1.1 --- /dev/null Thu Jan 01 00:00:00 1970 +0000
1.2 +++ b/doc-src/isac/jrocnik/Inverse_Z_Transform/Inverse_Z_Transform.thy Thu Sep 08 23:17:35 2011 +0200
1.3 @@ -0,0 +1,449 @@
1.4 +(* Title: Test_Z_Transform
1.5 + Author: Jan Rocnik
1.6 + (c) copyright due to lincense terms.
1.7 +12345678901234567890123456789012345678901234567890123456789012345678901234567890
1.8 + 10 20 30 40 50 60 70 80
1.9 +*)
1.10 +
1.11 +theory Inverse_Z_Transform imports Isac begin
1.12 +
1.13 +section {*trials towards Z transform *}
1.14 +text{*===============================*}
1.15 +subsection {*terms*}
1.16 +ML {*
1.17 +@{term "1 < || z ||"};
1.18 +@{term "z / (z - 1)"};
1.19 +@{term "-u -n - 1"};
1.20 +@{term "-u [-n - 1]"}; (*[ ] denotes lists !!!*)
1.21 +@{term "z /(z - 1) = -u [-n - 1]"};Isac
1.22 +@{term "1 < || z || ==> z / (z - 1) = -u [-n - 1]"};
1.23 +term2str @{term "1 < || z || ==> z / (z - 1) = -u [-n - 1]"};
1.24 +*}
1.25 +ML {*
1.26 +(*alpha --> "</alpha>" *)
1.27 +
1.28 +@{term "\<alpha> "};
1.29 +@{term "\<delta> "};
1.30 +@{term "\<phi> "};
1.31 +@{term "\<rho> "};
1.32 +term2str @{term "\<rho> "};
1.33 +*}
1.34 +
1.35 +subsection {*rules*}
1.36 +(*axiomatization "z / (z - 1) = -u [-n - 1]" Illegal variable name: "z / (z - 1) = -u [-n - 1]" *)
1.37 +(*definition "z / (z - 1) = -u [-n - 1]" Bad head of lhs: existing constant "op /"*)
1.38 +axiomatization where
1.39 + rule1: "1 = \<delta>[n]" and
1.40 + rule2: "|| z || > 1 ==> z / (z - 1) = u [n]" and
1.41 + rule3: "|| z || < 1 ==> z / (z - 1) = -u [-n - 1]" and
1.42 + rule4: "|| z || > || \<alpha> || ==> z / (z - \<alpha>) = \<alpha>^n * u [n]" and
1.43 + rule5: "|| z || < || \<alpha> || ==> z / (z - \<alpha>) = -(\<alpha>^n) * u [-n - 1]" and
1.44 + rule6: "|| z || > 1 ==> z/(z - 1)^2 = n * u [n]"
1.45 +ML {*
1.46 +@{thm rule1};
1.47 +@{thm rule2};
1.48 +@{thm rule3};
1.49 +@{thm rule4};
1.50 +*}
1.51 +
1.52 +subsection {*apply rules*}
1.53 +ML {*
1.54 +val inverse_Z = append_rls "inverse_Z" e_rls
1.55 + [ Thm ("rule3",num_str @{thm rule3}),
1.56 + Thm ("rule4",num_str @{thm rule4}),
1.57 + Thm ("rule1",num_str @{thm rule1})
1.58 + ];
1.59 +
1.60 +val t = str2term "z / (z - 1) + z / (z - \<alpha>) + 1";
1.61 +val SOME (t', asm) = rewrite_set_ thy true inverse_Z t;
1.62 +term2str t' = "z / (z - ?\<delta> [?n]) + z / (z - \<alpha>) + ?\<delta> [?n]"; (*attention rule1 !!!*)
1.63 +*}
1.64 +ML {*
1.65 +val (thy, ro, er) = (@{theory}, tless_true, eval_rls);
1.66 +*}
1.67 +ML {*
1.68 +val SOME (t, asm1) = rewrite_ thy ro er true (num_str @{thm rule3}) t;
1.69 +term2str t = "- ?u [- ?n - 1] + z / (z - \<alpha>) + 1"; (*- real *)
1.70 +term2str t;
1.71 +*}
1.72 +ML {*
1.73 +val SOME (t, asm2) = rewrite_ thy ro er true (num_str @{thm rule4}) t;
1.74 +term2str t = "- ?u [- ?n - 1] + \<alpha> ^ ?n * ?u [?n] + 1"; (*- real *)
1.75 +term2str t;
1.76 +*}
1.77 +ML {*
1.78 +val SOME (t, asm3) = rewrite_ thy ro er true (num_str @{thm rule1}) t;
1.79 +term2str t = "- ?u [- ?n - 1] + \<alpha> ^ ?n * ?u [?n] + ?\<delta> [?n]"; (*- real *)
1.80 +term2str t;
1.81 +*}
1.82 +ML {*
1.83 +terms2str (asm1 @ asm2 @ asm3);
1.84 +*}
1.85 +
1.86 +section {*Prepare steps in CTP-based programming language*}
1.87 +text{*===================================================*}
1.88 +subsection {*prepare expression*}
1.89 +ML {*
1.90 +val ctxt = ProofContext.init_global @{theory};
1.91 +val ctxt = declare_constraints' [@{term "z::real"}] ctxt;
1.92 +
1.93 +val SOME fun1 = parseNEW ctxt "X z = 3 / (z - 1/4 + -1/8 * z ^ -1)"; term2str fun1;
1.94 +val SOME fun1' = parseNEW ctxt "X z = 3 / (z - 1/4 + -1/8 * (1/z))"; term2str fun1';
1.95 +*}
1.96 +
1.97 +axiomatization where
1.98 + ruleZY: "(X z = a / b) = (X' z = a / (z * b))"
1.99 +
1.100 +ML {*
1.101 +val (thy, ro, er) = (@{theory}, tless_true, eval_rls);
1.102 +val SOME (fun2, asm1) = rewrite_ thy ro er true @{thm ruleZY} fun1; term2str fun2;
1.103 +val SOME (fun2', asm1) = rewrite_ thy ro er true @{thm ruleZY} fun1'; term2str fun2';
1.104 +
1.105 +val SOME (fun3,_) = rewrite_set_ @{theory Isac} false norm_Rational fun2;
1.106 +term2str fun3; (*fails on x^(-1) TODO*)
1.107 +val SOME (fun3',_) = rewrite_set_ @{theory Isac} false norm_Rational fun2';
1.108 +term2str fun3'; (*OK*)
1.109 +
1.110 +val (_, expr) = HOLogic.dest_eq fun3'; term2str expr;
1.111 +*}
1.112 +
1.113 +subsection {*solve equation*}
1.114 +ML {*(*from test/Tools/isac/Minisubpbl/100-init-rootpbl.sml*)
1.115 +"----------- Minisubplb/100-init-rootp (*OK*)bl.sml ---------------------";
1.116 +val denominator = parseNEW ctxt "z^2 - 1/4*z - 1/8 = 0";
1.117 +val fmz = ["equality (z^2 - 1/4*z - 1/8 = (0::real))", "solveFor z","solutions L"];
1.118 +val (dI',pI',mI') =("Isac", ["univariate","equation"], ["no_met"]);
1.119 +(* ^^^^^^^^^^^^^^^^^^^^^^ TODO: ISAC determines type of eq*)
1.120 +*}
1.121 +ML {*
1.122 +val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
1.123 +val (p,_,f,nxt,_,pt) = me nxt p [] pt;
1.124 +(*[
1.125 +(([], Frm), solve (z ^ 2 - 1 / 4 * z - 1 / 8 = 0, z)),
1.126 +(([1], Frm), z ^ 2 - 1 / 4 * z - 1 / 8 = 0), bad rewrite order
1.127 +(([1], Res), -1 / 8 + z ^ 2 + -1 / 4 * z = 0), bad pattern
1.128 +(([2], Pbl), solve (-1 / 8 + z ^ 2 + -1 / 4 * z = 0, z)),
1.129 +(([2,1], Pbl), solve (-1 / 8 + z ^ 2 + -1 / 4 * z = 0, z)),
1.130 +(([2,1,1], Pbl), solve (-1 / 8 + z ^ 2 + -1 / 4 * z = 0, z)),
1.131 +(([2,1,1,1], Frm), -1 / 8 + z ^ 2 + -1 / 4 * z = 0)]
1.132 +*)
1.133 +*}
1.134 +ML {*
1.135 +val denominator = parseNEW ctxt "-1/8 + -1/4*z + z^2 = 0";
1.136 +(*ergebnis: [gleichung, was tun?, lösung]*)
1.137 +val fmz = ["equality (-1/8 + -1/4*z + z^2 = (0::real))", "solveFor z","solutions L"];
1.138 +(*liste der theoreme die zum lösen benötigt werden, aus isac, keine spezielle methode (no met)*)
1.139 +val (dI',pI',mI') =
1.140 + ("Isac", ["pqFormula","degree_2","polynomial","univariate","equation"], ["no_met"]);
1.141 +(*schritte abarbeiten*)
1.142 +val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
1.143 +val (p,_,f,nxt,_,pt) = me nxt p [] pt;
1.144 +val (p,_,f,nxt,_,pt) = me nxt p [] pt;
1.145 +val (p,_,f,nxt,_,pt) = me nxt p [] pt;
1.146 +val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*val nxt = ("Empty_Tac", ...): tac'_*)
1.147 +show_pt pt;
1.148 +*}
1.149 +
1.150 +subsection {*partial fraction decomposition*}
1.151 +subsubsection {*solution of the equation*}
1.152 +ML {*
1.153 +val SOME solutions = parseNEW ctxt "[z=1/2, z=-1/4]";
1.154 +term2str solutions;
1.155 +atomty solutions;
1.156 +*}
1.157 +
1.158 +subsubsection {*get solutions out of list*}
1.159 +text {*in isac's CTP-based programming language: $let s_1 = NTH 1 solutions; s_2 = NTH 2...$*}
1.160 +ML {*
1.161 +val Const ("List.list.Cons", _) $ s_1 $ (Const ("List.list.Cons", _) $
1.162 + s_2 $ Const ("List.list.Nil", _)) = solutions;
1.163 +term2str s_1;
1.164 +term2str s_2;
1.165 +*}
1.166 +
1.167 +ML {* (*Solutions as Denominator --> Denominator1 = z - Zeropoint1, Denominator2 = z-Zeropoint2,...*)
1.168 +val xx = HOLogic.dest_eq s_1;
1.169 +val s_1' = HOLogic.mk_binop "Groups.minus_class.minus" xx;
1.170 +val xx = HOLogic.dest_eq s_2;
1.171 +val s_2' = HOLogic.mk_binop "Groups.minus_class.minus" xx;
1.172 +term2str s_1';
1.173 +term2str s_2';
1.174 +*}
1.175 +
1.176 +subsubsection {*build expression*}
1.177 +text {*in isac's CTP-based programming language: $let s_1 = Take numerator / (s_1 * s_2)$*}
1.178 +ML {*
1.179 +(*The Main Denominator is the multiplikation of the partial fraction denominators*)
1.180 +val denominator' = HOLogic.mk_binop "Groups.times_class.times" (s_1', s_2') ;
1.181 +val SOME numerator = parseNEW ctxt "3::real";
1.182 +
1.183 +val expr' = HOLogic.mk_binop "Rings.inverse_class.divide" (numerator, denominator');
1.184 +term2str expr';
1.185 +*}
1.186 +
1.187 +subsubsection {*Ansatz - create partial fractions out of our expression*}
1.188 +
1.189 +axiomatization where
1.190 + ansatz2: "n / (a*b) = A/a + B/(b::real)" and
1.191 + multiply_eq2: "(n / (a*b) = A/a + B/b) = (a*b*(n / (a*b)) = a*b*(A/a + B/b))"
1.192 +
1.193 +ML {*
1.194 +(*we use our ansatz2 to rewrite our expression and get an equilation with our expression on the left and the partial fractions of it on the right side*)
1.195 +val SOME (t1,_) = rewrite_ @{theory Isac} e_rew_ord e_rls false @{thm ansatz2} expr';
1.196 +term2str t1;
1.197 +atomty t1;
1.198 +val eq1 = HOLogic.mk_eq (expr', t1);
1.199 +term2str eq1;
1.200 +*}
1.201 +ML {*
1.202 +(*eliminate the demoninators by multiplying the left and the right side with the main denominator*)
1.203 +val SOME (eq2,_) = rewrite_ @{theory Isac} e_rew_ord e_rls false @{thm multiply_eq2} eq1;
1.204 +term2str eq2;
1.205 +*}
1.206 +ML {*
1.207 +(*simplificatoin*)
1.208 +val SOME (eq3,_) = rewrite_set_ @{theory Isac} false norm_Rational eq2;
1.209 +term2str eq3; (*?A ?B not simplified*)
1.210 +*}
1.211 +ML {*
1.212 +val SOME fract1 =
1.213 + parseNEW ctxt "(z - 1 / 2) * (z - -1 / 4) * (A / (z - 1 / 2) + B / (z - -1 / 4))"; (*A B !*)
1.214 +val SOME (fract2,_) = rewrite_set_ @{theory Isac} false norm_Rational fract1;
1.215 +term2str fract2 = "(A + -2 * B + 4 * A * z + 4 * B * z) / 4";
1.216 +(*term2str fract2 = "A * (1 / 4 + z) + B * (-1 / 2 + z)" would be more traditional*)
1.217 +*}
1.218 +ML {*
1.219 +val (numerator, denominator) = HOLogic.dest_eq eq3;
1.220 +val eq3' = HOLogic.mk_eq (numerator, fract1); (*A B !*)
1.221 +term2str eq3';
1.222 +*}
1.223 +ML {* (*MANDATORY: otherwise 3 = 0*)
1.224 +val SOME (eq3'' ,_) = rewrite_set_ @{theory Isac} false norm_Rational eq3';
1.225 +term2str eq3'';
1.226 +*}
1.227 +
1.228 +subsubsection {*get first koeffizient*}
1.229 +
1.230 +ML {*
1.231 +(*substitude z with the first zeropoint to get A*)
1.232 +val SOME (eq4_1,_) = rewrite_terms_ @{theory Isac} e_rew_ord e_rls [s_1] eq3'';
1.233 +term2str eq4_1;
1.234 +*}
1.235 +ML {*
1.236 +val SOME (eq4_2,_) = rewrite_set_ @{theory Isac} false norm_Rational eq4_1;
1.237 +term2str eq4_2;
1.238 +*}
1.239 +ML {*
1.240 +val fmz = ["equality (3 = 3 * A / (4::real))", "solveFor A","solutions L"];
1.241 +val (dI',pI',mI') =("Isac", ["univariate","equation"], ["no_met"]);
1.242 +
1.243 +*}
1.244 +ML {*
1.245 +(*solve the simple linear equilation for A TODO: return eq, not list of eq*)
1.246 +val (p,_,fa,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
1.247 +val (p,_,fa,nxt,_,pt) = me nxt p [] pt;
1.248 +val (p,_,fa,nxt,_,pt) = me nxt p [] pt;
1.249 +val (p,_,fa,nxt,_,pt) = me nxt p [] pt;
1.250 +val (p,_,fa,nxt,_,pt) = me nxt p [] pt;
1.251 +val (p,_,fa,nxt,_,pt) = me nxt p [] pt;
1.252 +val (p,_,fa,nxt,_,pt) = me nxt p [] pt;
1.253 +val (p,_,fa,nxt,_,pt) = me nxt p [] pt;
1.254 +val (p,_,fa,nxt,_,pt) = me nxt p [] pt;
1.255 +val (p,_,fa,nxt,_,pt) = me nxt p [] pt;
1.256 +val (p,_,fa,nxt,_,pt) = me nxt p [] pt;
1.257 +val (p,_,fa,nxt,_,pt) = me nxt p [] pt;
1.258 +val (p,_,fa,nxt,_,pt) = me nxt p [] pt;
1.259 +val (p,_,fa,nxt,_,pt) = me nxt p [] pt;
1.260 +val (p,_,fa,nxt,_,pt) = me nxt p [] pt;
1.261 +val (p,_,fa,nxt,_,pt) = me nxt p [] pt;
1.262 +val (p,_,fa,nxt,_,pt) = me nxt p [] pt;
1.263 +val (p,_,fa,nxt,_,pt) = me nxt p [] pt;
1.264 +val (p,_,fa,nxt,_,pt) = me nxt p [] pt;
1.265 +val (p,_,fa,nxt,_,pt) = me nxt p [] pt;
1.266 +val (p,_,fa,nxt,_,pt) = me nxt p [] pt;
1.267 +val (p,_,fa,nxt,_,pt) = me nxt p [] pt;
1.268 +val (p,_,fa,nxt,_,pt) = me nxt p [] pt;
1.269 +val (p,_,fa,nxt,_,pt) = me nxt p [] pt;
1.270 +val (p,_,fa,nxt,_,pt) = me nxt p [] pt;
1.271 +val (p,_,fa,nxt,_,pt) = me nxt p [] pt;
1.272 +val (p,_,fa,nxt,_,pt) = me nxt p [] pt;
1.273 +*}
1.274 +ML {*
1.275 +val (p,_,fa,nxt,_,pt) = me nxt p [] pt;
1.276 +f2str fa;
1.277 +*}
1.278 +
1.279 +subsubsection {*get second koeffizient*}
1.280 +
1.281 +ML {*
1.282 +(*substitude z with the second zeropoint to get B*)
1.283 +val SOME (eq4b_1,_) = rewrite_terms_ @{theory Isac} e_rew_ord e_rls [s_2] eq3'';
1.284 +term2str eq4b_1;
1.285 +*}
1.286 +
1.287 +ML {*
1.288 +val SOME (eq4b_2,_) = rewrite_set_ @{theory Isac} false norm_Rational eq4b_1;
1.289 +term2str eq4b_2;
1.290 +*}
1.291 +
1.292 +ML {*
1.293 +(*solve the simple linear equilation for B TODO: return eq, not list of eq*)
1.294 +val fmz = ["equality (3 = -3 * B / (4::real))", "solveFor B","solutions L"];
1.295 +val (dI',pI',mI') =("Isac", ["univariate","equation"], ["no_met"]);
1.296 +val (p,_,fb,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
1.297 +val (p,_,fb,nxt,_,pt) = me nxt p [] pt;
1.298 +val (p,_,fb,nxt,_,pt) = me nxt p [] pt;
1.299 +val (p,_,fb,nxt,_,pt) = me nxt p [] pt;
1.300 +val (p,_,fb,nxt,_,pt) = me nxt p [] pt;
1.301 +val (p,_,fb,nxt,_,pt) = me nxt p [] pt;
1.302 +val (p,_,fb,nxt,_,pt) = me nxt p [] pt;
1.303 +val (p,_,fb,nxt,_,pt) = me nxt p [] pt;
1.304 +val (p,_,fb,nxt,_,pt) = me nxt p [] pt;
1.305 +val (p,_,fb,nxt,_,pt) = me nxt p [] pt;
1.306 +val (p,_,fb,nxt,_,pt) = me nxt p [] pt;
1.307 +val (p,_,fb,nxt,_,pt) = me nxt p [] pt;
1.308 +val (p,_,fb,nxt,_,pt) = me nxt p [] pt;
1.309 +val (p,_,fb,nxt,_,pt) = me nxt p [] pt;
1.310 +val (p,_,fb,nxt,_,pt) = me nxt p [] pt;
1.311 +val (p,_,fb,nxt,_,pt) = me nxt p [] pt;
1.312 +val (p,_,fb,nxt,_,pt) = me nxt p [] pt;
1.313 +val (p,_,fb,nxt,_,pt) = me nxt p [] pt;
1.314 +val (p,_,fb,nxt,_,pt) = me nxt p [] pt;
1.315 +val (p,_,fb,nxt,_,pt) = me nxt p [] pt;
1.316 +val (p,_,fb,nxt,_,pt) = me nxt p [] pt;
1.317 +val (p,_,fb,nxt,_,pt) = me nxt p [] pt;
1.318 +val (p,_,fb,nxt,_,pt) = me nxt p [] pt;
1.319 +val (p,_,fb,nxt,_,pt) = me nxt p [] pt;
1.320 +val (p,_,fb,nxt,_,pt) = me nxt p [] pt;
1.321 +val (p,_,fb,nxt,_,pt) = me nxt p [] pt;
1.322 +val (p,_,fb,nxt,_,pt) = me nxt p [] pt;
1.323 +val (p,_,fb,nxt,_,pt) = me nxt p [] pt;
1.324 +f2str fb;
1.325 +*}
1.326 +
1.327 +ML {* (*check koeffizients*)
1.328 +if f2str fa = "[A = 4]" then () else error "part.fract. eq4_1";
1.329 +if f2str fb = "[B = -4]" then () else error "part.fract. eq4_1";
1.330 +*}
1.331 +
1.332 +subsubsection {*substitute expression with solutions*}
1.333 +ML {*
1.334 +*}
1.335 +
1.336 +section {*Implement the Specification and the Method*}
1.337 +text{*==============================================*}
1.338 +subsection{*Define the Specification*}
1.339 +ML {*
1.340 +val thy = @{theory};
1.341 +*}
1.342 +ML {*
1.343 +store_pbt
1.344 + (prep_pbt thy "pbl_SP" [] e_pblID
1.345 + (["SignalProcessing"], [], e_rls, NONE, []));
1.346 +store_pbt
1.347 + (prep_pbt thy "pbl_SP_Ztrans" [] e_pblID
1.348 + (["Z_Transform","SignalProcessing"], [], e_rls, NONE, []));
1.349 +store_pbt
1.350 + (prep_pbt thy "pbl_SP_Ztrans_inv" [] e_pblID
1.351 + (["inverse", "Z_Transform", "SignalProcessing"],
1.352 + [("#Given" ,["equality X_eq"]),
1.353 + ("#Find" ,["equality n_eq"])
1.354 + ],
1.355 + append_rls "e_rls" e_rls [(*for preds in where_*)], NONE,
1.356 + [["TODO: path to method"]]));
1.357 +
1.358 +show_ptyps();
1.359 +get_pbt ["inverse","Z_Transform","SignalProcessing"];
1.360 +*}
1.361 +
1.362 +subsection{*Define the (Dummy-)Method*}
1.363 +subsection {*Define Name and Signature for the Method*}
1.364 +consts
1.365 + InverseZTransform :: "[bool, bool] => bool"
1.366 + ("((Script InverseZTransform (_ =))// (_))" 9)
1.367 +
1.368 +ML {*
1.369 +store_met
1.370 + (prep_met thy "met_SP" [] e_metID
1.371 + (["SignalProcessing"], [],
1.372 + {rew_ord'="tless_true", rls'= e_rls, calc = [], srls = e_rls, prls = e_rls,
1.373 + crls = e_rls, nrls = e_rls}, "empty_script"));
1.374 +store_met
1.375 + (prep_met thy "met_SP_Ztrans" [] e_metID
1.376 + (["SignalProcessing", "Z_Transform"], [],
1.377 + {rew_ord'="tless_true", rls'= e_rls, calc = [], srls = e_rls, prls = e_rls,
1.378 + crls = e_rls, nrls = e_rls}, "empty_script"));
1.379 +*}
1.380 +ML {*
1.381 +store_met
1.382 + (prep_met thy "met_SP_Ztrans_inv" [] e_metID
1.383 + (["SignalProcessing", "Z_Transform", "inverse"], [],
1.384 + {rew_ord'="tless_true", rls'= e_rls, calc = [], srls = e_rls, prls = e_rls,
1.385 + crls = e_rls, nrls = e_rls},
1.386 + "empty_script"
1.387 + ));
1.388 +*}
1.389 +ML {*(*
1.390 +store_met
1.391 + (prep_met thy "met_SP_Ztrans_inv" [] e_metID
1.392 + (["SignalProcessing", "Z_Transform", "inverse"], [],
1.393 + {rew_ord'="tless_true", rls'= e_rls, calc = [], srls = e_rls, prls = e_rls,
1.394 + crls = e_rls, nrls = e_rls},
1.395 + "Script InverseZTransform (Xeq::bool) =" ^
1.396 + " (let X = Take Xeq;" ^
1.397 + " X = Rewrite ruleZY False X" ^
1.398 + " in X)"
1.399 + ));
1.400 +*)*}
1.401 +ML {*
1.402 +show_mets();
1.403 +get_met ["SignalProcessing","Z_Transform","inverse"];
1.404 +*}
1.405 +
1.406 +
1.407 +section {*Program in CTP-based language*}
1.408 +text{*=================================*}
1.409 +subsection {*Stepwise extend Program*}
1.410 +ML {*
1.411 +val str =
1.412 +"Script InverseZTransform (Xeq::bool) =" ^
1.413 +" Xeq";
1.414 +*}
1.415 +ML {*
1.416 +val str =
1.417 +"Script InverseZTransform (Xeq::bool) =" ^
1.418 +" (let X = Take Xeq;" ^
1.419 +" X = Rewrite ruleZY False X" ^
1.420 +" in X)";
1.421 +*}
1.422 +ML {*
1.423 +val thy = @{theory};
1.424 +val sc = ((inst_abs thy) o term_of o the o (parse thy)) str;
1.425 +*}
1.426 +ML {*
1.427 +term2str sc;
1.428 +atomty sc
1.429 +*}
1.430 +
1.431 +subsection {*Stepwise Execute the Program*}
1.432 +
1.433 +
1.434 +
1.435 +
1.436 +
1.437 +
1.438 +
1.439 +
1.440 +section {*Write Tests for Crucial Details*}
1.441 +text{*===================================*}
1.442 +ML {*
1.443 +
1.444 +*}
1.445 +
1.446 +section {*Integrate Program into Knowledge*}
1.447 +ML {*
1.448 +
1.449 +*}
1.450 +
1.451 +end
1.452 +
2.1 --- /dev/null Thu Jan 01 00:00:00 1970 +0000
2.2 +++ b/doc-src/isac/jrocnik/Inverse_Z_Transform/ROOT.ML Thu Sep 08 23:17:35 2011 +0200
2.3 @@ -0,0 +1,9 @@
2.4 +(*
2.5 + no_document use_thys ["This_Theory1", "This_Theory2"];
2.6 + use_thys ["That_Theory1", "That_Theory2", "That_Theory3"];
2.7 +*)
2.8 +
2.9 +Thy_Output.source_default := true;
2.10 +use "antiquote_setup.ML";
2.11 +
2.12 +use_thys ["Inverse_Z_Transform"];
2.13 \ No newline at end of file
3.1 --- /dev/null Thu Jan 01 00:00:00 1970 +0000
3.2 +++ b/doc-src/isac/jrocnik/Inverse_Z_Transform/antiquote_setup.ML Thu Sep 08 23:17:35 2011 +0200
3.3 @@ -0,0 +1,198 @@
3.4 +(* Title: doc-src/antiquote_setup.ML
3.5 + Author: Makarius
3.6 +
3.7 +Auxiliary antiquotations for the Isabelle manuals.
3.8 +*)
3.9 +
3.10 +structure Antiquote_Setup: sig end =
3.11 +struct
3.12 +
3.13 +(* misc utils *)
3.14 +
3.15 +fun translate f = Symbol.explode #> map f #> implode;
3.16 +
3.17 +val clean_string = translate
3.18 + (fn "_" => "\\_"
3.19 + | "#" => "\\#"
3.20 + | "<" => "$<$"
3.21 + | ">" => "$>$"
3.22 + | "{" => "\\{"
3.23 + | "|" => "$\\mid$"
3.24 + | "}" => "\\}"
3.25 + | "\<dash>" => "-"
3.26 + | c => c);
3.27 +
3.28 +fun clean_name "\<dots>" = "dots"
3.29 + | clean_name ".." = "ddot"
3.30 + | clean_name "." = "dot"
3.31 + | clean_name "_" = "underscore"
3.32 + | clean_name "{" = "braceleft"
3.33 + | clean_name "}" = "braceright"
3.34 + | clean_name s = s |> translate (fn "_" => "-" | "\<dash>" => "-" | c => c);
3.35 +
3.36 +
3.37 +(* verbatim text *)
3.38 +
3.39 +val verbatim = space_implode "\\verb,|," o map (enclose "\\verb|" "|") o space_explode "|";
3.40 +
3.41 +val _ = Thy_Output.antiquotation "verbatim" (Scan.lift Args.name)
3.42 + (K (split_lines #> map verbatim #> space_implode "\\isasep\\isanewline%\n"));
3.43 +
3.44 +
3.45 +(* ML text *)
3.46 +
3.47 +local
3.48 +
3.49 +fun ml_val (txt1, "") = "fn _ => (" ^ txt1 ^ ");"
3.50 + | ml_val (txt1, txt2) = "fn _ => (" ^ txt1 ^ " : " ^ txt2 ^ ");";
3.51 +
3.52 +fun ml_type (txt1, "") = "val _ = NONE : (" ^ txt1 ^ ") option;"
3.53 + | ml_type (txt1, txt2) = "val _ = [NONE : (" ^ txt1 ^ ") option, NONE : (" ^ txt2 ^ ") option];";
3.54 +
3.55 +fun ml_exn (txt1, "") = "fn _ => (" ^ txt1 ^ " : exn);"
3.56 + | ml_exn (txt1, txt2) = "fn _ => (" ^ txt1 ^ " : " ^ txt2 ^ " -> exn);";
3.57 +
3.58 +fun ml_structure (txt, _) = "functor XXX() = struct structure XX = " ^ txt ^ " end;";
3.59 +
3.60 +fun ml_functor (txt, _) = "ML_Env.check_functor " ^ ML_Syntax.print_string txt;
3.61 +
3.62 +val is_name = ML_Lex.kind_of #> (fn kind => kind = ML_Lex.Ident orelse kind = ML_Lex.LongIdent);
3.63 +
3.64 +fun ml_name txt =
3.65 + (case filter is_name (ML_Lex.tokenize txt) of
3.66 + toks as [_] => ML_Lex.flatten toks
3.67 + | _ => error ("Single ML name expected in input: " ^ quote txt));
3.68 +
3.69 +fun index_ml name kind ml = Thy_Output.antiquotation name
3.70 + (Scan.lift (Args.name -- Scan.optional (Args.colon |-- Args.name) ""))
3.71 + (fn {context = ctxt, ...} => fn (txt1, txt2) =>
3.72 + let
3.73 + val txt =
3.74 + if txt2 = "" then txt1
3.75 + else if kind = "type" then txt1 ^ " = " ^ txt2
3.76 + else if kind = "exception" then txt1 ^ " of " ^ txt2
3.77 + else if Syntax.is_identifier (Long_Name.base_name (ml_name txt1)) then txt1 ^ ": " ^ txt2
3.78 + else txt1 ^ " : " ^ txt2;
3.79 + val txt' = if kind = "" then txt else kind ^ " " ^ txt;
3.80 + val _ = ML_Context.eval_text_in (SOME ctxt) false Position.none (ml (txt1, txt2)); (* ML_Lex.read (!?) *)
3.81 + val kind' = if kind = "" then "ML" else "ML " ^ kind;
3.82 + in
3.83 + "\\indexdef{}{" ^ kind' ^ "}{" ^ clean_string (ml_name txt1) ^ "}" ^
3.84 + (txt'
3.85 + |> (if Config.get ctxt Thy_Output.quotes then quote else I)
3.86 + |> (if Config.get ctxt Thy_Output.display then enclose "\\begin{verbatim}\n" "\n\\end{verbatim}"
3.87 + else split_lines #> map verbatim #> space_implode "\\isasep\\isanewline%\n"))
3.88 + end);
3.89 +
3.90 +in
3.91 +
3.92 +val _ = index_ml "index_ML" "" ml_val;
3.93 +val _ = index_ml "index_ML_type" "type" ml_type;
3.94 +val _ = index_ml "index_ML_exn" "exception" ml_exn;
3.95 +val _ = index_ml "index_ML_structure" "structure" ml_structure;
3.96 +val _ = index_ml "index_ML_functor" "functor" ml_functor;
3.97 +
3.98 +end;
3.99 +
3.100 +
3.101 +(* named theorems *)
3.102 +
3.103 +val _ = Thy_Output.antiquotation "named_thms"
3.104 + (Scan.repeat (Attrib.thm -- Scan.lift (Args.parens Args.name)))
3.105 + (fn {context = ctxt, ...} =>
3.106 + map (apfst (Thy_Output.pretty_thm ctxt))
3.107 + #> (if Config.get ctxt Thy_Output.quotes then map (apfst Pretty.quote) else I)
3.108 + #> (if Config.get ctxt Thy_Output.display
3.109 + then
3.110 + map (fn (p, name) =>
3.111 + Output.output (Pretty.string_of (Pretty.indent (Config.get ctxt Thy_Output.indent) p)) ^
3.112 + "\\rulename{" ^ Output.output (Pretty.str_of (Thy_Output.pretty_text ctxt name)) ^ "}")
3.113 + #> space_implode "\\par\\smallskip%\n"
3.114 + #> enclose "\\begin{isabelle}%\n" "%\n\\end{isabelle}"
3.115 + else
3.116 + map (fn (p, name) =>
3.117 + Output.output (Pretty.str_of p) ^
3.118 + "\\rulename{" ^ Output.output (Pretty.str_of (Thy_Output.pretty_text ctxt name)) ^ "}")
3.119 + #> space_implode "\\par\\smallskip%\n"
3.120 + #> enclose "\\isa{" "}"));
3.121 +
3.122 +
3.123 +(* theory file *)
3.124 +
3.125 +val _ = Thy_Output.antiquotation "thy_file" (Scan.lift Args.name)
3.126 + (fn {context = ctxt, ...} =>
3.127 + fn name => (Thy_Load.check_thy Path.current name; Thy_Output.output ctxt [Pretty.str name]));
3.128 +
3.129 +
3.130 +(* Isabelle/Isar entities (with index) *)
3.131 +
3.132 +local
3.133 +
3.134 +fun no_check _ _ = true;
3.135 +
3.136 +fun thy_check intern defined ctxt =
3.137 + let val thy = ProofContext.theory_of ctxt
3.138 + in defined thy o intern thy end;
3.139 +
3.140 +fun check_tool name =
3.141 + File.exists (Path.append (Path.explode "~~/lib/Tools") (Path.basic name));
3.142 +
3.143 +val arg = enclose "{" "}" o clean_string;
3.144 +
3.145 +fun entity check markup kind index =
3.146 + Thy_Output.antiquotation
3.147 + (translate (fn " " => "_" | c => c) kind ^
3.148 + (case index of NONE => "" | SOME true => "_def" | SOME false => "_ref"))
3.149 + (Scan.lift (Scan.optional (Args.parens Args.name) "" -- Args.name))
3.150 + (fn {context = ctxt, ...} => fn (logic, name) =>
3.151 + let
3.152 + val hyper_name =
3.153 + "{" ^ Long_Name.append kind (Long_Name.append logic (clean_name name)) ^ "}";
3.154 + val hyper =
3.155 + enclose ("\\hyperlink" ^ hyper_name ^ "{") "}" #>
3.156 + index = SOME true ? enclose ("\\hypertarget" ^ hyper_name ^ "{") "}";
3.157 + val idx =
3.158 + (case index of
3.159 + NONE => ""
3.160 + | SOME is_def =>
3.161 + "\\index" ^ (if is_def then "def" else "ref") ^ arg logic ^ arg kind ^ arg name);
3.162 + in
3.163 + if check ctxt name then
3.164 + idx ^
3.165 + (Output.output name
3.166 + |> (if markup = "" then I else enclose ("\\" ^ markup ^ "{") "}")
3.167 + |> (if Config.get ctxt Thy_Output.quotes then quote else I)
3.168 + |> (if Config.get ctxt Thy_Output.display
3.169 + then enclose "\\begin{isabelle}%\n" "%\n\\end{isabelle}"
3.170 + else hyper o enclose "\\mbox{\\isa{" "}}"))
3.171 + else error ("Bad " ^ kind ^ " " ^ quote name)
3.172 + end);
3.173 +
3.174 +fun entity_antiqs check markup kind =
3.175 + ((entity check markup kind NONE);
3.176 + (entity check markup kind (SOME true));
3.177 + (entity check markup kind (SOME false)));
3.178 +
3.179 +in
3.180 +
3.181 +val _ = entity_antiqs no_check "" "syntax";
3.182 +val _ = entity_antiqs (K (is_some o Keyword.command_keyword)) "isacommand" "command";
3.183 +val _ = entity_antiqs (K Keyword.is_keyword) "isakeyword" "keyword";
3.184 +val _ = entity_antiqs (K Keyword.is_keyword) "isakeyword" "element";
3.185 +val _ = entity_antiqs (thy_check Method.intern Method.defined) "" "method";
3.186 +val _ = entity_antiqs (thy_check Attrib.intern Attrib.defined) "" "attribute";
3.187 +val _ = entity_antiqs no_check "" "fact";
3.188 +val _ = entity_antiqs no_check "" "variable";
3.189 +val _ = entity_antiqs no_check "" "case";
3.190 +val _ = entity_antiqs (K Thy_Output.defined_command) "" "antiquotation";
3.191 +val _ = entity_antiqs (K Thy_Output.defined_option) "" "antiquotation option";
3.192 +val _ = entity_antiqs (fn _ => fn name => is_some (OS.Process.getEnv name)) "isatt" "setting";
3.193 +val _ = entity_antiqs no_check "" "inference";
3.194 +val _ = entity_antiqs no_check "isatt" "executable";
3.195 +val _ = entity_antiqs (K check_tool) "isatt" "tool";
3.196 +val _ = entity_antiqs (K (can Thy_Info.get_theory)) "" "theory";
3.197 +val _ = entity_antiqs no_check "" "ML antiquotation"; (* FIXME proper check *)
3.198 +
3.199 +end;
3.200 +
3.201 +end;
4.1 --- /dev/null Thu Jan 01 00:00:00 1970 +0000
4.2 +++ b/doc-src/isac/jrocnik/Inverse_Z_Transform/document/Inverse_Z_Transform.tex Thu Sep 08 23:17:35 2011 +0200
4.3 @@ -0,0 +1,988 @@
4.4 +%
4.5 +\begin{isabellebody}%
4.6 +\def\isabellecontext{Inverse{\isaliteral{5F}{\isacharunderscore}}Z{\isaliteral{5F}{\isacharunderscore}}Transform}%
4.7 +%
4.8 +\isadelimtheory
4.9 +\isanewline
4.10 +\isanewline
4.11 +%
4.12 +\endisadelimtheory
4.13 +%
4.14 +\isatagtheory
4.15 +\isacommand{theory}\isamarkupfalse%
4.16 +\ Inverse{\isaliteral{5F}{\isacharunderscore}}Z{\isaliteral{5F}{\isacharunderscore}}Transform\ \isakeyword{imports}\ Isac\ \isakeyword{begin}%
4.17 +\endisatagtheory
4.18 +{\isafoldtheory}%
4.19 +%
4.20 +\isadelimtheory
4.21 +%
4.22 +\endisadelimtheory
4.23 +%
4.24 +\isamarkupsection{trials towards Z transform%
4.25 +}
4.26 +\isamarkuptrue%
4.27 +%
4.28 +\begin{isamarkuptext}%
4.29 +===============================%
4.30 +\end{isamarkuptext}%
4.31 +\isamarkuptrue%
4.32 +%
4.33 +\isamarkupsubsection{terms%
4.34 +}
4.35 +\isamarkuptrue%
4.36 +%
4.37 +\isadelimML
4.38 +%
4.39 +\endisadelimML
4.40 +%
4.41 +\isatagML
4.42 +\isacommand{ML}\isamarkupfalse%
4.43 +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
4.44 +%
4.45 +\isaantiq
4.46 +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}}{}%
4.47 +\endisaantiq
4.48 +{\isaliteral{3B}{\isacharsemicolon}}\isanewline
4.49 +%
4.50 +\isaantiq
4.51 +term\ {\isaliteral{22}{\isachardoublequote}}z\ {\isaliteral{2F}{\isacharslash}}\ {\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{1}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}{}%
4.52 +\endisaantiq
4.53 +{\isaliteral{3B}{\isacharsemicolon}}\isanewline
4.54 +%
4.55 +\isaantiq
4.56 +term\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{2D}{\isacharminus}}u\ {\isaliteral{2D}{\isacharminus}}n\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}{}%
4.57 +\endisaantiq
4.58 +{\isaliteral{3B}{\isacharsemicolon}}\isanewline
4.59 +%
4.60 +\isaantiq
4.61 +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}}{}%
4.62 +\endisaantiq
4.63 +{\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
4.64 +%
4.65 +\isaantiq
4.66 +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}}{}%
4.67 +\endisaantiq
4.68 +{\isaliteral{3B}{\isacharsemicolon}}Isac\isanewline
4.69 +%
4.70 +\isaantiq
4.71 +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}}{}%
4.72 +\endisaantiq
4.73 +{\isaliteral{3B}{\isacharsemicolon}}\isanewline
4.74 +term{\isadigit{2}}str\ %
4.75 +\isaantiq
4.76 +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}}{}%
4.77 +\endisaantiq
4.78 +{\isaliteral{3B}{\isacharsemicolon}}\isanewline
4.79 +{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline
4.80 +\isacommand{ML}\isamarkupfalse%
4.81 +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
4.82 +{\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
4.83 +\isanewline
4.84 +%
4.85 +\isaantiq
4.86 +term\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ {\isaliteral{22}{\isachardoublequote}}{}%
4.87 +\endisaantiq
4.88 +{\isaliteral{3B}{\isacharsemicolon}}\isanewline
4.89 +%
4.90 +\isaantiq
4.91 +term\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C64656C74613E}{\isasymdelta}}\ {\isaliteral{22}{\isachardoublequote}}{}%
4.92 +\endisaantiq
4.93 +{\isaliteral{3B}{\isacharsemicolon}}\isanewline
4.94 +%
4.95 +\isaantiq
4.96 +term\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C7068693E}{\isasymphi}}\ {\isaliteral{22}{\isachardoublequote}}{}%
4.97 +\endisaantiq
4.98 +{\isaliteral{3B}{\isacharsemicolon}}\isanewline
4.99 +%
4.100 +\isaantiq
4.101 +term\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C72686F3E}{\isasymrho}}\ {\isaliteral{22}{\isachardoublequote}}{}%
4.102 +\endisaantiq
4.103 +{\isaliteral{3B}{\isacharsemicolon}}\isanewline
4.104 +term{\isadigit{2}}str\ %
4.105 +\isaantiq
4.106 +term\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C72686F3E}{\isasymrho}}\ {\isaliteral{22}{\isachardoublequote}}{}%
4.107 +\endisaantiq
4.108 +{\isaliteral{3B}{\isacharsemicolon}}\isanewline
4.109 +{\isaliteral{2A7D}{\isacharverbatimclose}}%
4.110 +\endisatagML
4.111 +{\isafoldML}%
4.112 +%
4.113 +\isadelimML
4.114 +%
4.115 +\endisadelimML
4.116 +%
4.117 +\isamarkupsubsection{rules%
4.118 +}
4.119 +\isamarkuptrue%
4.120 +\isacommand{axiomatization}\isamarkupfalse%
4.121 +\ \isakeyword{where}\ \isanewline
4.122 +\ \ 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
4.123 +\ \ 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
4.124 +\ \ 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
4.125 +\ \ 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}}n\ {\isaliteral{2A}{\isacharasterisk}}\ u\ {\isaliteral{5B}{\isacharbrackleft}}n{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequoteclose}}\ \isakeyword{and}\isanewline
4.126 +\ \ 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}}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
4.127 +\ \ 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}}{\isadigit{2}}\ {\isaliteral{3D}{\isacharequal}}\ n\ {\isaliteral{2A}{\isacharasterisk}}\ u\ {\isaliteral{5B}{\isacharbrackleft}}n{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline
4.128 +%
4.129 +\isadelimML
4.130 +%
4.131 +\endisadelimML
4.132 +%
4.133 +\isatagML
4.134 +\isacommand{ML}\isamarkupfalse%
4.135 +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
4.136 +%
4.137 +\isaantiq
4.138 +thm\ rule{\isadigit{1}}{}%
4.139 +\endisaantiq
4.140 +{\isaliteral{3B}{\isacharsemicolon}}\isanewline
4.141 +%
4.142 +\isaantiq
4.143 +thm\ rule{\isadigit{2}}{}%
4.144 +\endisaantiq
4.145 +{\isaliteral{3B}{\isacharsemicolon}}\isanewline
4.146 +%
4.147 +\isaantiq
4.148 +thm\ rule{\isadigit{3}}{}%
4.149 +\endisaantiq
4.150 +{\isaliteral{3B}{\isacharsemicolon}}\isanewline
4.151 +%
4.152 +\isaantiq
4.153 +thm\ rule{\isadigit{4}}{}%
4.154 +\endisaantiq
4.155 +{\isaliteral{3B}{\isacharsemicolon}}\isanewline
4.156 +{\isaliteral{2A7D}{\isacharverbatimclose}}%
4.157 +\endisatagML
4.158 +{\isafoldML}%
4.159 +%
4.160 +\isadelimML
4.161 +%
4.162 +\endisadelimML
4.163 +%
4.164 +\isamarkupsubsection{apply rules%
4.165 +}
4.166 +\isamarkuptrue%
4.167 +%
4.168 +\isadelimML
4.169 +%
4.170 +\endisadelimML
4.171 +%
4.172 +\isatagML
4.173 +\isacommand{ML}\isamarkupfalse%
4.174 +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
4.175 +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
4.176 +\ \ {\isaliteral{5B}{\isacharbrackleft}}\ Thm\ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}rule{\isadigit{3}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}num{\isaliteral{5F}{\isacharunderscore}}str\ %
4.177 +\isaantiq
4.178 +thm\ rule{\isadigit{3}}{}%
4.179 +\endisaantiq
4.180 +{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\isanewline
4.181 +\ \ \ \ Thm\ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}rule{\isadigit{4}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}num{\isaliteral{5F}{\isacharunderscore}}str\ %
4.182 +\isaantiq
4.183 +thm\ rule{\isadigit{4}}{}%
4.184 +\endisaantiq
4.185 +{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\isanewline
4.186 +\ \ \ \ Thm\ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}rule{\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}num{\isaliteral{5F}{\isacharunderscore}}str\ %
4.187 +\isaantiq
4.188 +thm\ rule{\isadigit{1}}{}%
4.189 +\endisaantiq
4.190 +{\isaliteral{29}{\isacharparenright}}\ \ \ \isanewline
4.191 +\ \ {\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
4.192 +\isanewline
4.193 +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
4.194 +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
4.195 +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
4.196 +{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline
4.197 +\isacommand{ML}\isamarkupfalse%
4.198 +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
4.199 +val\ {\isaliteral{28}{\isacharparenleft}}thy{\isaliteral{2C}{\isacharcomma}}\ ro{\isaliteral{2C}{\isacharcomma}}\ er{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}%
4.200 +\isaantiq
4.201 +theory{}%
4.202 +\endisaantiq
4.203 +{\isaliteral{2C}{\isacharcomma}}\ tless{\isaliteral{5F}{\isacharunderscore}}true{\isaliteral{2C}{\isacharcomma}}\ eval{\isaliteral{5F}{\isacharunderscore}}rls{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
4.204 +{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline
4.205 +\isacommand{ML}\isamarkupfalse%
4.206 +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
4.207 +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\ %
4.208 +\isaantiq
4.209 +thm\ rule{\isadigit{3}}{}%
4.210 +\endisaantiq
4.211 +{\isaliteral{29}{\isacharparenright}}\ t{\isaliteral{3B}{\isacharsemicolon}}\isanewline
4.212 +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
4.213 +term{\isadigit{2}}str\ t{\isaliteral{3B}{\isacharsemicolon}}\isanewline
4.214 +{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline
4.215 +\isacommand{ML}\isamarkupfalse%
4.216 +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
4.217 +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\ %
4.218 +\isaantiq
4.219 +thm\ rule{\isadigit{4}}{}%
4.220 +\endisaantiq
4.221 +{\isaliteral{29}{\isacharparenright}}\ t{\isaliteral{3B}{\isacharsemicolon}}\isanewline
4.222 +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{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
4.223 +term{\isadigit{2}}str\ t{\isaliteral{3B}{\isacharsemicolon}}\isanewline
4.224 +{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline
4.225 +\isacommand{ML}\isamarkupfalse%
4.226 +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
4.227 +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\ %
4.228 +\isaantiq
4.229 +thm\ rule{\isadigit{1}}{}%
4.230 +\endisaantiq
4.231 +{\isaliteral{29}{\isacharparenright}}\ t{\isaliteral{3B}{\isacharsemicolon}}\isanewline
4.232 +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{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
4.233 +term{\isadigit{2}}str\ t{\isaliteral{3B}{\isacharsemicolon}}\isanewline
4.234 +{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline
4.235 +\isacommand{ML}\isamarkupfalse%
4.236 +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
4.237 +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
4.238 +{\isaliteral{2A7D}{\isacharverbatimclose}}%
4.239 +\endisatagML
4.240 +{\isafoldML}%
4.241 +%
4.242 +\isadelimML
4.243 +%
4.244 +\endisadelimML
4.245 +%
4.246 +\isamarkupsection{Prepare steps in CTP-based programming language%
4.247 +}
4.248 +\isamarkuptrue%
4.249 +%
4.250 +\begin{isamarkuptext}%
4.251 +===================================================%
4.252 +\end{isamarkuptext}%
4.253 +\isamarkuptrue%
4.254 +%
4.255 +\isamarkupsubsection{prepare expression%
4.256 +}
4.257 +\isamarkuptrue%
4.258 +%
4.259 +\isadelimML
4.260 +%
4.261 +\endisadelimML
4.262 +%
4.263 +\isatagML
4.264 +\isacommand{ML}\isamarkupfalse%
4.265 +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
4.266 +val\ ctxt\ {\isaliteral{3D}{\isacharequal}}\ ProofContext{\isaliteral{2E}{\isachardot}}init{\isaliteral{5F}{\isacharunderscore}}global\ %
4.267 +\isaantiq
4.268 +theory{}%
4.269 +\endisaantiq
4.270 +{\isaliteral{3B}{\isacharsemicolon}}\isanewline
4.271 +val\ ctxt\ {\isaliteral{3D}{\isacharequal}}\ declare{\isaliteral{5F}{\isacharunderscore}}constraints{\isaliteral{27}{\isacharprime}}\ {\isaliteral{5B}{\isacharbrackleft}}%
4.272 +\isaantiq
4.273 +term\ {\isaliteral{22}{\isachardoublequote}}z{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}real{\isaliteral{22}{\isachardoublequote}}{}%
4.274 +\endisaantiq
4.275 +{\isaliteral{5D}{\isacharbrackright}}\ ctxt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
4.276 +\isanewline
4.277 +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{2D}{\isacharminus}}{\isadigit{1}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\ term{\isadigit{2}}str\ fun{\isadigit{1}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
4.278 +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
4.279 +{\isaliteral{2A7D}{\isacharverbatimclose}}%
4.280 +\endisatagML
4.281 +{\isafoldML}%
4.282 +%
4.283 +\isadelimML
4.284 +%
4.285 +\endisadelimML
4.286 +\isanewline
4.287 +\isanewline
4.288 +\isacommand{axiomatization}\isamarkupfalse%
4.289 +\ \isakeyword{where}\isanewline
4.290 +\ \ 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
4.291 +%
4.292 +\isadelimML
4.293 +\isanewline
4.294 +%
4.295 +\endisadelimML
4.296 +%
4.297 +\isatagML
4.298 +\isacommand{ML}\isamarkupfalse%
4.299 +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
4.300 +val\ {\isaliteral{28}{\isacharparenleft}}thy{\isaliteral{2C}{\isacharcomma}}\ ro{\isaliteral{2C}{\isacharcomma}}\ er{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}%
4.301 +\isaantiq
4.302 +theory{}%
4.303 +\endisaantiq
4.304 +{\isaliteral{2C}{\isacharcomma}}\ tless{\isaliteral{5F}{\isacharunderscore}}true{\isaliteral{2C}{\isacharcomma}}\ eval{\isaliteral{5F}{\isacharunderscore}}rls{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
4.305 +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\ \ %
4.306 +\isaantiq
4.307 +thm\ ruleZY{}%
4.308 +\endisaantiq
4.309 +\ fun{\isadigit{1}}{\isaliteral{3B}{\isacharsemicolon}}\ term{\isadigit{2}}str\ fun{\isadigit{2}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
4.310 +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\ \ %
4.311 +\isaantiq
4.312 +thm\ ruleZY{}%
4.313 +\endisaantiq
4.314 +\ fun{\isadigit{1}}{\isaliteral{27}{\isacharprime}}{\isaliteral{3B}{\isacharsemicolon}}\ term{\isadigit{2}}str\ fun{\isadigit{2}}{\isaliteral{27}{\isacharprime}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
4.315 +\isanewline
4.316 +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}}\ %
4.317 +\isaantiq
4.318 +theory\ Isac{}%
4.319 +\endisaantiq
4.320 +\ false\ norm{\isaliteral{5F}{\isacharunderscore}}Rational\ fun{\isadigit{2}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
4.321 +term{\isadigit{2}}str\ fun{\isadigit{3}}{\isaliteral{3B}{\isacharsemicolon}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}fails\ on\ x{\isaliteral{5E}{\isacharcircum}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{2D}{\isacharminus}}{\isadigit{1}}{\isaliteral{29}{\isacharparenright}}\ TODO{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
4.322 +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}}\ %
4.323 +\isaantiq
4.324 +theory\ Isac{}%
4.325 +\endisaantiq
4.326 +\ false\ norm{\isaliteral{5F}{\isacharunderscore}}Rational\ fun{\isadigit{2}}{\isaliteral{27}{\isacharprime}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
4.327 +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
4.328 +\isanewline
4.329 +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
4.330 +{\isaliteral{2A7D}{\isacharverbatimclose}}%
4.331 +\endisatagML
4.332 +{\isafoldML}%
4.333 +%
4.334 +\isadelimML
4.335 +%
4.336 +\endisadelimML
4.337 +%
4.338 +\isamarkupsubsection{solve equation%
4.339 +}
4.340 +\isamarkuptrue%
4.341 +%
4.342 +\isadelimML
4.343 +%
4.344 +\endisadelimML
4.345 +%
4.346 +\isatagML
4.347 +\isacommand{ML}\isamarkupfalse%
4.348 +\ {\isaliteral{7B2A}{\isacharverbatimopen}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}from\ test{\isaliteral{2F}{\isacharslash}}Tools{\isaliteral{2F}{\isacharslash}}isac{\isaliteral{2F}{\isacharslash}}Minisubpbl{\isaliteral{2F}{\isacharslash}}{\isadigit{1}}{\isadigit{0}}{\isadigit{0}}{\isaliteral{2D}{\isacharminus}}init{\isaliteral{2D}{\isacharminus}}rootpbl{\isaliteral{2E}{\isachardot}}sml{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
4.349 +{\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
4.350 +val\ denominator\ {\isaliteral{3D}{\isacharequal}}\ parseNEW\ ctxt\ {\isaliteral{22}{\isachardoublequote}}z{\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
4.351 +val\ fmz\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}equality\ {\isaliteral{28}{\isacharparenleft}}z{\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
4.352 +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
4.353 +{\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
4.354 +{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline
4.355 +\isacommand{ML}\isamarkupfalse%
4.356 +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
4.357 +val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\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
4.358 +val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
4.359 +{\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{5B}{\isacharbrackleft}}\isanewline
4.360 +{\isaliteral{28}{\isacharparenleft}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ Frm{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\ solve\ {\isaliteral{28}{\isacharparenleft}}z\ {\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{2C}{\isacharcomma}}\ z{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\isanewline
4.361 +{\isaliteral{28}{\isacharparenleft}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5B}{\isacharbrackleft}}{\isadigit{1}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ Frm{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\ z\ {\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{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\ \ \ \ \ \ \ \ \ \ \ \ \ \ bad\ rewrite\ order\isanewline
4.362 +{\isaliteral{28}{\isacharparenleft}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5B}{\isacharbrackleft}}{\isadigit{1}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ Res{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{1}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{8}}\ {\isaliteral{2B}{\isacharplus}}\ z\ {\isaliteral{5E}{\isacharcircum}}\ {\isadigit{2}}\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{1}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{4}}\ {\isaliteral{2A}{\isacharasterisk}}\ z\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{0}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\ \ \ \ \ \ \ \ \ \ \ \ bad\ pattern\isanewline
4.363 +{\isaliteral{28}{\isacharparenleft}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5B}{\isacharbrackleft}}{\isadigit{2}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ Pbl{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\ solve\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2D}{\isacharminus}}{\isadigit{1}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{8}}\ {\isaliteral{2B}{\isacharplus}}\ z\ {\isaliteral{5E}{\isacharcircum}}\ {\isadigit{2}}\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{1}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{4}}\ {\isaliteral{2A}{\isacharasterisk}}\ z\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{0}}{\isaliteral{2C}{\isacharcomma}}\ z{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\isanewline
4.364 +{\isaliteral{28}{\isacharparenleft}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5B}{\isacharbrackleft}}{\isadigit{2}}{\isaliteral{2C}{\isacharcomma}}{\isadigit{1}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ Pbl{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\ solve\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2D}{\isacharminus}}{\isadigit{1}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{8}}\ {\isaliteral{2B}{\isacharplus}}\ z\ {\isaliteral{5E}{\isacharcircum}}\ {\isadigit{2}}\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{1}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{4}}\ {\isaliteral{2A}{\isacharasterisk}}\ z\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{0}}{\isaliteral{2C}{\isacharcomma}}\ z{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\isanewline
4.365 +{\isaliteral{28}{\isacharparenleft}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5B}{\isacharbrackleft}}{\isadigit{2}}{\isaliteral{2C}{\isacharcomma}}{\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}{\isadigit{1}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ Pbl{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\ solve\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2D}{\isacharminus}}{\isadigit{1}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{8}}\ {\isaliteral{2B}{\isacharplus}}\ z\ {\isaliteral{5E}{\isacharcircum}}\ {\isadigit{2}}\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{1}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{4}}\ {\isaliteral{2A}{\isacharasterisk}}\ z\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{0}}{\isaliteral{2C}{\isacharcomma}}\ z{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\isanewline
4.366 +{\isaliteral{28}{\isacharparenleft}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{5B}{\isacharbrackleft}}{\isadigit{2}}{\isaliteral{2C}{\isacharcomma}}{\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}{\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}{\isadigit{1}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ Frm{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{1}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{8}}\ {\isaliteral{2B}{\isacharplus}}\ z\ {\isaliteral{5E}{\isacharcircum}}\ {\isadigit{2}}\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{1}}\ {\isaliteral{2F}{\isacharslash}}\ {\isadigit{4}}\ {\isaliteral{2A}{\isacharasterisk}}\ z\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{0}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{5D}{\isacharbrackright}}\ \isanewline
4.367 +{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
4.368 +{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline
4.369 +\isacommand{ML}\isamarkupfalse%
4.370 +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
4.371 +val\ denominator\ {\isaliteral{3D}{\isacharequal}}\ parseNEW\ ctxt\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{2D}{\isacharminus}}{\isadigit{1}}{\isaliteral{2F}{\isacharslash}}{\isadigit{8}}\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{1}}{\isaliteral{2F}{\isacharslash}}{\isadigit{4}}{\isaliteral{2A}{\isacharasterisk}}z\ {\isaliteral{2B}{\isacharplus}}\ z{\isaliteral{5E}{\isacharcircum}}{\isadigit{2}}\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{0}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
4.372 +{\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}ergebnis{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5B}{\isacharbrackleft}}gleichung{\isaliteral{2C}{\isacharcomma}}\ was\ tun{\isaliteral{3F}{\isacharquery}}{\isaliteral{2C}{\isacharcomma}}\ lösung{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
4.373 +val\ fmz\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}equality\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2D}{\isacharminus}}{\isadigit{1}}{\isaliteral{2F}{\isacharslash}}{\isadigit{8}}\ {\isaliteral{2B}{\isacharplus}}\ {\isaliteral{2D}{\isacharminus}}{\isadigit{1}}{\isaliteral{2F}{\isacharslash}}{\isadigit{4}}{\isaliteral{2A}{\isacharasterisk}}z\ {\isaliteral{2B}{\isacharplus}}\ z{\isaliteral{5E}{\isacharcircum}}{\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{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
4.374 +{\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}liste\ der\ theoreme\ die\ zum\ lösen\ benötigt\ werden{\isaliteral{2C}{\isacharcomma}}\ aus\ isac{\isaliteral{2C}{\isacharcomma}}\ keine\ spezielle\ methode\ {\isaliteral{28}{\isacharparenleft}}no\ met{\isaliteral{29}{\isacharparenright}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
4.375 +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
4.376 +\ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}Isac{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}pqFormula{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}degree{\isaliteral{5F}{\isacharunderscore}}{\isadigit{2}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}polynomial{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}univariate{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{22}{\isachardoublequote}}equation{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}no{\isaliteral{5F}{\isacharunderscore}}met{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
4.377 +{\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}schritte\ abarbeiten{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
4.378 +val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\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
4.379 +val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
4.380 +val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
4.381 +val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
4.382 +val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\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}}val\ nxt\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}Empty{\isaliteral{5F}{\isacharunderscore}}Tac{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}\ {\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}{\isaliteral{2E}{\isachardot}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3A}{\isacharcolon}}\ tac{\isaliteral{27}{\isacharprime}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
4.383 +show{\isaliteral{5F}{\isacharunderscore}}pt\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline
4.384 +{\isaliteral{2A7D}{\isacharverbatimclose}}%
4.385 +\endisatagML
4.386 +{\isafoldML}%
4.387 +%
4.388 +\isadelimML
4.389 +%
4.390 +\endisadelimML
4.391 +%
4.392 +\isamarkupsubsection{partial fraction decomposition%
4.393 +}
4.394 +\isamarkuptrue%
4.395 +%
4.396 +\isamarkupsubsubsection{solution of the equation%
4.397 +}
4.398 +\isamarkuptrue%
4.399 +%
4.400 +\isadelimML
4.401 +%
4.402 +\endisadelimML
4.403 +%
4.404 +\isatagML
4.405 +\isacommand{ML}\isamarkupfalse%
4.406 +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
4.407 +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
4.408 +term{\isadigit{2}}str\ solutions{\isaliteral{3B}{\isacharsemicolon}}\isanewline
4.409 +atomty\ solutions{\isaliteral{3B}{\isacharsemicolon}}\isanewline
4.410 +{\isaliteral{2A7D}{\isacharverbatimclose}}%
4.411 +\endisatagML
4.412 +{\isafoldML}%
4.413 +%
4.414 +\isadelimML
4.415 +%
4.416 +\endisadelimML
4.417 +%
4.418 +\isamarkupsubsubsection{get solutions out of list%
4.419 +}
4.420 +\isamarkuptrue%
4.421 +%
4.422 +\begin{isamarkuptext}%
4.423 +in isac's CTP-based programming language: $let s_1 = NTH 1 solutions; s_2 = NTH 2...$%
4.424 +\end{isamarkuptext}%
4.425 +\isamarkuptrue%
4.426 +%
4.427 +\isadelimML
4.428 +%
4.429 +\endisadelimML
4.430 +%
4.431 +\isatagML
4.432 +\isacommand{ML}\isamarkupfalse%
4.433 +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
4.434 +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
4.435 +\ \ \ \ \ \ 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
4.436 +term{\isadigit{2}}str\ s{\isaliteral{5F}{\isacharunderscore}}{\isadigit{1}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
4.437 +term{\isadigit{2}}str\ s{\isaliteral{5F}{\isacharunderscore}}{\isadigit{2}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
4.438 +{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline
4.439 +\isanewline
4.440 +\isacommand{ML}\isamarkupfalse%
4.441 +\ {\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
4.442 +val\ xx\ {\isaliteral{3D}{\isacharequal}}\ HOLogic{\isaliteral{2E}{\isachardot}}dest{\isaliteral{5F}{\isacharunderscore}}eq\ s{\isaliteral{5F}{\isacharunderscore}}{\isadigit{1}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
4.443 +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
4.444 +val\ xx\ {\isaliteral{3D}{\isacharequal}}\ HOLogic{\isaliteral{2E}{\isachardot}}dest{\isaliteral{5F}{\isacharunderscore}}eq\ s{\isaliteral{5F}{\isacharunderscore}}{\isadigit{2}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
4.445 +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
4.446 +term{\isadigit{2}}str\ s{\isaliteral{5F}{\isacharunderscore}}{\isadigit{1}}{\isaliteral{27}{\isacharprime}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
4.447 +term{\isadigit{2}}str\ s{\isaliteral{5F}{\isacharunderscore}}{\isadigit{2}}{\isaliteral{27}{\isacharprime}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
4.448 +{\isaliteral{2A7D}{\isacharverbatimclose}}%
4.449 +\endisatagML
4.450 +{\isafoldML}%
4.451 +%
4.452 +\isadelimML
4.453 +%
4.454 +\endisadelimML
4.455 +%
4.456 +\isamarkupsubsubsection{build expression%
4.457 +}
4.458 +\isamarkuptrue%
4.459 +%
4.460 +\begin{isamarkuptext}%
4.461 +in isac's CTP-based programming language: $let s_1 = Take numerator / (s_1 * s_2)$%
4.462 +\end{isamarkuptext}%
4.463 +\isamarkuptrue%
4.464 +%
4.465 +\isadelimML
4.466 +%
4.467 +\endisadelimML
4.468 +%
4.469 +\isatagML
4.470 +\isacommand{ML}\isamarkupfalse%
4.471 +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
4.472 +{\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}The\ Main\ Denominator\ is\ the\ multiplikation\ of\ the\ partial\ fraction\ denominators{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
4.473 +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
4.474 +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
4.475 +\isanewline
4.476 +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
4.477 +term{\isadigit{2}}str\ expr{\isaliteral{27}{\isacharprime}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
4.478 +{\isaliteral{2A7D}{\isacharverbatimclose}}%
4.479 +\endisatagML
4.480 +{\isafoldML}%
4.481 +%
4.482 +\isadelimML
4.483 +%
4.484 +\endisadelimML
4.485 +%
4.486 +\isamarkupsubsubsection{Ansatz - create partial fractions out of our expression%
4.487 +}
4.488 +\isamarkuptrue%
4.489 +\isacommand{axiomatization}\isamarkupfalse%
4.490 +\ \isakeyword{where}\isanewline
4.491 +\ \ 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
4.492 +\ \ 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
4.493 +%
4.494 +\isadelimML
4.495 +\isanewline
4.496 +%
4.497 +\endisadelimML
4.498 +%
4.499 +\isatagML
4.500 +\isacommand{ML}\isamarkupfalse%
4.501 +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
4.502 +{\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
4.503 +val\ SOME\ {\isaliteral{28}{\isacharparenleft}}t{\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ rewrite{\isaliteral{5F}{\isacharunderscore}}\ %
4.504 +\isaantiq
4.505 +theory\ Isac{}%
4.506 +\endisaantiq
4.507 +\ e{\isaliteral{5F}{\isacharunderscore}}rew{\isaliteral{5F}{\isacharunderscore}}ord\ e{\isaliteral{5F}{\isacharunderscore}}rls\ false\ %
4.508 +\isaantiq
4.509 +thm\ ansatz{\isadigit{2}}{}%
4.510 +\endisaantiq
4.511 +\ expr{\isaliteral{27}{\isacharprime}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
4.512 +term{\isadigit{2}}str\ t{\isadigit{1}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
4.513 +atomty\ t{\isadigit{1}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
4.514 +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
4.515 +term{\isadigit{2}}str\ eq{\isadigit{1}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
4.516 +{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline
4.517 +\isacommand{ML}\isamarkupfalse%
4.518 +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
4.519 +{\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
4.520 +val\ SOME\ {\isaliteral{28}{\isacharparenleft}}eq{\isadigit{2}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ rewrite{\isaliteral{5F}{\isacharunderscore}}\ %
4.521 +\isaantiq
4.522 +theory\ Isac{}%
4.523 +\endisaantiq
4.524 +\ e{\isaliteral{5F}{\isacharunderscore}}rew{\isaliteral{5F}{\isacharunderscore}}ord\ e{\isaliteral{5F}{\isacharunderscore}}rls\ false\ %
4.525 +\isaantiq
4.526 +thm\ multiply{\isaliteral{5F}{\isacharunderscore}}eq{\isadigit{2}}{}%
4.527 +\endisaantiq
4.528 +\ eq{\isadigit{1}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
4.529 +term{\isadigit{2}}str\ eq{\isadigit{2}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
4.530 +{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline
4.531 +\isacommand{ML}\isamarkupfalse%
4.532 +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
4.533 +{\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}simplificatoin{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
4.534 +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}}\ %
4.535 +\isaantiq
4.536 +theory\ Isac{}%
4.537 +\endisaantiq
4.538 +\ false\ norm{\isaliteral{5F}{\isacharunderscore}}Rational\ eq{\isadigit{2}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
4.539 +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
4.540 +{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline
4.541 +\isacommand{ML}\isamarkupfalse%
4.542 +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
4.543 +val\ SOME\ fract{\isadigit{1}}\ {\isaliteral{3D}{\isacharequal}}\isanewline
4.544 +\ \ 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
4.545 +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}}\ %
4.546 +\isaantiq
4.547 +theory\ Isac{}%
4.548 +\endisaantiq
4.549 +\ false\ norm{\isaliteral{5F}{\isacharunderscore}}Rational\ fract{\isadigit{1}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
4.550 +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
4.551 +{\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
4.552 +{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline
4.553 +\isacommand{ML}\isamarkupfalse%
4.554 +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
4.555 +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
4.556 +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
4.557 +term{\isadigit{2}}str\ eq{\isadigit{3}}{\isaliteral{27}{\isacharprime}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
4.558 +{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline
4.559 +\isacommand{ML}\isamarkupfalse%
4.560 +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}MANDATORY{\isaliteral{3A}{\isacharcolon}}\ otherwise\ {\isadigit{3}}\ {\isaliteral{3D}{\isacharequal}}\ {\isadigit{0}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
4.561 +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}}\ %
4.562 +\isaantiq
4.563 +theory\ Isac{}%
4.564 +\endisaantiq
4.565 +\ false\ norm{\isaliteral{5F}{\isacharunderscore}}Rational\ eq{\isadigit{3}}{\isaliteral{27}{\isacharprime}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
4.566 +term{\isadigit{2}}str\ eq{\isadigit{3}}{\isaliteral{27}{\isacharprime}}{\isaliteral{27}{\isacharprime}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
4.567 +{\isaliteral{2A7D}{\isacharverbatimclose}}%
4.568 +\endisatagML
4.569 +{\isafoldML}%
4.570 +%
4.571 +\isadelimML
4.572 +%
4.573 +\endisadelimML
4.574 +%
4.575 +\isamarkupsubsubsection{get first koeffizient%
4.576 +}
4.577 +\isamarkuptrue%
4.578 +%
4.579 +\isadelimML
4.580 +%
4.581 +\endisadelimML
4.582 +%
4.583 +\isatagML
4.584 +\isacommand{ML}\isamarkupfalse%
4.585 +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
4.586 +{\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}substitude\ z\ with\ the\ first\ zeropoint\ to\ get\ A{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
4.587 +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}}\ %
4.588 +\isaantiq
4.589 +theory\ Isac{}%
4.590 +\endisaantiq
4.591 +\ 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
4.592 +term{\isadigit{2}}str\ eq{\isadigit{4}}{\isaliteral{5F}{\isacharunderscore}}{\isadigit{1}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
4.593 +{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline
4.594 +\isacommand{ML}\isamarkupfalse%
4.595 +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
4.596 +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}}\ %
4.597 +\isaantiq
4.598 +theory\ Isac{}%
4.599 +\endisaantiq
4.600 +\ false\ norm{\isaliteral{5F}{\isacharunderscore}}Rational\ eq{\isadigit{4}}{\isaliteral{5F}{\isacharunderscore}}{\isadigit{1}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
4.601 +term{\isadigit{2}}str\ eq{\isadigit{4}}{\isaliteral{5F}{\isacharunderscore}}{\isadigit{2}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
4.602 +{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline
4.603 +\isacommand{ML}\isamarkupfalse%
4.604 +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
4.605 +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
4.606 +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
4.607 +\isanewline
4.608 +{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline
4.609 +\isacommand{ML}\isamarkupfalse%
4.610 +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
4.611 +{\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
4.612 +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
4.613 +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
4.614 +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
4.615 +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
4.616 +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
4.617 +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
4.618 +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
4.619 +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
4.620 +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
4.621 +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
4.622 +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
4.623 +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
4.624 +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
4.625 +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
4.626 +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
4.627 +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
4.628 +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
4.629 +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
4.630 +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
4.631 +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
4.632 +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
4.633 +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
4.634 +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
4.635 +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
4.636 +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
4.637 +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
4.638 +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
4.639 +{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline
4.640 +\isacommand{ML}\isamarkupfalse%
4.641 +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
4.642 +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
4.643 +f{\isadigit{2}}str\ fa{\isaliteral{3B}{\isacharsemicolon}}\isanewline
4.644 +{\isaliteral{2A7D}{\isacharverbatimclose}}%
4.645 +\endisatagML
4.646 +{\isafoldML}%
4.647 +%
4.648 +\isadelimML
4.649 +%
4.650 +\endisadelimML
4.651 +%
4.652 +\isamarkupsubsubsection{get second koeffizient%
4.653 +}
4.654 +\isamarkuptrue%
4.655 +%
4.656 +\isadelimML
4.657 +%
4.658 +\endisadelimML
4.659 +%
4.660 +\isatagML
4.661 +\isacommand{ML}\isamarkupfalse%
4.662 +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
4.663 +{\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}substitude\ z\ with\ the\ second\ zeropoint\ to\ get\ B{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
4.664 +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}}\ %
4.665 +\isaantiq
4.666 +theory\ Isac{}%
4.667 +\endisaantiq
4.668 +\ 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
4.669 +term{\isadigit{2}}str\ eq{\isadigit{4}}b{\isaliteral{5F}{\isacharunderscore}}{\isadigit{1}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
4.670 +{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline
4.671 +\isanewline
4.672 +\isacommand{ML}\isamarkupfalse%
4.673 +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
4.674 +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}}\ %
4.675 +\isaantiq
4.676 +theory\ Isac{}%
4.677 +\endisaantiq
4.678 +\ false\ norm{\isaliteral{5F}{\isacharunderscore}}Rational\ eq{\isadigit{4}}b{\isaliteral{5F}{\isacharunderscore}}{\isadigit{1}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
4.679 +term{\isadigit{2}}str\ eq{\isadigit{4}}b{\isaliteral{5F}{\isacharunderscore}}{\isadigit{2}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
4.680 +{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline
4.681 +\isanewline
4.682 +\isacommand{ML}\isamarkupfalse%
4.683 +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
4.684 +{\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
4.685 +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
4.686 +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
4.687 +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
4.688 +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
4.689 +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
4.690 +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
4.691 +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
4.692 +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
4.693 +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
4.694 +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
4.695 +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
4.696 +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
4.697 +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
4.698 +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
4.699 +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
4.700 +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
4.701 +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
4.702 +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
4.703 +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
4.704 +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
4.705 +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
4.706 +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
4.707 +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
4.708 +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
4.709 +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
4.710 +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
4.711 +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
4.712 +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
4.713 +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
4.714 +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
4.715 +f{\isadigit{2}}str\ fb{\isaliteral{3B}{\isacharsemicolon}}\isanewline
4.716 +{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline
4.717 +\isanewline
4.718 +\isacommand{ML}\isamarkupfalse%
4.719 +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}check\ koeffizients{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline
4.720 +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
4.721 +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
4.722 +{\isaliteral{2A7D}{\isacharverbatimclose}}%
4.723 +\endisatagML
4.724 +{\isafoldML}%
4.725 +%
4.726 +\isadelimML
4.727 +%
4.728 +\endisadelimML
4.729 +%
4.730 +\isamarkupsubsubsection{substitute expression with solutions%
4.731 +}
4.732 +\isamarkuptrue%
4.733 +%
4.734 +\isadelimML
4.735 +%
4.736 +\endisadelimML
4.737 +%
4.738 +\isatagML
4.739 +\isacommand{ML}\isamarkupfalse%
4.740 +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
4.741 +{\isaliteral{2A7D}{\isacharverbatimclose}}%
4.742 +\endisatagML
4.743 +{\isafoldML}%
4.744 +%
4.745 +\isadelimML
4.746 +%
4.747 +\endisadelimML
4.748 +%
4.749 +\isamarkupsection{Implement the Specification and the Method%
4.750 +}
4.751 +\isamarkuptrue%
4.752 +%
4.753 +\begin{isamarkuptext}%
4.754 +==============================================%
4.755 +\end{isamarkuptext}%
4.756 +\isamarkuptrue%
4.757 +%
4.758 +\isamarkupsubsection{Define the Specification%
4.759 +}
4.760 +\isamarkuptrue%
4.761 +%
4.762 +\isadelimML
4.763 +%
4.764 +\endisadelimML
4.765 +%
4.766 +\isatagML
4.767 +\isacommand{ML}\isamarkupfalse%
4.768 +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
4.769 +val\ thy\ {\isaliteral{3D}{\isacharequal}}\ %
4.770 +\isaantiq
4.771 +theory{}%
4.772 +\endisaantiq
4.773 +{\isaliteral{3B}{\isacharsemicolon}}\isanewline
4.774 +{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline
4.775 +\isacommand{ML}\isamarkupfalse%
4.776 +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
4.777 +store{\isaliteral{5F}{\isacharunderscore}}pbt\isanewline
4.778 +\ {\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
4.779 +\ {\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
4.780 +store{\isaliteral{5F}{\isacharunderscore}}pbt\isanewline
4.781 +\ {\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
4.782 +\ {\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
4.783 +store{\isaliteral{5F}{\isacharunderscore}}pbt\isanewline
4.784 +\ {\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
4.785 +\ {\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
4.786 +\ \ {\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}}equality\ X{\isaliteral{5F}{\isacharunderscore}}eq{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\isanewline
4.787 +\ \ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{23}{\isacharhash}}Find{\isaliteral{22}{\isachardoublequote}}\ \ {\isaliteral{2C}{\isacharcomma}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}equality\ n{\isaliteral{5F}{\isacharunderscore}}eq{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}\isanewline
4.788 +\ \ {\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\isanewline
4.789 +\ \ 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
4.790 +\ \ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{22}{\isachardoublequote}}TODO{\isaliteral{3A}{\isacharcolon}}\ path\ to\ method{\isaliteral{22}{\isachardoublequote}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
4.791 +\isanewline
4.792 +show{\isaliteral{5F}{\isacharunderscore}}ptyps{\isaliteral{28}{\isacharparenleft}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
4.793 +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
4.794 +{\isaliteral{2A7D}{\isacharverbatimclose}}%
4.795 +\endisatagML
4.796 +{\isafoldML}%
4.797 +%
4.798 +\isadelimML
4.799 +%
4.800 +\endisadelimML
4.801 +%
4.802 +\isamarkupsubsection{Define the (Dummy-)Method%
4.803 +}
4.804 +\isamarkuptrue%
4.805 +%
4.806 +\isamarkupsubsection{Define Name and Signature for the Method%
4.807 +}
4.808 +\isamarkuptrue%
4.809 +\isacommand{consts}\isamarkupfalse%
4.810 +\isanewline
4.811 +\ \ 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
4.812 +\ \ \ \ {\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}}\isanewline
4.813 +%
4.814 +\isadelimML
4.815 +\isanewline
4.816 +%
4.817 +\endisadelimML
4.818 +%
4.819 +\isatagML
4.820 +\isacommand{ML}\isamarkupfalse%
4.821 +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
4.822 +store{\isaliteral{5F}{\isacharunderscore}}met\isanewline
4.823 +\ {\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
4.824 +\ {\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
4.825 +\ \ \ {\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
4.826 +\ \ \ \ 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
4.827 +store{\isaliteral{5F}{\isacharunderscore}}met\isanewline
4.828 +\ {\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
4.829 +\ {\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
4.830 +\ \ \ {\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
4.831 +\ \ \ \ 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
4.832 +{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline
4.833 +\isacommand{ML}\isamarkupfalse%
4.834 +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
4.835 +store{\isaliteral{5F}{\isacharunderscore}}met\isanewline
4.836 +\ {\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
4.837 +\ {\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}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\isanewline
4.838 +\ \ \ {\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
4.839 +\ \ \ \ 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
4.840 +\ \ {\isaliteral{22}{\isachardoublequote}}empty{\isaliteral{5F}{\isacharunderscore}}script{\isaliteral{22}{\isachardoublequote}}\isanewline
4.841 +\ {\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
4.842 +{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline
4.843 +\isacommand{ML}\isamarkupfalse%
4.844 +\ {\isaliteral{7B2A}{\isacharverbatimopen}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}\isanewline
4.845 +store{\isaliteral{5F}{\isacharunderscore}}met\isanewline
4.846 +\ {\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
4.847 +\ {\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}}\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\isanewline
4.848 +\ \ \ {\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
4.849 +\ \ \ \ 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
4.850 +\ \ {\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
4.851 +\ \ {\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{28}{\isacharparenleft}}let\ X\ {\isaliteral{3D}{\isacharequal}}\ Take\ Xeq{\isaliteral{3B}{\isacharsemicolon}}{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5E}{\isacharcircum}}\isanewline
4.852 +\ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ X\ {\isaliteral{3D}{\isacharequal}}\ Rewrite\ ruleZY\ False\ X{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5E}{\isacharcircum}}\isanewline
4.853 +\ \ {\isaliteral{22}{\isachardoublequote}}\ \ in\ X{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}\isanewline
4.854 +\ {\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
4.855 +{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline
4.856 +\isacommand{ML}\isamarkupfalse%
4.857 +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
4.858 +show{\isaliteral{5F}{\isacharunderscore}}mets{\isaliteral{28}{\isacharparenleft}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
4.859 +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
4.860 +{\isaliteral{2A7D}{\isacharverbatimclose}}%
4.861 +\endisatagML
4.862 +{\isafoldML}%
4.863 +%
4.864 +\isadelimML
4.865 +%
4.866 +\endisadelimML
4.867 +%
4.868 +\isamarkupsection{Program in CTP-based language%
4.869 +}
4.870 +\isamarkuptrue%
4.871 +%
4.872 +\begin{isamarkuptext}%
4.873 +=================================%
4.874 +\end{isamarkuptext}%
4.875 +\isamarkuptrue%
4.876 +%
4.877 +\isamarkupsubsection{Stepwise extend Program%
4.878 +}
4.879 +\isamarkuptrue%
4.880 +%
4.881 +\isadelimML
4.882 +%
4.883 +\endisadelimML
4.884 +%
4.885 +\isatagML
4.886 +\isacommand{ML}\isamarkupfalse%
4.887 +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
4.888 +val\ str\ {\isaliteral{3D}{\isacharequal}}\ \isanewline
4.889 +{\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
4.890 +{\isaliteral{22}{\isachardoublequote}}\ Xeq{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
4.891 +{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline
4.892 +\isacommand{ML}\isamarkupfalse%
4.893 +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
4.894 +val\ str\ {\isaliteral{3D}{\isacharequal}}\ \isanewline
4.895 +{\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
4.896 +{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{28}{\isacharparenleft}}let\ X\ {\isaliteral{3D}{\isacharequal}}\ Take\ Xeq{\isaliteral{3B}{\isacharsemicolon}}{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5E}{\isacharcircum}}\isanewline
4.897 +{\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ X\ {\isaliteral{3D}{\isacharequal}}\ Rewrite\ ruleZY\ False\ X{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5E}{\isacharcircum}}\isanewline
4.898 +{\isaliteral{22}{\isachardoublequote}}\ \ in\ X{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline
4.899 +{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline
4.900 +\isacommand{ML}\isamarkupfalse%
4.901 +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
4.902 +val\ thy\ {\isaliteral{3D}{\isacharequal}}\ %
4.903 +\isaantiq
4.904 +theory{}%
4.905 +\endisaantiq
4.906 +{\isaliteral{3B}{\isacharsemicolon}}\isanewline
4.907 +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
4.908 +{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline
4.909 +\isacommand{ML}\isamarkupfalse%
4.910 +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
4.911 +term{\isadigit{2}}str\ sc{\isaliteral{3B}{\isacharsemicolon}}\isanewline
4.912 +atomty\ sc\isanewline
4.913 +{\isaliteral{2A7D}{\isacharverbatimclose}}%
4.914 +\endisatagML
4.915 +{\isafoldML}%
4.916 +%
4.917 +\isadelimML
4.918 +%
4.919 +\endisadelimML
4.920 +%
4.921 +\isamarkupsubsection{Stepwise Execute the Program%
4.922 +}
4.923 +\isamarkuptrue%
4.924 +%
4.925 +\isamarkupsection{Write Tests for Crucial Details%
4.926 +}
4.927 +\isamarkuptrue%
4.928 +%
4.929 +\begin{isamarkuptext}%
4.930 +===================================%
4.931 +\end{isamarkuptext}%
4.932 +\isamarkuptrue%
4.933 +%
4.934 +\isadelimML
4.935 +%
4.936 +\endisadelimML
4.937 +%
4.938 +\isatagML
4.939 +\isacommand{ML}\isamarkupfalse%
4.940 +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
4.941 +\isanewline
4.942 +{\isaliteral{2A7D}{\isacharverbatimclose}}%
4.943 +\endisatagML
4.944 +{\isafoldML}%
4.945 +%
4.946 +\isadelimML
4.947 +%
4.948 +\endisadelimML
4.949 +%
4.950 +\isamarkupsection{Integrate Program into Knowledge%
4.951 +}
4.952 +\isamarkuptrue%
4.953 +%
4.954 +\isadelimML
4.955 +%
4.956 +\endisadelimML
4.957 +%
4.958 +\isatagML
4.959 +\isacommand{ML}\isamarkupfalse%
4.960 +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline
4.961 +\isanewline
4.962 +{\isaliteral{2A7D}{\isacharverbatimclose}}%
4.963 +\endisatagML
4.964 +{\isafoldML}%
4.965 +%
4.966 +\isadelimML
4.967 +%
4.968 +\endisadelimML
4.969 +\isanewline
4.970 +%
4.971 +\isadelimtheory
4.972 +\isanewline
4.973 +%
4.974 +\endisadelimtheory
4.975 +%
4.976 +\isatagtheory
4.977 +\isacommand{end}\isamarkupfalse%
4.978 +%
4.979 +\endisatagtheory
4.980 +{\isafoldtheory}%
4.981 +%
4.982 +\isadelimtheory
4.983 +%
4.984 +\endisadelimtheory
4.985 +\isanewline
4.986 +\isanewline
4.987 +\end{isabellebody}%
4.988 +%%% Local Variables:
4.989 +%%% mode: latex
4.990 +%%% TeX-master: "root"
4.991 +%%% End:
5.1 --- /dev/null Thu Jan 01 00:00:00 1970 +0000
5.2 +++ b/doc-src/isac/jrocnik/Inverse_Z_Transform/document/isabelle.sty Thu Sep 08 23:17:35 2011 +0200
5.3 @@ -0,0 +1,218 @@
5.4 +%%
5.5 +%% macros for Isabelle generated LaTeX output
5.6 +%%
5.7 +
5.8 +%%% Simple document preparation (based on theory token language and symbols)
5.9 +
5.10 +% isabelle environments
5.11 +
5.12 +\newcommand{\isabellecontext}{UNKNOWN}
5.13 +
5.14 +\newcommand{\isastyle}{\UNDEF}
5.15 +\newcommand{\isastyleminor}{\UNDEF}
5.16 +\newcommand{\isastylescript}{\UNDEF}
5.17 +\newcommand{\isastyletext}{\normalsize\rm}
5.18 +\newcommand{\isastyletxt}{\rm}
5.19 +\newcommand{\isastylecmt}{\rm}
5.20 +
5.21 +%symbol markup -- \emph achieves decent spacing via italic corrections
5.22 +\newcommand{\isamath}[1]{\emph{$#1$}}
5.23 +\newcommand{\isatext}[1]{\emph{#1}}
5.24 +\DeclareRobustCommand{\isascriptstyle}{\def\isamath##1{##1}\def\isatext##1{\mbox{\isastylescript##1}}}
5.25 +\newcommand{\isactrlsub}[1]{\emph{\isascriptstyle${}\sb{#1}$}}
5.26 +\newcommand{\isactrlsup}[1]{\emph{\isascriptstyle${}\sp{#1}$}}
5.27 +\newcommand{\isactrlisub}[1]{\emph{\isascriptstyle${}\sb{#1}$}}
5.28 +\newcommand{\isactrlisup}[1]{\emph{\isascriptstyle${}\sp{#1}$}}
5.29 +\DeclareRobustCommand{\isactrlbsub}{\emph\bgroup\math{}\sb\bgroup\mbox\bgroup\isastylescript}
5.30 +\DeclareRobustCommand{\isactrlesub}{\egroup\egroup\endmath\egroup}
5.31 +\DeclareRobustCommand{\isactrlbsup}{\emph\bgroup\math{}\sp\bgroup\mbox\bgroup\isastylescript}
5.32 +\DeclareRobustCommand{\isactrlesup}{\egroup\egroup\endmath\egroup}
5.33 +\newcommand{\isactrlbold}[1]{{\bfseries\upshape\boldmath#1}}
5.34 +\newcommand{\isactrlloc}[1]{{\bfseries\upshape\boldmath#1}}
5.35 +
5.36 +\newenvironment{isaantiq}{{\isacharat\isacharbraceleft}}{{\isacharbraceright}}
5.37 +\newcommand{\isaantiqopen}{\isakeyword{\isacharbraceleft}}
5.38 +\newcommand{\isaantiqclose}{\isakeyword{\isacharbraceright}}
5.39 +
5.40 +\newdimen\isa@parindent\newdimen\isa@parskip
5.41 +
5.42 +\newenvironment{isabellebody}{%
5.43 +\isamarkuptrue\par%
5.44 +\isa@parindent\parindent\parindent0pt%
5.45 +\isa@parskip\parskip\parskip0pt%
5.46 +\isastyle}{\par}
5.47 +
5.48 +\newenvironment{isabelle}
5.49 +{\begin{trivlist}\begin{isabellebody}\item\relax}
5.50 +{\end{isabellebody}\end{trivlist}}
5.51 +
5.52 +\newcommand{\isa}[1]{\emph{\isastyleminor #1}}
5.53 +
5.54 +\newcommand{\isaindent}[1]{\hphantom{#1}}
5.55 +\newcommand{\isanewline}{\mbox{}\par\mbox{}}
5.56 +\newcommand{\isasep}{}
5.57 +\newcommand{\isadigit}[1]{#1}
5.58 +
5.59 +\newcommand{\isachardefaults}{%
5.60 +\chardef\isacharbang=`\!%
5.61 +\chardef\isachardoublequote=`\"%
5.62 +\chardef\isachardoublequoteopen=`\"%
5.63 +\chardef\isachardoublequoteclose=`\"%
5.64 +\chardef\isacharhash=`\#%
5.65 +\chardef\isachardollar=`\$%
5.66 +\chardef\isacharpercent=`\%%
5.67 +\chardef\isacharampersand=`\&%
5.68 +\chardef\isacharprime=`\'%
5.69 +\chardef\isacharparenleft=`\(%
5.70 +\chardef\isacharparenright=`\)%
5.71 +\chardef\isacharasterisk=`\*%
5.72 +\chardef\isacharplus=`\+%
5.73 +\chardef\isacharcomma=`\,%
5.74 +\chardef\isacharminus=`\-%
5.75 +\chardef\isachardot=`\.%
5.76 +\chardef\isacharslash=`\/%
5.77 +\chardef\isacharcolon=`\:%
5.78 +\chardef\isacharsemicolon=`\;%
5.79 +\chardef\isacharless=`\<%
5.80 +\chardef\isacharequal=`\=%
5.81 +\chardef\isachargreater=`\>%
5.82 +\chardef\isacharquery=`\?%
5.83 +\chardef\isacharat=`\@%
5.84 +\chardef\isacharbrackleft=`\[%
5.85 +\chardef\isacharbackslash=`\\%
5.86 +\chardef\isacharbrackright=`\]%
5.87 +\chardef\isacharcircum=`\^%
5.88 +\chardef\isacharunderscore=`\_%
5.89 +\def\isacharunderscorekeyword{\_}%
5.90 +\chardef\isacharbackquote=`\`%
5.91 +\chardef\isacharbackquoteopen=`\`%
5.92 +\chardef\isacharbackquoteclose=`\`%
5.93 +\chardef\isacharbraceleft=`\{%
5.94 +\chardef\isacharbar=`\|%
5.95 +\chardef\isacharbraceright=`\}%
5.96 +\chardef\isachartilde=`\~%
5.97 +\def\isacharverbatimopen{\isacharbraceleft\isacharasterisk}%
5.98 +\def\isacharverbatimclose{\isacharasterisk\isacharbraceright}%
5.99 +}
5.100 +
5.101 +\newcommand{\isaliteral}[2]{#2}
5.102 +\newcommand{\isanil}{}
5.103 +
5.104 +
5.105 +% keyword and section markup
5.106 +
5.107 +\newcommand{\isakeyword}[1]
5.108 +{\emph{\bf\def\isachardot{.}\def\isacharunderscore{\isacharunderscorekeyword}%
5.109 +\def\isacharbraceleft{\{}\def\isacharbraceright{\}}#1}}
5.110 +\newcommand{\isacommand}[1]{\isakeyword{#1}}
5.111 +
5.112 +\newcommand{\isamarkupheader}[1]{\section{#1}}
5.113 +\newcommand{\isamarkupchapter}[1]{\chapter{#1}}
5.114 +\newcommand{\isamarkupsection}[1]{\section{#1}}
5.115 +\newcommand{\isamarkupsubsection}[1]{\subsection{#1}}
5.116 +\newcommand{\isamarkupsubsubsection}[1]{\subsubsection{#1}}
5.117 +\newcommand{\isamarkupsect}[1]{\section{#1}}
5.118 +\newcommand{\isamarkupsubsect}[1]{\subsection{#1}}
5.119 +\newcommand{\isamarkupsubsubsect}[1]{\subsubsection{#1}}
5.120 +
5.121 +\newif\ifisamarkup
5.122 +\newcommand{\isabeginpar}{\par\ifisamarkup\relax\else\medskip\fi}
5.123 +\newcommand{\isaendpar}{\par\medskip}
5.124 +\newenvironment{isapar}{\parindent\isa@parindent\parskip\isa@parskip\isabeginpar}{\isaendpar}
5.125 +\newenvironment{isamarkuptext}{\par\isastyletext\begin{isapar}}{\end{isapar}}
5.126 +\newenvironment{isamarkuptxt}{\par\isastyletxt\begin{isapar}}{\end{isapar}}
5.127 +\newcommand{\isamarkupcmt}[1]{{\isastylecmt--- #1}}
5.128 +
5.129 +
5.130 +% styles
5.131 +
5.132 +\def\isabellestyle#1{\csname isabellestyle#1\endcsname}
5.133 +
5.134 +\newcommand{\isabellestyledefault}{%
5.135 +\renewcommand{\isastyle}{\small\tt\slshape}%
5.136 +\renewcommand{\isastyleminor}{\small\tt\slshape}%
5.137 +\renewcommand{\isastylescript}{\footnotesize\tt\slshape}%
5.138 +\isachardefaults%
5.139 +}
5.140 +\isabellestyledefault
5.141 +
5.142 +\newcommand{\isabellestylett}{%
5.143 +\renewcommand{\isastyle}{\small\tt}%
5.144 +\renewcommand{\isastyleminor}{\small\tt}%
5.145 +\renewcommand{\isastylescript}{\footnotesize\tt}%
5.146 +\isachardefaults%
5.147 +}
5.148 +
5.149 +\newcommand{\isabellestyleit}{%
5.150 +\renewcommand{\isastyle}{\small\it}%
5.151 +\renewcommand{\isastyleminor}{\it}%
5.152 +\renewcommand{\isastylescript}{\footnotesize\it}%
5.153 +\renewcommand{\isacharunderscorekeyword}{\mbox{-}}%
5.154 +\renewcommand{\isacharbang}{\isamath{!}}%
5.155 +\renewcommand{\isachardoublequote}{\isanil}%
5.156 +\renewcommand{\isachardoublequoteopen}{\isanil}%
5.157 +\renewcommand{\isachardoublequoteclose}{\isanil}%
5.158 +\renewcommand{\isacharhash}{\isamath{\#}}%
5.159 +\renewcommand{\isachardollar}{\isamath{\$}}%
5.160 +\renewcommand{\isacharpercent}{\isamath{\%}}%
5.161 +\renewcommand{\isacharampersand}{\isamath{\&}}%
5.162 +\renewcommand{\isacharprime}{\isamath{\mskip2mu{'}\mskip-2mu}}%
5.163 +\renewcommand{\isacharparenleft}{\isamath{(}}%
5.164 +\renewcommand{\isacharparenright}{\isamath{)}}%
5.165 +\renewcommand{\isacharasterisk}{\isamath{*}}%
5.166 +\renewcommand{\isacharplus}{\isamath{+}}%
5.167 +\renewcommand{\isacharcomma}{\isamath{\mathord,}}%
5.168 +\renewcommand{\isacharminus}{\isamath{-}}%
5.169 +\renewcommand{\isachardot}{\isamath{\mathord.}}%
5.170 +\renewcommand{\isacharslash}{\isamath{/}}%
5.171 +\renewcommand{\isacharcolon}{\isamath{\mathord:}}%
5.172 +\renewcommand{\isacharsemicolon}{\isamath{\mathord;}}%
5.173 +\renewcommand{\isacharless}{\isamath{<}}%
5.174 +\renewcommand{\isacharequal}{\isamath{=}}%
5.175 +\renewcommand{\isachargreater}{\isamath{>}}%
5.176 +\renewcommand{\isacharat}{\isamath{@}}%
5.177 +\renewcommand{\isacharbrackleft}{\isamath{[}}%
5.178 +\renewcommand{\isacharbackslash}{\isamath{\backslash}}%
5.179 +\renewcommand{\isacharbrackright}{\isamath{]}}%
5.180 +\renewcommand{\isacharunderscore}{\mbox{-}}%
5.181 +\renewcommand{\isacharbraceleft}{\isamath{\{}}%
5.182 +\renewcommand{\isacharbar}{\isamath{\mid}}%
5.183 +\renewcommand{\isacharbraceright}{\isamath{\}}}%
5.184 +\renewcommand{\isachartilde}{\isamath{{}\sp{\sim}}}%
5.185 +\renewcommand{\isacharbackquoteopen}{\isatext{\raise.3ex\hbox{$\scriptscriptstyle\langle$}}}%
5.186 +\renewcommand{\isacharbackquoteclose}{\isatext{\raise.3ex\hbox{$\scriptscriptstyle\rangle$}}}%
5.187 +\renewcommand{\isacharverbatimopen}{\isamath{\langle\!\langle}}%
5.188 +\renewcommand{\isacharverbatimclose}{\isamath{\rangle\!\rangle}}%
5.189 +}
5.190 +
5.191 +\newcommand{\isabellestylesl}{%
5.192 +\isabellestyleit%
5.193 +\renewcommand{\isastyle}{\small\sl}%
5.194 +\renewcommand{\isastyleminor}{\sl}%
5.195 +\renewcommand{\isastylescript}{\footnotesize\sl}%
5.196 +}
5.197 +
5.198 +
5.199 +% tagged regions
5.200 +
5.201 +%plain TeX version of comment package -- much faster!
5.202 +\let\isafmtname\fmtname\def\fmtname{plain}
5.203 +\usepackage{comment}
5.204 +\let\fmtname\isafmtname
5.205 +
5.206 +\newcommand{\isafold}[1]{\emph{$\langle\mathord{\mathit{#1}}\rangle$}}
5.207 +
5.208 +\newcommand{\isakeeptag}[1]%
5.209 +{\includecomment{isadelim#1}\includecomment{isatag#1}\csarg\def{isafold#1}{}}
5.210 +\newcommand{\isadroptag}[1]%
5.211 +{\excludecomment{isadelim#1}\excludecomment{isatag#1}\csarg\def{isafold#1}{}}
5.212 +\newcommand{\isafoldtag}[1]%
5.213 +{\includecomment{isadelim#1}\excludecomment{isatag#1}\csarg\def{isafold#1}{\isafold{#1}}}
5.214 +
5.215 +\isakeeptag{theory}
5.216 +\isakeeptag{proof}
5.217 +\isakeeptag{ML}
5.218 +\isakeeptag{visible}
5.219 +\isadroptag{invisible}
5.220 +
5.221 +\IfFileExists{isabelletags.sty}{\usepackage{isabelletags}}{}
6.1 --- /dev/null Thu Jan 01 00:00:00 1970 +0000
6.2 +++ b/doc-src/isac/jrocnik/Inverse_Z_Transform/document/isabellesym.sty Thu Sep 08 23:17:35 2011 +0200
6.3 @@ -0,0 +1,358 @@
6.4 +%%
6.5 +%% definitions of standard Isabelle symbols
6.6 +%%
6.7 +
6.8 +\newcommand{\isasymzero}{\isamath{\mathbf{0}}} %requires amssymb
6.9 +\newcommand{\isasymone}{\isamath{\mathbf{1}}} %requires amssymb
6.10 +\newcommand{\isasymtwo}{\isamath{\mathbf{2}}} %requires amssymb
6.11 +\newcommand{\isasymthree}{\isamath{\mathbf{3}}} %requires amssymb
6.12 +\newcommand{\isasymfour}{\isamath{\mathbf{4}}} %requires amssymb
6.13 +\newcommand{\isasymfive}{\isamath{\mathbf{5}}} %requires amssymb
6.14 +\newcommand{\isasymsix}{\isamath{\mathbf{6}}} %requires amssymb
6.15 +\newcommand{\isasymseven}{\isamath{\mathbf{7}}} %requires amssymb
6.16 +\newcommand{\isasymeight}{\isamath{\mathbf{8}}} %requires amssymb
6.17 +\newcommand{\isasymnine}{\isamath{\mathbf{9}}} %requires amssymb
6.18 +\newcommand{\isasymA}{\isamath{\mathcal{A}}}
6.19 +\newcommand{\isasymB}{\isamath{\mathcal{B}}}
6.20 +\newcommand{\isasymC}{\isamath{\mathcal{C}}}
6.21 +\newcommand{\isasymD}{\isamath{\mathcal{D}}}
6.22 +\newcommand{\isasymE}{\isamath{\mathcal{E}}}
6.23 +\newcommand{\isasymF}{\isamath{\mathcal{F}}}
6.24 +\newcommand{\isasymG}{\isamath{\mathcal{G}}}
6.25 +\newcommand{\isasymH}{\isamath{\mathcal{H}}}
6.26 +\newcommand{\isasymI}{\isamath{\mathcal{I}}}
6.27 +\newcommand{\isasymJ}{\isamath{\mathcal{J}}}
6.28 +\newcommand{\isasymK}{\isamath{\mathcal{K}}}
6.29 +\newcommand{\isasymL}{\isamath{\mathcal{L}}}
6.30 +\newcommand{\isasymM}{\isamath{\mathcal{M}}}
6.31 +\newcommand{\isasymN}{\isamath{\mathcal{N}}}
6.32 +\newcommand{\isasymO}{\isamath{\mathcal{O}}}
6.33 +\newcommand{\isasymP}{\isamath{\mathcal{P}}}
6.34 +\newcommand{\isasymQ}{\isamath{\mathcal{Q}}}
6.35 +\newcommand{\isasymR}{\isamath{\mathcal{R}}}
6.36 +\newcommand{\isasymS}{\isamath{\mathcal{S}}}
6.37 +\newcommand{\isasymT}{\isamath{\mathcal{T}}}
6.38 +\newcommand{\isasymU}{\isamath{\mathcal{U}}}
6.39 +\newcommand{\isasymV}{\isamath{\mathcal{V}}}
6.40 +\newcommand{\isasymW}{\isamath{\mathcal{W}}}
6.41 +\newcommand{\isasymX}{\isamath{\mathcal{X}}}
6.42 +\newcommand{\isasymY}{\isamath{\mathcal{Y}}}
6.43 +\newcommand{\isasymZ}{\isamath{\mathcal{Z}}}
6.44 +\newcommand{\isasyma}{\isamath{\mathrm{a}}}
6.45 +\newcommand{\isasymb}{\isamath{\mathrm{b}}}
6.46 +\newcommand{\isasymc}{\isamath{\mathrm{c}}}
6.47 +\newcommand{\isasymd}{\isamath{\mathrm{d}}}
6.48 +\newcommand{\isasyme}{\isamath{\mathrm{e}}}
6.49 +\newcommand{\isasymf}{\isamath{\mathrm{f}}}
6.50 +\newcommand{\isasymg}{\isamath{\mathrm{g}}}
6.51 +\newcommand{\isasymh}{\isamath{\mathrm{h}}}
6.52 +\newcommand{\isasymi}{\isamath{\mathrm{i}}}
6.53 +\newcommand{\isasymj}{\isamath{\mathrm{j}}}
6.54 +\newcommand{\isasymk}{\isamath{\mathrm{k}}}
6.55 +\newcommand{\isasyml}{\isamath{\mathrm{l}}}
6.56 +\newcommand{\isasymm}{\isamath{\mathrm{m}}}
6.57 +\newcommand{\isasymn}{\isamath{\mathrm{n}}}
6.58 +\newcommand{\isasymo}{\isamath{\mathrm{o}}}
6.59 +\newcommand{\isasymp}{\isamath{\mathrm{p}}}
6.60 +\newcommand{\isasymq}{\isamath{\mathrm{q}}}
6.61 +\newcommand{\isasymr}{\isamath{\mathrm{r}}}
6.62 +\newcommand{\isasyms}{\isamath{\mathrm{s}}}
6.63 +\newcommand{\isasymt}{\isamath{\mathrm{t}}}
6.64 +\newcommand{\isasymu}{\isamath{\mathrm{u}}}
6.65 +\newcommand{\isasymv}{\isamath{\mathrm{v}}}
6.66 +\newcommand{\isasymw}{\isamath{\mathrm{w}}}
6.67 +\newcommand{\isasymx}{\isamath{\mathrm{x}}}
6.68 +\newcommand{\isasymy}{\isamath{\mathrm{y}}}
6.69 +\newcommand{\isasymz}{\isamath{\mathrm{z}}}
6.70 +\newcommand{\isasymAA}{\isamath{\mathfrak{A}}} %requires eufrak
6.71 +\newcommand{\isasymBB}{\isamath{\mathfrak{B}}} %requires eufrak
6.72 +\newcommand{\isasymCC}{\isamath{\mathfrak{C}}} %requires eufrak
6.73 +\newcommand{\isasymDD}{\isamath{\mathfrak{D}}} %requires eufrak
6.74 +\newcommand{\isasymEE}{\isamath{\mathfrak{E}}} %requires eufrak
6.75 +\newcommand{\isasymFF}{\isamath{\mathfrak{F}}} %requires eufrak
6.76 +\newcommand{\isasymGG}{\isamath{\mathfrak{G}}} %requires eufrak
6.77 +\newcommand{\isasymHH}{\isamath{\mathfrak{H}}} %requires eufrak
6.78 +\newcommand{\isasymII}{\isamath{\mathfrak{I}}} %requires eufrak
6.79 +\newcommand{\isasymJJ}{\isamath{\mathfrak{J}}} %requires eufrak
6.80 +\newcommand{\isasymKK}{\isamath{\mathfrak{K}}} %requires eufrak
6.81 +\newcommand{\isasymLL}{\isamath{\mathfrak{L}}} %requires eufrak
6.82 +\newcommand{\isasymMM}{\isamath{\mathfrak{M}}} %requires eufrak
6.83 +\newcommand{\isasymNN}{\isamath{\mathfrak{N}}} %requires eufrak
6.84 +\newcommand{\isasymOO}{\isamath{\mathfrak{O}}} %requires eufrak
6.85 +\newcommand{\isasymPP}{\isamath{\mathfrak{P}}} %requires eufrak
6.86 +\newcommand{\isasymQQ}{\isamath{\mathfrak{Q}}} %requires eufrak
6.87 +\newcommand{\isasymRR}{\isamath{\mathfrak{R}}} %requires eufrak
6.88 +\newcommand{\isasymSS}{\isamath{\mathfrak{S}}} %requires eufrak
6.89 +\newcommand{\isasymTT}{\isamath{\mathfrak{T}}} %requires eufrak
6.90 +\newcommand{\isasymUU}{\isamath{\mathfrak{U}}} %requires eufrak
6.91 +\newcommand{\isasymVV}{\isamath{\mathfrak{V}}} %requires eufrak
6.92 +\newcommand{\isasymWW}{\isamath{\mathfrak{W}}} %requires eufrak
6.93 +\newcommand{\isasymXX}{\isamath{\mathfrak{X}}} %requires eufrak
6.94 +\newcommand{\isasymYY}{\isamath{\mathfrak{Y}}} %requires eufrak
6.95 +\newcommand{\isasymZZ}{\isamath{\mathfrak{Z}}} %requires eufrak
6.96 +\newcommand{\isasymaa}{\isamath{\mathfrak{a}}} %requires eufrak
6.97 +\newcommand{\isasymbb}{\isamath{\mathfrak{b}}} %requires eufrak
6.98 +\newcommand{\isasymcc}{\isamath{\mathfrak{c}}} %requires eufrak
6.99 +\newcommand{\isasymdd}{\isamath{\mathfrak{d}}} %requires eufrak
6.100 +\newcommand{\isasymee}{\isamath{\mathfrak{e}}} %requires eufrak
6.101 +\newcommand{\isasymff}{\isamath{\mathfrak{f}}} %requires eufrak
6.102 +\newcommand{\isasymgg}{\isamath{\mathfrak{g}}} %requires eufrak
6.103 +\newcommand{\isasymhh}{\isamath{\mathfrak{h}}} %requires eufrak
6.104 +\newcommand{\isasymii}{\isamath{\mathfrak{i}}} %requires eufrak
6.105 +\newcommand{\isasymjj}{\isamath{\mathfrak{j}}} %requires eufrak
6.106 +\newcommand{\isasymkk}{\isamath{\mathfrak{k}}} %requires eufrak
6.107 +\newcommand{\isasymll}{\isamath{\mathfrak{l}}} %requires eufrak
6.108 +\newcommand{\isasymmm}{\isamath{\mathfrak{m}}} %requires eufrak
6.109 +\newcommand{\isasymnn}{\isamath{\mathfrak{n}}} %requires eufrak
6.110 +\newcommand{\isasymoo}{\isamath{\mathfrak{o}}} %requires eufrak
6.111 +\newcommand{\isasympp}{\isamath{\mathfrak{p}}} %requires eufrak
6.112 +\newcommand{\isasymqq}{\isamath{\mathfrak{q}}} %requires eufrak
6.113 +\newcommand{\isasymrr}{\isamath{\mathfrak{r}}} %requires eufrak
6.114 +\newcommand{\isasymss}{\isamath{\mathfrak{s}}} %requires eufrak
6.115 +\newcommand{\isasymtt}{\isamath{\mathfrak{t}}} %requires eufrak
6.116 +\newcommand{\isasymuu}{\isamath{\mathfrak{u}}} %requires eufrak
6.117 +\newcommand{\isasymvv}{\isamath{\mathfrak{v}}} %requires eufrak
6.118 +\newcommand{\isasymww}{\isamath{\mathfrak{w}}} %requires eufrak
6.119 +\newcommand{\isasymxx}{\isamath{\mathfrak{x}}} %requires eufrak
6.120 +\newcommand{\isasymyy}{\isamath{\mathfrak{y}}} %requires eufrak
6.121 +\newcommand{\isasymzz}{\isamath{\mathfrak{z}}} %requires eufrak
6.122 +\newcommand{\isasymalpha}{\isamath{\alpha}}
6.123 +\newcommand{\isasymbeta}{\isamath{\beta}}
6.124 +\newcommand{\isasymgamma}{\isamath{\gamma}}
6.125 +\newcommand{\isasymdelta}{\isamath{\delta}}
6.126 +\newcommand{\isasymepsilon}{\isamath{\varepsilon}}
6.127 +\newcommand{\isasymzeta}{\isamath{\zeta}}
6.128 +\newcommand{\isasymeta}{\isamath{\eta}}
6.129 +\newcommand{\isasymtheta}{\isamath{\vartheta}}
6.130 +\newcommand{\isasymiota}{\isamath{\iota}}
6.131 +\newcommand{\isasymkappa}{\isamath{\kappa}}
6.132 +\newcommand{\isasymlambda}{\isamath{\lambda}}
6.133 +\newcommand{\isasymmu}{\isamath{\mu}}
6.134 +\newcommand{\isasymnu}{\isamath{\nu}}
6.135 +\newcommand{\isasymxi}{\isamath{\xi}}
6.136 +\newcommand{\isasympi}{\isamath{\pi}}
6.137 +\newcommand{\isasymrho}{\isamath{\varrho}}
6.138 +\newcommand{\isasymsigma}{\isamath{\sigma}}
6.139 +\newcommand{\isasymtau}{\isamath{\tau}}
6.140 +\newcommand{\isasymupsilon}{\isamath{\upsilon}}
6.141 +\newcommand{\isasymphi}{\isamath{\varphi}}
6.142 +\newcommand{\isasymchi}{\isamath{\chi}}
6.143 +\newcommand{\isasympsi}{\isamath{\psi}}
6.144 +\newcommand{\isasymomega}{\isamath{\omega}}
6.145 +\newcommand{\isasymGamma}{\isamath{\Gamma}}
6.146 +\newcommand{\isasymDelta}{\isamath{\Delta}}
6.147 +\newcommand{\isasymTheta}{\isamath{\Theta}}
6.148 +\newcommand{\isasymLambda}{\isamath{\Lambda}}
6.149 +\newcommand{\isasymXi}{\isamath{\Xi}}
6.150 +\newcommand{\isasymPi}{\isamath{\Pi}}
6.151 +\newcommand{\isasymSigma}{\isamath{\Sigma}}
6.152 +\newcommand{\isasymUpsilon}{\isamath{\Upsilon}}
6.153 +\newcommand{\isasymPhi}{\isamath{\Phi}}
6.154 +\newcommand{\isasymPsi}{\isamath{\Psi}}
6.155 +\newcommand{\isasymOmega}{\isamath{\Omega}}
6.156 +\newcommand{\isasymbool}{\isamath{\mathrm{I}\mkern-3.8mu\mathrm{B}}}
6.157 +\newcommand{\isasymcomplex}{\isamath{\mathrm{C}\mkern-15mu{\phantom{\mathrm{t}}\vrule}\mkern9mu}}
6.158 +\newcommand{\isasymnat}{\isamath{\mathrm{I}\mkern-3.8mu\mathrm{N}}}
6.159 +\newcommand{\isasymrat}{\isamath{\mathrm{Q}\mkern-16mu{\phantom{\mathrm{t}}\vrule}\mkern10mu}}
6.160 +\newcommand{\isasymreal}{\isamath{\mathrm{I}\mkern-3.8mu\mathrm{R}}}
6.161 +\newcommand{\isasymint}{\isamath{\mathsf{Z}\mkern-7.5mu\mathsf{Z}}}
6.162 +\newcommand{\isasymleftarrow}{\isamath{\leftarrow}}
6.163 +\newcommand{\isasymlongleftarrow}{\isamath{\longleftarrow}}
6.164 +\newcommand{\isasymrightarrow}{\isamath{\rightarrow}}
6.165 +\newcommand{\isasymlongrightarrow}{\isamath{\longrightarrow}}
6.166 +\newcommand{\isasymLeftarrow}{\isamath{\Leftarrow}}
6.167 +\newcommand{\isasymLongleftarrow}{\isamath{\Longleftarrow}}
6.168 +\newcommand{\isasymRightarrow}{\isamath{\Rightarrow}}
6.169 +\newcommand{\isasymLongrightarrow}{\isamath{\Longrightarrow}}
6.170 +\newcommand{\isasymleftrightarrow}{\isamath{\leftrightarrow}}
6.171 +\newcommand{\isasymlongleftrightarrow}{\isamath{\longleftrightarrow}}
6.172 +\newcommand{\isasymLeftrightarrow}{\isamath{\Leftrightarrow}}
6.173 +\newcommand{\isasymLongleftrightarrow}{\isamath{\Longleftrightarrow}}
6.174 +\newcommand{\isasymmapsto}{\isamath{\mapsto}}
6.175 +\newcommand{\isasymlongmapsto}{\isamath{\longmapsto}}
6.176 +\newcommand{\isasymmidarrow}{\isamath{\relbar}}
6.177 +\newcommand{\isasymMidarrow}{\isamath{\Relbar}}
6.178 +\newcommand{\isasymhookleftarrow}{\isamath{\hookleftarrow}}
6.179 +\newcommand{\isasymhookrightarrow}{\isamath{\hookrightarrow}}
6.180 +\newcommand{\isasymleftharpoondown}{\isamath{\leftharpoondown}}
6.181 +\newcommand{\isasymrightharpoondown}{\isamath{\rightharpoondown}}
6.182 +\newcommand{\isasymleftharpoonup}{\isamath{\leftharpoonup}}
6.183 +\newcommand{\isasymrightharpoonup}{\isamath{\rightharpoonup}}
6.184 +\newcommand{\isasymrightleftharpoons}{\isamath{\rightleftharpoons}}
6.185 +\newcommand{\isasymleadsto}{\isamath{\leadsto}} %requires amssymb
6.186 +\newcommand{\isasymdownharpoonleft}{\isamath{\downharpoonleft}} %requires amssymb
6.187 +\newcommand{\isasymdownharpoonright}{\isamath{\downharpoonright}} %requires amssymb
6.188 +\newcommand{\isasymupharpoonleft}{\isamath{\upharpoonleft}} %requires amssymb
6.189 +\newcommand{\isasymupharpoonright}{\isamath{\upharpoonright}} %requires amssymb
6.190 +\newcommand{\isasymrestriction}{\isamath{\restriction}} %requires amssymb
6.191 +\newcommand{\isasymColon}{\isamath{\mathrel{::}}}
6.192 +\newcommand{\isasymup}{\isamath{\uparrow}}
6.193 +\newcommand{\isasymUp}{\isamath{\Uparrow}}
6.194 +\newcommand{\isasymdown}{\isamath{\downarrow}}
6.195 +\newcommand{\isasymDown}{\isamath{\Downarrow}}
6.196 +\newcommand{\isasymupdown}{\isamath{\updownarrow}}
6.197 +\newcommand{\isasymUpdown}{\isamath{\Updownarrow}}
6.198 +\newcommand{\isasymlangle}{\isamath{\langle}}
6.199 +\newcommand{\isasymrangle}{\isamath{\rangle}}
6.200 +\newcommand{\isasymlceil}{\isamath{\lceil}}
6.201 +\newcommand{\isasymrceil}{\isamath{\rceil}}
6.202 +\newcommand{\isasymlfloor}{\isamath{\lfloor}}
6.203 +\newcommand{\isasymrfloor}{\isamath{\rfloor}}
6.204 +\newcommand{\isasymlparr}{\isamath{\mathopen{(\mkern-3mu\mid}}}
6.205 +\newcommand{\isasymrparr}{\isamath{\mathclose{\mid\mkern-3mu)}}}
6.206 +\newcommand{\isasymlbrakk}{\isamath{\mathopen{\lbrack\mkern-3mu\lbrack}}}
6.207 +\newcommand{\isasymrbrakk}{\isamath{\mathclose{\rbrack\mkern-3mu\rbrack}}}
6.208 +\newcommand{\isasymlbrace}{\isamath{\mathopen{\lbrace\mkern-4.5mu\mid}}}
6.209 +\newcommand{\isasymrbrace}{\isamath{\mathclose{\mid\mkern-4.5mu\rbrace}}}
6.210 +\newcommand{\isasymguillemotleft}{\isatext{\flqq}} %requires babel
6.211 +\newcommand{\isasymguillemotright}{\isatext{\frqq}} %requires babel
6.212 +\newcommand{\isasymbottom}{\isamath{\bot}}
6.213 +\newcommand{\isasymtop}{\isamath{\top}}
6.214 +\newcommand{\isasymand}{\isamath{\wedge}}
6.215 +\newcommand{\isasymAnd}{\isamath{\bigwedge}}
6.216 +\newcommand{\isasymor}{\isamath{\vee}}
6.217 +\newcommand{\isasymOr}{\isamath{\bigvee}}
6.218 +\newcommand{\isasymforall}{\isamath{\forall\,}}
6.219 +\newcommand{\isasymexists}{\isamath{\exists\,}}
6.220 +\newcommand{\isasymnexists}{\isamath{\nexists\,}} %requires amssymb
6.221 +\newcommand{\isasymnot}{\isamath{\neg}}
6.222 +\newcommand{\isasymbox}{\isamath{\Box}} %requires amssymb
6.223 +\newcommand{\isasymdiamond}{\isamath{\Diamond}} %requires amssymb
6.224 +\newcommand{\isasymturnstile}{\isamath{\vdash}}
6.225 +\newcommand{\isasymTurnstile}{\isamath{\models}}
6.226 +\newcommand{\isasymtturnstile}{\isamath{\vdash\!\!\!\vdash}}
6.227 +\newcommand{\isasymTTurnstile}{\isamath{\mid\!\models}}
6.228 +\newcommand{\isasymstileturn}{\isamath{\dashv}}
6.229 +\newcommand{\isasymsurd}{\isamath{\surd}}
6.230 +\newcommand{\isasymle}{\isamath{\le}}
6.231 +\newcommand{\isasymge}{\isamath{\ge}}
6.232 +\newcommand{\isasymlless}{\isamath{\ll}}
6.233 +\newcommand{\isasymggreater}{\isamath{\gg}}
6.234 +\newcommand{\isasymlesssim}{\isamath{\lesssim}} %requires amssymb
6.235 +\newcommand{\isasymgreatersim}{\isamath{\gtrsim}} %requires amssymb
6.236 +\newcommand{\isasymlessapprox}{\isamath{\lessapprox}} %requires amssymb
6.237 +\newcommand{\isasymgreaterapprox}{\isamath{\gtrapprox}} %requires amssymb
6.238 +\newcommand{\isasymin}{\isamath{\in}}
6.239 +\newcommand{\isasymnotin}{\isamath{\notin}}
6.240 +\newcommand{\isasymsubset}{\isamath{\subset}}
6.241 +\newcommand{\isasymsupset}{\isamath{\supset}}
6.242 +\newcommand{\isasymsubseteq}{\isamath{\subseteq}}
6.243 +\newcommand{\isasymsupseteq}{\isamath{\supseteq}}
6.244 +\newcommand{\isasymsqsubset}{\isamath{\sqsubset}} %requires amssymb
6.245 +\newcommand{\isasymsqsupset}{\isamath{\sqsupset}} %requires amssymb
6.246 +\newcommand{\isasymsqsubseteq}{\isamath{\sqsubseteq}}
6.247 +\newcommand{\isasymsqsupseteq}{\isamath{\sqsupseteq}}
6.248 +\newcommand{\isasyminter}{\isamath{\cap}}
6.249 +\newcommand{\isasymInter}{\isamath{\bigcap\,}}
6.250 +\newcommand{\isasymunion}{\isamath{\cup}}
6.251 +\newcommand{\isasymUnion}{\isamath{\bigcup\,}}
6.252 +\newcommand{\isasymsqunion}{\isamath{\sqcup}}
6.253 +\newcommand{\isasymSqunion}{\isamath{\bigsqcup\,}}
6.254 +\newcommand{\isasymsqinter}{\isamath{\sqcap}}
6.255 +\newcommand{\isasymSqinter}{\isamath{\bigsqcap\,}} %requires stmaryrd
6.256 +\newcommand{\isasymsetminus}{\isamath{\setminus}}
6.257 +\newcommand{\isasympropto}{\isamath{\propto}}
6.258 +\newcommand{\isasymuplus}{\isamath{\uplus}}
6.259 +\newcommand{\isasymUplus}{\isamath{\biguplus\,}}
6.260 +\newcommand{\isasymnoteq}{\isamath{\not=}}
6.261 +\newcommand{\isasymsim}{\isamath{\sim}}
6.262 +\newcommand{\isasymdoteq}{\isamath{\doteq}}
6.263 +\newcommand{\isasymsimeq}{\isamath{\simeq}}
6.264 +\newcommand{\isasymapprox}{\isamath{\approx}}
6.265 +\newcommand{\isasymasymp}{\isamath{\asymp}}
6.266 +\newcommand{\isasymcong}{\isamath{\cong}}
6.267 +\newcommand{\isasymsmile}{\isamath{\smile}}
6.268 +\newcommand{\isasymequiv}{\isamath{\equiv}}
6.269 +\newcommand{\isasymfrown}{\isamath{\frown}}
6.270 +\newcommand{\isasymJoin}{\isamath{\Join}} %requires amssymb
6.271 +\newcommand{\isasymbowtie}{\isamath{\bowtie}}
6.272 +\newcommand{\isasymprec}{\isamath{\prec}}
6.273 +\newcommand{\isasymsucc}{\isamath{\succ}}
6.274 +\newcommand{\isasympreceq}{\isamath{\preceq}}
6.275 +\newcommand{\isasymsucceq}{\isamath{\succeq}}
6.276 +\newcommand{\isasymparallel}{\isamath{\parallel}}
6.277 +\newcommand{\isasymbar}{\isamath{\mid}}
6.278 +\newcommand{\isasymplusminus}{\isamath{\pm}}
6.279 +\newcommand{\isasymminusplus}{\isamath{\mp}}
6.280 +\newcommand{\isasymtimes}{\isamath{\times}}
6.281 +\newcommand{\isasymdiv}{\isamath{\div}}
6.282 +\newcommand{\isasymcdot}{\isamath{\cdot}}
6.283 +\newcommand{\isasymstar}{\isamath{\star}}
6.284 +\newcommand{\isasymbullet}{\boldmath\isamath{\mathchoice{\displaystyle{\cdot}}{\textstyle{\cdot}}{\scriptstyle{\bullet}}{\scriptscriptstyle{\bullet}}}}
6.285 +\newcommand{\isasymcirc}{\isamath{\circ}}
6.286 +\newcommand{\isasymdagger}{\isamath{\dagger}}
6.287 +\newcommand{\isasymddagger}{\isamath{\ddagger}}
6.288 +\newcommand{\isasymlhd}{\isamath{\lhd}} %requires amssymb
6.289 +\newcommand{\isasymrhd}{\isamath{\rhd}} %requires amssymb
6.290 +\newcommand{\isasymunlhd}{\isamath{\unlhd}} %requires amssymb
6.291 +\newcommand{\isasymunrhd}{\isamath{\unrhd}} %requires amssymb
6.292 +\newcommand{\isasymtriangleleft}{\isamath{\triangleleft}}
6.293 +\newcommand{\isasymtriangleright}{\isamath{\triangleright}}
6.294 +\newcommand{\isasymtriangle}{\isamath{\triangle}}
6.295 +\newcommand{\isasymtriangleq}{\isamath{\triangleq}} %requires amssymb
6.296 +\newcommand{\isasymoplus}{\isamath{\oplus}}
6.297 +\newcommand{\isasymOplus}{\isamath{\bigoplus\,}}
6.298 +\newcommand{\isasymotimes}{\isamath{\otimes}}
6.299 +\newcommand{\isasymOtimes}{\isamath{\bigotimes\,}}
6.300 +\newcommand{\isasymodot}{\isamath{\odot}}
6.301 +\newcommand{\isasymOdot}{\isamath{\bigodot\,}}
6.302 +\newcommand{\isasymominus}{\isamath{\ominus}}
6.303 +\newcommand{\isasymoslash}{\isamath{\oslash}}
6.304 +\newcommand{\isasymdots}{\isamath{\dots}}
6.305 +\newcommand{\isasymcdots}{\isamath{\cdots}}
6.306 +\newcommand{\isasymSum}{\isamath{\sum\,}}
6.307 +\newcommand{\isasymProd}{\isamath{\prod\,}}
6.308 +\newcommand{\isasymCoprod}{\isamath{\coprod\,}}
6.309 +\newcommand{\isasyminfinity}{\isamath{\infty}}
6.310 +\newcommand{\isasymintegral}{\isamath{\int\,}}
6.311 +\newcommand{\isasymointegral}{\isamath{\oint\,}}
6.312 +\newcommand{\isasymclubsuit}{\isamath{\clubsuit}}
6.313 +\newcommand{\isasymdiamondsuit}{\isamath{\diamondsuit}}
6.314 +\newcommand{\isasymheartsuit}{\isamath{\heartsuit}}
6.315 +\newcommand{\isasymspadesuit}{\isamath{\spadesuit}}
6.316 +\newcommand{\isasymaleph}{\isamath{\aleph}}
6.317 +\newcommand{\isasymemptyset}{\isamath{\emptyset}}
6.318 +\newcommand{\isasymnabla}{\isamath{\nabla}}
6.319 +\newcommand{\isasympartial}{\isamath{\partial}}
6.320 +\newcommand{\isasymRe}{\isamath{\Re}}
6.321 +\newcommand{\isasymIm}{\isamath{\Im}}
6.322 +\newcommand{\isasymflat}{\isamath{\flat}}
6.323 +\newcommand{\isasymnatural}{\isamath{\natural}}
6.324 +\newcommand{\isasymsharp}{\isamath{\sharp}}
6.325 +\newcommand{\isasymangle}{\isamath{\angle}}
6.326 +\newcommand{\isasymcopyright}{\isatext{\rm\copyright}}
6.327 +\newcommand{\isasymregistered}{\isatext{\rm\textregistered}}
6.328 +\newcommand{\isasymhyphen}{\isatext{\rm-}}
6.329 +\newcommand{\isasyminverse}{\isamath{{}^{-1}}}
6.330 +\newcommand{\isasymonesuperior}{\isamath{{}^1}}
6.331 +\newcommand{\isasymonequarter}{\isatext{\rm\textonequarter}} %requires textcomp
6.332 +\newcommand{\isasymtwosuperior}{\isamath{{}^2}}
6.333 +\newcommand{\isasymonehalf}{\isatext{\rm\textonehalf}} %requires textcomp
6.334 +\newcommand{\isasymthreesuperior}{\isamath{{}^3}}
6.335 +\newcommand{\isasymthreequarters}{\isatext{\rm\textthreequarters}} %requires textcomp
6.336 +\newcommand{\isasymordfeminine}{\isatext{\rm\textordfeminine}}
6.337 +\newcommand{\isasymordmasculine}{\isatext{\rm\textordmasculine}}
6.338 +\newcommand{\isasymsection}{\isatext{\rm\S}}
6.339 +\newcommand{\isasymparagraph}{\isatext{\rm\P}}
6.340 +\newcommand{\isasymexclamdown}{\isatext{\rm\textexclamdown}}
6.341 +\newcommand{\isasymquestiondown}{\isatext{\rm\textquestiondown}}
6.342 +\newcommand{\isasymeuro}{\isatext{\textgreek{\euro}}} %requires greek babel
6.343 +\newcommand{\isasympounds}{\isamath{\pounds}}
6.344 +\newcommand{\isasymyen}{\isatext{\yen}} %requires amssymb
6.345 +\newcommand{\isasymcent}{\isatext{\textcent}} %requires textcomp
6.346 +\newcommand{\isasymcurrency}{\isatext{\textcurrency}} %requires textcomp
6.347 +\newcommand{\isasymdegree}{\isatext{\rm\textdegree}} %requires textcomp
6.348 +\newcommand{\isasymamalg}{\isamath{\amalg}}
6.349 +\newcommand{\isasymmho}{\isamath{\mho}} %requires amssymb
6.350 +\newcommand{\isasymlozenge}{\isamath{\lozenge}} %requires amssymb
6.351 +\newcommand{\isasymwp}{\isamath{\wp}}
6.352 +\newcommand{\isasymwrong}{\isamath{\wr}}
6.353 +\newcommand{\isasymstruct}{\isamath{\diamond}}
6.354 +\newcommand{\isasymacute}{\isatext{\'\relax}}
6.355 +\newcommand{\isasymindex}{\isatext{\i}}
6.356 +\newcommand{\isasymdieresis}{\isatext{\"\relax}}
6.357 +\newcommand{\isasymcedilla}{\isatext{\c\relax}}
6.358 +\newcommand{\isasymhungarumlaut}{\isatext{\H\relax}}
6.359 +\newcommand{\isasymspacespace}{\isamath{~~}}
6.360 +\newcommand{\isasymmodule}{\isamath{\langle}\isakeyword{module}\isamath{\rangle}}
6.361 +\newcommand{\isasymsome}{\isamath{\epsilon\,}}
7.1 --- /dev/null Thu Jan 01 00:00:00 1970 +0000
7.2 +++ b/doc-src/isac/jrocnik/Inverse_Z_Transform/document/pdfsetup.sty Thu Sep 08 23:17:35 2011 +0200
7.3 @@ -0,0 +1,7 @@
7.4 +%%
7.5 +%% default hyperref setup (both for pdf and dvi output)
7.6 +%%
7.7 +
7.8 +\usepackage{color}
7.9 +\definecolor{linkcolor}{rgb}{0,0,0.5}
7.10 +\usepackage[colorlinks=true,linkcolor=linkcolor,citecolor=linkcolor,filecolor=linkcolor,pagecolor=linkcolor,urlcolor=linkcolor]{hyperref}
8.1 --- /dev/null Thu Jan 01 00:00:00 1970 +0000
8.2 +++ b/doc-src/isac/jrocnik/Inverse_Z_Transform/document/root.tex Thu Sep 08 23:17:35 2011 +0200
8.3 @@ -0,0 +1,60 @@
8.4 +\documentclass[11pt,a4paper]{article}
8.5 +\usepackage{isabelle,isabellesym}
8.6 +
8.7 +% further packages required for unusual symbols (see also
8.8 +% isabellesym.sty), use only when needed
8.9 +
8.10 +%\usepackage{amssymb}
8.11 + %for \<leadsto>, \<box>, \<diamond>, \<sqsupset>, \<mho>, \<Join>,
8.12 + %\<lhd>, \<lesssim>, \<greatersim>, \<lessapprox>, \<greaterapprox>,
8.13 + %\<triangleq>, \<yen>, \<lozenge>
8.14 +
8.15 +%\usepackage[greek,english]{babel}
8.16 + %option greek for \<euro>
8.17 + %option english (default language) for \<guillemotleft>, \<guillemotright>
8.18 +
8.19 +%\usepackage[only,bigsqcap]{stmaryrd}
8.20 + %for \<Sqinter>
8.21 +
8.22 +%\usepackage{eufrak}
8.23 + %for \<AA> ... \<ZZ>, \<aa> ... \<zz> (also included in amssymb)
8.24 +
8.25 +%\usepackage{textcomp}
8.26 + %for \<onequarter>, \<onehalf>, \<threequarters>, \<degree>, \<cent>,
8.27 + %\<currency>
8.28 +
8.29 +% this should be the last package used
8.30 +\usepackage{pdfsetup}
8.31 +
8.32 +% urls in roman style, theory text in math-similar italics
8.33 +\urlstyle{rm}
8.34 +\isabellestyle{it}
8.35 +
8.36 +% for uniform font size
8.37 +%\renewcommand{\isastyle}{\isastyleminor}
8.38 +
8.39 +
8.40 +\begin{document}
8.41 +
8.42 +\title{Inverse-Z-Transform}
8.43 +\author{By jan}
8.44 +\maketitle
8.45 +
8.46 +\tableofcontents
8.47 +
8.48 +% sane default for proof documents
8.49 +\parindent 0pt\parskip 0.5ex
8.50 +
8.51 +% generated text of all theories
8.52 +\input{session}
8.53 +
8.54 +% optional bibliography
8.55 +%\bibliographystyle{abbrv}
8.56 +%\bibliography{root}
8.57 +
8.58 +\end{document}
8.59 +
8.60 +%%% Local Variables:
8.61 +%%% mode: latex
8.62 +%%% TeX-master: t
8.63 +%%% End:
9.1 --- /dev/null Thu Jan 01 00:00:00 1970 +0000
9.2 +++ b/doc-src/isac/jrocnik/Inverse_Z_Transform/document/session.tex Thu Sep 08 23:17:35 2011 +0200
9.3 @@ -0,0 +1,6 @@
9.4 +\input{Inverse_Z_Transform.tex}
9.5 +
9.6 +%%% Local Variables:
9.7 +%%% mode: latex
9.8 +%%% TeX-master: "root"
9.9 +%%% End:
10.1 --- /dev/null Thu Jan 01 00:00:00 1970 +0000
10.2 +++ b/doc-src/isac/jrocnik/IsaMakefile Thu Sep 08 23:17:35 2011 +0200
10.3 @@ -0,0 +1,31 @@
10.4 +
10.5 +## targets
10.6 +
10.7 +default: Inverse_Z_Transform
10.8 +images:
10.9 +test: Inverse_Z_Transform
10.10 +
10.11 +all: images test
10.12 +
10.13 +
10.14 +## global settings
10.15 +
10.16 +SRC = $(ISABELLE_HOME)/src
10.17 +OUT = $(ISABELLE_OUTPUT)
10.18 +LOG = $(OUT)/log
10.19 +
10.20 +USEDIR = $(ISABELLE_TOOL) usedir -v true -i false -d false -C false -D document
10.21 +
10.22 +
10.23 +## Inverse_Z_Transform
10.24 +
10.25 +Inverse_Z_Transform: $(LOG)/Isac-Inverse_Z_Transform.gz
10.26 +
10.27 +$(LOG)/Isac-Inverse_Z_Transform.gz: ## Inverse_Z_Transform/ROOT.ML Inverse_Z_Transform/document/root.tex Inverse_Z_Transform/*.thy
10.28 + @$(USEDIR) Isac Inverse_Z_Transform
10.29 +
10.30 +
10.31 +## clean
10.32 +
10.33 +clean:
10.34 + @rm -f $(LOG)/Isac-Inverse_Z_Transform.gz
11.1 --- a/doc-src/isac/jrocnik/bakkarbeit_jrocnik.tex Thu Sep 08 23:06:39 2011 +0200
11.2 +++ b/doc-src/isac/jrocnik/bakkarbeit_jrocnik.tex Thu Sep 08 23:17:35 2011 +0200
11.3 @@ -174,7 +174,7 @@
11.4 %\section*{Anhang}
11.5 \section{Demobeispiel}
11.6
11.7 -\input{./Inverse_Z-Transform/document/Inverse_Z_Transform.tex}
11.8 +\input{./Inverse_Z_Transform/document/Inverse_Z_Transform.tex}
11.9
11.10 \begin{verbatim}
11.11
12.1 --- /dev/null Thu Jan 01 00:00:00 1970 +0000
12.2 +++ b/doc-src/isac/jrocnik/isabelle.sty Thu Sep 08 23:17:35 2011 +0200
12.3 @@ -0,0 +1,218 @@
12.4 +%%
12.5 +%% macros for Isabelle generated LaTeX output
12.6 +%%
12.7 +
12.8 +%%% Simple document preparation (based on theory token language and symbols)
12.9 +
12.10 +% isabelle environments
12.11 +
12.12 +\newcommand{\isabellecontext}{UNKNOWN}
12.13 +
12.14 +\newcommand{\isastyle}{\UNDEF}
12.15 +\newcommand{\isastyleminor}{\UNDEF}
12.16 +\newcommand{\isastylescript}{\UNDEF}
12.17 +\newcommand{\isastyletext}{\normalsize\rm}
12.18 +\newcommand{\isastyletxt}{\rm}
12.19 +\newcommand{\isastylecmt}{\rm}
12.20 +
12.21 +%symbol markup -- \emph achieves decent spacing via italic corrections
12.22 +\newcommand{\isamath}[1]{\emph{$#1$}}
12.23 +\newcommand{\isatext}[1]{\emph{#1}}
12.24 +\DeclareRobustCommand{\isascriptstyle}{\def\isamath##1{##1}\def\isatext##1{\mbox{\isastylescript##1}}}
12.25 +\newcommand{\isactrlsub}[1]{\emph{\isascriptstyle${}\sb{#1}$}}
12.26 +\newcommand{\isactrlsup}[1]{\emph{\isascriptstyle${}\sp{#1}$}}
12.27 +\newcommand{\isactrlisub}[1]{\emph{\isascriptstyle${}\sb{#1}$}}
12.28 +\newcommand{\isactrlisup}[1]{\emph{\isascriptstyle${}\sp{#1}$}}
12.29 +\DeclareRobustCommand{\isactrlbsub}{\emph\bgroup\math{}\sb\bgroup\mbox\bgroup\isastylescript}
12.30 +\DeclareRobustCommand{\isactrlesub}{\egroup\egroup\endmath\egroup}
12.31 +\DeclareRobustCommand{\isactrlbsup}{\emph\bgroup\math{}\sp\bgroup\mbox\bgroup\isastylescript}
12.32 +\DeclareRobustCommand{\isactrlesup}{\egroup\egroup\endmath\egroup}
12.33 +\newcommand{\isactrlbold}[1]{{\bfseries\upshape\boldmath#1}}
12.34 +\newcommand{\isactrlloc}[1]{{\bfseries\upshape\boldmath#1}}
12.35 +
12.36 +\newenvironment{isaantiq}{{\isacharat\isacharbraceleft}}{{\isacharbraceright}}
12.37 +\newcommand{\isaantiqopen}{\isakeyword{\isacharbraceleft}}
12.38 +\newcommand{\isaantiqclose}{\isakeyword{\isacharbraceright}}
12.39 +
12.40 +\newdimen\isa@parindent\newdimen\isa@parskip
12.41 +
12.42 +\newenvironment{isabellebody}{%
12.43 +\isamarkuptrue\par%
12.44 +\isa@parindent\parindent\parindent0pt%
12.45 +\isa@parskip\parskip\parskip0pt%
12.46 +\isastyle}{\par}
12.47 +
12.48 +\newenvironment{isabelle}
12.49 +{\begin{trivlist}\begin{isabellebody}\item\relax}
12.50 +{\end{isabellebody}\end{trivlist}}
12.51 +
12.52 +\newcommand{\isa}[1]{\emph{\isastyleminor #1}}
12.53 +
12.54 +\newcommand{\isaindent}[1]{\hphantom{#1}}
12.55 +\newcommand{\isanewline}{\mbox{}\par\mbox{}}
12.56 +\newcommand{\isasep}{}
12.57 +\newcommand{\isadigit}[1]{#1}
12.58 +
12.59 +\newcommand{\isachardefaults}{%
12.60 +\chardef\isacharbang=`\!%
12.61 +\chardef\isachardoublequote=`\"%
12.62 +\chardef\isachardoublequoteopen=`\"%
12.63 +\chardef\isachardoublequoteclose=`\"%
12.64 +\chardef\isacharhash=`\#%
12.65 +\chardef\isachardollar=`\$%
12.66 +\chardef\isacharpercent=`\%%
12.67 +\chardef\isacharampersand=`\&%
12.68 +\chardef\isacharprime=`\'%
12.69 +\chardef\isacharparenleft=`\(%
12.70 +\chardef\isacharparenright=`\)%
12.71 +\chardef\isacharasterisk=`\*%
12.72 +\chardef\isacharplus=`\+%
12.73 +\chardef\isacharcomma=`\,%
12.74 +\chardef\isacharminus=`\-%
12.75 +\chardef\isachardot=`\.%
12.76 +\chardef\isacharslash=`\/%
12.77 +\chardef\isacharcolon=`\:%
12.78 +\chardef\isacharsemicolon=`\;%
12.79 +\chardef\isacharless=`\<%
12.80 +\chardef\isacharequal=`\=%
12.81 +\chardef\isachargreater=`\>%
12.82 +\chardef\isacharquery=`\?%
12.83 +\chardef\isacharat=`\@%
12.84 +\chardef\isacharbrackleft=`\[%
12.85 +\chardef\isacharbackslash=`\\%
12.86 +\chardef\isacharbrackright=`\]%
12.87 +\chardef\isacharcircum=`\^%
12.88 +\chardef\isacharunderscore=`\_%
12.89 +\def\isacharunderscorekeyword{\_}%
12.90 +\chardef\isacharbackquote=`\`%
12.91 +\chardef\isacharbackquoteopen=`\`%
12.92 +\chardef\isacharbackquoteclose=`\`%
12.93 +\chardef\isacharbraceleft=`\{%
12.94 +\chardef\isacharbar=`\|%
12.95 +\chardef\isacharbraceright=`\}%
12.96 +\chardef\isachartilde=`\~%
12.97 +\def\isacharverbatimopen{\isacharbraceleft\isacharasterisk}%
12.98 +\def\isacharverbatimclose{\isacharasterisk\isacharbraceright}%
12.99 +}
12.100 +
12.101 +\newcommand{\isaliteral}[2]{#2}
12.102 +\newcommand{\isanil}{}
12.103 +
12.104 +
12.105 +% keyword and section markup
12.106 +
12.107 +\newcommand{\isakeyword}[1]
12.108 +{\emph{\bf\def\isachardot{.}\def\isacharunderscore{\isacharunderscorekeyword}%
12.109 +\def\isacharbraceleft{\{}\def\isacharbraceright{\}}#1}}
12.110 +\newcommand{\isacommand}[1]{\isakeyword{#1}}
12.111 +
12.112 +\newcommand{\isamarkupheader}[1]{\section{#1}}
12.113 +\newcommand{\isamarkupchapter}[1]{\chapter{#1}}
12.114 +\newcommand{\isamarkupsection}[1]{\section{#1}}
12.115 +\newcommand{\isamarkupsubsection}[1]{\subsection{#1}}
12.116 +\newcommand{\isamarkupsubsubsection}[1]{\subsubsection{#1}}
12.117 +\newcommand{\isamarkupsect}[1]{\section{#1}}
12.118 +\newcommand{\isamarkupsubsect}[1]{\subsection{#1}}
12.119 +\newcommand{\isamarkupsubsubsect}[1]{\subsubsection{#1}}
12.120 +
12.121 +\newif\ifisamarkup
12.122 +\newcommand{\isabeginpar}{\par\ifisamarkup\relax\else\medskip\fi}
12.123 +\newcommand{\isaendpar}{\par\medskip}
12.124 +\newenvironment{isapar}{\parindent\isa@parindent\parskip\isa@parskip\isabeginpar}{\isaendpar}
12.125 +\newenvironment{isamarkuptext}{\par\isastyletext\begin{isapar}}{\end{isapar}}
12.126 +\newenvironment{isamarkuptxt}{\par\isastyletxt\begin{isapar}}{\end{isapar}}
12.127 +\newcommand{\isamarkupcmt}[1]{{\isastylecmt--- #1}}
12.128 +
12.129 +
12.130 +% styles
12.131 +
12.132 +\def\isabellestyle#1{\csname isabellestyle#1\endcsname}
12.133 +
12.134 +\newcommand{\isabellestyledefault}{%
12.135 +\renewcommand{\isastyle}{\small\tt\slshape}%
12.136 +\renewcommand{\isastyleminor}{\small\tt\slshape}%
12.137 +\renewcommand{\isastylescript}{\footnotesize\tt\slshape}%
12.138 +\isachardefaults%
12.139 +}
12.140 +\isabellestyledefault
12.141 +
12.142 +\newcommand{\isabellestylett}{%
12.143 +\renewcommand{\isastyle}{\small\tt}%
12.144 +\renewcommand{\isastyleminor}{\small\tt}%
12.145 +\renewcommand{\isastylescript}{\footnotesize\tt}%
12.146 +\isachardefaults%
12.147 +}
12.148 +
12.149 +\newcommand{\isabellestyleit}{%
12.150 +\renewcommand{\isastyle}{\small\it}%
12.151 +\renewcommand{\isastyleminor}{\it}%
12.152 +\renewcommand{\isastylescript}{\footnotesize\it}%
12.153 +\renewcommand{\isacharunderscorekeyword}{\mbox{-}}%
12.154 +\renewcommand{\isacharbang}{\isamath{!}}%
12.155 +\renewcommand{\isachardoublequote}{\isanil}%
12.156 +\renewcommand{\isachardoublequoteopen}{\isanil}%
12.157 +\renewcommand{\isachardoublequoteclose}{\isanil}%
12.158 +\renewcommand{\isacharhash}{\isamath{\#}}%
12.159 +\renewcommand{\isachardollar}{\isamath{\$}}%
12.160 +\renewcommand{\isacharpercent}{\isamath{\%}}%
12.161 +\renewcommand{\isacharampersand}{\isamath{\&}}%
12.162 +\renewcommand{\isacharprime}{\isamath{\mskip2mu{'}\mskip-2mu}}%
12.163 +\renewcommand{\isacharparenleft}{\isamath{(}}%
12.164 +\renewcommand{\isacharparenright}{\isamath{)}}%
12.165 +\renewcommand{\isacharasterisk}{\isamath{*}}%
12.166 +\renewcommand{\isacharplus}{\isamath{+}}%
12.167 +\renewcommand{\isacharcomma}{\isamath{\mathord,}}%
12.168 +\renewcommand{\isacharminus}{\isamath{-}}%
12.169 +\renewcommand{\isachardot}{\isamath{\mathord.}}%
12.170 +\renewcommand{\isacharslash}{\isamath{/}}%
12.171 +\renewcommand{\isacharcolon}{\isamath{\mathord:}}%
12.172 +\renewcommand{\isacharsemicolon}{\isamath{\mathord;}}%
12.173 +\renewcommand{\isacharless}{\isamath{<}}%
12.174 +\renewcommand{\isacharequal}{\isamath{=}}%
12.175 +\renewcommand{\isachargreater}{\isamath{>}}%
12.176 +\renewcommand{\isacharat}{\isamath{@}}%
12.177 +\renewcommand{\isacharbrackleft}{\isamath{[}}%
12.178 +\renewcommand{\isacharbackslash}{\isamath{\backslash}}%
12.179 +\renewcommand{\isacharbrackright}{\isamath{]}}%
12.180 +\renewcommand{\isacharunderscore}{\mbox{-}}%
12.181 +\renewcommand{\isacharbraceleft}{\isamath{\{}}%
12.182 +\renewcommand{\isacharbar}{\isamath{\mid}}%
12.183 +\renewcommand{\isacharbraceright}{\isamath{\}}}%
12.184 +\renewcommand{\isachartilde}{\isamath{{}\sp{\sim}}}%
12.185 +\renewcommand{\isacharbackquoteopen}{\isatext{\raise.3ex\hbox{$\scriptscriptstyle\langle$}}}%
12.186 +\renewcommand{\isacharbackquoteclose}{\isatext{\raise.3ex\hbox{$\scriptscriptstyle\rangle$}}}%
12.187 +\renewcommand{\isacharverbatimopen}{\isamath{\langle\!\langle}}%
12.188 +\renewcommand{\isacharverbatimclose}{\isamath{\rangle\!\rangle}}%
12.189 +}
12.190 +
12.191 +\newcommand{\isabellestylesl}{%
12.192 +\isabellestyleit%
12.193 +\renewcommand{\isastyle}{\small\sl}%
12.194 +\renewcommand{\isastyleminor}{\sl}%
12.195 +\renewcommand{\isastylescript}{\footnotesize\sl}%
12.196 +}
12.197 +
12.198 +
12.199 +% tagged regions
12.200 +
12.201 +%plain TeX version of comment package -- much faster!
12.202 +\let\isafmtname\fmtname\def\fmtname{plain}
12.203 +\usepackage{comment}
12.204 +\let\fmtname\isafmtname
12.205 +
12.206 +\newcommand{\isafold}[1]{\emph{$\langle\mathord{\mathit{#1}}\rangle$}}
12.207 +
12.208 +\newcommand{\isakeeptag}[1]%
12.209 +{\includecomment{isadelim#1}\includecomment{isatag#1}\csarg\def{isafold#1}{}}
12.210 +\newcommand{\isadroptag}[1]%
12.211 +{\excludecomment{isadelim#1}\excludecomment{isatag#1}\csarg\def{isafold#1}{}}
12.212 +\newcommand{\isafoldtag}[1]%
12.213 +{\includecomment{isadelim#1}\excludecomment{isatag#1}\csarg\def{isafold#1}{\isafold{#1}}}
12.214 +
12.215 +\isakeeptag{theory}
12.216 +\isakeeptag{proof}
12.217 +\isakeeptag{ML}
12.218 +\isakeeptag{visible}
12.219 +\isadroptag{invisible}
12.220 +
12.221 +\IfFileExists{isabelletags.sty}{\usepackage{isabelletags}}{}
13.1 --- /dev/null Thu Jan 01 00:00:00 1970 +0000
13.2 +++ b/doc-src/isac/jrocnik/isabellesym.sty Thu Sep 08 23:17:35 2011 +0200
13.3 @@ -0,0 +1,358 @@
13.4 +%%
13.5 +%% definitions of standard Isabelle symbols
13.6 +%%
13.7 +
13.8 +\newcommand{\isasymzero}{\isamath{\mathbf{0}}} %requires amssymb
13.9 +\newcommand{\isasymone}{\isamath{\mathbf{1}}} %requires amssymb
13.10 +\newcommand{\isasymtwo}{\isamath{\mathbf{2}}} %requires amssymb
13.11 +\newcommand{\isasymthree}{\isamath{\mathbf{3}}} %requires amssymb
13.12 +\newcommand{\isasymfour}{\isamath{\mathbf{4}}} %requires amssymb
13.13 +\newcommand{\isasymfive}{\isamath{\mathbf{5}}} %requires amssymb
13.14 +\newcommand{\isasymsix}{\isamath{\mathbf{6}}} %requires amssymb
13.15 +\newcommand{\isasymseven}{\isamath{\mathbf{7}}} %requires amssymb
13.16 +\newcommand{\isasymeight}{\isamath{\mathbf{8}}} %requires amssymb
13.17 +\newcommand{\isasymnine}{\isamath{\mathbf{9}}} %requires amssymb
13.18 +\newcommand{\isasymA}{\isamath{\mathcal{A}}}
13.19 +\newcommand{\isasymB}{\isamath{\mathcal{B}}}
13.20 +\newcommand{\isasymC}{\isamath{\mathcal{C}}}
13.21 +\newcommand{\isasymD}{\isamath{\mathcal{D}}}
13.22 +\newcommand{\isasymE}{\isamath{\mathcal{E}}}
13.23 +\newcommand{\isasymF}{\isamath{\mathcal{F}}}
13.24 +\newcommand{\isasymG}{\isamath{\mathcal{G}}}
13.25 +\newcommand{\isasymH}{\isamath{\mathcal{H}}}
13.26 +\newcommand{\isasymI}{\isamath{\mathcal{I}}}
13.27 +\newcommand{\isasymJ}{\isamath{\mathcal{J}}}
13.28 +\newcommand{\isasymK}{\isamath{\mathcal{K}}}
13.29 +\newcommand{\isasymL}{\isamath{\mathcal{L}}}
13.30 +\newcommand{\isasymM}{\isamath{\mathcal{M}}}
13.31 +\newcommand{\isasymN}{\isamath{\mathcal{N}}}
13.32 +\newcommand{\isasymO}{\isamath{\mathcal{O}}}
13.33 +\newcommand{\isasymP}{\isamath{\mathcal{P}}}
13.34 +\newcommand{\isasymQ}{\isamath{\mathcal{Q}}}
13.35 +\newcommand{\isasymR}{\isamath{\mathcal{R}}}
13.36 +\newcommand{\isasymS}{\isamath{\mathcal{S}}}
13.37 +\newcommand{\isasymT}{\isamath{\mathcal{T}}}
13.38 +\newcommand{\isasymU}{\isamath{\mathcal{U}}}
13.39 +\newcommand{\isasymV}{\isamath{\mathcal{V}}}
13.40 +\newcommand{\isasymW}{\isamath{\mathcal{W}}}
13.41 +\newcommand{\isasymX}{\isamath{\mathcal{X}}}
13.42 +\newcommand{\isasymY}{\isamath{\mathcal{Y}}}
13.43 +\newcommand{\isasymZ}{\isamath{\mathcal{Z}}}
13.44 +\newcommand{\isasyma}{\isamath{\mathrm{a}}}
13.45 +\newcommand{\isasymb}{\isamath{\mathrm{b}}}
13.46 +\newcommand{\isasymc}{\isamath{\mathrm{c}}}
13.47 +\newcommand{\isasymd}{\isamath{\mathrm{d}}}
13.48 +\newcommand{\isasyme}{\isamath{\mathrm{e}}}
13.49 +\newcommand{\isasymf}{\isamath{\mathrm{f}}}
13.50 +\newcommand{\isasymg}{\isamath{\mathrm{g}}}
13.51 +\newcommand{\isasymh}{\isamath{\mathrm{h}}}
13.52 +\newcommand{\isasymi}{\isamath{\mathrm{i}}}
13.53 +\newcommand{\isasymj}{\isamath{\mathrm{j}}}
13.54 +\newcommand{\isasymk}{\isamath{\mathrm{k}}}
13.55 +\newcommand{\isasyml}{\isamath{\mathrm{l}}}
13.56 +\newcommand{\isasymm}{\isamath{\mathrm{m}}}
13.57 +\newcommand{\isasymn}{\isamath{\mathrm{n}}}
13.58 +\newcommand{\isasymo}{\isamath{\mathrm{o}}}
13.59 +\newcommand{\isasymp}{\isamath{\mathrm{p}}}
13.60 +\newcommand{\isasymq}{\isamath{\mathrm{q}}}
13.61 +\newcommand{\isasymr}{\isamath{\mathrm{r}}}
13.62 +\newcommand{\isasyms}{\isamath{\mathrm{s}}}
13.63 +\newcommand{\isasymt}{\isamath{\mathrm{t}}}
13.64 +\newcommand{\isasymu}{\isamath{\mathrm{u}}}
13.65 +\newcommand{\isasymv}{\isamath{\mathrm{v}}}
13.66 +\newcommand{\isasymw}{\isamath{\mathrm{w}}}
13.67 +\newcommand{\isasymx}{\isamath{\mathrm{x}}}
13.68 +\newcommand{\isasymy}{\isamath{\mathrm{y}}}
13.69 +\newcommand{\isasymz}{\isamath{\mathrm{z}}}
13.70 +\newcommand{\isasymAA}{\isamath{\mathfrak{A}}} %requires eufrak
13.71 +\newcommand{\isasymBB}{\isamath{\mathfrak{B}}} %requires eufrak
13.72 +\newcommand{\isasymCC}{\isamath{\mathfrak{C}}} %requires eufrak
13.73 +\newcommand{\isasymDD}{\isamath{\mathfrak{D}}} %requires eufrak
13.74 +\newcommand{\isasymEE}{\isamath{\mathfrak{E}}} %requires eufrak
13.75 +\newcommand{\isasymFF}{\isamath{\mathfrak{F}}} %requires eufrak
13.76 +\newcommand{\isasymGG}{\isamath{\mathfrak{G}}} %requires eufrak
13.77 +\newcommand{\isasymHH}{\isamath{\mathfrak{H}}} %requires eufrak
13.78 +\newcommand{\isasymII}{\isamath{\mathfrak{I}}} %requires eufrak
13.79 +\newcommand{\isasymJJ}{\isamath{\mathfrak{J}}} %requires eufrak
13.80 +\newcommand{\isasymKK}{\isamath{\mathfrak{K}}} %requires eufrak
13.81 +\newcommand{\isasymLL}{\isamath{\mathfrak{L}}} %requires eufrak
13.82 +\newcommand{\isasymMM}{\isamath{\mathfrak{M}}} %requires eufrak
13.83 +\newcommand{\isasymNN}{\isamath{\mathfrak{N}}} %requires eufrak
13.84 +\newcommand{\isasymOO}{\isamath{\mathfrak{O}}} %requires eufrak
13.85 +\newcommand{\isasymPP}{\isamath{\mathfrak{P}}} %requires eufrak
13.86 +\newcommand{\isasymQQ}{\isamath{\mathfrak{Q}}} %requires eufrak
13.87 +\newcommand{\isasymRR}{\isamath{\mathfrak{R}}} %requires eufrak
13.88 +\newcommand{\isasymSS}{\isamath{\mathfrak{S}}} %requires eufrak
13.89 +\newcommand{\isasymTT}{\isamath{\mathfrak{T}}} %requires eufrak
13.90 +\newcommand{\isasymUU}{\isamath{\mathfrak{U}}} %requires eufrak
13.91 +\newcommand{\isasymVV}{\isamath{\mathfrak{V}}} %requires eufrak
13.92 +\newcommand{\isasymWW}{\isamath{\mathfrak{W}}} %requires eufrak
13.93 +\newcommand{\isasymXX}{\isamath{\mathfrak{X}}} %requires eufrak
13.94 +\newcommand{\isasymYY}{\isamath{\mathfrak{Y}}} %requires eufrak
13.95 +\newcommand{\isasymZZ}{\isamath{\mathfrak{Z}}} %requires eufrak
13.96 +\newcommand{\isasymaa}{\isamath{\mathfrak{a}}} %requires eufrak
13.97 +\newcommand{\isasymbb}{\isamath{\mathfrak{b}}} %requires eufrak
13.98 +\newcommand{\isasymcc}{\isamath{\mathfrak{c}}} %requires eufrak
13.99 +\newcommand{\isasymdd}{\isamath{\mathfrak{d}}} %requires eufrak
13.100 +\newcommand{\isasymee}{\isamath{\mathfrak{e}}} %requires eufrak
13.101 +\newcommand{\isasymff}{\isamath{\mathfrak{f}}} %requires eufrak
13.102 +\newcommand{\isasymgg}{\isamath{\mathfrak{g}}} %requires eufrak
13.103 +\newcommand{\isasymhh}{\isamath{\mathfrak{h}}} %requires eufrak
13.104 +\newcommand{\isasymii}{\isamath{\mathfrak{i}}} %requires eufrak
13.105 +\newcommand{\isasymjj}{\isamath{\mathfrak{j}}} %requires eufrak
13.106 +\newcommand{\isasymkk}{\isamath{\mathfrak{k}}} %requires eufrak
13.107 +\newcommand{\isasymll}{\isamath{\mathfrak{l}}} %requires eufrak
13.108 +\newcommand{\isasymmm}{\isamath{\mathfrak{m}}} %requires eufrak
13.109 +\newcommand{\isasymnn}{\isamath{\mathfrak{n}}} %requires eufrak
13.110 +\newcommand{\isasymoo}{\isamath{\mathfrak{o}}} %requires eufrak
13.111 +\newcommand{\isasympp}{\isamath{\mathfrak{p}}} %requires eufrak
13.112 +\newcommand{\isasymqq}{\isamath{\mathfrak{q}}} %requires eufrak
13.113 +\newcommand{\isasymrr}{\isamath{\mathfrak{r}}} %requires eufrak
13.114 +\newcommand{\isasymss}{\isamath{\mathfrak{s}}} %requires eufrak
13.115 +\newcommand{\isasymtt}{\isamath{\mathfrak{t}}} %requires eufrak
13.116 +\newcommand{\isasymuu}{\isamath{\mathfrak{u}}} %requires eufrak
13.117 +\newcommand{\isasymvv}{\isamath{\mathfrak{v}}} %requires eufrak
13.118 +\newcommand{\isasymww}{\isamath{\mathfrak{w}}} %requires eufrak
13.119 +\newcommand{\isasymxx}{\isamath{\mathfrak{x}}} %requires eufrak
13.120 +\newcommand{\isasymyy}{\isamath{\mathfrak{y}}} %requires eufrak
13.121 +\newcommand{\isasymzz}{\isamath{\mathfrak{z}}} %requires eufrak
13.122 +\newcommand{\isasymalpha}{\isamath{\alpha}}
13.123 +\newcommand{\isasymbeta}{\isamath{\beta}}
13.124 +\newcommand{\isasymgamma}{\isamath{\gamma}}
13.125 +\newcommand{\isasymdelta}{\isamath{\delta}}
13.126 +\newcommand{\isasymepsilon}{\isamath{\varepsilon}}
13.127 +\newcommand{\isasymzeta}{\isamath{\zeta}}
13.128 +\newcommand{\isasymeta}{\isamath{\eta}}
13.129 +\newcommand{\isasymtheta}{\isamath{\vartheta}}
13.130 +\newcommand{\isasymiota}{\isamath{\iota}}
13.131 +\newcommand{\isasymkappa}{\isamath{\kappa}}
13.132 +\newcommand{\isasymlambda}{\isamath{\lambda}}
13.133 +\newcommand{\isasymmu}{\isamath{\mu}}
13.134 +\newcommand{\isasymnu}{\isamath{\nu}}
13.135 +\newcommand{\isasymxi}{\isamath{\xi}}
13.136 +\newcommand{\isasympi}{\isamath{\pi}}
13.137 +\newcommand{\isasymrho}{\isamath{\varrho}}
13.138 +\newcommand{\isasymsigma}{\isamath{\sigma}}
13.139 +\newcommand{\isasymtau}{\isamath{\tau}}
13.140 +\newcommand{\isasymupsilon}{\isamath{\upsilon}}
13.141 +\newcommand{\isasymphi}{\isamath{\varphi}}
13.142 +\newcommand{\isasymchi}{\isamath{\chi}}
13.143 +\newcommand{\isasympsi}{\isamath{\psi}}
13.144 +\newcommand{\isasymomega}{\isamath{\omega}}
13.145 +\newcommand{\isasymGamma}{\isamath{\Gamma}}
13.146 +\newcommand{\isasymDelta}{\isamath{\Delta}}
13.147 +\newcommand{\isasymTheta}{\isamath{\Theta}}
13.148 +\newcommand{\isasymLambda}{\isamath{\Lambda}}
13.149 +\newcommand{\isasymXi}{\isamath{\Xi}}
13.150 +\newcommand{\isasymPi}{\isamath{\Pi}}
13.151 +\newcommand{\isasymSigma}{\isamath{\Sigma}}
13.152 +\newcommand{\isasymUpsilon}{\isamath{\Upsilon}}
13.153 +\newcommand{\isasymPhi}{\isamath{\Phi}}
13.154 +\newcommand{\isasymPsi}{\isamath{\Psi}}
13.155 +\newcommand{\isasymOmega}{\isamath{\Omega}}
13.156 +\newcommand{\isasymbool}{\isamath{\mathrm{I}\mkern-3.8mu\mathrm{B}}}
13.157 +\newcommand{\isasymcomplex}{\isamath{\mathrm{C}\mkern-15mu{\phantom{\mathrm{t}}\vrule}\mkern9mu}}
13.158 +\newcommand{\isasymnat}{\isamath{\mathrm{I}\mkern-3.8mu\mathrm{N}}}
13.159 +\newcommand{\isasymrat}{\isamath{\mathrm{Q}\mkern-16mu{\phantom{\mathrm{t}}\vrule}\mkern10mu}}
13.160 +\newcommand{\isasymreal}{\isamath{\mathrm{I}\mkern-3.8mu\mathrm{R}}}
13.161 +\newcommand{\isasymint}{\isamath{\mathsf{Z}\mkern-7.5mu\mathsf{Z}}}
13.162 +\newcommand{\isasymleftarrow}{\isamath{\leftarrow}}
13.163 +\newcommand{\isasymlongleftarrow}{\isamath{\longleftarrow}}
13.164 +\newcommand{\isasymrightarrow}{\isamath{\rightarrow}}
13.165 +\newcommand{\isasymlongrightarrow}{\isamath{\longrightarrow}}
13.166 +\newcommand{\isasymLeftarrow}{\isamath{\Leftarrow}}
13.167 +\newcommand{\isasymLongleftarrow}{\isamath{\Longleftarrow}}
13.168 +\newcommand{\isasymRightarrow}{\isamath{\Rightarrow}}
13.169 +\newcommand{\isasymLongrightarrow}{\isamath{\Longrightarrow}}
13.170 +\newcommand{\isasymleftrightarrow}{\isamath{\leftrightarrow}}
13.171 +\newcommand{\isasymlongleftrightarrow}{\isamath{\longleftrightarrow}}
13.172 +\newcommand{\isasymLeftrightarrow}{\isamath{\Leftrightarrow}}
13.173 +\newcommand{\isasymLongleftrightarrow}{\isamath{\Longleftrightarrow}}
13.174 +\newcommand{\isasymmapsto}{\isamath{\mapsto}}
13.175 +\newcommand{\isasymlongmapsto}{\isamath{\longmapsto}}
13.176 +\newcommand{\isasymmidarrow}{\isamath{\relbar}}
13.177 +\newcommand{\isasymMidarrow}{\isamath{\Relbar}}
13.178 +\newcommand{\isasymhookleftarrow}{\isamath{\hookleftarrow}}
13.179 +\newcommand{\isasymhookrightarrow}{\isamath{\hookrightarrow}}
13.180 +\newcommand{\isasymleftharpoondown}{\isamath{\leftharpoondown}}
13.181 +\newcommand{\isasymrightharpoondown}{\isamath{\rightharpoondown}}
13.182 +\newcommand{\isasymleftharpoonup}{\isamath{\leftharpoonup}}
13.183 +\newcommand{\isasymrightharpoonup}{\isamath{\rightharpoonup}}
13.184 +\newcommand{\isasymrightleftharpoons}{\isamath{\rightleftharpoons}}
13.185 +\newcommand{\isasymleadsto}{\isamath{\leadsto}} %requires amssymb
13.186 +\newcommand{\isasymdownharpoonleft}{\isamath{\downharpoonleft}} %requires amssymb
13.187 +\newcommand{\isasymdownharpoonright}{\isamath{\downharpoonright}} %requires amssymb
13.188 +\newcommand{\isasymupharpoonleft}{\isamath{\upharpoonleft}} %requires amssymb
13.189 +\newcommand{\isasymupharpoonright}{\isamath{\upharpoonright}} %requires amssymb
13.190 +\newcommand{\isasymrestriction}{\isamath{\restriction}} %requires amssymb
13.191 +\newcommand{\isasymColon}{\isamath{\mathrel{::}}}
13.192 +\newcommand{\isasymup}{\isamath{\uparrow}}
13.193 +\newcommand{\isasymUp}{\isamath{\Uparrow}}
13.194 +\newcommand{\isasymdown}{\isamath{\downarrow}}
13.195 +\newcommand{\isasymDown}{\isamath{\Downarrow}}
13.196 +\newcommand{\isasymupdown}{\isamath{\updownarrow}}
13.197 +\newcommand{\isasymUpdown}{\isamath{\Updownarrow}}
13.198 +\newcommand{\isasymlangle}{\isamath{\langle}}
13.199 +\newcommand{\isasymrangle}{\isamath{\rangle}}
13.200 +\newcommand{\isasymlceil}{\isamath{\lceil}}
13.201 +\newcommand{\isasymrceil}{\isamath{\rceil}}
13.202 +\newcommand{\isasymlfloor}{\isamath{\lfloor}}
13.203 +\newcommand{\isasymrfloor}{\isamath{\rfloor}}
13.204 +\newcommand{\isasymlparr}{\isamath{\mathopen{(\mkern-3mu\mid}}}
13.205 +\newcommand{\isasymrparr}{\isamath{\mathclose{\mid\mkern-3mu)}}}
13.206 +\newcommand{\isasymlbrakk}{\isamath{\mathopen{\lbrack\mkern-3mu\lbrack}}}
13.207 +\newcommand{\isasymrbrakk}{\isamath{\mathclose{\rbrack\mkern-3mu\rbrack}}}
13.208 +\newcommand{\isasymlbrace}{\isamath{\mathopen{\lbrace\mkern-4.5mu\mid}}}
13.209 +\newcommand{\isasymrbrace}{\isamath{\mathclose{\mid\mkern-4.5mu\rbrace}}}
13.210 +\newcommand{\isasymguillemotleft}{\isatext{\flqq}} %requires babel
13.211 +\newcommand{\isasymguillemotright}{\isatext{\frqq}} %requires babel
13.212 +\newcommand{\isasymbottom}{\isamath{\bot}}
13.213 +\newcommand{\isasymtop}{\isamath{\top}}
13.214 +\newcommand{\isasymand}{\isamath{\wedge}}
13.215 +\newcommand{\isasymAnd}{\isamath{\bigwedge}}
13.216 +\newcommand{\isasymor}{\isamath{\vee}}
13.217 +\newcommand{\isasymOr}{\isamath{\bigvee}}
13.218 +\newcommand{\isasymforall}{\isamath{\forall\,}}
13.219 +\newcommand{\isasymexists}{\isamath{\exists\,}}
13.220 +\newcommand{\isasymnexists}{\isamath{\nexists\,}} %requires amssymb
13.221 +\newcommand{\isasymnot}{\isamath{\neg}}
13.222 +\newcommand{\isasymbox}{\isamath{\Box}} %requires amssymb
13.223 +\newcommand{\isasymdiamond}{\isamath{\Diamond}} %requires amssymb
13.224 +\newcommand{\isasymturnstile}{\isamath{\vdash}}
13.225 +\newcommand{\isasymTurnstile}{\isamath{\models}}
13.226 +\newcommand{\isasymtturnstile}{\isamath{\vdash\!\!\!\vdash}}
13.227 +\newcommand{\isasymTTurnstile}{\isamath{\mid\!\models}}
13.228 +\newcommand{\isasymstileturn}{\isamath{\dashv}}
13.229 +\newcommand{\isasymsurd}{\isamath{\surd}}
13.230 +\newcommand{\isasymle}{\isamath{\le}}
13.231 +\newcommand{\isasymge}{\isamath{\ge}}
13.232 +\newcommand{\isasymlless}{\isamath{\ll}}
13.233 +\newcommand{\isasymggreater}{\isamath{\gg}}
13.234 +\newcommand{\isasymlesssim}{\isamath{\lesssim}} %requires amssymb
13.235 +\newcommand{\isasymgreatersim}{\isamath{\gtrsim}} %requires amssymb
13.236 +\newcommand{\isasymlessapprox}{\isamath{\lessapprox}} %requires amssymb
13.237 +\newcommand{\isasymgreaterapprox}{\isamath{\gtrapprox}} %requires amssymb
13.238 +\newcommand{\isasymin}{\isamath{\in}}
13.239 +\newcommand{\isasymnotin}{\isamath{\notin}}
13.240 +\newcommand{\isasymsubset}{\isamath{\subset}}
13.241 +\newcommand{\isasymsupset}{\isamath{\supset}}
13.242 +\newcommand{\isasymsubseteq}{\isamath{\subseteq}}
13.243 +\newcommand{\isasymsupseteq}{\isamath{\supseteq}}
13.244 +\newcommand{\isasymsqsubset}{\isamath{\sqsubset}} %requires amssymb
13.245 +\newcommand{\isasymsqsupset}{\isamath{\sqsupset}} %requires amssymb
13.246 +\newcommand{\isasymsqsubseteq}{\isamath{\sqsubseteq}}
13.247 +\newcommand{\isasymsqsupseteq}{\isamath{\sqsupseteq}}
13.248 +\newcommand{\isasyminter}{\isamath{\cap}}
13.249 +\newcommand{\isasymInter}{\isamath{\bigcap\,}}
13.250 +\newcommand{\isasymunion}{\isamath{\cup}}
13.251 +\newcommand{\isasymUnion}{\isamath{\bigcup\,}}
13.252 +\newcommand{\isasymsqunion}{\isamath{\sqcup}}
13.253 +\newcommand{\isasymSqunion}{\isamath{\bigsqcup\,}}
13.254 +\newcommand{\isasymsqinter}{\isamath{\sqcap}}
13.255 +\newcommand{\isasymSqinter}{\isamath{\bigsqcap\,}} %requires stmaryrd
13.256 +\newcommand{\isasymsetminus}{\isamath{\setminus}}
13.257 +\newcommand{\isasympropto}{\isamath{\propto}}
13.258 +\newcommand{\isasymuplus}{\isamath{\uplus}}
13.259 +\newcommand{\isasymUplus}{\isamath{\biguplus\,}}
13.260 +\newcommand{\isasymnoteq}{\isamath{\not=}}
13.261 +\newcommand{\isasymsim}{\isamath{\sim}}
13.262 +\newcommand{\isasymdoteq}{\isamath{\doteq}}
13.263 +\newcommand{\isasymsimeq}{\isamath{\simeq}}
13.264 +\newcommand{\isasymapprox}{\isamath{\approx}}
13.265 +\newcommand{\isasymasymp}{\isamath{\asymp}}
13.266 +\newcommand{\isasymcong}{\isamath{\cong}}
13.267 +\newcommand{\isasymsmile}{\isamath{\smile}}
13.268 +\newcommand{\isasymequiv}{\isamath{\equiv}}
13.269 +\newcommand{\isasymfrown}{\isamath{\frown}}
13.270 +\newcommand{\isasymJoin}{\isamath{\Join}} %requires amssymb
13.271 +\newcommand{\isasymbowtie}{\isamath{\bowtie}}
13.272 +\newcommand{\isasymprec}{\isamath{\prec}}
13.273 +\newcommand{\isasymsucc}{\isamath{\succ}}
13.274 +\newcommand{\isasympreceq}{\isamath{\preceq}}
13.275 +\newcommand{\isasymsucceq}{\isamath{\succeq}}
13.276 +\newcommand{\isasymparallel}{\isamath{\parallel}}
13.277 +\newcommand{\isasymbar}{\isamath{\mid}}
13.278 +\newcommand{\isasymplusminus}{\isamath{\pm}}
13.279 +\newcommand{\isasymminusplus}{\isamath{\mp}}
13.280 +\newcommand{\isasymtimes}{\isamath{\times}}
13.281 +\newcommand{\isasymdiv}{\isamath{\div}}
13.282 +\newcommand{\isasymcdot}{\isamath{\cdot}}
13.283 +\newcommand{\isasymstar}{\isamath{\star}}
13.284 +\newcommand{\isasymbullet}{\boldmath\isamath{\mathchoice{\displaystyle{\cdot}}{\textstyle{\cdot}}{\scriptstyle{\bullet}}{\scriptscriptstyle{\bullet}}}}
13.285 +\newcommand{\isasymcirc}{\isamath{\circ}}
13.286 +\newcommand{\isasymdagger}{\isamath{\dagger}}
13.287 +\newcommand{\isasymddagger}{\isamath{\ddagger}}
13.288 +\newcommand{\isasymlhd}{\isamath{\lhd}} %requires amssymb
13.289 +\newcommand{\isasymrhd}{\isamath{\rhd}} %requires amssymb
13.290 +\newcommand{\isasymunlhd}{\isamath{\unlhd}} %requires amssymb
13.291 +\newcommand{\isasymunrhd}{\isamath{\unrhd}} %requires amssymb
13.292 +\newcommand{\isasymtriangleleft}{\isamath{\triangleleft}}
13.293 +\newcommand{\isasymtriangleright}{\isamath{\triangleright}}
13.294 +\newcommand{\isasymtriangle}{\isamath{\triangle}}
13.295 +\newcommand{\isasymtriangleq}{\isamath{\triangleq}} %requires amssymb
13.296 +\newcommand{\isasymoplus}{\isamath{\oplus}}
13.297 +\newcommand{\isasymOplus}{\isamath{\bigoplus\,}}
13.298 +\newcommand{\isasymotimes}{\isamath{\otimes}}
13.299 +\newcommand{\isasymOtimes}{\isamath{\bigotimes\,}}
13.300 +\newcommand{\isasymodot}{\isamath{\odot}}
13.301 +\newcommand{\isasymOdot}{\isamath{\bigodot\,}}
13.302 +\newcommand{\isasymominus}{\isamath{\ominus}}
13.303 +\newcommand{\isasymoslash}{\isamath{\oslash}}
13.304 +\newcommand{\isasymdots}{\isamath{\dots}}
13.305 +\newcommand{\isasymcdots}{\isamath{\cdots}}
13.306 +\newcommand{\isasymSum}{\isamath{\sum\,}}
13.307 +\newcommand{\isasymProd}{\isamath{\prod\,}}
13.308 +\newcommand{\isasymCoprod}{\isamath{\coprod\,}}
13.309 +\newcommand{\isasyminfinity}{\isamath{\infty}}
13.310 +\newcommand{\isasymintegral}{\isamath{\int\,}}
13.311 +\newcommand{\isasymointegral}{\isamath{\oint\,}}
13.312 +\newcommand{\isasymclubsuit}{\isamath{\clubsuit}}
13.313 +\newcommand{\isasymdiamondsuit}{\isamath{\diamondsuit}}
13.314 +\newcommand{\isasymheartsuit}{\isamath{\heartsuit}}
13.315 +\newcommand{\isasymspadesuit}{\isamath{\spadesuit}}
13.316 +\newcommand{\isasymaleph}{\isamath{\aleph}}
13.317 +\newcommand{\isasymemptyset}{\isamath{\emptyset}}
13.318 +\newcommand{\isasymnabla}{\isamath{\nabla}}
13.319 +\newcommand{\isasympartial}{\isamath{\partial}}
13.320 +\newcommand{\isasymRe}{\isamath{\Re}}
13.321 +\newcommand{\isasymIm}{\isamath{\Im}}
13.322 +\newcommand{\isasymflat}{\isamath{\flat}}
13.323 +\newcommand{\isasymnatural}{\isamath{\natural}}
13.324 +\newcommand{\isasymsharp}{\isamath{\sharp}}
13.325 +\newcommand{\isasymangle}{\isamath{\angle}}
13.326 +\newcommand{\isasymcopyright}{\isatext{\rm\copyright}}
13.327 +\newcommand{\isasymregistered}{\isatext{\rm\textregistered}}
13.328 +\newcommand{\isasymhyphen}{\isatext{\rm-}}
13.329 +\newcommand{\isasyminverse}{\isamath{{}^{-1}}}
13.330 +\newcommand{\isasymonesuperior}{\isamath{{}^1}}
13.331 +\newcommand{\isasymonequarter}{\isatext{\rm\textonequarter}} %requires textcomp
13.332 +\newcommand{\isasymtwosuperior}{\isamath{{}^2}}
13.333 +\newcommand{\isasymonehalf}{\isatext{\rm\textonehalf}} %requires textcomp
13.334 +\newcommand{\isasymthreesuperior}{\isamath{{}^3}}
13.335 +\newcommand{\isasymthreequarters}{\isatext{\rm\textthreequarters}} %requires textcomp
13.336 +\newcommand{\isasymordfeminine}{\isatext{\rm\textordfeminine}}
13.337 +\newcommand{\isasymordmasculine}{\isatext{\rm\textordmasculine}}
13.338 +\newcommand{\isasymsection}{\isatext{\rm\S}}
13.339 +\newcommand{\isasymparagraph}{\isatext{\rm\P}}
13.340 +\newcommand{\isasymexclamdown}{\isatext{\rm\textexclamdown}}
13.341 +\newcommand{\isasymquestiondown}{\isatext{\rm\textquestiondown}}
13.342 +\newcommand{\isasymeuro}{\isatext{\textgreek{\euro}}} %requires greek babel
13.343 +\newcommand{\isasympounds}{\isamath{\pounds}}
13.344 +\newcommand{\isasymyen}{\isatext{\yen}} %requires amssymb
13.345 +\newcommand{\isasymcent}{\isatext{\textcent}} %requires textcomp
13.346 +\newcommand{\isasymcurrency}{\isatext{\textcurrency}} %requires textcomp
13.347 +\newcommand{\isasymdegree}{\isatext{\rm\textdegree}} %requires textcomp
13.348 +\newcommand{\isasymamalg}{\isamath{\amalg}}
13.349 +\newcommand{\isasymmho}{\isamath{\mho}} %requires amssymb
13.350 +\newcommand{\isasymlozenge}{\isamath{\lozenge}} %requires amssymb
13.351 +\newcommand{\isasymwp}{\isamath{\wp}}
13.352 +\newcommand{\isasymwrong}{\isamath{\wr}}
13.353 +\newcommand{\isasymstruct}{\isamath{\diamond}}
13.354 +\newcommand{\isasymacute}{\isatext{\'\relax}}
13.355 +\newcommand{\isasymindex}{\isatext{\i}}
13.356 +\newcommand{\isasymdieresis}{\isatext{\"\relax}}
13.357 +\newcommand{\isasymcedilla}{\isatext{\c\relax}}
13.358 +\newcommand{\isasymhungarumlaut}{\isatext{\H\relax}}
13.359 +\newcommand{\isasymspacespace}{\isamath{~~}}
13.360 +\newcommand{\isasymmodule}{\isamath{\langle}\isakeyword{module}\isamath{\rangle}}
13.361 +\newcommand{\isasymsome}{\isamath{\epsilon\,}}