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 Inverse_Z_Transform.thy as an exercise.

    25   Because subsection "Stepwise Check the Program" requires

    26   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 \begin{isamarkuptext}%

   413 ---------------------------begin partial fractions snip--------------------------%

   414 \end{isamarkuptext}%

   415 \isamarkuptrue%

   416 %

   417 \isamarkupsubsubsection{get the denominator out of a fraction%

   418 }

   419 \isamarkuptrue%

   420 %

   421 \begin{isamarkuptext}%

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

   423 \end{isamarkuptext}%

   424 \isamarkuptrue%

   425 \isacommand{consts}\isamarkupfalse%

   426 \isanewline

   427 \ \ 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}}%

   428 \begin{isamarkuptext}%

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

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

   431   to Rationa.thy and re-building Isac.

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

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

   434 \end{isamarkuptext}%

   435 \isamarkuptrue%

   436 %

   437 \isadelimML

   438 %

   439 \endisadelimML

   440 %

   441 \isatagML

   442 \isacommand{ML}\isamarkupfalse%

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

   444 {\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

   445 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

   446 		\ \ \ \ \ \ {\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

   447 \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\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

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

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

   450 \ \ \ \ \ \ \ \ \ \ \ \ {\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

   451 	\ \ \ \ \ \ \ \ \ \ 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

   452 \ \ {\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

   453 \isanewline

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

   455 \endisatagML

   456 {\isafoldML}%

   457 %

   458 \isadelimML

   459 %

   460 \endisadelimML

   461 %

   462 \begin{isamarkuptext}%

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

   464 \end{isamarkuptext}%

   465 \isamarkuptrue%

   466 %

   467 \begin{isamarkuptext}%

   468 ---------------------------end partial fractions snip--------------------------%

   469 \end{isamarkuptext}%

   470 \isamarkuptrue%

   471 %

   472 \isamarkupsubsection{solve equation%

   473 }

   474 \isamarkuptrue%

   475 %

   476 \begin{isamarkuptext}%

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

   478 \end{isamarkuptext}%

   479 \isamarkuptrue%

   480 %

   481 \isadelimML

   482 %

   483 \endisadelimML

   484 %

   485 \isatagML

   486 \isacommand{ML}\isamarkupfalse%

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

   488 {\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

   489 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

   490 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

   491 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

   492 {\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

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

   494 \endisatagML

   495 {\isafoldML}%

   496 %

   497 \isadelimML

   498 %

   499 \endisadelimML

   500 %

   501 \begin{isamarkuptext}%

   502 Does the Equation Match the Specification ?%

   503 \end{isamarkuptext}%

   504 \isamarkuptrue%

   505 %

   506 \isadelimML

   507 %

   508 \endisadelimML

   509 %

   510 \isatagML

   511 \isacommand{ML}\isamarkupfalse%

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

   513 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

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

   515 \isacommand{ML}\isamarkupfalse%

   516 \ {\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

   517 \isanewline

   518 \isacommand{ML}\isamarkupfalse%

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

   520 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

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

   522 \ \ {\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

   523 \ \ \ {\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

   524 \ \ \ {\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

   525 \isanewline

   526 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

   527 \ \ {\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

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

   529 \endisatagML

   530 {\isafoldML}%

   531 %

   532 \isadelimML

   533 %

   534 \endisadelimML

   535 %

   536 \begin{isamarkuptext}%

   537 Does the Other Equation Match the Specification ?%

   538 \end{isamarkuptext}%

   539 \isamarkuptrue%

   540 %

   541 \isadelimML

   542 %

   543 \endisadelimML

   544 %

   545 \isatagML

   546 \isacommand{ML}\isamarkupfalse%

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

   548 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

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

   550 \endisatagML

   551 {\isafoldML}%

   552 %

   553 \isadelimML

   554 %

   555 \endisadelimML

   556 %

   557 \begin{isamarkuptext}%

   558 Solve Equation Stepwise%

   559 \end{isamarkuptext}%

   560 \isamarkuptrue%

   561 %

   562 \isadelimML

   563 %

   564 \endisadelimML

   565 %

   566 \isatagML

   567 \isacommand{ML}\isamarkupfalse%

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

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

   570 \isacommand{ML}\isamarkupfalse%

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

   572 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\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

   573 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\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

   574 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\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

   575 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\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

   576 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\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

   577 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\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

   578 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\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

   579 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\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

   580 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\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

   581 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\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

   582 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\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

   583 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\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

   584 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\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

   585 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\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

   586 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\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

   587 {\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

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

   589 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

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

   591 \endisatagML

   592 {\isafoldML}%

   593 %

   594 \isadelimML

   595 %

   596 \endisadelimML

   597 %

   598 \isamarkupsubsection{partial fraction decomposition%

   599 }

   600 \isamarkuptrue%

   601 %

   602 \isamarkupsubsubsection{solution of the equation%

   603 }

   604 \isamarkuptrue%

   605 %

   606 \isadelimML

   607 %

   608 \endisadelimML

   609 %

   610 \isatagML

   611 \isacommand{ML}\isamarkupfalse%

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

   613 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

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

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

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

   617 \endisatagML

   618 {\isafoldML}%

   619 %

   620 \isadelimML

   621 %

   622 \endisadelimML

   623 %

   624 \isamarkupsubsubsection{get solutions out of list%

   625 }

   626 \isamarkuptrue%

   627 %

   628 \begin{isamarkuptext}%

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

   630 \end{isamarkuptext}%

   631 \isamarkuptrue%

   632 %

   633 \isadelimML

   634 %

   635 \endisadelimML

   636 %

   637 \isatagML

   638 \isacommand{ML}\isamarkupfalse%

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

   640 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

   641 \ \ \ \ \ \ 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

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

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

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

   645 \isanewline

   646 \isacommand{ML}\isamarkupfalse%

   647 \ {\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

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

   649 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

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

   651 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

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

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

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

   655 \endisatagML

   656 {\isafoldML}%

   657 %

   658 \isadelimML

   659 %

   660 \endisadelimML

   661 %

   662 \isamarkupsubsubsection{build expression%

   663 }

   664 \isamarkuptrue%

   665 %

   666 \begin{isamarkuptext}%

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

   668 \end{isamarkuptext}%

   669 \isamarkuptrue%

   670 %

   671 \isadelimML

   672 %

   673 \endisadelimML

   674 %

   675 \isatagML

   676 \isacommand{ML}\isamarkupfalse%

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

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

   679 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

   680 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

   681 \isanewline

   682 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

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

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

   685 \endisatagML

   686 {\isafoldML}%

   687 %

   688 \isadelimML

   689 %

   690 \endisadelimML

   691 %

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

   693 }

   694 \isamarkuptrue%

   695 %

   696 \isadelimML

   697 %

   698 \endisadelimML

   699 %

   700 \isatagML

   701 \isacommand{ML}\isamarkupfalse%

   702 \ {\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}}%

   703 \endisatagML

   704 {\isafoldML}%

   705 %

   706 \isadelimML

   707 %

   708 \endisadelimML

   709 \isanewline

   710 \isanewline

   711 \isacommand{axiomatization}\isamarkupfalse%

   712 \ \isakeyword{where}\isanewline

   713 \ \ 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

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

   715 %

   716 \isadelimML

   717 \isanewline

   718 %

   719 \endisadelimML

   720 %

   721 \isatagML

   722 \isacommand{ML}\isamarkupfalse%

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

   724 {\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

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

   726 \isaantiq

   727 theory\ Isac{}%

   728 \endisaantiq

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

   730 \isaantiq

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

   732 \endisaantiq

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

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

   735 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

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

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

   738 \isacommand{ML}\isamarkupfalse%

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

   740 {\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

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

   742 \isaantiq

   743 theory\ Isac{}%

   744 \endisaantiq

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

   746 \isaantiq

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

   748 \endisaantiq

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

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

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

   752 \isacommand{ML}\isamarkupfalse%

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

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

   755 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}}\ %

   756 \isaantiq

   757 theory\ Isac{}%

   758 \endisaantiq

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

   760 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

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

   762 \isacommand{ML}\isamarkupfalse%

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

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

   765 \ \ 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

   766 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}}\ %

   767 \isaantiq

   768 theory\ Isac{}%

   769 \endisaantiq

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

   771 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

   772 {\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

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

   774 \isacommand{ML}\isamarkupfalse%

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

   776 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

   777 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

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

   779 {\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

   780 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}}\ %

   781 \isaantiq

   782 theory\ Isac{}%

   783 \endisaantiq

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

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

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

   787 \isacommand{ML}\isamarkupfalse%

   788 \ {\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}}%

   789 \endisatagML

   790 {\isafoldML}%

   791 %

   792 \isadelimML

   793 %

   794 \endisadelimML

   795 %

   796 \isamarkupsubsubsection{get first koeffizient%

   797 }

   798 \isamarkuptrue%

   799 %

   800 \isadelimML

   801 %

   802 \endisadelimML

   803 %

   804 \isatagML

   805 \isacommand{ML}\isamarkupfalse%

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

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

   808 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}}\ %

   809 \isaantiq

   810 theory\ Isac{}%

   811 \endisaantiq

   812 \ 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

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

   814 \isanewline

   815 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}}\ %

   816 \isaantiq

   817 theory\ Isac{}%

   818 \endisaantiq

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

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

   821 \isanewline

   822 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

   823 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

   824 {\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

   825 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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

   855 \endisatagML

   856 {\isafoldML}%

   857 %

   858 \isadelimML

   859 %

   860 \endisadelimML

   861 %

   862 \isamarkupsubsubsection{get second koeffizient%

   863 }

   864 \isamarkuptrue%

   865 %

   866 \isadelimML

   867 %

   868 \endisadelimML

   869 %

   870 \isatagML

   871 \isacommand{ML}\isamarkupfalse%

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

   873 \isanewline

   874 \isacommand{ML}\isamarkupfalse%

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

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

   877 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}}\ %

   878 \isaantiq

   879 theory\ Isac{}%

   880 \endisaantiq

   881 \ 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

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

   883 \isanewline

   884 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}}\ %

   885 \isaantiq

   886 theory\ Isac{}%

   887 \endisaantiq

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

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

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

   891 \isacommand{ML}\isamarkupfalse%

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

   893 {\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

   894 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

   895 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

   896 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

   897 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

   898 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

   899 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

   900 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

   901 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

   902 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

   903 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

   904 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

   905 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

   906 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

   907 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

   908 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

   909 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

   910 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

   911 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

   912 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

   913 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

   914 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

   915 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

   916 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

   917 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

   918 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

   919 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

   920 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

   921 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

   922 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

   923 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

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

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

   926 \isanewline

   927 \isacommand{ML}\isamarkupfalse%

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

   929 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

   930 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

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

   932 \endisatagML

   933 {\isafoldML}%

   934 %

   935 \isadelimML

   936 %

   937 \endisadelimML

   938 %

   939 \isamarkupsubsubsection{substitute expression with solutions%

   940 }

   941 \isamarkuptrue%

   942 %

   943 \isadelimML

   944 %

   945 \endisadelimML

   946 %

   947 \isatagML

   948 \isacommand{ML}\isamarkupfalse%

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

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

   951 \isacommand{ML}\isamarkupfalse%

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

   953 \endisatagML

   954 {\isafoldML}%

   955 %

   956 \isadelimML

   957 %

   958 \endisadelimML

   959 %

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

   961 }

   962 \isamarkuptrue%

   963 %

   964 \begin{isamarkuptext}%

   965 ==============================================%

   966 \end{isamarkuptext}%

   967 \isamarkuptrue%

   968 %

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

   970 }

   971 \isamarkuptrue%

   972 \isacommand{consts}\isamarkupfalse%

   973 \isanewline

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

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

   976 \isamarkupsubsection{Define the Specification%

   977 }

   978 \isamarkuptrue%

   979 %

   980 \isadelimML

   981 %

   982 \endisadelimML

   983 %

   984 \isatagML

   985 \isacommand{ML}\isamarkupfalse%

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

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

   988 \ {\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

   989 \ {\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

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

   991 \ {\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

   992 \ {\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

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

   994 \isacommand{ML}\isamarkupfalse%

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

   996 \isacommand{ML}\isamarkupfalse%

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

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

   999 \ {\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

  1000 \ {\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

  1001 \ \ {\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

  1002 \ \ \ {\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

  1003 \ \ {\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\isanewline

  1004 \ \ 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

  1005 \ \ {\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

  1006 \isanewline

  1007 show{\isaliteral{5F}{\isacharunderscore}}ptyps{\isaliteral{28}{\isacharparenleft}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1008 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

  1009 {\isaliteral{2A7D}{\isacharverbatimclose}}%

  1010 \endisatagML

  1011 {\isafoldML}%

  1012 %

  1013 \isadelimML

  1014 %

  1015 \endisadelimML

  1016 %

  1017 \isamarkupsubsection{Define Name and Signature for the Method%

  1018 }

  1019 \isamarkuptrue%

  1020 \isacommand{consts}\isamarkupfalse%

  1021 \isanewline

  1022 \ \ 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

  1023 \ \ \ \ {\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}}%

  1024 \isamarkupsubsection{Setup Parent Nodes in Hierarchy of Method%

  1025 }

  1026 \isamarkuptrue%

  1027 %

  1028 \isadelimML

  1029 %

  1030 \endisadelimML

  1031 %

  1032 \isatagML

  1033 \isacommand{ML}\isamarkupfalse%

  1034 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

  1035 store{\isaliteral{5F}{\isacharunderscore}}met\isanewline

  1036 \ {\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

  1037 \ {\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

  1038 \ \ \ {\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

  1039 \ \ \ \ 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

  1040 store{\isaliteral{5F}{\isacharunderscore}}met\isanewline

  1041 \ {\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

  1042 \ {\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

  1043 \ \ \ {\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

  1044 \ \ \ \ 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

  1045 {\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline

  1046 \isacommand{ML}\isamarkupfalse%

  1047 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

  1048 store{\isaliteral{5F}{\isacharunderscore}}met\isanewline

  1049 \ {\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

  1050 \ {\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

  1051 \ \ {\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

  1052 \ \ \ {\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

  1053 \ \ {\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\isanewline

  1054 \ \ \ {\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

  1055 \ \ \ \ 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

  1056 \ \ {\isaliteral{22}{\isachardoublequote}}empty{\isaliteral{5F}{\isacharunderscore}}script{\isaliteral{22}{\isachardoublequote}}\isanewline

  1057 \ {\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1058 {\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline

  1059 \isacommand{ML}\isamarkupfalse%

  1060 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

  1061 store{\isaliteral{5F}{\isacharunderscore}}met\isanewline

  1062 \ {\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

  1063 \ {\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

  1064 \ \ {\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

  1065 \ \ \ {\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

  1066 \ \ {\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\isanewline

  1067 \ \ \ {\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

  1068 \ \ \ \ 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

  1069 \ \ {\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

  1070 \ \ {\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{28}{\isacharparenleft}}let\ X\ {\isaliteral{3D}{\isacharequal}}\ Take\ Xeq{\isaliteral{3B}{\isacharsemicolon}}{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5E}{\isacharcircum}}\isanewline

  1071 \ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ X\ {\isaliteral{3D}{\isacharequal}}\ Rewrite\ ruleZY\ False\ X{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5E}{\isacharcircum}}\isanewline

  1072 \ \ {\isaliteral{22}{\isachardoublequote}}\ \ in\ X{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}\isanewline

  1073 \ {\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1074 {\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline

  1075 \isacommand{ML}\isamarkupfalse%

  1076 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

  1077 show{\isaliteral{5F}{\isacharunderscore}}mets{\isaliteral{28}{\isacharparenleft}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1078 {\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline

  1079 \isacommand{ML}\isamarkupfalse%

  1080 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

  1081 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

  1082 {\isaliteral{2A7D}{\isacharverbatimclose}}%

  1083 \endisatagML

  1084 {\isafoldML}%

  1085 %

  1086 \isadelimML

  1087 %

  1088 \endisadelimML

  1089 %

  1090 \isamarkupsection{Program in CTP-based language \label{prog-steps}%

  1091 }

  1092 \isamarkuptrue%

  1093 %

  1094 \begin{isamarkuptext}%

  1095 =================================%

  1096 \end{isamarkuptext}%

  1097 \isamarkuptrue%

  1098 %

  1099 \isamarkupsubsection{Stepwise extend Program%

  1100 }

  1101 \isamarkuptrue%

  1102 %

  1103 \isadelimML

  1104 %

  1105 \endisadelimML

  1106 %

  1107 \isatagML

  1108 \isacommand{ML}\isamarkupfalse%

  1109 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

  1110 val\ str\ {\isaliteral{3D}{\isacharequal}}\ \isanewline

  1111 {\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

  1112 {\isaliteral{22}{\isachardoublequote}}\ Xeq{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1113 {\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline

  1114 \isacommand{ML}\isamarkupfalse%

  1115 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

  1116 val\ str\ {\isaliteral{3D}{\isacharequal}}\ \isanewline

  1117 {\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

  1118 {\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{28}{\isacharparenleft}}let\ X\ {\isaliteral{3D}{\isacharequal}}\ Take\ Xeq{\isaliteral{3B}{\isacharsemicolon}}{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5E}{\isacharcircum}}\isanewline

  1119 {\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

  1120 {\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

  1121 {\isaliteral{22}{\isachardoublequote}}\ \ in\ X{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1122 {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}NONE{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1123 {\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

  1124 {\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{28}{\isacharparenleft}}let\ X\ {\isaliteral{3D}{\isacharequal}}\ Take\ Xeq{\isaliteral{3B}{\isacharsemicolon}}{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5E}{\isacharcircum}}\isanewline

  1125 {\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

  1126 {\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

  1127 {\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

  1128 \ \ \ \ {\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

  1129 {\isaliteral{22}{\isachardoublequote}}\ \ in\ X{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1130 {\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline

  1131 \isacommand{ML}\isamarkupfalse%

  1132 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

  1133 val\ str\ {\isaliteral{3D}{\isacharequal}}\ \isanewline

  1134 {\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

  1135 {\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{28}{\isacharparenleft}}let\ X\ {\isaliteral{3D}{\isacharequal}}\ Take\ Xeq{\isaliteral{3B}{\isacharsemicolon}}{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5E}{\isacharcircum}}\isanewline

  1136 {\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

  1137 {\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

  1138 {\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

  1139 {\isaliteral{22}{\isachardoublequote}}\ \ in\ X{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1140 {\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline

  1141 \isacommand{ML}\isamarkupfalse%

  1142 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

  1143 val\ str\ {\isaliteral{3D}{\isacharequal}}\ \isanewline

  1144 {\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

  1145 {\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

  1146 {\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

  1147 {\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

  1148 {\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

  1149 {\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

  1150 {\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

  1151 {\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

  1152 {\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

  1153 {\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

  1154 {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{28}{\isacharparenleft}}SubProblem\ {\isaliteral{28}{\isacharparenleft}}Test{\isaliteral{27}{\isacharprime}}{\isaliteral{2C}{\isacharcomma}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5E}{\isacharcircum}}\isanewline

  1155 {\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

  1156 {\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

  1157 {\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

  1158 {\isaliteral{22}{\isachardoublequote}}\ \ in\ X{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}\isanewline

  1159 {\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1160 \isanewline

  1161 parse\ thy\ str{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1162 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

  1163 atomty\ sc{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1164 \isanewline

  1165 {\isaliteral{2A7D}{\isacharverbatimclose}}%

  1166 \endisatagML

  1167 {\isafoldML}%

  1168 %

  1169 \isadelimML

  1170 %

  1171 \endisadelimML

  1172 %

  1173 \begin{isamarkuptext}%

  1174 This ruleset contains all functions that are in the script;

  1175 The evaluation of the functions is done by rewriting using this ruleset.%

  1176 \end{isamarkuptext}%

  1177 \isamarkuptrue%

  1178 %

  1179 \isadelimML

  1180 %

  1181 \endisadelimML

  1182 %

  1183 \isatagML

  1184 \isacommand{ML}\isamarkupfalse%

  1185 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

  1186 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

  1187 		\ \ 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

  1188 		\ \ 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

  1189 				\ \ \ \ {\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

  1190 				\ \ \ \ \ {\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

  1191 				\ \ \ \ {\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ \isanewline

  1192 \ \ srls\ {\isaliteral{3D}{\isacharequal}}\ Erls{\isaliteral{2C}{\isacharcomma}}\ calc\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\isanewline

  1193 		\ \ rules\ {\isaliteral{3D}{\isacharequal}}\isanewline

  1194 \ \ \ \ {\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\ %

  1195 \isaantiq

  1196 thm\ NTH{\isaliteral{5F}{\isacharunderscore}}CONS{}%

  1197 \endisaantiq

  1198 {\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\isanewline

  1199 			\ \ \ \ \ 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

  1200 			\ \ \ \ \ Thm\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}NTH{\isaliteral{5F}{\isacharunderscore}}NIL{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}num{\isaliteral{5F}{\isacharunderscore}}str\ %

  1201 \isaantiq

  1202 thm\ NTH{\isaliteral{5F}{\isacharunderscore}}NIL{}%

  1203 \endisaantiq

  1204 {\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\isanewline

  1205 			\ \ \ \ \ 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

  1206 			\ \ \ \ \ 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

  1207 			\ \ \ \ \ 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

  1208 \ \ \ \ \ Calc{\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}Rational{\isaliteral{2E}{\isachardot}}get{\isaliteral{5F}{\isacharunderscore}}denominator{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\isanewline

  1209 \ \ \ \ \ \ \ eval{\isaliteral{5F}{\isacharunderscore}}get{\isaliteral{5F}{\isacharunderscore}}denominator\ {\isaliteral{22}{\isachardoublequote}}Rational{\isaliteral{2E}{\isachardot}}get{\isaliteral{5F}{\isacharunderscore}}denominator{\isaliteral{22}{\isachardoublequote}}{\isaliteral{29}{\isacharparenright}}\isanewline

  1210 			\ \ \ \ {\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\isanewline

  1211 		\ \ scr\ {\isaliteral{3D}{\isacharequal}}\ EmptyScr{\isaliteral{7D}{\isacharbraceright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1212 {\isaliteral{2A7D}{\isacharverbatimclose}}%

  1213 \endisatagML

  1214 {\isafoldML}%

  1215 %

  1216 \isadelimML

  1217 %

  1218 \endisadelimML

  1219 %

  1220 \isamarkupsubsection{Store Final Version of Program for Execution%

  1221 }

  1222 \isamarkuptrue%

  1223 %

  1224 \isadelimML

  1225 %

  1226 \endisadelimML

  1227 %

  1228 \isatagML

  1229 \isacommand{ML}\isamarkupfalse%

  1230 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

  1231 store{\isaliteral{5F}{\isacharunderscore}}met\isanewline

  1232 \ {\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

  1233 \ {\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

  1234 \ \ {\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

  1235 \ \ \ {\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

  1236 \ \ {\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\isanewline

  1237 \ \ \ {\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

  1238 \ \ \ \ prls\ {\isaliteral{3D}{\isacharequal}}\ e{\isaliteral{5F}{\isacharunderscore}}rls{\isaliteral{2C}{\isacharcomma}}\isanewline

  1239 \ \ \ \ 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

  1240 {\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

  1241 {\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

  1242 {\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

  1243 {\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

  1244 {\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

  1245 {\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

  1246 {\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

  1247 {\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

  1248 {\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

  1249 \isanewline

  1250 {\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

  1251 {\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}}meth{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5E}{\isacharcircum}}\isanewline

  1252 {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ \ \ {\isaliteral{5B}{\isacharbrackleft}}BOOL\ equ{\isaliteral{2C}{\isacharcomma}}\ REAL\ zzz{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ {\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5E}{\isacharcircum}}\isanewline

  1253 {\isaliteral{22}{\isachardoublequote}}\ \ in\ X{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}\isanewline

  1254 \ {\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1255 {\isaliteral{2A7D}{\isacharverbatimclose}}%

  1256 \endisatagML

  1257 {\isafoldML}%

  1258 %

  1259 \isadelimML

  1260 %

  1261 \endisadelimML

  1262 %

  1263 \isamarkupsubsection{Check the Program%

  1264 }

  1265 \isamarkuptrue%

  1266 %

  1267 \isamarkupsubsubsection{Check the formalization%

  1268 }

  1269 \isamarkuptrue%

  1270 %

  1271 \isadelimML

  1272 %

  1273 \endisadelimML

  1274 %

  1275 \isatagML

  1276 \isacommand{ML}\isamarkupfalse%

  1277 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

  1278 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

  1279 \ \ {\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

  1280 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

  1281 \ \ {\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

  1282 \isanewline

  1283 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

  1284 \ \ \ \ \ \ \ \ \ \ \ \ {\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

  1285 \ \ \ \ \ \ \ \ \ \ \ {\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

  1286 \ \ \ \ \ \ \ \ \ \ \ \ {\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

  1287 \ \ \ \ \ \ \ \ \ \ {\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

  1288 {\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline

  1289 \isacommand{ML}\isamarkupfalse%

  1290 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

  1291 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

  1292 atomty\ sc{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1293 {\isaliteral{2A7D}{\isacharverbatimclose}}%

  1294 \endisatagML

  1295 {\isafoldML}%

  1296 %

  1297 \isadelimML

  1298 %

  1299 \endisadelimML

  1300 %

  1301 \isamarkupsubsubsection{Stepwise check the program%

  1302 }

  1303 \isamarkuptrue%

  1304 %

  1305 \isadelimML

  1306 %

  1307 \endisadelimML

  1308 %

  1309 \isatagML

  1310 \isacommand{ML}\isamarkupfalse%

  1311 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

  1312 trace{\isaliteral{5F}{\isacharunderscore}}rewrite\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3D}{\isacharequal}}\ false{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1313 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

  1314 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

  1315 \ \ {\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

  1316 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

  1317 \ \ {\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

  1318 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\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

  1319 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\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

  1320 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\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

  1321 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\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

  1322 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\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

  1323 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\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

  1324 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\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

  1325 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\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

  1326 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\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

  1327 {\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline

  1328 \isacommand{ML}\isamarkupfalse%

  1329 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

  1330 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\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}}\ Empty{\isaliteral{5F}{\isacharunderscore}}Tac\ instead\ of\ SubProblem{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1331 {\isaliteral{2A7D}{\isacharverbatimclose}}%

  1332 \endisatagML

  1333 {\isafoldML}%

  1334 %

  1335 \isadelimML

  1336 %

  1337 \endisadelimML

  1338 %

  1339 \begin{isamarkuptext}%

  1340 Instead of nxt = Subproblem above we had Empty_Tac; the search for the reason

  1341   considered the following points:

  1342   # what shows show_pt pt; ...

  1343     (([2], Res), ?X' z = 24 / (-1 + -2 * z + 8 * z ^^^ 2))] ..calculation ok,

  1344     but no "next" step found: should be "nxt = Subproblem" ?!?

  1345   # what shows trace_script := true; we read bottom up ...

  1346     @@@ next   leaf 'SubProbfrom

  1347      (PolyEq', [abcFormula, degree_2, polynomial, univariate, equation],

  1348       no_meth)

  1349      [BOOL equ, REAL z]' ---> STac 'SubProblem

  1350      (PolyEq', [abcFormula, degree_2, polynomial, univariate, equation],

  1351       no_meth)

  1352      [BOOL (-1 + -2 * z + 8 * z ^^^ 2 = 0), REAL z]'

  1353     ... and see the SubProblem with correct arguments from searching next step

  1354     (program text !!!--->!!! STac (script tactic) with arguments evaluated.)

  1355   # do we have the right Script ...

  1356     val Script s = (#scr o get_met) ["SignalProcessing","Z_Transform","inverse"];

  1357     writeln (term2str s);

  1358     ... shows the right script.

  1359   # test --- why helpless here ? --- shows: replace no_meth by [no_meth] in Script%

  1360 \end{isamarkuptext}%

  1361 \isamarkuptrue%

  1362 %

  1363 \isadelimML

  1364 %

  1365 \endisadelimML

  1366 %

  1367 \isatagML

  1368 \isacommand{ML}\isamarkupfalse%

  1369 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

  1370 print{\isaliteral{5F}{\isacharunderscore}}depth\ {\isadigit{9}}{\isadigit{9}}{\isadigit{9}}{\isadigit{9}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1371 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\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}}\ Empty{\isaliteral{5F}{\isacharunderscore}}Tac\ instead\ Model{\isaliteral{5F}{\isacharunderscore}}Problem{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1372 print{\isaliteral{5F}{\isacharunderscore}}depth\ {\isadigit{9}}{\isadigit{9}}{\isadigit{9}}{\isadigit{9}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1373 {\isaliteral{2A7D}{\isacharverbatimclose}}%

  1374 \endisatagML

  1375 {\isafoldML}%

  1376 %

  1377 \isadelimML

  1378 %

  1379 \endisadelimML

  1380 %

  1381 \begin{isamarkuptext}%

  1382 Instead of nxt = Model_Problem above we had Empty_Tac; the search for the reason

  1383   considered the following points:

  1384   # comparison with subsection { *solve equation* }: there solving this equation works,

  1385     so there must be some difference in the arguments of the Subproblem.%

  1386 \end{isamarkuptext}%

  1387 \isamarkuptrue%

  1388 %

  1389 \isadelimML

  1390 %

  1391 \endisadelimML

  1392 %

  1393 \isatagML

  1394 \isacommand{ML}\isamarkupfalse%

  1395 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

  1396 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{22}{\isachardoublequote}}equality\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2D}{\isacharminus}}{\isadigit{1}}\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{2}}\ {\isaliteral{2A}{\isacharasterisk}}\ z\ {\isaliteral{2B}{\isacharplus}}\ {\isadigit{8}}\ {\isaliteral{2A}{\isacharasterisk}}\ z\ {\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}{\isaliteral{5E}{\isacharcircum}}\ {\isadigit{2}}\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{0}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1397 {\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline

  1398 \isacommand{ML}\isamarkupfalse%

  1399 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

  1400 \isanewline

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

  1402 \isacommand{ML}\isamarkupfalse%

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

  1404 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{22}{\isachardoublequote}}solveFor\ z{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1405 {\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline

  1406 \isacommand{ML}\isamarkupfalse%

  1407 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

  1408 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{22}{\isachardoublequote}}nxt\ {\isaliteral{3D}{\isacharequal}}\ Add{\isaliteral{5F}{\isacharunderscore}}Find{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1409 {\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline

  1410 \isacommand{ML}\isamarkupfalse%

  1411 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

  1412 show{\isaliteral{5F}{\isacharunderscore}}pt\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1413 {\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline

  1414 \isacommand{ML}\isamarkupfalse%

  1415 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

  1416 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{22}{\isachardoublequote}}nxt\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}Empty{\isaliteral{5F}{\isacharunderscore}}Tac{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1417 {\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline

  1418 \isacommand{ML}\isamarkupfalse%

  1419 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

  1420 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{22}{\isachardoublequote}}nxt\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}Empty{\isaliteral{5F}{\isacharunderscore}}Tac\ instead\ Specify{\isaliteral{5F}{\isacharunderscore}}Theory{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1421 {\isaliteral{2A7D}{\isacharverbatimclose}}%

  1422 \endisatagML

  1423 {\isafoldML}%

  1424 %

  1425 \isadelimML

  1426 %

  1427 \endisadelimML

  1428 %

  1429 \begin{isamarkuptext}%

  1430 We had "nxt = (Empty_Tac"; the search for the reason considered the following points:

  1431   # was there an error message ? NO --ok

  1432   # has "nxt = Add_Find" been inserted in pt: get_obj g_pbl pt (fst p); YES --ok

  1433   # what is the returned "formula": print_depth 999; f; print_depth 999; --

  1434     {Find = [Correct "solutions z_i"], With = [],

  1435      Given = [Correct "equality (-1 + -2 * z + 8 * z ^^^ 2 = 0)", Correct "solveFor z"],

  1436      Where = [False "matches (z = 0) (-1 + -2 * z + 8 * z ^^^ 2 = 0) |\n

  1437                      matches (?b * z = 0) (-1 + -2 * z + 8 * z ^^^ 2 = 0) |\n

  1438                      matches (?a + z = 0) (-1 + -2 * z + 8 * z ^^^ 2 = 0) |\n

  1439                      matches (?a + ?b * z = 0) (-1 + -2 * z + 8 * z ^^^ 2 = 0)"],

  1440      Relate = []}

  1441      -- the only False is the reason: the Where (the precondition) is False for good reasons:

  1442      the precondition seems to check for linear equations, not for the one we want to solve!

  1443   Removed this error by correcting the Script

  1444   from SubProblem (PolyEq', [linear,univariate,equation,test], [Test,solve_linear]

  1445   to   SubProblem (PolyEq', [abcFormula,degree_2,polynomial,univariate,equation],

  1446                    [PolyEq,solve_d2_polyeq_abc_equation]

  1447   You find the appropriate type of equation at

  1448     http://www.ist.tugraz.at/projects/isac/www/kbase/pbl/index_pbl.html

  1449   and the respective method in Knowledge/PolyEq.thy at the respective store_pbt.

  1450   Or you leave the selection of the appropriate type to isac as done in the final Script ;-))%

  1451 \end{isamarkuptext}%

  1452 \isamarkuptrue%

  1453 %

  1454 \isadelimML

  1455 %

  1456 \endisadelimML

  1457 %

  1458 \isatagML

  1459 \isacommand{ML}\isamarkupfalse%

  1460 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

  1461 val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\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

  1462 {\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline

  1463 \isacommand{ML}\isamarkupfalse%

  1464 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

  1465 \isanewline

  1466 {\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline

  1467 \isacommand{ML}\isamarkupfalse%

  1468 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

  1469 show{\isaliteral{5F}{\isacharunderscore}}pt\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline

  1470 {\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline

  1471 \isacommand{ML}\isamarkupfalse%

  1472 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

  1473 {\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline

  1474 \isacommand{ML}\isamarkupfalse%

  1475 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

  1476 \isanewline

  1477 {\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline

  1478 \isacommand{ML}\isamarkupfalse%

  1479 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

  1480 \isanewline

  1481 {\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline

  1482 \isacommand{ML}\isamarkupfalse%

  1483 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

  1484 \isanewline

  1485 {\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline

  1486 \isacommand{ML}\isamarkupfalse%

  1487 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

  1488 \isanewline

  1489 {\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline

  1490 \isanewline

  1491 \isacommand{ML}\isamarkupfalse%

  1492 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

  1493 \isanewline

  1494 {\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline

  1495 \isacommand{ML}\isamarkupfalse%

  1496 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

  1497 %

  1498 \isaantiq

  1499 theory\ Isac{}%

  1500 \endisaantiq

  1501 \isanewline

  1502 {\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline

  1503 \isanewline

  1504 \isacommand{ML}\isamarkupfalse%

  1505 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

  1506 {\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline

  1507 \isacommand{ML}\isamarkupfalse%

  1508 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

  1509 {\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline

  1510 \isacommand{ML}\isamarkupfalse%

  1511 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

  1512 {\isaliteral{2A7D}{\isacharverbatimclose}}%

  1513 \endisatagML

  1514 {\isafoldML}%

  1515 %

  1516 \isadelimML

  1517 %

  1518 \endisadelimML

  1519 %

  1520 \isamarkupsection{Write Tests for Crucial Details%

  1521 }

  1522 \isamarkuptrue%

  1523 %

  1524 \begin{isamarkuptext}%

  1525 ===================================%

  1526 \end{isamarkuptext}%

  1527 \isamarkuptrue%

  1528 %

  1529 \isadelimML

  1530 %

  1531 \endisadelimML

  1532 %

  1533 \isatagML

  1534 \isacommand{ML}\isamarkupfalse%

  1535 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

  1536 \isanewline

  1537 {\isaliteral{2A7D}{\isacharverbatimclose}}%

  1538 \endisatagML

  1539 {\isafoldML}%

  1540 %

  1541 \isadelimML

  1542 %

  1543 \endisadelimML

  1544 %

  1545 \isamarkupsection{Integrate Program into Knowledge%

  1546 }

  1547 \isamarkuptrue%

  1548 %

  1549 \isadelimML

  1550 %

  1551 \endisadelimML

  1552 %

  1553 \isatagML

  1554 \isacommand{ML}\isamarkupfalse%

  1555 \ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline

  1556 %

  1557 \isaantiq

  1558 theory\ Isac{}%

  1559 \endisaantiq

  1560 \isanewline

  1561 {\isaliteral{2A7D}{\isacharverbatimclose}}%

  1562 \endisatagML

  1563 {\isafoldML}%

  1564 %

  1565 \isadelimML

  1566 %

  1567 \endisadelimML

  1568 \isanewline

  1569 %

  1570 \isadelimtheory

  1571 \isanewline

  1572 %

  1573 \endisadelimtheory

  1574 %

  1575 \isatagtheory

  1576 \isacommand{end}\isamarkupfalse%

  1577 %

  1578 \endisatagtheory

  1579 {\isafoldtheory}%

  1580 %

  1581 \isadelimtheory

  1582 %

  1583 \endisadelimtheory

  1584 \isanewline

  1585 \isanewline

  1586 \end{isabellebody}%

  1587 %%% Local Variables:

  1588 %%% mode: latex

  1589 %%% TeX-master: "root"

  1590 %%% End:

author	Jan Rocnik <jan.rocnik@student.tugraz.at>
	Fri, 14 Oct 2011 09:03:25 +0200
branch	decompose-isar
changeset 42316	cd1ccadd11c9
parent 42304	68a2fbbac02e
child 42339	564e35533772
permissions	-rw-r--r--