

  1441 {\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

  1442 {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}SubProblem\ {\isaliteral{28}{\isacharparenleft}}Test{\isaliteral{27}{\isacharprime}}{\isaliteral{2C}{\isacharcomma}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5E}{\isacharcircum}}\isanewline

  1443 {\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

  1444 {\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

  1445 {\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

  1446 {\isaliteral{22}{\isachardoublequote}}\ \ in\ X{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}\isanewline

  1447 {\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1448 \isanewline

  1449 parse\ thy\ str{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1450 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

  1451 atomty\ sc{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1452 \isanewline

  1453 {\isaliteral{2A7D}{\isacharverbatimclose}}%

  1454 \endisatagML

  1455 {\isafoldML}%

  1456 %

  1457 \isadelimML

  1458 %

  1459 \endisadelimML

  1460 %

  1461 \begin{isamarkuptext}%

  1462 This ruleset contains all functions that are in the script;

  1463 The evaluation of the functions is done by rewriting using this ruleset.%

  1464 \end{isamarkuptext}%

  1465 \isamarkuptrue%

  1466 %

  1467 \isadelimML

  1468 %

  1469 \endisadelimML

  1470 %

  1471 \isatagML

  1472 \isacommand{ML}\isamarkupfalse%

  1473 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

  1474 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

  1475 		\ \ preconds\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ rew{\isaliteral{5F}{\isacharunderscore}}ord\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}termlessI{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}termlessI{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\ \isanewline

  1476 		\ \ erls\ {\isaliteral{3D}{\isacharequal}}\ append{\isaliteral{5F}{\isacharunderscore}}rls\ {\isaliteral{22}{\isachardoublequote}}erls{\isaliteral{5F}{\isacharunderscore}}in{\isaliteral{5F}{\isacharunderscore}}srls{\isaliteral{5F}{\isacharunderscore}}InverseZTransform{\isaliteral{22}{\isachardoublequote}}\ e{\isaliteral{5F}{\isacharunderscore}}rls\isanewline

  1477 				\ \ \ \ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}for\ asm\ in\ NTH{\isaliteral{5F}{\isacharunderscore}}CONS\ {\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\ Calc\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}Orderings{\isaliteral{2E}{\isachardot}}ord{\isaliteral{5F}{\isacharunderscore}}class{\isaliteral{2E}{\isachardot}}less{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}eval{\isaliteral{5F}{\isacharunderscore}}equ\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{23}{\isacharhash}}less{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\isanewline

  1478 				\ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}{\isadigit{2}}nd\ NTH{\isaliteral{5F}{\isacharunderscore}}CONS\ pushes\ n{\isaliteral{2B}{\isacharplus}}{\isaliteral{2D}{\isacharminus}}{\isadigit{1}}\ into\ asms{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\ Calc{\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}Groups{\isaliteral{2E}{\isachardot}}plus{\isaliteral{5F}{\isacharunderscore}}class{\isaliteral{2E}{\isachardot}}plus{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ eval{\isaliteral{5F}{\isacharunderscore}}binop\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{23}{\isacharhash}}add{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1479 				\ \ \ \ {\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ \isanewline

  1480 \ \ srls\ {\isaliteral{3D}{\isacharequal}}\ Erls{\isaliteral{2C}{\isacharcomma}}\ calc\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\isanewline

  1481 		\ \ rules\ {\isaliteral{3D}{\isacharequal}}\isanewline

  1482 \ \ \ \ {\isaliteral{5B}{\isacharbrackleft}}Thm\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}NTH{\isaliteral{5F}{\isacharunderscore}}CONS{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}num{\isaliteral{5F}{\isacharunderscore}}str\ %

  1483 \isaantiq

  1484 thm\ NTH{\isaliteral{5F}{\isacharunderscore}}CONS{}%

  1485 \endisaantiq

  1486 {\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\isanewline

  1487 			\ \ \ \ \ Calc{\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}Groups{\isaliteral{2E}{\isachardot}}plus{\isaliteral{5F}{\isacharunderscore}}class{\isaliteral{2E}{\isachardot}}plus{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ eval{\isaliteral{5F}{\isacharunderscore}}binop\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{23}{\isacharhash}}add{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\isanewline

  1488 			\ \ \ \ \ Thm\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}NTH{\isaliteral{5F}{\isacharunderscore}}NIL{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}num{\isaliteral{5F}{\isacharunderscore}}str\ %

  1489 \isaantiq

  1490 thm\ NTH{\isaliteral{5F}{\isacharunderscore}}NIL{}%

  1491 \endisaantiq

  1492 {\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\isanewline

  1493 			\ \ \ \ \ 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

  1494 			\ \ \ \ \ 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

  1495 			\ \ \ \ \ 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

  1496 \ \ \ \ \ Calc{\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{23}{\isacharhash}}get{\isaliteral{5F}{\isacharunderscore}}denominator{\isaliteral{22}{\isachardoublequote}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\isanewline

  1497 \ \ \ \ \ Calc{\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}Rational{\isaliteral{2E}{\isachardot}}get{\isaliteral{5F}{\isacharunderscore}}numerator{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ eval{\isaliteral{5F}{\isacharunderscore}}get{\isaliteral{5F}{\isacharunderscore}}numerator\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{23}{\isacharhash}}get{\isaliteral{5F}{\isacharunderscore}}numerator{\isaliteral{22}{\isachardoublequote}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\isanewline

  1498 \ \ \ \ \ Calc{\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}Partial{\isaliteral{5F}{\isacharunderscore}}Fractions{\isaliteral{2E}{\isachardot}}factors{\isaliteral{5F}{\isacharunderscore}}from{\isaliteral{5F}{\isacharunderscore}}solution{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\isanewline

  1499 \ \ \ \ \ \ \ eval{\isaliteral{5F}{\isacharunderscore}}factors{\isaliteral{5F}{\isacharunderscore}}from{\isaliteral{5F}{\isacharunderscore}}solution\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{23}{\isacharhash}}factors{\isaliteral{5F}{\isacharunderscore}}from{\isaliteral{5F}{\isacharunderscore}}solution{\isaliteral{22}{\isachardoublequote}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\isanewline

  1500 \ \ \ \ \ Calc{\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}Partial{\isaliteral{5F}{\isacharunderscore}}Fractions{\isaliteral{2E}{\isachardot}}drop{\isaliteral{5F}{\isacharunderscore}}questionmarks{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ eval{\isaliteral{5F}{\isacharunderscore}}drop{\isaliteral{5F}{\isacharunderscore}}questionmarks\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{23}{\isacharhash}}drop{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{3F}{\isacharquery}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1501 			\ \ \ \ {\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\isanewline

  1502 		\ \ scr\ {\isaliteral{3D}{\isacharequal}}\ EmptyScr{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1503 {\isaliteral{2A7D}{\isacharverbatimclose}}%

  1504 \endisatagML

  1505 {\isafoldML}%

  1506 %

  1507 \isadelimML

  1508 %

  1509 \endisadelimML

  1510 %

  1511 \isamarkupsubsection{Store Final Version of Program for Execution%

  1512 }

  1513 \isamarkuptrue%

  1514 %

  1515 \isadelimML

  1516 %

  1517 \endisadelimML

  1518 %

  1519 \isatagML

  1520 \isacommand{ML}\isamarkupfalse%

  1521 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

  1522 store{\isaliteral{5F}{\isacharunderscore}}met\isanewline

  1523 \ {\isaliteral{28}{\isacharparenleft}}prep{\isaliteral{5F}{\isacharunderscore}}met\ thy\ {\isaliteral{22}{\isachardoublequote}}met{\isaliteral{5F}{\isacharunderscore}}SP{\isaliteral{5F}{\isacharunderscore}}Ztrans{\isaliteral{5F}{\isacharunderscore}}inv{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ e{\isaliteral{5F}{\isacharunderscore}}metID\isanewline

  1524 \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}SignalProcessing{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}Z{\isaliteral{5F}{\isacharunderscore}}Transform{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}inverse{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ \isanewline

  1525 \ \ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{23}{\isacharhash}}Given{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{2C}{\isacharcomma}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}filterExpression\ X{\isaliteral{5F}{\isacharunderscore}}eq{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\isanewline

  1526 \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{23}{\isacharhash}}Find{\isaliteral{22}{\isachardoublequote}}\ \ {\isaliteral{2C}{\isacharcomma}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}stepResponse\ n{\isaliteral{5F}{\isacharunderscore}}eq{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1527 \ \ {\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\isanewline

  1528 \ \ \ {\isaliteral{7B}{\isacharbraceleft}}rew{\isaliteral{5F}{\isacharunderscore}}ord{\isaliteral{27}{\isacharprime}}{\isaliteral{3D}{\isacharequal}}{\isaliteral{22}{\isachardoublequote}}tless{\isaliteral{5F}{\isacharunderscore}}true{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ rls{\isaliteral{27}{\isacharprime}}{\isaliteral{3D}{\isacharequal}}\ e{\isaliteral{5F}{\isacharunderscore}}rls{\isaliteral{2C}{\isacharcomma}}\ calc\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ srls\ {\isaliteral{3D}{\isacharequal}}\ srls{\isaliteral{2C}{\isacharcomma}}\ \isanewline

  1529 \ \ \ \ prls\ {\isaliteral{3D}{\isacharequal}}\ e{\isaliteral{5F}{\isacharunderscore}}rls{\isaliteral{2C}{\isacharcomma}}\isanewline

  1530 \ \ \ \ crls\ {\isaliteral{3D}{\isacharequal}}\ e{\isaliteral{5F}{\isacharunderscore}}rls{\isaliteral{2C}{\isacharcomma}}\ nrls\ {\isaliteral{3D}{\isacharequal}}\ e{\isaliteral{5F}{\isacharunderscore}}rls{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{2C}{\isacharcomma}}\isanewline

  1531 \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}Script\ InverseZTransform\ {\isaliteral{28}{\isacharparenleft}}X{\isaliteral{5F}{\isacharunderscore}}eq{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}bool{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5E}{\isacharcircum}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{28}{\isacharparenleft}}{\isadigit{1}}{\isaliteral{2F}{\isacharslash}}z{\isaliteral{29}{\isacharparenright}}\ instead\ of\ z\ {\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{1}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1532 \ \ \ \ \ \ {\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

  1533 {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5B}{\isacharbrackleft}}{\isadigit{1}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ Frm{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\ 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{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1534 \ \ \ \ \ \ {\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

  1535 {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5B}{\isacharbrackleft}}{\isadigit{1}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ Res{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{3F}{\isacharquery}}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{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1536 \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}num{\isaliteral{5F}{\isacharunderscore}}orig{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}real{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ get{\isaliteral{5F}{\isacharunderscore}}numerator\ {\isaliteral{28}{\isacharparenleft}}rhs\ X{\isaliteral{27}{\isacharprime}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline

  1537 \ \ \ \ \ \ {\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

  1538 {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5B}{\isacharbrackleft}}{\isadigit{2}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ Res{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{3F}{\isacharquery}}X{\isaliteral{27}{\isacharprime}}\ z\ {\isaliteral{3D}{\isacharequal}}\ {\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{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1539 \ \ \ \ \ \ {\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

  1540 \ \ \ \ \ \ {\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

  1541 \ \ \ \ \ \ {\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

  1542 \ \ \ \ \ \ {\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

  1543 \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}num{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}real{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ get{\isaliteral{5F}{\isacharunderscore}}numerator\ funterm{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5E}{\isacharcircum}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}get{\isaliteral{5F}{\isacharunderscore}}numerator{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1544 \ \ \ \ \ \ {\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

  1545 \ \ \ \ \ \ {\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

  1546 \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ \ \ \ {\isaliteral{5B}{\isacharbrackleft}}abcFormula{\isaliteral{2C}{\isacharcomma}}degree{\isaliteral{5F}{\isacharunderscore}}{\isadigit{2}}{\isaliteral{2C}{\isacharcomma}}polynomial{\isaliteral{2C}{\isacharcomma}}univariate{\isaliteral{2C}{\isacharcomma}}equation{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5B}{\isacharbrackleft}}no{\isaliteral{5F}{\isacharunderscore}}met{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5E}{\isacharcircum}}\isanewline

  1547 \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ \ \ \ {\isaliteral{5B}{\isacharbrackleft}}BOOL\ equ{\isaliteral{2C}{\isacharcomma}}\ REAL\ zzz{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5E}{\isacharcircum}}\isanewline

  1548 \isanewline

  1549 {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5B}{\isacharbrackleft}}{\isadigit{3}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ Pbl{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\ solve\ {\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{2C}{\isacharcomma}}\ z{\isaliteral{29}{\isacharparenright}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1550 {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5B}{\isacharbrackleft}}{\isadigit{3}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ Res{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\ {\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

  1551 \isanewline

  1552 \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}facs{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}real{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ factors{\isaliteral{5F}{\isacharunderscore}}from{\isaliteral{5F}{\isacharunderscore}}solution\ L{\isaliteral{5F}{\isacharunderscore}}L{\isaliteral{3B}{\isacharsemicolon}}{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5E}{\isacharcircum}}\isanewline

  1553 \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}eql{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}real{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ Take\ {\isaliteral{28}{\isacharparenleft}}num{\isaliteral{5F}{\isacharunderscore}}orig\ {\isaliteral{2F}{\isacharslash}}\ facs{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5E}{\isacharcircum}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5B}{\isacharbrackleft}}{\isadigit{4}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ Frm{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\ {\isadigit{2}}{\isadigit{4}}\ {\isaliteral{2F}{\isacharslash}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{1}}\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{1}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{2}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{1}}\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2D}{\isacharminus}}{\isadigit{1}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{4}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1554 \isanewline

  1555 \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}eqr{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}real{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}Try\ {\isaliteral{28}{\isacharparenleft}}Rewrite{\isaliteral{5F}{\isacharunderscore}}Set\ ansatz{\isaliteral{5F}{\isacharunderscore}}rls\ False{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ eql{\isaliteral{3B}{\isacharsemicolon}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\ \ \ \ \ \ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5B}{\isacharbrackleft}}{\isadigit{4}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ Res{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{3F}{\isacharquery}}A\ {\isaliteral{2F}{\isacharslash}}\ {\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{1}}\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{1}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{2}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{3F}{\isacharquery}}B\ {\isaliteral{2F}{\isacharslash}}\ {\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{1}}\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2D}{\isacharminus}}{\isadigit{1}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{4}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1556 \isanewline

  1557 \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}eq{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}bool{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ Take\ {\isaliteral{28}{\isacharparenleft}}eql\ {\isaliteral{3D}{\isacharequal}}\ eqr{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}Maybe\ possible\ to\ use\ HOLogic{\isaliteral{2E}{\isachardot}}mk{\isaliteral{5F}{\isacharunderscore}}eq\ {\isaliteral{3F}{\isacharquery}}{\isaliteral{3F}{\isacharquery}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5B}{\isacharbrackleft}}{\isadigit{5}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ Frm{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\ {\isadigit{2}}{\isadigit{4}}\ {\isaliteral{2F}{\isacharslash}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{1}}\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{1}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{2}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{1}}\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2D}{\isacharminus}}{\isadigit{1}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{4}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{3F}{\isacharquery}}A\ {\isaliteral{2F}{\isacharslash}}\ {\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{1}}\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{1}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{2}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{3F}{\isacharquery}}B\ {\isaliteral{2F}{\isacharslash}}\ {\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{1}}\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2D}{\isacharminus}}{\isadigit{1}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{4}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1558 \isanewline

  1559 \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ eq\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}Try\ {\isaliteral{28}{\isacharparenleft}}Rewrite{\isaliteral{5F}{\isacharunderscore}}Set\ equival{\isaliteral{5F}{\isacharunderscore}}trans\ False{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ eq{\isaliteral{3B}{\isacharsemicolon}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5B}{\isacharbrackleft}}{\isadigit{5}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ Res{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\ {\isadigit{2}}{\isadigit{4}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{3F}{\isacharquery}}A\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{1}}\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2D}{\isacharminus}}{\isadigit{1}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{4}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{3F}{\isacharquery}}B\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{1}}\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{1}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{2}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1560 \isanewline

  1561 \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ eq\ {\isaliteral{3D}{\isacharequal}}\ drop{\isaliteral{5F}{\isacharunderscore}}questionmarks\ eq{\isaliteral{3B}{\isacharsemicolon}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline

  1562 \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}z{\isadigit{1}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}real{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}rhs\ {\isaliteral{28}{\isacharparenleft}}NTH\ {\isadigit{1}}\ L{\isaliteral{5F}{\isacharunderscore}}L{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}prepare\ equliation\ for\ a\ {\isaliteral{2D}{\isacharminus}}\ eq{\isaliteral{5F}{\isacharunderscore}}a\ therfor\ subsitude\ z\ with\ solution\ {\isadigit{1}}\ {\isaliteral{2D}{\isacharminus}}\ z{\isadigit{1}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1563 \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}z{\isadigit{2}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}real{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}rhs\ {\isaliteral{28}{\isacharparenleft}}NTH\ {\isadigit{2}}\ L{\isaliteral{5F}{\isacharunderscore}}L{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline

  1564 \ \isanewline

  1565 \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}eq{\isaliteral{5F}{\isacharunderscore}}a{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}bool{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ Take\ eq{\isaliteral{3B}{\isacharsemicolon}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline

  1566 \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ eq{\isaliteral{5F}{\isacharunderscore}}a\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}Substitute\ {\isaliteral{5B}{\isacharbrackleft}}zzz{\isaliteral{3D}{\isacharequal}}z{\isadigit{1}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\ eq{\isaliteral{3B}{\isacharsemicolon}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5B}{\isacharbrackleft}}{\isadigit{6}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ Res{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\ {\isadigit{2}}{\isadigit{4}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{3F}{\isacharquery}}A\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{1}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{2}}\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{1}}\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2D}{\isacharminus}}{\isadigit{1}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{4}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{3F}{\isacharquery}}B\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{1}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{2}}\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{1}}\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{1}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{2}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1567 \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ eq{\isaliteral{5F}{\isacharunderscore}}a\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}Rewrite{\isaliteral{5F}{\isacharunderscore}}Set\ norm{\isaliteral{5F}{\isacharunderscore}}Rational\ False{\isaliteral{29}{\isacharparenright}}\ eq{\isaliteral{5F}{\isacharunderscore}}a{\isaliteral{3B}{\isacharsemicolon}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5B}{\isacharbrackleft}}{\isadigit{7}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ Res{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\ {\isadigit{2}}{\isadigit{4}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{3F}{\isacharquery}}A\ {\isaliteral{2A}{\isacharasterisk}}\ {\isadigit{3}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{4}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1568 \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}sol{\isaliteral{5F}{\isacharunderscore}}a{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}bool\ list{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}SubProblem\ {\isaliteral{28}{\isacharparenleft}}Isac{\isaliteral{27}{\isacharprime}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5E}{\isacharcircum}}\isanewline

  1569 \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ \ \ \ \ {\isaliteral{5B}{\isacharbrackleft}}univariate{\isaliteral{2C}{\isacharcomma}}equation{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5B}{\isacharbrackleft}}no{\isaliteral{5F}{\isacharunderscore}}met{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5E}{\isacharcircum}}\isanewline

  1570 \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ \ \ {\isaliteral{5B}{\isacharbrackleft}}BOOL\ eq{\isaliteral{5F}{\isacharunderscore}}a{\isaliteral{2C}{\isacharcomma}}\ REAL\ {\isaliteral{28}{\isacharparenleft}}A{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}real{\isaliteral{29}{\isacharparenright}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline

  1571 \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}a{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}real{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}rhs{\isaliteral{28}{\isacharparenleft}}NTH\ {\isadigit{1}}\ sol{\isaliteral{5F}{\isacharunderscore}}a{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline

  1572 {\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}aarg{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}real{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}lhs{\isaliteral{28}{\isacharparenleft}}NTH\ {\isadigit{1}}\ sol{\isaliteral{5F}{\isacharunderscore}}a{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline

  1573 \isanewline

  1574 \isanewline

  1575 \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}eq{\isaliteral{5F}{\isacharunderscore}}b{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}bool{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ Take\ eq{\isaliteral{3B}{\isacharsemicolon}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline

  1576 \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ eq{\isaliteral{5F}{\isacharunderscore}}b\ {\isaliteral{3D}{\isacharequal}}\ \ {\isaliteral{28}{\isacharparenleft}}Substitute\ {\isaliteral{5B}{\isacharbrackleft}}zzz{\isaliteral{3D}{\isacharequal}}z{\isadigit{2}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\ eq{\isaliteral{5F}{\isacharunderscore}}b{\isaliteral{3B}{\isacharsemicolon}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline

  1577 \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ eq{\isaliteral{5F}{\isacharunderscore}}b\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}Rewrite{\isaliteral{5F}{\isacharunderscore}}Set\ norm{\isaliteral{5F}{\isacharunderscore}}Rational\ False{\isaliteral{29}{\isacharparenright}}\ eq{\isaliteral{5F}{\isacharunderscore}}b{\isaliteral{3B}{\isacharsemicolon}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline

  1578 \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}sol{\isaliteral{5F}{\isacharunderscore}}b{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}bool\ list{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}SubProblem\ {\isaliteral{28}{\isacharparenleft}}Isac{\isaliteral{27}{\isacharprime}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5E}{\isacharcircum}}\isanewline

  1579 \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ \ \ \ \ {\isaliteral{5B}{\isacharbrackleft}}univariate{\isaliteral{2C}{\isacharcomma}}equation{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5B}{\isacharbrackleft}}no{\isaliteral{5F}{\isacharunderscore}}met{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5E}{\isacharcircum}}\isanewline

  1580 \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ \ \ {\isaliteral{5B}{\isacharbrackleft}}BOOL\ eq{\isaliteral{5F}{\isacharunderscore}}b{\isaliteral{2C}{\isacharcomma}}\ REAL\ {\isaliteral{28}{\isacharparenleft}}B{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}real{\isaliteral{29}{\isacharparenright}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline

  1581 \isanewline

  1582 \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}pbz{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}real{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ Take\ eqr{\isaliteral{3B}{\isacharsemicolon}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline

  1583 \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ pbz\ {\isaliteral{3D}{\isacharequal}}\ drop{\isaliteral{5F}{\isacharunderscore}}questionmarks\ pbz{\isaliteral{3B}{\isacharsemicolon}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline

  1584 \isanewline

  1585 \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}pbz{\isadigit{2}}{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}real{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}Substitute\ {\isaliteral{5B}{\isacharbrackleft}}A{\isaliteral{3D}{\isacharequal}}a{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\ pbz{\isaliteral{3B}{\isacharsemicolon}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline

  1586 \isanewline

  1587 \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}real{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ Take\ pbz{\isadigit{2}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5E}{\isacharcircum}}\isanewline

  1588 \isanewline

  1589 \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ \ in\ X{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}\ \isanewline

  1590 \ \ \ \ \ \ {\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1591 {\isaliteral{2A7D}{\isacharverbatimclose}}%

  1592 \endisatagML

  1593 {\isafoldML}%

  1594 %

  1595 \isadelimML

  1596 %

  1597 \endisadelimML

  1598 %

  1599 \isamarkupsubsection{Check the Program%

  1600 }

  1601 \isamarkuptrue%

  1602 %

  1603 \isamarkupsubsubsection{Check the formalization%

  1604 }

  1605 \isamarkuptrue%

  1606 %

  1607 \isadelimML

  1608 %

  1609 \endisadelimML

  1610 %

  1611 \isatagML

  1612 \isacommand{ML}\isamarkupfalse%

  1613 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

  1614 val\ fmz\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}filterExpression\ {\isaliteral{28}{\isacharparenleft}}X\ \ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{3}}\ {\isaliteral{2F}{\isacharslash}}\ {\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{1}}{\isaliteral{2F}{\isacharslash}}{\isadigit{4}}\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{1}}{\isaliteral{2F}{\isacharslash}}{\isadigit{8}}\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{1}}{\isaliteral{2F}{\isacharslash}}{\isaliteral{28}{\isacharparenleft}}z{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}real{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ \isanewline

  1615 \ \ {\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

  1616 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

  1617 \ \ {\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

  1618 \isanewline

  1619 val\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{28}{\isacharparenleft}}{\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isadigit{1}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{23}{\isacharhash}}Given{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ Const\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}Inverse{\isaliteral{5F}{\isacharunderscore}}Z{\isaliteral{5F}{\isacharunderscore}}Transform{\isaliteral{2E}{\isachardot}}filterExpression{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5F}{\isacharunderscore}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\isanewline

  1620 \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{5B}{\isacharbrackleft}}Const\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}HOL{\isaliteral{2E}{\isachardot}}eq{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5F}{\isacharunderscore}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{24}{\isachardollar}}\ {\isaliteral{5F}{\isacharunderscore}}\ {\isaliteral{24}{\isachardollar}}\ {\isaliteral{5F}{\isacharunderscore}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\isanewline

  1621 \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}{\isadigit{2}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isadigit{1}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{23}{\isacharhash}}Find{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ Const\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}Inverse{\isaliteral{5F}{\isacharunderscore}}Z{\isaliteral{5F}{\isacharunderscore}}Transform{\isaliteral{2E}{\isachardot}}stepResponse{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5F}{\isacharunderscore}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\isanewline

  1622 \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{5B}{\isacharbrackleft}}Free\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}x{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5F}{\isacharunderscore}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{24}{\isachardollar}}\ {\isaliteral{5F}{\isacharunderscore}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\isanewline

  1623 \ \ \ \ \ \ \ \ \ \ {\isaliteral{5F}{\isacharunderscore}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ prep{\isaliteral{5F}{\isacharunderscore}}ori\ fmz\ thy\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{23}{\isacharhash}}ppc\ o\ get{\isaliteral{5F}{\isacharunderscore}}pbt{\isaliteral{29}{\isacharparenright}}\ pI{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1624 {\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline

  1625 \isacommand{ML}\isamarkupfalse%

  1626 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

  1627 val\ Script\ sc\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{23}{\isacharhash}}scr\ o\ get{\isaliteral{5F}{\isacharunderscore}}met{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}SignalProcessing{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\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

  1628 atomty\ sc{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1629 {\isaliteral{2A7D}{\isacharverbatimclose}}%

  1630 \endisatagML

  1631 {\isafoldML}%

  1632 %

  1633 \isadelimML

  1634 %

  1635 \endisadelimML

  1636 %

  1637 \isamarkupsubsubsection{Stepwise check the program%

  1638 }

  1639 \isamarkuptrue%

  1640 %

  1641 \isadelimML

  1642 %

  1643 \endisadelimML

  1644 %

  1645 \isatagML

  1646 \isacommand{ML}\isamarkupfalse%

  1647 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

  1648 trace{\isaliteral{5F}{\isacharunderscore}}rewrite\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ false{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1649 trace{\isaliteral{5F}{\isacharunderscore}}script\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ false{\isaliteral{3B}{\isacharsemicolon}}\ print{\isaliteral{5F}{\isacharunderscore}}depth\ {\isadigit{9}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1650 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

  1651 \ \ {\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

  1652 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

  1653 \ \ {\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

  1654 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

  1655 {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ Frm{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\ Problem\ {\isaliteral{28}{\isacharparenleft}}Isac{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5B}{\isacharbrackleft}}inverse{\isaliteral{2C}{\isacharcomma}}\ Z{\isaliteral{5F}{\isacharunderscore}}Transform{\isaliteral{2C}{\isacharcomma}}\ SignalProcessing{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1656 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

  1657 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

  1658 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

  1659 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

  1660 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

  1661 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

  1662 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

  1663 {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5B}{\isacharbrackleft}}{\isadigit{1}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ Frm{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\ 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{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1664 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

  1665 {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5B}{\isacharbrackleft}}{\isadigit{1}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ Res{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{3F}{\isacharquery}}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{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1666 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}}\ SubProblem{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1667 {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5B}{\isacharbrackleft}}{\isadigit{2}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ Res{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{3F}{\isacharquery}}X{\isaliteral{27}{\isacharprime}}\ z\ {\isaliteral{3D}{\isacharequal}}\ {\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{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1668 {\isaliteral{2A7D}{\isacharverbatimclose}}%

  1669 \endisatagML

  1670 {\isafoldML}%

  1671 %

  1672 \isadelimML

  1673 %

  1674 \endisadelimML

  1675 %

  1676 \begin{isamarkuptext}%

  1677 Instead of nxt = Subproblem above we had Empty_Tac; the search for the reason

  1678   considered the following points:

  1679   # what shows show_pt pt; ...

  1680     (([2], Res), ?X' z = 24 / (-1 + -2 * z + 8 * z ^^^ 2))] ..calculation ok,

  1681     but no "next" step found: should be "nxt = Subproblem" ?!?

  1682   # what shows trace_script := true; we read bottom up ...

  1683     @@@ next   leaf 'SubProbfrom

  1684      (PolyEq', [abcFormula, degree_2, polynomial, univariate, equation],

  1685       no_meth)

  1686      [BOOL equ, REAL z]' ---> STac 'SubProblem

  1687      (PolyEq', [abcFormula, degree_2, polynomial, univariate, equation],

  1688       no_meth)

  1689      [BOOL (-1 + -2 * z + 8 * z ^^^ 2 = 0), REAL z]'

  1690     ... and see the SubProblem with correct arguments from searching next step

  1691     (program text !!!--->!!! STac (script tactic) with arguments evaluated.)

  1692   # do we have the right Script ...difference in the argumentsdifference in the arguments

  1693     val Script s = (#scr o get_met) ["SignalProcessing","Z_Transform","inverse"];

  1694     writeln (term2str s);

  1695     ... shows the right script.difference in the arguments

  1696   # test --- why helpless here ? --- shows: replace no_meth by [no_meth] in Script%

  1697 \end{isamarkuptext}%

  1698 \isamarkuptrue%

  1699 %

  1700 \isadelimML

  1701 %

  1702 \endisadelimML

  1703 %

  1704 \isatagML

  1705 \isacommand{ML}\isamarkupfalse%

  1706 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

  1707 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

  1708 {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5B}{\isacharbrackleft}}{\isadigit{3}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ Pbl{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\ solve\ {\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{2C}{\isacharcomma}}\ z{\isaliteral{29}{\isacharparenright}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1709 {\isaliteral{2A7D}{\isacharverbatimclose}}%

  1710 \endisatagML

  1711 {\isafoldML}%

  1712 %

  1713 \isadelimML

  1714 %

  1715 \endisadelimML

  1716 %

  1717 \begin{isamarkuptext}%

  1718 Instead of nxt = Model_Problem above we had Empty_Tac; the search for the reason

  1719   considered the following points:difference in the arguments

  1720   # comparison with subsection { *solve equation* }: there solving this equation works,

  1721     so there must be some difference in the arguments of the Subproblem:

  1722     RIGHT: we had [no_meth] instead of [no_met] ;-))%

  1723 \end{isamarkuptext}%

  1724 \isamarkuptrue%

  1725 %

  1726 \isadelimML

  1727 %

  1728 \endisadelimML

  1729 %

  1730 \isatagML

  1731 \isacommand{ML}\isamarkupfalse%

  1732 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

  1733 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}}Given\ equality\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2D}{\isacharminus}}{\isadigit{1}}\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{2}}\ {\isaliteral{2A}{\isacharasterisk}}\ z\ {\isaliteral{2B}{\isacharplus}}\ {\isadigit{8}}\ {\isaliteral{2A}{\isacharasterisk}}\ z\ {\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}\ {\isadigit{2}}\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{0}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1734 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}}Given\ solveFor\ z{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1735 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\ solutions\ z{\isaliteral{5F}{\isacharunderscore}}i{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1736 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}}\ Specify{\isaliteral{5F}{\isacharunderscore}}Theory\ Isac{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1737 {\isaliteral{2A7D}{\isacharverbatimclose}}%

  1738 \endisatagML

  1739 {\isafoldML}%

  1740 %

  1741 \isadelimML

  1742 %

  1743 \endisadelimML

  1744 %

  1745 \begin{isamarkuptext}%

  1746 We had "nxt = Empty_Tac instead Specify_Theory;

  1747   the search for the reason considered the following points:

  1748   # was there an error message ? NO --ok

  1749   # has "nxt = Add_Find" been inserted in pt: get_obj g_pbl pt (fst p); YES --ok

  1750   # what is the returned "formula": print_depth 999; f; print_depth 999; --

  1751     {Find = [Correct "solutions z_i"], With = [],

  1752      Given = [Correct "equality (-1 + -2 * z + 8 * z ^^^ 2 = 0)", Correct "solveFor z"],

  1753      Where = [False "matches (z = 0) (-1 + -2 * z + 8 * z ^^^ 2 = 0) |\n

  1754                      matches (?b * z = 0) (-1 + -2 * z + 8 * z ^^^ 2 = 0) |\n

  1755                      matches (?a + z = 0) (-1 + -2 * z + 8 * z ^^^ 2 = 0) |\n

  1756                      matches (?a + ?b * z = 0) (-1 + -2 * z + 8 * z ^^^ 2 = 0)"],

  1757      Relate = []}

  1758      -- the only False is the reason: the Where (the precondition) is False for good reasons:

  1759      the precondition seems to check for linear equations, not for the one we want to solve!

  1760   Removed this error by correcting the Script

  1761   from SubProblem (PolyEq', [linear,univariate,equation,test], [Test,solve_linear]

  1762   to   SubProblem (PolyEq', [abcFormula,degree_2,polynomial,univariate,equation],

  1763                    [PolyEq,solve_d2_polyeq_abc_equation]

  1764   You find the appropriate type of equation at

  1765     http://www.ist.tugraz.at/projects/isac/www/kbase/pbl/index_pbl.html

  1766   and the respective method in Knowledge/PolyEq.thy at the respective store_pbt.

  1767   Or you leave the selection of the appropriate type to isac as done in the final Script ;-))%

  1768 \end{isamarkuptext}%

  1769 \isamarkuptrue%

  1770 %

  1771 \isadelimML

  1772 %

  1773 \endisadelimML

  1774 %

  1775 \isatagML

  1776 \isacommand{ML}\isamarkupfalse%

  1777 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

  1778 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}}\ Specify{\isaliteral{5F}{\isacharunderscore}}Problem\ {\isaliteral{5B}{\isacharbrackleft}}abcFormula{\isaliteral{2C}{\isacharcomma}}{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1779 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}}\ Specify{\isaliteral{5F}{\isacharunderscore}}Method\ {\isaliteral{5B}{\isacharbrackleft}}PolyEq{\isaliteral{2C}{\isacharcomma}}solve{\isaliteral{5F}{\isacharunderscore}}d{\isadigit{2}}{\isaliteral{5F}{\isacharunderscore}}polyeq{\isaliteral{5F}{\isacharunderscore}}abc{\isaliteral{5F}{\isacharunderscore}}equation{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1780 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{5B}{\isacharbrackleft}}PolyEq{\isaliteral{2C}{\isacharcomma}}solve{\isaliteral{5F}{\isacharunderscore}}d{\isadigit{2}}{\isaliteral{5F}{\isacharunderscore}}polyeq{\isaliteral{5F}{\isacharunderscore}}abc{\isaliteral{5F}{\isacharunderscore}}equation{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1781 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{\isaliteral{5F}{\isacharunderscore}}Inst\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{28}{\isacharparenleft}}bdv{\isaliteral{2C}{\isacharcomma}}\ z{\isaliteral{29}{\isacharparenright}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ d{\isadigit{2}}{\isaliteral{5F}{\isacharunderscore}}polyeq{\isaliteral{5F}{\isacharunderscore}}abcFormula{\isaliteral{5F}{\isacharunderscore}}simplify{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1782 {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5B}{\isacharbrackleft}}{\isadigit{3}}{\isaliteral{2C}{\isacharcomma}}{\isadigit{1}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ Frm{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\ {\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{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1783 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

  1784 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

  1785 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

  1786 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

  1787 {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5B}{\isacharbrackleft}}{\isadigit{3}}{\isaliteral{2C}{\isacharcomma}}{\isadigit{4}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ Res{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\ {\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{29}{\isacharparenright}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1788 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

  1789 {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5B}{\isacharbrackleft}}{\isadigit{3}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ Res{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\ {\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

  1790 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

  1791 {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5B}{\isacharbrackleft}}{\isadigit{4}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ Frm{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\ {\isadigit{2}}{\isadigit{4}}\ {\isaliteral{2F}{\isacharslash}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{1}}\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{1}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{2}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{1}}\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2D}{\isacharminus}}{\isadigit{1}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{4}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1792 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

  1793 {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5B}{\isacharbrackleft}}{\isadigit{4}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ Res{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{3F}{\isacharquery}}A\ {\isaliteral{2F}{\isacharslash}}\ {\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{1}}\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{1}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{2}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{3F}{\isacharquery}}B\ {\isaliteral{2F}{\isacharslash}}\ {\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{1}}\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2D}{\isacharminus}}{\isadigit{1}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{4}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1794 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

  1795 {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5B}{\isacharbrackleft}}{\isadigit{5}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ Frm{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\ {\isadigit{2}}{\isadigit{4}}\ {\isaliteral{2F}{\isacharslash}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{1}}\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{1}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{2}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{1}}\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2D}{\isacharminus}}{\isadigit{1}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{4}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{3F}{\isacharquery}}A\ {\isaliteral{2F}{\isacharslash}}\ {\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{1}}\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{1}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{2}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{3F}{\isacharquery}}B\ {\isaliteral{2F}{\isacharslash}}\ {\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{1}}\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2D}{\isacharminus}}{\isadigit{1}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{4}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1796 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

  1797 {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5B}{\isacharbrackleft}}{\isadigit{5}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ Res{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\ {\isadigit{2}}{\isadigit{4}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{3F}{\isacharquery}}A\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{1}}\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2D}{\isacharminus}}{\isadigit{1}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{4}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{3F}{\isacharquery}}B\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{1}}\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{1}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{2}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1798 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

  1799 {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5B}{\isacharbrackleft}}{\isadigit{6}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ Res{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\ {\isadigit{2}}{\isadigit{4}}\ {\isaliteral{3D}{\isacharequal}}\ A\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{1}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{2}}\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{1}}\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2D}{\isacharminus}}{\isadigit{1}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{4}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{2B}{\isacharplus}}\ B\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{1}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{2}}\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{1}}\ {\isaliteral{2A}{\isacharasterisk}}\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{1}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{2}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1800 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

  1801 {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5B}{\isacharbrackleft}}{\isadigit{7}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ Res{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\ {\isadigit{2}}{\isadigit{4}}\ {\isaliteral{3D}{\isacharequal}}\ A\ {\isaliteral{2A}{\isacharasterisk}}\ {\isadigit{3}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{4}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1802 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

  1803 {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5B}{\isacharbrackleft}}{\isadigit{8}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ Pbl{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\ solve\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{2}}{\isadigit{4}}\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{3}}\ {\isaliteral{2A}{\isacharasterisk}}\ A\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{4}}{\isaliteral{2C}{\isacharcomma}}\ A{\isaliteral{29}{\isacharparenright}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1804 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}}Add{\isaliteral{5F}{\isacharunderscore}}Given\ {\isaliteral{22}{\isachardoublequote}}equality\ {\isaliteral{28}{\isacharparenleft}}{\isadigit{2}}{\isadigit{4}}\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{3}}\ {\isaliteral{2A}{\isacharasterisk}}\ A\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{4}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1805 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}}Add{\isaliteral{5F}{\isacharunderscore}}Given\ {\isaliteral{22}{\isachardoublequote}}solveFor\ A{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1806 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}}Add{\isaliteral{5F}{\isacharunderscore}}Find\ {\isaliteral{22}{\isachardoublequote}}solutions\ A{\isaliteral{5F}{\isacharunderscore}}i{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1807 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}}Specify{\isaliteral{5F}{\isacharunderscore}}Theory\ {\isaliteral{22}{\isachardoublequote}}Isac{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}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}}Specify{\isaliteral{5F}{\isacharunderscore}}Problem\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}normalize{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}polynomial{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ \isanewline

  1808 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}univariate{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}equation{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1809 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}}Specify{\isaliteral{5F}{\isacharunderscore}}Method\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}PolyEq{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}normalize{\isaliteral{5F}{\isacharunderscore}}poly{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1810 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}}Apply{\isaliteral{5F}{\isacharunderscore}}Method\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}PolyEq{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}normalize{\isaliteral{5F}{\isacharunderscore}}poly{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1811 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}}Rewrite\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}all{\isaliteral{5F}{\isacharunderscore}}left{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}PolyEq{\isaliteral{2E}{\isachardot}}all{\isaliteral{5F}{\isacharunderscore}}left{\isaliteral{22}{\isachardoublequote}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1812 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}}Rewrite{\isaliteral{5F}{\isacharunderscore}}Set{\isaliteral{5F}{\isacharunderscore}}Inst\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{28}{\isacharparenleft}}bdv{\isaliteral{2C}{\isacharcomma}}\ A{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}make{\isaliteral{5F}{\isacharunderscore}}ratpoly{\isaliteral{5F}{\isacharunderscore}}in{\isaliteral{22}{\isachardoublequote}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1813 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}}Rewrite{\isaliteral{5F}{\isacharunderscore}}Set\ {\isaliteral{22}{\isachardoublequote}}polyeq{\isaliteral{5F}{\isacharunderscore}}simplify{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1814 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}}Subproblem\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}Isac{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}degree{\isaliteral{5F}{\isacharunderscore}}{\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}polynomial{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ \isanewline

  1815 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}univariate{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{22}{\isachardoublequote}}equation{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1816 {\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline

  1817 \isanewline

  1818 \isanewline

  1819 \isacommand{ML}\isamarkupfalse%

  1820 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

  1821 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

  1822 show{\isaliteral{5F}{\isacharunderscore}}pt\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1823 {\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline

  1824 \isanewline

  1825 \isacommand{ML}\isamarkupfalse%

  1826 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

  1827 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

  1828 show{\isaliteral{5F}{\isacharunderscore}}pt\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1829 {\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline

  1830 \isanewline

  1831 \isacommand{ML}\isamarkupfalse%

  1832 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

  1833 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

  1834 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

  1835 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

  1836 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

  1837 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

  1838 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

  1839 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

  1840 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

  1841 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

  1842 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

  1843 {\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline

  1844 \isanewline

  1845 \isacommand{ML}\isamarkupfalse%

  1846 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

  1847 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

  1848 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

  1849 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

  1850 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

  1851 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

  1852 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

  1853 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

  1854 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

  1855 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

  1856 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

  1857 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

  1858 {\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline

  1859 \isanewline

  1860 \isacommand{ML}\isamarkupfalse%

  1861 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

  1862 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

  1863 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

  1864 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

  1865 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

  1866 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

  1867 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

  1868 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

  1869 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

  1870 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

  1871 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

  1872 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

  1873 {\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline

  1874 \isanewline

  1875 \isacommand{ML}\isamarkupfalse%

  1876 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

  1877 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

  1878 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

  1879 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

  1880 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

  1881 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

  1882 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

  1883 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

  1884 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

  1885 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

  1886 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

  1887 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

  1888 {\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline

  1889 \isanewline

  1890 \isacommand{ML}\isamarkupfalse%

  1891 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

  1892 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

  1893 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

  1894 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

  1895 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

  1896 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

  1897 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

  1898 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

  1899 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

  1900 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

  1901 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

  1902 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

  1903 {\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline

  1904 \isanewline

  1905 \isanewline

  1906 \isacommand{ML}\isamarkupfalse%

  1907 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

  1908 trace{\isaliteral{5F}{\isacharunderscore}}script\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ true{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1909 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

  1910 show{\isaliteral{5F}{\isacharunderscore}}pt\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1911 {\isaliteral{2A7D}{\isacharverbatimclose}}%

  1912 \endisatagML

  1913 {\isafoldML}%

  1914 %

  1915 \isadelimML

  1916 %

  1917 \endisadelimML

  1918 %

  1919 \isamarkupsection{Write Tests for Crucial Details%

  1920 }

  1921 \isamarkuptrue%

  1922 %

  1923 \begin{isamarkuptext}%

  1924 ===================================%

  1925 \end{isamarkuptext}%

  1926 \isamarkuptrue%

  1927 %

  1928 \isadelimML

  1929 %

  1930 \endisadelimML

  1931 %

  1932 \isatagML

  1933 \isacommand{ML}\isamarkupfalse%

  1934 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

  1935 {\isaliteral{2A7D}{\isacharverbatimclose}}%

  1936 \endisatagML

  1937 {\isafoldML}%

  1938 %

  1939 \isadelimML

  1940 %

  1941 \endisadelimML

  1942 %

  1943 \isamarkupsection{Integrate Program into Knowledge%

  1944 }

  1945 \isamarkuptrue%

  1946 %

  1947 \isadelimML

  1948 %

  1949 \endisadelimML

  1950 %

  1951 \isatagML

  1952 \isacommand{ML}\isamarkupfalse%

  1953 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

  1954 print{\isaliteral{5F}{\isacharunderscore}}depth\ {\isadigit{9}}{\isadigit{9}}{\isadigit{9}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1955 {\isaliteral{2A7D}{\isacharverbatimclose}}%

  1956 \endisatagML

  1957 {\isafoldML}%

  1958 %

  1959 \isadelimML

  1960 %

  1961 \endisadelimML

  1962 \isanewline

  1963 %

  1964 \isadelimtheory

  1965 \isanewline

  1966 %

  1967 \endisadelimtheory

  1968 %

  1969 \isatagtheory

  1970 \isacommand{end}\isamarkupfalse%

  1971 %

  1972 \endisatagtheory

  1973 {\isafoldtheory}%

  1974 %

  1975 \isadelimtheory

  1976 %

  1977 \endisadelimtheory

  1978 \isanewline

  1979 \isanewline

  1980 \end{isabellebody}%

  1981 %%% Local Variables:

  1982 %%% mode: latex

  1983 %%% TeX-master: "root"

  1984 %%% End:

author	Jan Rocnik <jan.rocnik@student.tugraz.at>
	Sun, 12 Feb 2012 12:17:48 +0100
changeset 42365	872589b4852c
parent 42339	564e35533772
child 42368	3afe632cd527
permissions	-rw-r--r--