# HG changeset patch # User Jan Rocnik # Date 1315516655 -7200 # Node ID e633bb41ea425544c9f64f5d55f08893700ca96e # Parent e41d91e86fa9d0b8fb3d10732abef3ac1e508ac3 setted up envoirement for latex includement (tuned) diff -r e41d91e86fa9 -r e633bb41ea42 doc-src/isac/jrocnik/Inverse_Z_Transform/Inverse_Z_Transform.thy --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/doc-src/isac/jrocnik/Inverse_Z_Transform/Inverse_Z_Transform.thy Thu Sep 08 23:17:35 2011 +0200 @@ -0,0 +1,449 @@ +(* Title: Test_Z_Transform + Author: Jan Rocnik + (c) copyright due to lincense terms. +12345678901234567890123456789012345678901234567890123456789012345678901234567890 + 10 20 30 40 50 60 70 80 +*) + +theory Inverse_Z_Transform imports Isac begin + +section {*trials towards Z transform *} +text{*===============================*} +subsection {*terms*} +ML {* +@{term "1 < || z ||"}; +@{term "z / (z - 1)"}; +@{term "-u -n - 1"}; +@{term "-u [-n - 1]"}; (*[ ] denotes lists !!!*) +@{term "z /(z - 1) = -u [-n - 1]"};Isac +@{term "1 < || z || ==> z / (z - 1) = -u [-n - 1]"}; +term2str @{term "1 < || z || ==> z / (z - 1) = -u [-n - 1]"}; +*} +ML {* +(*alpha --> "" *) + +@{term "\ "}; +@{term "\ "}; +@{term "\ "}; +@{term "\ "}; +term2str @{term "\ "}; +*} + +subsection {*rules*} +(*axiomatization "z / (z - 1) = -u [-n - 1]" Illegal variable name: "z / (z - 1) = -u [-n - 1]" *) +(*definition "z / (z - 1) = -u [-n - 1]" Bad head of lhs: existing constant "op /"*) +axiomatization where + rule1: "1 = \[n]" and + rule2: "|| z || > 1 ==> z / (z - 1) = u [n]" and + rule3: "|| z || < 1 ==> z / (z - 1) = -u [-n - 1]" and + rule4: "|| z || > || \ || ==> z / (z - \) = \^n * u [n]" and + rule5: "|| z || < || \ || ==> z / (z - \) = -(\^n) * u [-n - 1]" and + rule6: "|| z || > 1 ==> z/(z - 1)^2 = n * u [n]" +ML {* +@{thm rule1}; +@{thm rule2}; +@{thm rule3}; +@{thm rule4}; +*} + +subsection {*apply rules*} +ML {* +val inverse_Z = append_rls "inverse_Z" e_rls + [ Thm ("rule3",num_str @{thm rule3}), + Thm ("rule4",num_str @{thm rule4}), + Thm ("rule1",num_str @{thm rule1}) + ]; + +val t = str2term "z / (z - 1) + z / (z - \) + 1"; +val SOME (t', asm) = rewrite_set_ thy true inverse_Z t; +term2str t' = "z / (z - ?\ [?n]) + z / (z - \) + ?\ [?n]"; (*attention rule1 !!!*) +*} +ML {* +val (thy, ro, er) = (@{theory}, tless_true, eval_rls); +*} +ML {* +val SOME (t, asm1) = rewrite_ thy ro er true (num_str @{thm rule3}) t; +term2str t = "- ?u [- ?n - 1] + z / (z - \) + 1"; (*- real *) +term2str t; +*} +ML {* +val SOME (t, asm2) = rewrite_ thy ro er true (num_str @{thm rule4}) t; +term2str t = "- ?u [- ?n - 1] + \ ^ ?n * ?u [?n] + 1"; (*- real *) +term2str t; +*} +ML {* +val SOME (t, asm3) = rewrite_ thy ro er true (num_str @{thm rule1}) t; +term2str t = "- ?u [- ?n - 1] + \ ^ ?n * ?u [?n] + ?\ [?n]"; (*- real *) +term2str t; +*} +ML {* +terms2str (asm1 @ asm2 @ asm3); +*} + +section {*Prepare steps in CTP-based programming language*} +text{*===================================================*} +subsection {*prepare expression*} +ML {* +val ctxt = ProofContext.init_global @{theory}; +val ctxt = declare_constraints' [@{term "z::real"}] ctxt; + +val SOME fun1 = parseNEW ctxt "X z = 3 / (z - 1/4 + -1/8 * z ^ -1)"; term2str fun1; +val SOME fun1' = parseNEW ctxt "X z = 3 / (z - 1/4 + -1/8 * (1/z))"; term2str fun1'; +*} + +axiomatization where + ruleZY: "(X z = a / b) = (X' z = a / (z * b))" + +ML {* +val (thy, ro, er) = (@{theory}, tless_true, eval_rls); +val SOME (fun2, asm1) = rewrite_ thy ro er true @{thm ruleZY} fun1; term2str fun2; +val SOME (fun2', asm1) = rewrite_ thy ro er true @{thm ruleZY} fun1'; term2str fun2'; + +val SOME (fun3,_) = rewrite_set_ @{theory Isac} false norm_Rational fun2; +term2str fun3; (*fails on x^(-1) TODO*) +val SOME (fun3',_) = rewrite_set_ @{theory Isac} false norm_Rational fun2'; +term2str fun3'; (*OK*) + +val (_, expr) = HOLogic.dest_eq fun3'; term2str expr; +*} + +subsection {*solve equation*} +ML {*(*from test/Tools/isac/Minisubpbl/100-init-rootpbl.sml*) +"----------- Minisubplb/100-init-rootp (*OK*)bl.sml ---------------------"; +val denominator = parseNEW ctxt "z^2 - 1/4*z - 1/8 = 0"; +val fmz = ["equality (z^2 - 1/4*z - 1/8 = (0::real))", "solveFor z","solutions L"]; +val (dI',pI',mI') =("Isac", ["univariate","equation"], ["no_met"]); +(* ^^^^^^^^^^^^^^^^^^^^^^ TODO: ISAC determines type of eq*) +*} +ML {* +val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))]; +val (p,_,f,nxt,_,pt) = me nxt p [] pt; +(*[ +(([], Frm), solve (z ^ 2 - 1 / 4 * z - 1 / 8 = 0, z)), +(([1], Frm), z ^ 2 - 1 / 4 * z - 1 / 8 = 0), bad rewrite order +(([1], Res), -1 / 8 + z ^ 2 + -1 / 4 * z = 0), bad pattern +(([2], Pbl), solve (-1 / 8 + z ^ 2 + -1 / 4 * z = 0, z)), +(([2,1], Pbl), solve (-1 / 8 + z ^ 2 + -1 / 4 * z = 0, z)), +(([2,1,1], Pbl), solve (-1 / 8 + z ^ 2 + -1 / 4 * z = 0, z)), +(([2,1,1,1], Frm), -1 / 8 + z ^ 2 + -1 / 4 * z = 0)] +*) +*} +ML {* +val denominator = parseNEW ctxt "-1/8 + -1/4*z + z^2 = 0"; +(*ergebnis: [gleichung, was tun?, lösung]*) +val fmz = ["equality (-1/8 + -1/4*z + z^2 = (0::real))", "solveFor z","solutions L"]; +(*liste der theoreme die zum lösen benötigt werden, aus isac, keine spezielle methode (no met)*) +val (dI',pI',mI') = + ("Isac", ["pqFormula","degree_2","polynomial","univariate","equation"], ["no_met"]); +(*schritte abarbeiten*) +val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))]; +val (p,_,f,nxt,_,pt) = me nxt p [] pt; +val (p,_,f,nxt,_,pt) = me nxt p [] pt; +val (p,_,f,nxt,_,pt) = me nxt p [] pt; +val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*val nxt = ("Empty_Tac", ...): tac'_*) +show_pt pt; +*} + +subsection {*partial fraction decomposition*} +subsubsection {*solution of the equation*} +ML {* +val SOME solutions = parseNEW ctxt "[z=1/2, z=-1/4]"; +term2str solutions; +atomty solutions; +*} + +subsubsection {*get solutions out of list*} +text {*in isac's CTP-based programming language: $let s_1 = NTH 1 solutions; s_2 = NTH 2...$*} +ML {* +val Const ("List.list.Cons", _) $ s_1 $ (Const ("List.list.Cons", _) $ + s_2 $ Const ("List.list.Nil", _)) = solutions; +term2str s_1; +term2str s_2; +*} + +ML {* (*Solutions as Denominator --> Denominator1 = z - Zeropoint1, Denominator2 = z-Zeropoint2,...*) +val xx = HOLogic.dest_eq s_1; +val s_1' = HOLogic.mk_binop "Groups.minus_class.minus" xx; +val xx = HOLogic.dest_eq s_2; +val s_2' = HOLogic.mk_binop "Groups.minus_class.minus" xx; +term2str s_1'; +term2str s_2'; +*} + +subsubsection {*build expression*} +text {*in isac's CTP-based programming language: $let s_1 = Take numerator / (s_1 * s_2)$*} +ML {* +(*The Main Denominator is the multiplikation of the partial fraction denominators*) +val denominator' = HOLogic.mk_binop "Groups.times_class.times" (s_1', s_2') ; +val SOME numerator = parseNEW ctxt "3::real"; + +val expr' = HOLogic.mk_binop "Rings.inverse_class.divide" (numerator, denominator'); +term2str expr'; +*} + +subsubsection {*Ansatz - create partial fractions out of our expression*} + +axiomatization where + ansatz2: "n / (a*b) = A/a + B/(b::real)" and + multiply_eq2: "(n / (a*b) = A/a + B/b) = (a*b*(n / (a*b)) = a*b*(A/a + B/b))" + +ML {* +(*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*) +val SOME (t1,_) = rewrite_ @{theory Isac} e_rew_ord e_rls false @{thm ansatz2} expr'; +term2str t1; +atomty t1; +val eq1 = HOLogic.mk_eq (expr', t1); +term2str eq1; +*} +ML {* +(*eliminate the demoninators by multiplying the left and the right side with the main denominator*) +val SOME (eq2,_) = rewrite_ @{theory Isac} e_rew_ord e_rls false @{thm multiply_eq2} eq1; +term2str eq2; +*} +ML {* +(*simplificatoin*) +val SOME (eq3,_) = rewrite_set_ @{theory Isac} false norm_Rational eq2; +term2str eq3; (*?A ?B not simplified*) +*} +ML {* +val SOME fract1 = + parseNEW ctxt "(z - 1 / 2) * (z - -1 / 4) * (A / (z - 1 / 2) + B / (z - -1 / 4))"; (*A B !*) +val SOME (fract2,_) = rewrite_set_ @{theory Isac} false norm_Rational fract1; +term2str fract2 = "(A + -2 * B + 4 * A * z + 4 * B * z) / 4"; +(*term2str fract2 = "A * (1 / 4 + z) + B * (-1 / 2 + z)" would be more traditional*) +*} +ML {* +val (numerator, denominator) = HOLogic.dest_eq eq3; +val eq3' = HOLogic.mk_eq (numerator, fract1); (*A B !*) +term2str eq3'; +*} +ML {* (*MANDATORY: otherwise 3 = 0*) +val SOME (eq3'' ,_) = rewrite_set_ @{theory Isac} false norm_Rational eq3'; +term2str eq3''; +*} + +subsubsection {*get first koeffizient*} + +ML {* +(*substitude z with the first zeropoint to get A*) +val SOME (eq4_1,_) = rewrite_terms_ @{theory Isac} e_rew_ord e_rls [s_1] eq3''; +term2str eq4_1; +*} +ML {* +val SOME (eq4_2,_) = rewrite_set_ @{theory Isac} false norm_Rational eq4_1; +term2str eq4_2; +*} +ML {* +val fmz = ["equality (3 = 3 * A / (4::real))", "solveFor A","solutions L"]; +val (dI',pI',mI') =("Isac", ["univariate","equation"], ["no_met"]); + +*} +ML {* +(*solve the simple linear equilation for A TODO: return eq, not list of eq*) +val (p,_,fa,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))]; +val (p,_,fa,nxt,_,pt) = me nxt p [] pt; +val (p,_,fa,nxt,_,pt) = me nxt p [] pt; +val (p,_,fa,nxt,_,pt) = me nxt p [] pt; +val (p,_,fa,nxt,_,pt) = me nxt p [] pt; +val (p,_,fa,nxt,_,pt) = me nxt p [] pt; +val (p,_,fa,nxt,_,pt) = me nxt p [] pt; +val (p,_,fa,nxt,_,pt) = me nxt p [] pt; +val (p,_,fa,nxt,_,pt) = me nxt p [] pt; +val (p,_,fa,nxt,_,pt) = me nxt p [] pt; +val (p,_,fa,nxt,_,pt) = me nxt p [] pt; +val (p,_,fa,nxt,_,pt) = me nxt p [] pt; +val (p,_,fa,nxt,_,pt) = me nxt p [] pt; +val (p,_,fa,nxt,_,pt) = me nxt p [] pt; +val (p,_,fa,nxt,_,pt) = me nxt p [] pt; +val (p,_,fa,nxt,_,pt) = me nxt p [] pt; +val (p,_,fa,nxt,_,pt) = me nxt p [] pt; +val (p,_,fa,nxt,_,pt) = me nxt p [] pt; +val (p,_,fa,nxt,_,pt) = me nxt p [] pt; +val (p,_,fa,nxt,_,pt) = me nxt p [] pt; +val (p,_,fa,nxt,_,pt) = me nxt p [] pt; +val (p,_,fa,nxt,_,pt) = me nxt p [] pt; +val (p,_,fa,nxt,_,pt) = me nxt p [] pt; +val (p,_,fa,nxt,_,pt) = me nxt p [] pt; +val (p,_,fa,nxt,_,pt) = me nxt p [] pt; +val (p,_,fa,nxt,_,pt) = me nxt p [] pt; +val (p,_,fa,nxt,_,pt) = me nxt p [] pt; +*} +ML {* +val (p,_,fa,nxt,_,pt) = me nxt p [] pt; +f2str fa; +*} + +subsubsection {*get second koeffizient*} + +ML {* +(*substitude z with the second zeropoint to get B*) +val SOME (eq4b_1,_) = rewrite_terms_ @{theory Isac} e_rew_ord e_rls [s_2] eq3''; +term2str eq4b_1; +*} + +ML {* +val SOME (eq4b_2,_) = rewrite_set_ @{theory Isac} false norm_Rational eq4b_1; +term2str eq4b_2; +*} + +ML {* +(*solve the simple linear equilation for B TODO: return eq, not list of eq*) +val fmz = ["equality (3 = -3 * B / (4::real))", "solveFor B","solutions L"]; +val (dI',pI',mI') =("Isac", ["univariate","equation"], ["no_met"]); +val (p,_,fb,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))]; +val (p,_,fb,nxt,_,pt) = me nxt p [] pt; +val (p,_,fb,nxt,_,pt) = me nxt p [] pt; +val (p,_,fb,nxt,_,pt) = me nxt p [] pt; +val (p,_,fb,nxt,_,pt) = me nxt p [] pt; +val (p,_,fb,nxt,_,pt) = me nxt p [] pt; +val (p,_,fb,nxt,_,pt) = me nxt p [] pt; +val (p,_,fb,nxt,_,pt) = me nxt p [] pt; +val (p,_,fb,nxt,_,pt) = me nxt p [] pt; +val (p,_,fb,nxt,_,pt) = me nxt p [] pt; +val (p,_,fb,nxt,_,pt) = me nxt p [] pt; +val (p,_,fb,nxt,_,pt) = me nxt p [] pt; +val (p,_,fb,nxt,_,pt) = me nxt p [] pt; +val (p,_,fb,nxt,_,pt) = me nxt p [] pt; +val (p,_,fb,nxt,_,pt) = me nxt p [] pt; +val (p,_,fb,nxt,_,pt) = me nxt p [] pt; +val (p,_,fb,nxt,_,pt) = me nxt p [] pt; +val (p,_,fb,nxt,_,pt) = me nxt p [] pt; +val (p,_,fb,nxt,_,pt) = me nxt p [] pt; +val (p,_,fb,nxt,_,pt) = me nxt p [] pt; +val (p,_,fb,nxt,_,pt) = me nxt p [] pt; +val (p,_,fb,nxt,_,pt) = me nxt p [] pt; +val (p,_,fb,nxt,_,pt) = me nxt p [] pt; +val (p,_,fb,nxt,_,pt) = me nxt p [] pt; +val (p,_,fb,nxt,_,pt) = me nxt p [] pt; +val (p,_,fb,nxt,_,pt) = me nxt p [] pt; +val (p,_,fb,nxt,_,pt) = me nxt p [] pt; +val (p,_,fb,nxt,_,pt) = me nxt p [] pt; +f2str fb; +*} + +ML {* (*check koeffizients*) +if f2str fa = "[A = 4]" then () else error "part.fract. eq4_1"; +if f2str fb = "[B = -4]" then () else error "part.fract. eq4_1"; +*} + +subsubsection {*substitute expression with solutions*} +ML {* +*} + +section {*Implement the Specification and the Method*} +text{*==============================================*} +subsection{*Define the Specification*} +ML {* +val thy = @{theory}; +*} +ML {* +store_pbt + (prep_pbt thy "pbl_SP" [] e_pblID + (["SignalProcessing"], [], e_rls, NONE, [])); +store_pbt + (prep_pbt thy "pbl_SP_Ztrans" [] e_pblID + (["Z_Transform","SignalProcessing"], [], e_rls, NONE, [])); +store_pbt + (prep_pbt thy "pbl_SP_Ztrans_inv" [] e_pblID + (["inverse", "Z_Transform", "SignalProcessing"], + [("#Given" ,["equality X_eq"]), + ("#Find" ,["equality n_eq"]) + ], + append_rls "e_rls" e_rls [(*for preds in where_*)], NONE, + [["TODO: path to method"]])); + +show_ptyps(); +get_pbt ["inverse","Z_Transform","SignalProcessing"]; +*} + +subsection{*Define the (Dummy-)Method*} +subsection {*Define Name and Signature for the Method*} +consts + InverseZTransform :: "[bool, bool] => bool" + ("((Script InverseZTransform (_ =))// (_))" 9) + +ML {* +store_met + (prep_met thy "met_SP" [] e_metID + (["SignalProcessing"], [], + {rew_ord'="tless_true", rls'= e_rls, calc = [], srls = e_rls, prls = e_rls, + crls = e_rls, nrls = e_rls}, "empty_script")); +store_met + (prep_met thy "met_SP_Ztrans" [] e_metID + (["SignalProcessing", "Z_Transform"], [], + {rew_ord'="tless_true", rls'= e_rls, calc = [], srls = e_rls, prls = e_rls, + crls = e_rls, nrls = e_rls}, "empty_script")); +*} +ML {* +store_met + (prep_met thy "met_SP_Ztrans_inv" [] e_metID + (["SignalProcessing", "Z_Transform", "inverse"], [], + {rew_ord'="tless_true", rls'= e_rls, calc = [], srls = e_rls, prls = e_rls, + crls = e_rls, nrls = e_rls}, + "empty_script" + )); +*} +ML {*(* +store_met + (prep_met thy "met_SP_Ztrans_inv" [] e_metID + (["SignalProcessing", "Z_Transform", "inverse"], [], + {rew_ord'="tless_true", rls'= e_rls, calc = [], srls = e_rls, prls = e_rls, + crls = e_rls, nrls = e_rls}, + "Script InverseZTransform (Xeq::bool) =" ^ + " (let X = Take Xeq;" ^ + " X = Rewrite ruleZY False X" ^ + " in X)" + )); +*)*} +ML {* +show_mets(); +get_met ["SignalProcessing","Z_Transform","inverse"]; +*} + + +section {*Program in CTP-based language*} +text{*=================================*} +subsection {*Stepwise extend Program*} +ML {* +val str = +"Script InverseZTransform (Xeq::bool) =" ^ +" Xeq"; +*} +ML {* +val str = +"Script InverseZTransform (Xeq::bool) =" ^ +" (let X = Take Xeq;" ^ +" X = Rewrite ruleZY False X" ^ +" in X)"; +*} +ML {* +val thy = @{theory}; +val sc = ((inst_abs thy) o term_of o the o (parse thy)) str; +*} +ML {* +term2str sc; +atomty sc +*} + +subsection {*Stepwise Execute the Program*} + + + + + + + + +section {*Write Tests for Crucial Details*} +text{*===================================*} +ML {* + +*} + +section {*Integrate Program into Knowledge*} +ML {* + +*} + +end + diff -r e41d91e86fa9 -r e633bb41ea42 doc-src/isac/jrocnik/Inverse_Z_Transform/ROOT.ML --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/doc-src/isac/jrocnik/Inverse_Z_Transform/ROOT.ML Thu Sep 08 23:17:35 2011 +0200 @@ -0,0 +1,9 @@ +(* + no_document use_thys ["This_Theory1", "This_Theory2"]; + use_thys ["That_Theory1", "That_Theory2", "That_Theory3"]; +*) + +Thy_Output.source_default := true; +use "antiquote_setup.ML"; + +use_thys ["Inverse_Z_Transform"]; \ No newline at end of file diff -r e41d91e86fa9 -r e633bb41ea42 doc-src/isac/jrocnik/Inverse_Z_Transform/antiquote_setup.ML --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/doc-src/isac/jrocnik/Inverse_Z_Transform/antiquote_setup.ML Thu Sep 08 23:17:35 2011 +0200 @@ -0,0 +1,198 @@ +(* Title: doc-src/antiquote_setup.ML + Author: Makarius + +Auxiliary antiquotations for the Isabelle manuals. +*) + +structure Antiquote_Setup: sig end = +struct + +(* misc utils *) + +fun translate f = Symbol.explode #> map f #> implode; + +val clean_string = translate + (fn "_" => "\\_" + | "#" => "\\#" + | "<" => "$<$" + | ">" => "$>$" + | "{" => "\\{" + | "|" => "$\\mid$" + | "}" => "\\}" + | "\" => "-" + | c => c); + +fun clean_name "\" = "dots" + | clean_name ".." = "ddot" + | clean_name "." = "dot" + | clean_name "_" = "underscore" + | clean_name "{" = "braceleft" + | clean_name "}" = "braceright" + | clean_name s = s |> translate (fn "_" => "-" | "\" => "-" | c => c); + + +(* verbatim text *) + +val verbatim = space_implode "\\verb,|," o map (enclose "\\verb|" "|") o space_explode "|"; + +val _ = Thy_Output.antiquotation "verbatim" (Scan.lift Args.name) + (K (split_lines #> map verbatim #> space_implode "\\isasep\\isanewline%\n")); + + +(* ML text *) + +local + +fun ml_val (txt1, "") = "fn _ => (" ^ txt1 ^ ");" + | ml_val (txt1, txt2) = "fn _ => (" ^ txt1 ^ " : " ^ txt2 ^ ");"; + +fun ml_type (txt1, "") = "val _ = NONE : (" ^ txt1 ^ ") option;" + | ml_type (txt1, txt2) = "val _ = [NONE : (" ^ txt1 ^ ") option, NONE : (" ^ txt2 ^ ") option];"; + +fun ml_exn (txt1, "") = "fn _ => (" ^ txt1 ^ " : exn);" + | ml_exn (txt1, txt2) = "fn _ => (" ^ txt1 ^ " : " ^ txt2 ^ " -> exn);"; + +fun ml_structure (txt, _) = "functor XXX() = struct structure XX = " ^ txt ^ " end;"; + +fun ml_functor (txt, _) = "ML_Env.check_functor " ^ ML_Syntax.print_string txt; + +val is_name = ML_Lex.kind_of #> (fn kind => kind = ML_Lex.Ident orelse kind = ML_Lex.LongIdent); + +fun ml_name txt = + (case filter is_name (ML_Lex.tokenize txt) of + toks as [_] => ML_Lex.flatten toks + | _ => error ("Single ML name expected in input: " ^ quote txt)); + +fun index_ml name kind ml = Thy_Output.antiquotation name + (Scan.lift (Args.name -- Scan.optional (Args.colon |-- Args.name) "")) + (fn {context = ctxt, ...} => fn (txt1, txt2) => + let + val txt = + if txt2 = "" then txt1 + else if kind = "type" then txt1 ^ " = " ^ txt2 + else if kind = "exception" then txt1 ^ " of " ^ txt2 + else if Syntax.is_identifier (Long_Name.base_name (ml_name txt1)) then txt1 ^ ": " ^ txt2 + else txt1 ^ " : " ^ txt2; + val txt' = if kind = "" then txt else kind ^ " " ^ txt; + val _ = ML_Context.eval_text_in (SOME ctxt) false Position.none (ml (txt1, txt2)); (* ML_Lex.read (!?) *) + val kind' = if kind = "" then "ML" else "ML " ^ kind; + in + "\\indexdef{}{" ^ kind' ^ "}{" ^ clean_string (ml_name txt1) ^ "}" ^ + (txt' + |> (if Config.get ctxt Thy_Output.quotes then quote else I) + |> (if Config.get ctxt Thy_Output.display then enclose "\\begin{verbatim}\n" "\n\\end{verbatim}" + else split_lines #> map verbatim #> space_implode "\\isasep\\isanewline%\n")) + end); + +in + +val _ = index_ml "index_ML" "" ml_val; +val _ = index_ml "index_ML_type" "type" ml_type; +val _ = index_ml "index_ML_exn" "exception" ml_exn; +val _ = index_ml "index_ML_structure" "structure" ml_structure; +val _ = index_ml "index_ML_functor" "functor" ml_functor; + +end; + + +(* named theorems *) + +val _ = Thy_Output.antiquotation "named_thms" + (Scan.repeat (Attrib.thm -- Scan.lift (Args.parens Args.name))) + (fn {context = ctxt, ...} => + map (apfst (Thy_Output.pretty_thm ctxt)) + #> (if Config.get ctxt Thy_Output.quotes then map (apfst Pretty.quote) else I) + #> (if Config.get ctxt Thy_Output.display + then + map (fn (p, name) => + Output.output (Pretty.string_of (Pretty.indent (Config.get ctxt Thy_Output.indent) p)) ^ + "\\rulename{" ^ Output.output (Pretty.str_of (Thy_Output.pretty_text ctxt name)) ^ "}") + #> space_implode "\\par\\smallskip%\n" + #> enclose "\\begin{isabelle}%\n" "%\n\\end{isabelle}" + else + map (fn (p, name) => + Output.output (Pretty.str_of p) ^ + "\\rulename{" ^ Output.output (Pretty.str_of (Thy_Output.pretty_text ctxt name)) ^ "}") + #> space_implode "\\par\\smallskip%\n" + #> enclose "\\isa{" "}")); + + +(* theory file *) + +val _ = Thy_Output.antiquotation "thy_file" (Scan.lift Args.name) + (fn {context = ctxt, ...} => + fn name => (Thy_Load.check_thy Path.current name; Thy_Output.output ctxt [Pretty.str name])); + + +(* Isabelle/Isar entities (with index) *) + +local + +fun no_check _ _ = true; + +fun thy_check intern defined ctxt = + let val thy = ProofContext.theory_of ctxt + in defined thy o intern thy end; + +fun check_tool name = + File.exists (Path.append (Path.explode "~~/lib/Tools") (Path.basic name)); + +val arg = enclose "{" "}" o clean_string; + +fun entity check markup kind index = + Thy_Output.antiquotation + (translate (fn " " => "_" | c => c) kind ^ + (case index of NONE => "" | SOME true => "_def" | SOME false => "_ref")) + (Scan.lift (Scan.optional (Args.parens Args.name) "" -- Args.name)) + (fn {context = ctxt, ...} => fn (logic, name) => + let + val hyper_name = + "{" ^ Long_Name.append kind (Long_Name.append logic (clean_name name)) ^ "}"; + val hyper = + enclose ("\\hyperlink" ^ hyper_name ^ "{") "}" #> + index = SOME true ? enclose ("\\hypertarget" ^ hyper_name ^ "{") "}"; + val idx = + (case index of + NONE => "" + | SOME is_def => + "\\index" ^ (if is_def then "def" else "ref") ^ arg logic ^ arg kind ^ arg name); + in + if check ctxt name then + idx ^ + (Output.output name + |> (if markup = "" then I else enclose ("\\" ^ markup ^ "{") "}") + |> (if Config.get ctxt Thy_Output.quotes then quote else I) + |> (if Config.get ctxt Thy_Output.display + then enclose "\\begin{isabelle}%\n" "%\n\\end{isabelle}" + else hyper o enclose "\\mbox{\\isa{" "}}")) + else error ("Bad " ^ kind ^ " " ^ quote name) + end); + +fun entity_antiqs check markup kind = + ((entity check markup kind NONE); + (entity check markup kind (SOME true)); + (entity check markup kind (SOME false))); + +in + +val _ = entity_antiqs no_check "" "syntax"; +val _ = entity_antiqs (K (is_some o Keyword.command_keyword)) "isacommand" "command"; +val _ = entity_antiqs (K Keyword.is_keyword) "isakeyword" "keyword"; +val _ = entity_antiqs (K Keyword.is_keyword) "isakeyword" "element"; +val _ = entity_antiqs (thy_check Method.intern Method.defined) "" "method"; +val _ = entity_antiqs (thy_check Attrib.intern Attrib.defined) "" "attribute"; +val _ = entity_antiqs no_check "" "fact"; +val _ = entity_antiqs no_check "" "variable"; +val _ = entity_antiqs no_check "" "case"; +val _ = entity_antiqs (K Thy_Output.defined_command) "" "antiquotation"; +val _ = entity_antiqs (K Thy_Output.defined_option) "" "antiquotation option"; +val _ = entity_antiqs (fn _ => fn name => is_some (OS.Process.getEnv name)) "isatt" "setting"; +val _ = entity_antiqs no_check "" "inference"; +val _ = entity_antiqs no_check "isatt" "executable"; +val _ = entity_antiqs (K check_tool) "isatt" "tool"; +val _ = entity_antiqs (K (can Thy_Info.get_theory)) "" "theory"; +val _ = entity_antiqs no_check "" "ML antiquotation"; (* FIXME proper check *) + +end; + +end; diff -r e41d91e86fa9 -r e633bb41ea42 doc-src/isac/jrocnik/Inverse_Z_Transform/document/Inverse_Z_Transform.tex --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/doc-src/isac/jrocnik/Inverse_Z_Transform/document/Inverse_Z_Transform.tex Thu Sep 08 23:17:35 2011 +0200 @@ -0,0 +1,988 @@ +% +\begin{isabellebody}% +\def\isabellecontext{Inverse{\isaliteral{5F}{\isacharunderscore}}Z{\isaliteral{5F}{\isacharunderscore}}Transform}% +% +\isadelimtheory +\isanewline +\isanewline +% +\endisadelimtheory +% +\isatagtheory +\isacommand{theory}\isamarkupfalse% +\ Inverse{\isaliteral{5F}{\isacharunderscore}}Z{\isaliteral{5F}{\isacharunderscore}}Transform\ \isakeyword{imports}\ Isac\ \isakeyword{begin}% +\endisatagtheory +{\isafoldtheory}% +% +\isadelimtheory +% +\endisadelimtheory +% +\isamarkupsection{trials towards Z transform% +} +\isamarkuptrue% +% +\begin{isamarkuptext}% +===============================% +\end{isamarkuptext}% +\isamarkuptrue% +% +\isamarkupsubsection{terms% +} +\isamarkuptrue% +% +\isadelimML +% +\endisadelimML +% +\isatagML +\isacommand{ML}\isamarkupfalse% +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline +% +\isaantiq +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}}{}% +\endisaantiq +{\isaliteral{3B}{\isacharsemicolon}}\isanewline +% +\isaantiq +term\ {\isaliteral{22}{\isachardoublequote}}z\ {\isaliteral{2F}{\isacharslash}}\ {\isaliteral{28}{\isacharparenleft}}z\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{1}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}{}% +\endisaantiq +{\isaliteral{3B}{\isacharsemicolon}}\isanewline +% +\isaantiq +term\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{2D}{\isacharminus}}u\ {\isaliteral{2D}{\isacharminus}}n\ {\isaliteral{2D}{\isacharminus}}\ {\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}{}% +\endisaantiq +{\isaliteral{3B}{\isacharsemicolon}}\isanewline +% +\isaantiq +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}}{}% +\endisaantiq +{\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 +% +\isaantiq +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}}{}% +\endisaantiq +{\isaliteral{3B}{\isacharsemicolon}}Isac\isanewline +% +\isaantiq +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}}{}% +\endisaantiq +{\isaliteral{3B}{\isacharsemicolon}}\isanewline +term{\isadigit{2}}str\ % +\isaantiq +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}}{}% +\endisaantiq +{\isaliteral{3B}{\isacharsemicolon}}\isanewline +{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline +\isacommand{ML}\isamarkupfalse% +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline +{\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 +\isanewline +% +\isaantiq +term\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C616C7068613E}{\isasymalpha}}\ {\isaliteral{22}{\isachardoublequote}}{}% +\endisaantiq +{\isaliteral{3B}{\isacharsemicolon}}\isanewline +% +\isaantiq +term\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C64656C74613E}{\isasymdelta}}\ {\isaliteral{22}{\isachardoublequote}}{}% +\endisaantiq +{\isaliteral{3B}{\isacharsemicolon}}\isanewline +% +\isaantiq +term\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C7068693E}{\isasymphi}}\ {\isaliteral{22}{\isachardoublequote}}{}% +\endisaantiq +{\isaliteral{3B}{\isacharsemicolon}}\isanewline +% +\isaantiq +term\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C72686F3E}{\isasymrho}}\ {\isaliteral{22}{\isachardoublequote}}{}% +\endisaantiq +{\isaliteral{3B}{\isacharsemicolon}}\isanewline +term{\isadigit{2}}str\ % +\isaantiq +term\ {\isaliteral{22}{\isachardoublequote}}{\isaliteral{5C3C72686F3E}{\isasymrho}}\ {\isaliteral{22}{\isachardoublequote}}{}% +\endisaantiq +{\isaliteral{3B}{\isacharsemicolon}}\isanewline +{\isaliteral{2A7D}{\isacharverbatimclose}}% +\endisatagML +{\isafoldML}% +% +\isadelimML +% +\endisadelimML +% +\isamarkupsubsection{rules% +} +\isamarkuptrue% +\isacommand{axiomatization}\isamarkupfalse% +\ \isakeyword{where}\ \isanewline +\ \ 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 +\ \ 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 +\ \ 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 +\ \ 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 +\ \ 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 +\ \ 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 +% +\isadelimML +% +\endisadelimML +% +\isatagML +\isacommand{ML}\isamarkupfalse% +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline +% +\isaantiq +thm\ rule{\isadigit{1}}{}% +\endisaantiq +{\isaliteral{3B}{\isacharsemicolon}}\isanewline +% +\isaantiq +thm\ rule{\isadigit{2}}{}% +\endisaantiq +{\isaliteral{3B}{\isacharsemicolon}}\isanewline +% +\isaantiq +thm\ rule{\isadigit{3}}{}% +\endisaantiq +{\isaliteral{3B}{\isacharsemicolon}}\isanewline +% +\isaantiq +thm\ rule{\isadigit{4}}{}% +\endisaantiq +{\isaliteral{3B}{\isacharsemicolon}}\isanewline +{\isaliteral{2A7D}{\isacharverbatimclose}}% +\endisatagML +{\isafoldML}% +% +\isadelimML +% +\endisadelimML +% +\isamarkupsubsection{apply rules% +} +\isamarkuptrue% +% +\isadelimML +% +\endisadelimML +% +\isatagML +\isacommand{ML}\isamarkupfalse% +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline +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 +\ \ {\isaliteral{5B}{\isacharbrackleft}}\ Thm\ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}rule{\isadigit{3}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}num{\isaliteral{5F}{\isacharunderscore}}str\ % +\isaantiq +thm\ rule{\isadigit{3}}{}% +\endisaantiq +{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\isanewline +\ \ \ \ Thm\ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}rule{\isadigit{4}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}num{\isaliteral{5F}{\isacharunderscore}}str\ % +\isaantiq +thm\ rule{\isadigit{4}}{}% +\endisaantiq +{\isaliteral{29}{\isacharparenright}}{\isaliteral{2C}{\isacharcomma}}\isanewline +\ \ \ \ Thm\ \ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{22}{\isachardoublequote}}rule{\isadigit{1}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{2C}{\isacharcomma}}num{\isaliteral{5F}{\isacharunderscore}}str\ % +\isaantiq +thm\ rule{\isadigit{1}}{}% +\endisaantiq +{\isaliteral{29}{\isacharparenright}}\ \ \ \isanewline +\ \ {\isaliteral{5D}{\isacharbrackright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline +\isanewline +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 +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 +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 +{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline +\isacommand{ML}\isamarkupfalse% +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline +val\ {\isaliteral{28}{\isacharparenleft}}thy{\isaliteral{2C}{\isacharcomma}}\ ro{\isaliteral{2C}{\isacharcomma}}\ er{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}% +\isaantiq +theory{}% +\endisaantiq +{\isaliteral{2C}{\isacharcomma}}\ tless{\isaliteral{5F}{\isacharunderscore}}true{\isaliteral{2C}{\isacharcomma}}\ eval{\isaliteral{5F}{\isacharunderscore}}rls{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline +{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline +\isacommand{ML}\isamarkupfalse% +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline +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\ % +\isaantiq +thm\ rule{\isadigit{3}}{}% +\endisaantiq +{\isaliteral{29}{\isacharparenright}}\ t{\isaliteral{3B}{\isacharsemicolon}}\isanewline +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 +term{\isadigit{2}}str\ t{\isaliteral{3B}{\isacharsemicolon}}\isanewline +{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline +\isacommand{ML}\isamarkupfalse% +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline +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\ % +\isaantiq +thm\ rule{\isadigit{4}}{}% +\endisaantiq +{\isaliteral{29}{\isacharparenright}}\ t{\isaliteral{3B}{\isacharsemicolon}}\isanewline +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 +term{\isadigit{2}}str\ t{\isaliteral{3B}{\isacharsemicolon}}\isanewline +{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline +\isacommand{ML}\isamarkupfalse% +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline +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\ % +\isaantiq +thm\ rule{\isadigit{1}}{}% +\endisaantiq +{\isaliteral{29}{\isacharparenright}}\ t{\isaliteral{3B}{\isacharsemicolon}}\isanewline +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 +term{\isadigit{2}}str\ t{\isaliteral{3B}{\isacharsemicolon}}\isanewline +{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline +\isacommand{ML}\isamarkupfalse% +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline +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 +{\isaliteral{2A7D}{\isacharverbatimclose}}% +\endisatagML +{\isafoldML}% +% +\isadelimML +% +\endisadelimML +% +\isamarkupsection{Prepare steps in CTP-based programming language% +} +\isamarkuptrue% +% +\begin{isamarkuptext}% +===================================================% +\end{isamarkuptext}% +\isamarkuptrue% +% +\isamarkupsubsection{prepare expression% +} +\isamarkuptrue% +% +\isadelimML +% +\endisadelimML +% +\isatagML +\isacommand{ML}\isamarkupfalse% +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline +val\ ctxt\ {\isaliteral{3D}{\isacharequal}}\ ProofContext{\isaliteral{2E}{\isachardot}}init{\isaliteral{5F}{\isacharunderscore}}global\ % +\isaantiq +theory{}% +\endisaantiq +{\isaliteral{3B}{\isacharsemicolon}}\isanewline +val\ ctxt\ {\isaliteral{3D}{\isacharequal}}\ declare{\isaliteral{5F}{\isacharunderscore}}constraints{\isaliteral{27}{\isacharprime}}\ {\isaliteral{5B}{\isacharbrackleft}}% +\isaantiq +term\ {\isaliteral{22}{\isachardoublequote}}z{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}real{\isaliteral{22}{\isachardoublequote}}{}% +\endisaantiq +{\isaliteral{5D}{\isacharbrackright}}\ ctxt{\isaliteral{3B}{\isacharsemicolon}}\isanewline +\isanewline +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 +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 +{\isaliteral{2A7D}{\isacharverbatimclose}}% +\endisatagML +{\isafoldML}% +% +\isadelimML +% +\endisadelimML +\isanewline +\isanewline +\isacommand{axiomatization}\isamarkupfalse% +\ \isakeyword{where}\isanewline +\ \ 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 +% +\isadelimML +\isanewline +% +\endisadelimML +% +\isatagML +\isacommand{ML}\isamarkupfalse% +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline +val\ {\isaliteral{28}{\isacharparenleft}}thy{\isaliteral{2C}{\isacharcomma}}\ ro{\isaliteral{2C}{\isacharcomma}}\ er{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}% +\isaantiq +theory{}% +\endisaantiq +{\isaliteral{2C}{\isacharcomma}}\ tless{\isaliteral{5F}{\isacharunderscore}}true{\isaliteral{2C}{\isacharcomma}}\ eval{\isaliteral{5F}{\isacharunderscore}}rls{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline +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\ \ % +\isaantiq +thm\ ruleZY{}% +\endisaantiq +\ fun{\isadigit{1}}{\isaliteral{3B}{\isacharsemicolon}}\ term{\isadigit{2}}str\ fun{\isadigit{2}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline +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\ \ % +\isaantiq +thm\ ruleZY{}% +\endisaantiq +\ fun{\isadigit{1}}{\isaliteral{27}{\isacharprime}}{\isaliteral{3B}{\isacharsemicolon}}\ term{\isadigit{2}}str\ fun{\isadigit{2}}{\isaliteral{27}{\isacharprime}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline +\isanewline +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}}\ % +\isaantiq +theory\ Isac{}% +\endisaantiq +\ false\ norm{\isaliteral{5F}{\isacharunderscore}}Rational\ fun{\isadigit{2}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline +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 +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}}\ % +\isaantiq +theory\ Isac{}% +\endisaantiq +\ false\ norm{\isaliteral{5F}{\isacharunderscore}}Rational\ fun{\isadigit{2}}{\isaliteral{27}{\isacharprime}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline +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 +\isanewline +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 +{\isaliteral{2A7D}{\isacharverbatimclose}}% +\endisatagML +{\isafoldML}% +% +\isadelimML +% +\endisadelimML +% +\isamarkupsubsection{solve equation% +} +\isamarkuptrue% +% +\isadelimML +% +\endisadelimML +% +\isatagML +\isacommand{ML}\isamarkupfalse% +\ {\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 +{\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 +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 +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 +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 +{\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 +{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline +\isacommand{ML}\isamarkupfalse% +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline +val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\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 +val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline +{\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{5B}{\isacharbrackleft}}\isanewline +{\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 +{\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 +{\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 +{\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 +{\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 +{\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 +{\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 +{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline +{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline +\isacommand{ML}\isamarkupfalse% +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline +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 +{\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 +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 +{\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 +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 +\ \ {\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 +{\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}schritte\ abarbeiten{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline +val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\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 +val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline +val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline +val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}pt{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ me\ nxt\ p\ {\isaliteral{5B}{\isacharbrackleft}}{\isaliteral{5D}{\isacharbrackright}}\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline +val\ {\isaliteral{28}{\isacharparenleft}}p{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{2C}{\isacharcomma}}f{\isaliteral{2C}{\isacharcomma}}nxt{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\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 +show{\isaliteral{5F}{\isacharunderscore}}pt\ pt{\isaliteral{3B}{\isacharsemicolon}}\isanewline +{\isaliteral{2A7D}{\isacharverbatimclose}}% +\endisatagML +{\isafoldML}% +% +\isadelimML +% +\endisadelimML +% +\isamarkupsubsection{partial fraction decomposition% +} +\isamarkuptrue% +% +\isamarkupsubsubsection{solution of the equation% +} +\isamarkuptrue% +% +\isadelimML +% +\endisadelimML +% +\isatagML +\isacommand{ML}\isamarkupfalse% +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline +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 +term{\isadigit{2}}str\ solutions{\isaliteral{3B}{\isacharsemicolon}}\isanewline +atomty\ solutions{\isaliteral{3B}{\isacharsemicolon}}\isanewline +{\isaliteral{2A7D}{\isacharverbatimclose}}% +\endisatagML +{\isafoldML}% +% +\isadelimML +% +\endisadelimML +% +\isamarkupsubsubsection{get solutions out of list% +} +\isamarkuptrue% +% +\begin{isamarkuptext}% +in isac's CTP-based programming language: $let s_1 = NTH 1 solutions; s_2 = NTH 2...$% +\end{isamarkuptext}% +\isamarkuptrue% +% +\isadelimML +% +\endisadelimML +% +\isatagML +\isacommand{ML}\isamarkupfalse% +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline +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 +\ \ \ \ \ \ 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 +term{\isadigit{2}}str\ s{\isaliteral{5F}{\isacharunderscore}}{\isadigit{1}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline +term{\isadigit{2}}str\ s{\isaliteral{5F}{\isacharunderscore}}{\isadigit{2}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline +{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline +\isanewline +\isacommand{ML}\isamarkupfalse% +\ {\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 +val\ xx\ {\isaliteral{3D}{\isacharequal}}\ HOLogic{\isaliteral{2E}{\isachardot}}dest{\isaliteral{5F}{\isacharunderscore}}eq\ s{\isaliteral{5F}{\isacharunderscore}}{\isadigit{1}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline +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 +val\ xx\ {\isaliteral{3D}{\isacharequal}}\ HOLogic{\isaliteral{2E}{\isachardot}}dest{\isaliteral{5F}{\isacharunderscore}}eq\ s{\isaliteral{5F}{\isacharunderscore}}{\isadigit{2}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline +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 +term{\isadigit{2}}str\ s{\isaliteral{5F}{\isacharunderscore}}{\isadigit{1}}{\isaliteral{27}{\isacharprime}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline +term{\isadigit{2}}str\ s{\isaliteral{5F}{\isacharunderscore}}{\isadigit{2}}{\isaliteral{27}{\isacharprime}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline +{\isaliteral{2A7D}{\isacharverbatimclose}}% +\endisatagML +{\isafoldML}% +% +\isadelimML +% +\endisadelimML +% +\isamarkupsubsubsection{build expression% +} +\isamarkuptrue% +% +\begin{isamarkuptext}% +in isac's CTP-based programming language: $let s_1 = Take numerator / (s_1 * s_2)$% +\end{isamarkuptext}% +\isamarkuptrue% +% +\isadelimML +% +\endisadelimML +% +\isatagML +\isacommand{ML}\isamarkupfalse% +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline +{\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}The\ Main\ Denominator\ is\ the\ multiplikation\ of\ the\ partial\ fraction\ denominators{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline +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 +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 +\isanewline +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 +term{\isadigit{2}}str\ expr{\isaliteral{27}{\isacharprime}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline +{\isaliteral{2A7D}{\isacharverbatimclose}}% +\endisatagML +{\isafoldML}% +% +\isadelimML +% +\endisadelimML +% +\isamarkupsubsubsection{Ansatz - create partial fractions out of our expression% +} +\isamarkuptrue% +\isacommand{axiomatization}\isamarkupfalse% +\ \isakeyword{where}\isanewline +\ \ 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 +\ \ 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 +% +\isadelimML +\isanewline +% +\endisadelimML +% +\isatagML +\isacommand{ML}\isamarkupfalse% +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline +{\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 +val\ SOME\ {\isaliteral{28}{\isacharparenleft}}t{\isadigit{1}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ rewrite{\isaliteral{5F}{\isacharunderscore}}\ % +\isaantiq +theory\ Isac{}% +\endisaantiq +\ e{\isaliteral{5F}{\isacharunderscore}}rew{\isaliteral{5F}{\isacharunderscore}}ord\ e{\isaliteral{5F}{\isacharunderscore}}rls\ false\ % +\isaantiq +thm\ ansatz{\isadigit{2}}{}% +\endisaantiq +\ expr{\isaliteral{27}{\isacharprime}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline +term{\isadigit{2}}str\ t{\isadigit{1}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline +atomty\ t{\isadigit{1}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline +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 +term{\isadigit{2}}str\ eq{\isadigit{1}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline +{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline +\isacommand{ML}\isamarkupfalse% +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline +{\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 +val\ SOME\ {\isaliteral{28}{\isacharparenleft}}eq{\isadigit{2}}{\isaliteral{2C}{\isacharcomma}}{\isaliteral{5F}{\isacharunderscore}}{\isaliteral{29}{\isacharparenright}}\ {\isaliteral{3D}{\isacharequal}}\ rewrite{\isaliteral{5F}{\isacharunderscore}}\ % +\isaantiq +theory\ Isac{}% +\endisaantiq +\ e{\isaliteral{5F}{\isacharunderscore}}rew{\isaliteral{5F}{\isacharunderscore}}ord\ e{\isaliteral{5F}{\isacharunderscore}}rls\ false\ % +\isaantiq +thm\ multiply{\isaliteral{5F}{\isacharunderscore}}eq{\isadigit{2}}{}% +\endisaantiq +\ eq{\isadigit{1}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline +term{\isadigit{2}}str\ eq{\isadigit{2}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline +{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline +\isacommand{ML}\isamarkupfalse% +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline +{\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}simplificatoin{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline +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}}\ % +\isaantiq +theory\ Isac{}% +\endisaantiq +\ false\ norm{\isaliteral{5F}{\isacharunderscore}}Rational\ eq{\isadigit{2}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline +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 +{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline +\isacommand{ML}\isamarkupfalse% +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline +val\ SOME\ fract{\isadigit{1}}\ {\isaliteral{3D}{\isacharequal}}\isanewline +\ \ 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 +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}}\ % +\isaantiq +theory\ Isac{}% +\endisaantiq +\ false\ norm{\isaliteral{5F}{\isacharunderscore}}Rational\ fract{\isadigit{1}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline +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 +{\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 +{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline +\isacommand{ML}\isamarkupfalse% +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline +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 +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 +term{\isadigit{2}}str\ eq{\isadigit{3}}{\isaliteral{27}{\isacharprime}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline +{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline +\isacommand{ML}\isamarkupfalse% +\ {\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 +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}}\ % +\isaantiq +theory\ Isac{}% +\endisaantiq +\ false\ norm{\isaliteral{5F}{\isacharunderscore}}Rational\ eq{\isadigit{3}}{\isaliteral{27}{\isacharprime}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline +term{\isadigit{2}}str\ eq{\isadigit{3}}{\isaliteral{27}{\isacharprime}}{\isaliteral{27}{\isacharprime}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline +{\isaliteral{2A7D}{\isacharverbatimclose}}% +\endisatagML +{\isafoldML}% +% +\isadelimML +% +\endisadelimML +% +\isamarkupsubsubsection{get first koeffizient% +} +\isamarkuptrue% +% +\isadelimML +% +\endisadelimML +% +\isatagML +\isacommand{ML}\isamarkupfalse% +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline +{\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}substitude\ z\ with\ the\ first\ zeropoint\ to\ get\ A{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline +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}}\ % +\isaantiq +theory\ Isac{}% +\endisaantiq +\ 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 +term{\isadigit{2}}str\ eq{\isadigit{4}}{\isaliteral{5F}{\isacharunderscore}}{\isadigit{1}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline +{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline +\isacommand{ML}\isamarkupfalse% +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline +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}}\ % +\isaantiq +theory\ Isac{}% +\endisaantiq +\ false\ norm{\isaliteral{5F}{\isacharunderscore}}Rational\ eq{\isadigit{4}}{\isaliteral{5F}{\isacharunderscore}}{\isadigit{1}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline +term{\isadigit{2}}str\ eq{\isadigit{4}}{\isaliteral{5F}{\isacharunderscore}}{\isadigit{2}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline +{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline +\isacommand{ML}\isamarkupfalse% +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline +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 +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 +\isanewline +{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline +\isacommand{ML}\isamarkupfalse% +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline +{\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 +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 +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 +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 +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 +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 +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 +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 +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 +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 +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 +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 +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 +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 +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 +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 +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 +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 +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 +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 +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 +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 +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 +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 +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 +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 +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 +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 +{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline +\isacommand{ML}\isamarkupfalse% +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline +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 +f{\isadigit{2}}str\ fa{\isaliteral{3B}{\isacharsemicolon}}\isanewline +{\isaliteral{2A7D}{\isacharverbatimclose}}% +\endisatagML +{\isafoldML}% +% +\isadelimML +% +\endisadelimML +% +\isamarkupsubsubsection{get second koeffizient% +} +\isamarkuptrue% +% +\isadelimML +% +\endisadelimML +% +\isatagML +\isacommand{ML}\isamarkupfalse% +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline +{\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}substitude\ z\ with\ the\ second\ zeropoint\ to\ get\ B{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline +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}}\ % +\isaantiq +theory\ Isac{}% +\endisaantiq +\ 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 +term{\isadigit{2}}str\ eq{\isadigit{4}}b{\isaliteral{5F}{\isacharunderscore}}{\isadigit{1}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline +{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline +\isanewline +\isacommand{ML}\isamarkupfalse% +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline +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}}\ % +\isaantiq +theory\ Isac{}% +\endisaantiq +\ false\ norm{\isaliteral{5F}{\isacharunderscore}}Rational\ eq{\isadigit{4}}b{\isaliteral{5F}{\isacharunderscore}}{\isadigit{1}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline +term{\isadigit{2}}str\ eq{\isadigit{4}}b{\isaliteral{5F}{\isacharunderscore}}{\isadigit{2}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline +{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline +\isanewline +\isacommand{ML}\isamarkupfalse% +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline +{\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 +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 +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 +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 +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 +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 +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 +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 +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 +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 +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 +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 +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 +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 +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 +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 +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 +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 +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 +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 +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 +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 +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 +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 +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 +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 +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 +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 +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 +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 +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 +f{\isadigit{2}}str\ fb{\isaliteral{3B}{\isacharsemicolon}}\isanewline +{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline +\isanewline +\isacommand{ML}\isamarkupfalse% +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\ {\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}check\ koeffizients{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}\isanewline +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 +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 +{\isaliteral{2A7D}{\isacharverbatimclose}}% +\endisatagML +{\isafoldML}% +% +\isadelimML +% +\endisadelimML +% +\isamarkupsubsubsection{substitute expression with solutions% +} +\isamarkuptrue% +% +\isadelimML +% +\endisadelimML +% +\isatagML +\isacommand{ML}\isamarkupfalse% +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline +{\isaliteral{2A7D}{\isacharverbatimclose}}% +\endisatagML +{\isafoldML}% +% +\isadelimML +% +\endisadelimML +% +\isamarkupsection{Implement the Specification and the Method% +} +\isamarkuptrue% +% +\begin{isamarkuptext}% +==============================================% +\end{isamarkuptext}% +\isamarkuptrue% +% +\isamarkupsubsection{Define the Specification% +} +\isamarkuptrue% +% +\isadelimML +% +\endisadelimML +% +\isatagML +\isacommand{ML}\isamarkupfalse% +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline +val\ thy\ {\isaliteral{3D}{\isacharequal}}\ % +\isaantiq +theory{}% +\endisaantiq +{\isaliteral{3B}{\isacharsemicolon}}\isanewline +{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline +\isacommand{ML}\isamarkupfalse% +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline +store{\isaliteral{5F}{\isacharunderscore}}pbt\isanewline +\ {\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 +\ {\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 +store{\isaliteral{5F}{\isacharunderscore}}pbt\isanewline +\ {\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 +\ {\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 +store{\isaliteral{5F}{\isacharunderscore}}pbt\isanewline +\ {\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 +\ {\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 +\ \ {\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 +\ \ \ {\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 +\ \ {\isaliteral{5D}{\isacharbrackright}}{\isaliteral{2C}{\isacharcomma}}\isanewline +\ \ 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 +\ \ {\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 +\isanewline +show{\isaliteral{5F}{\isacharunderscore}}ptyps{\isaliteral{28}{\isacharparenleft}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline +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 +{\isaliteral{2A7D}{\isacharverbatimclose}}% +\endisatagML +{\isafoldML}% +% +\isadelimML +% +\endisadelimML +% +\isamarkupsubsection{Define the (Dummy-)Method% +} +\isamarkuptrue% +% +\isamarkupsubsection{Define Name and Signature for the Method% +} +\isamarkuptrue% +\isacommand{consts}\isamarkupfalse% +\isanewline +\ \ 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 +\ \ \ \ {\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 +% +\isadelimML +\isanewline +% +\endisadelimML +% +\isatagML +\isacommand{ML}\isamarkupfalse% +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline +store{\isaliteral{5F}{\isacharunderscore}}met\isanewline +\ {\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 +\ {\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 +\ \ \ {\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 +\ \ \ \ 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 +store{\isaliteral{5F}{\isacharunderscore}}met\isanewline +\ {\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 +\ {\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 +\ \ \ {\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 +\ \ \ \ 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 +{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline +\isacommand{ML}\isamarkupfalse% +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline +store{\isaliteral{5F}{\isacharunderscore}}met\isanewline +\ {\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 +\ {\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 +\ \ \ {\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 +\ \ \ \ 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 +\ \ {\isaliteral{22}{\isachardoublequote}}empty{\isaliteral{5F}{\isacharunderscore}}script{\isaliteral{22}{\isachardoublequote}}\isanewline +\ {\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline +{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline +\isacommand{ML}\isamarkupfalse% +\ {\isaliteral{7B2A}{\isacharverbatimopen}}{\isaliteral{28}{\isacharparenleft}}{\isaliteral{2A}{\isacharasterisk}}\isanewline +store{\isaliteral{5F}{\isacharunderscore}}met\isanewline +\ {\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 +\ {\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 +\ \ \ {\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 +\ \ \ \ 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 +\ \ {\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 +\ \ {\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{28}{\isacharparenleft}}let\ X\ {\isaliteral{3D}{\isacharequal}}\ Take\ Xeq{\isaliteral{3B}{\isacharsemicolon}}{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5E}{\isacharcircum}}\isanewline +\ \ {\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ X\ {\isaliteral{3D}{\isacharequal}}\ Rewrite\ ruleZY\ False\ X{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5E}{\isacharcircum}}\isanewline +\ \ {\isaliteral{22}{\isachardoublequote}}\ \ in\ X{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}\isanewline +\ {\isaliteral{29}{\isacharparenright}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline +{\isaliteral{2A}{\isacharasterisk}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline +\isacommand{ML}\isamarkupfalse% +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline +show{\isaliteral{5F}{\isacharunderscore}}mets{\isaliteral{28}{\isacharparenleft}}{\isaliteral{29}{\isacharparenright}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline +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 +{\isaliteral{2A7D}{\isacharverbatimclose}}% +\endisatagML +{\isafoldML}% +% +\isadelimML +% +\endisadelimML +% +\isamarkupsection{Program in CTP-based language% +} +\isamarkuptrue% +% +\begin{isamarkuptext}% +=================================% +\end{isamarkuptext}% +\isamarkuptrue% +% +\isamarkupsubsection{Stepwise extend Program% +} +\isamarkuptrue% +% +\isadelimML +% +\endisadelimML +% +\isatagML +\isacommand{ML}\isamarkupfalse% +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline +val\ str\ {\isaliteral{3D}{\isacharequal}}\ \isanewline +{\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 +{\isaliteral{22}{\isachardoublequote}}\ Xeq{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline +{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline +\isacommand{ML}\isamarkupfalse% +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline +val\ str\ {\isaliteral{3D}{\isacharequal}}\ \isanewline +{\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 +{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{28}{\isacharparenleft}}let\ X\ {\isaliteral{3D}{\isacharequal}}\ Take\ Xeq{\isaliteral{3B}{\isacharsemicolon}}{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5E}{\isacharcircum}}\isanewline +{\isaliteral{22}{\isachardoublequote}}\ \ \ \ \ \ X\ {\isaliteral{3D}{\isacharequal}}\ Rewrite\ ruleZY\ False\ X{\isaliteral{22}{\isachardoublequote}}\ {\isaliteral{5E}{\isacharcircum}}\isanewline +{\isaliteral{22}{\isachardoublequote}}\ \ in\ X{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequote}}{\isaliteral{3B}{\isacharsemicolon}}\isanewline +{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline +\isacommand{ML}\isamarkupfalse% +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline +val\ thy\ {\isaliteral{3D}{\isacharequal}}\ % +\isaantiq +theory{}% +\endisaantiq +{\isaliteral{3B}{\isacharsemicolon}}\isanewline +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 +{\isaliteral{2A7D}{\isacharverbatimclose}}\isanewline +\isacommand{ML}\isamarkupfalse% +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline +term{\isadigit{2}}str\ sc{\isaliteral{3B}{\isacharsemicolon}}\isanewline +atomty\ sc\isanewline +{\isaliteral{2A7D}{\isacharverbatimclose}}% +\endisatagML +{\isafoldML}% +% +\isadelimML +% +\endisadelimML +% +\isamarkupsubsection{Stepwise Execute the Program% +} +\isamarkuptrue% +% +\isamarkupsection{Write Tests for Crucial Details% +} +\isamarkuptrue% +% +\begin{isamarkuptext}% +===================================% +\end{isamarkuptext}% +\isamarkuptrue% +% +\isadelimML +% +\endisadelimML +% +\isatagML +\isacommand{ML}\isamarkupfalse% +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline +\isanewline +{\isaliteral{2A7D}{\isacharverbatimclose}}% +\endisatagML +{\isafoldML}% +% +\isadelimML +% +\endisadelimML +% +\isamarkupsection{Integrate Program into Knowledge% +} +\isamarkuptrue% +% +\isadelimML +% +\endisadelimML +% +\isatagML +\isacommand{ML}\isamarkupfalse% +\ {\isaliteral{7B2A}{\isacharverbatimopen}}\isanewline +\isanewline +{\isaliteral{2A7D}{\isacharverbatimclose}}% +\endisatagML +{\isafoldML}% +% +\isadelimML +% +\endisadelimML +\isanewline +% +\isadelimtheory +\isanewline +% +\endisadelimtheory +% +\isatagtheory +\isacommand{end}\isamarkupfalse% +% +\endisatagtheory +{\isafoldtheory}% +% +\isadelimtheory +% +\endisadelimtheory +\isanewline +\isanewline +\end{isabellebody}% +%%% Local Variables: +%%% mode: latex +%%% TeX-master: "root" +%%% End: diff -r e41d91e86fa9 -r e633bb41ea42 doc-src/isac/jrocnik/Inverse_Z_Transform/document/isabelle.sty --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/doc-src/isac/jrocnik/Inverse_Z_Transform/document/isabelle.sty Thu Sep 08 23:17:35 2011 +0200 @@ -0,0 +1,218 @@ +%% +%% macros for Isabelle generated LaTeX output +%% + +%%% Simple document preparation (based on theory token language and symbols) + +% isabelle environments + +\newcommand{\isabellecontext}{UNKNOWN} + +\newcommand{\isastyle}{\UNDEF} +\newcommand{\isastyleminor}{\UNDEF} +\newcommand{\isastylescript}{\UNDEF} +\newcommand{\isastyletext}{\normalsize\rm} +\newcommand{\isastyletxt}{\rm} +\newcommand{\isastylecmt}{\rm} + +%symbol markup -- \emph achieves decent spacing via italic corrections +\newcommand{\isamath}[1]{\emph{$#1$}} +\newcommand{\isatext}[1]{\emph{#1}} +\DeclareRobustCommand{\isascriptstyle}{\def\isamath##1{##1}\def\isatext##1{\mbox{\isastylescript##1}}} +\newcommand{\isactrlsub}[1]{\emph{\isascriptstyle${}\sb{#1}$}} +\newcommand{\isactrlsup}[1]{\emph{\isascriptstyle${}\sp{#1}$}} +\newcommand{\isactrlisub}[1]{\emph{\isascriptstyle${}\sb{#1}$}} +\newcommand{\isactrlisup}[1]{\emph{\isascriptstyle${}\sp{#1}$}} +\DeclareRobustCommand{\isactrlbsub}{\emph\bgroup\math{}\sb\bgroup\mbox\bgroup\isastylescript} +\DeclareRobustCommand{\isactrlesub}{\egroup\egroup\endmath\egroup} +\DeclareRobustCommand{\isactrlbsup}{\emph\bgroup\math{}\sp\bgroup\mbox\bgroup\isastylescript} +\DeclareRobustCommand{\isactrlesup}{\egroup\egroup\endmath\egroup} +\newcommand{\isactrlbold}[1]{{\bfseries\upshape\boldmath#1}} +\newcommand{\isactrlloc}[1]{{\bfseries\upshape\boldmath#1}} + +\newenvironment{isaantiq}{{\isacharat\isacharbraceleft}}{{\isacharbraceright}} +\newcommand{\isaantiqopen}{\isakeyword{\isacharbraceleft}} +\newcommand{\isaantiqclose}{\isakeyword{\isacharbraceright}} + +\newdimen\isa@parindent\newdimen\isa@parskip + +\newenvironment{isabellebody}{% +\isamarkuptrue\par% +\isa@parindent\parindent\parindent0pt% +\isa@parskip\parskip\parskip0pt% +\isastyle}{\par} + +\newenvironment{isabelle} +{\begin{trivlist}\begin{isabellebody}\item\relax} +{\end{isabellebody}\end{trivlist}} + +\newcommand{\isa}[1]{\emph{\isastyleminor #1}} + +\newcommand{\isaindent}[1]{\hphantom{#1}} +\newcommand{\isanewline}{\mbox{}\par\mbox{}} +\newcommand{\isasep}{} +\newcommand{\isadigit}[1]{#1} + +\newcommand{\isachardefaults}{% +\chardef\isacharbang=`\!% +\chardef\isachardoublequote=`\"% +\chardef\isachardoublequoteopen=`\"% +\chardef\isachardoublequoteclose=`\"% +\chardef\isacharhash=`\#% +\chardef\isachardollar=`\$% +\chardef\isacharpercent=`\%% +\chardef\isacharampersand=`\&% +\chardef\isacharprime=`\'% +\chardef\isacharparenleft=`\(% +\chardef\isacharparenright=`\)% +\chardef\isacharasterisk=`\*% +\chardef\isacharplus=`\+% +\chardef\isacharcomma=`\,% +\chardef\isacharminus=`\-% +\chardef\isachardot=`\.% +\chardef\isacharslash=`\/% +\chardef\isacharcolon=`\:% +\chardef\isacharsemicolon=`\;% +\chardef\isacharless=`\<% +\chardef\isacharequal=`\=% +\chardef\isachargreater=`\>% +\chardef\isacharquery=`\?% +\chardef\isacharat=`\@% +\chardef\isacharbrackleft=`\[% +\chardef\isacharbackslash=`\\% +\chardef\isacharbrackright=`\]% +\chardef\isacharcircum=`\^% +\chardef\isacharunderscore=`\_% +\def\isacharunderscorekeyword{\_}% +\chardef\isacharbackquote=`\`% +\chardef\isacharbackquoteopen=`\`% +\chardef\isacharbackquoteclose=`\`% +\chardef\isacharbraceleft=`\{% +\chardef\isacharbar=`\|% +\chardef\isacharbraceright=`\}% +\chardef\isachartilde=`\~% +\def\isacharverbatimopen{\isacharbraceleft\isacharasterisk}% +\def\isacharverbatimclose{\isacharasterisk\isacharbraceright}% +} + +\newcommand{\isaliteral}[2]{#2} +\newcommand{\isanil}{} + + +% keyword and section markup + +\newcommand{\isakeyword}[1] +{\emph{\bf\def\isachardot{.}\def\isacharunderscore{\isacharunderscorekeyword}% +\def\isacharbraceleft{\{}\def\isacharbraceright{\}}#1}} +\newcommand{\isacommand}[1]{\isakeyword{#1}} + +\newcommand{\isamarkupheader}[1]{\section{#1}} +\newcommand{\isamarkupchapter}[1]{\chapter{#1}} +\newcommand{\isamarkupsection}[1]{\section{#1}} +\newcommand{\isamarkupsubsection}[1]{\subsection{#1}} +\newcommand{\isamarkupsubsubsection}[1]{\subsubsection{#1}} +\newcommand{\isamarkupsect}[1]{\section{#1}} +\newcommand{\isamarkupsubsect}[1]{\subsection{#1}} +\newcommand{\isamarkupsubsubsect}[1]{\subsubsection{#1}} + +\newif\ifisamarkup +\newcommand{\isabeginpar}{\par\ifisamarkup\relax\else\medskip\fi} +\newcommand{\isaendpar}{\par\medskip} +\newenvironment{isapar}{\parindent\isa@parindent\parskip\isa@parskip\isabeginpar}{\isaendpar} +\newenvironment{isamarkuptext}{\par\isastyletext\begin{isapar}}{\end{isapar}} +\newenvironment{isamarkuptxt}{\par\isastyletxt\begin{isapar}}{\end{isapar}} +\newcommand{\isamarkupcmt}[1]{{\isastylecmt--- #1}} + + +% styles + +\def\isabellestyle#1{\csname isabellestyle#1\endcsname} + +\newcommand{\isabellestyledefault}{% +\renewcommand{\isastyle}{\small\tt\slshape}% +\renewcommand{\isastyleminor}{\small\tt\slshape}% +\renewcommand{\isastylescript}{\footnotesize\tt\slshape}% +\isachardefaults% +} +\isabellestyledefault + +\newcommand{\isabellestylett}{% +\renewcommand{\isastyle}{\small\tt}% +\renewcommand{\isastyleminor}{\small\tt}% +\renewcommand{\isastylescript}{\footnotesize\tt}% +\isachardefaults% +} + +\newcommand{\isabellestyleit}{% +\renewcommand{\isastyle}{\small\it}% +\renewcommand{\isastyleminor}{\it}% +\renewcommand{\isastylescript}{\footnotesize\it}% +\renewcommand{\isacharunderscorekeyword}{\mbox{-}}% +\renewcommand{\isacharbang}{\isamath{!}}% +\renewcommand{\isachardoublequote}{\isanil}% +\renewcommand{\isachardoublequoteopen}{\isanil}% +\renewcommand{\isachardoublequoteclose}{\isanil}% +\renewcommand{\isacharhash}{\isamath{\#}}% +\renewcommand{\isachardollar}{\isamath{\$}}% +\renewcommand{\isacharpercent}{\isamath{\%}}% +\renewcommand{\isacharampersand}{\isamath{\&}}% +\renewcommand{\isacharprime}{\isamath{\mskip2mu{'}\mskip-2mu}}% +\renewcommand{\isacharparenleft}{\isamath{(}}% +\renewcommand{\isacharparenright}{\isamath{)}}% +\renewcommand{\isacharasterisk}{\isamath{*}}% +\renewcommand{\isacharplus}{\isamath{+}}% +\renewcommand{\isacharcomma}{\isamath{\mathord,}}% +\renewcommand{\isacharminus}{\isamath{-}}% +\renewcommand{\isachardot}{\isamath{\mathord.}}% +\renewcommand{\isacharslash}{\isamath{/}}% +\renewcommand{\isacharcolon}{\isamath{\mathord:}}% +\renewcommand{\isacharsemicolon}{\isamath{\mathord;}}% +\renewcommand{\isacharless}{\isamath{<}}% +\renewcommand{\isacharequal}{\isamath{=}}% +\renewcommand{\isachargreater}{\isamath{>}}% +\renewcommand{\isacharat}{\isamath{@}}% +\renewcommand{\isacharbrackleft}{\isamath{[}}% +\renewcommand{\isacharbackslash}{\isamath{\backslash}}% +\renewcommand{\isacharbrackright}{\isamath{]}}% +\renewcommand{\isacharunderscore}{\mbox{-}}% +\renewcommand{\isacharbraceleft}{\isamath{\{}}% +\renewcommand{\isacharbar}{\isamath{\mid}}% +\renewcommand{\isacharbraceright}{\isamath{\}}}% +\renewcommand{\isachartilde}{\isamath{{}\sp{\sim}}}% +\renewcommand{\isacharbackquoteopen}{\isatext{\raise.3ex\hbox{$\scriptscriptstyle\langle$}}}% +\renewcommand{\isacharbackquoteclose}{\isatext{\raise.3ex\hbox{$\scriptscriptstyle\rangle$}}}% +\renewcommand{\isacharverbatimopen}{\isamath{\langle\!\langle}}% +\renewcommand{\isacharverbatimclose}{\isamath{\rangle\!\rangle}}% +} + +\newcommand{\isabellestylesl}{% +\isabellestyleit% +\renewcommand{\isastyle}{\small\sl}% +\renewcommand{\isastyleminor}{\sl}% +\renewcommand{\isastylescript}{\footnotesize\sl}% +} + + +% tagged regions + +%plain TeX version of comment package -- much faster! +\let\isafmtname\fmtname\def\fmtname{plain} +\usepackage{comment} +\let\fmtname\isafmtname + +\newcommand{\isafold}[1]{\emph{$\langle\mathord{\mathit{#1}}\rangle$}} + +\newcommand{\isakeeptag}[1]% +{\includecomment{isadelim#1}\includecomment{isatag#1}\csarg\def{isafold#1}{}} +\newcommand{\isadroptag}[1]% +{\excludecomment{isadelim#1}\excludecomment{isatag#1}\csarg\def{isafold#1}{}} +\newcommand{\isafoldtag}[1]% +{\includecomment{isadelim#1}\excludecomment{isatag#1}\csarg\def{isafold#1}{\isafold{#1}}} + +\isakeeptag{theory} +\isakeeptag{proof} +\isakeeptag{ML} +\isakeeptag{visible} +\isadroptag{invisible} + +\IfFileExists{isabelletags.sty}{\usepackage{isabelletags}}{} diff -r e41d91e86fa9 -r e633bb41ea42 doc-src/isac/jrocnik/Inverse_Z_Transform/document/isabellesym.sty --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/doc-src/isac/jrocnik/Inverse_Z_Transform/document/isabellesym.sty Thu Sep 08 23:17:35 2011 +0200 @@ -0,0 +1,358 @@ +%% +%% definitions of standard Isabelle symbols +%% + +\newcommand{\isasymzero}{\isamath{\mathbf{0}}} %requires amssymb +\newcommand{\isasymone}{\isamath{\mathbf{1}}} %requires amssymb +\newcommand{\isasymtwo}{\isamath{\mathbf{2}}} %requires amssymb +\newcommand{\isasymthree}{\isamath{\mathbf{3}}} %requires amssymb +\newcommand{\isasymfour}{\isamath{\mathbf{4}}} %requires amssymb +\newcommand{\isasymfive}{\isamath{\mathbf{5}}} %requires amssymb +\newcommand{\isasymsix}{\isamath{\mathbf{6}}} %requires amssymb +\newcommand{\isasymseven}{\isamath{\mathbf{7}}} %requires amssymb +\newcommand{\isasymeight}{\isamath{\mathbf{8}}} %requires amssymb +\newcommand{\isasymnine}{\isamath{\mathbf{9}}} %requires amssymb +\newcommand{\isasymA}{\isamath{\mathcal{A}}} +\newcommand{\isasymB}{\isamath{\mathcal{B}}} +\newcommand{\isasymC}{\isamath{\mathcal{C}}} +\newcommand{\isasymD}{\isamath{\mathcal{D}}} +\newcommand{\isasymE}{\isamath{\mathcal{E}}} +\newcommand{\isasymF}{\isamath{\mathcal{F}}} +\newcommand{\isasymG}{\isamath{\mathcal{G}}} +\newcommand{\isasymH}{\isamath{\mathcal{H}}} +\newcommand{\isasymI}{\isamath{\mathcal{I}}} +\newcommand{\isasymJ}{\isamath{\mathcal{J}}} +\newcommand{\isasymK}{\isamath{\mathcal{K}}} +\newcommand{\isasymL}{\isamath{\mathcal{L}}} +\newcommand{\isasymM}{\isamath{\mathcal{M}}} +\newcommand{\isasymN}{\isamath{\mathcal{N}}} +\newcommand{\isasymO}{\isamath{\mathcal{O}}} +\newcommand{\isasymP}{\isamath{\mathcal{P}}} +\newcommand{\isasymQ}{\isamath{\mathcal{Q}}} +\newcommand{\isasymR}{\isamath{\mathcal{R}}} +\newcommand{\isasymS}{\isamath{\mathcal{S}}} +\newcommand{\isasymT}{\isamath{\mathcal{T}}} +\newcommand{\isasymU}{\isamath{\mathcal{U}}} +\newcommand{\isasymV}{\isamath{\mathcal{V}}} +\newcommand{\isasymW}{\isamath{\mathcal{W}}} +\newcommand{\isasymX}{\isamath{\mathcal{X}}} +\newcommand{\isasymY}{\isamath{\mathcal{Y}}} +\newcommand{\isasymZ}{\isamath{\mathcal{Z}}} +\newcommand{\isasyma}{\isamath{\mathrm{a}}} +\newcommand{\isasymb}{\isamath{\mathrm{b}}} +\newcommand{\isasymc}{\isamath{\mathrm{c}}} +\newcommand{\isasymd}{\isamath{\mathrm{d}}} +\newcommand{\isasyme}{\isamath{\mathrm{e}}} +\newcommand{\isasymf}{\isamath{\mathrm{f}}} +\newcommand{\isasymg}{\isamath{\mathrm{g}}} +\newcommand{\isasymh}{\isamath{\mathrm{h}}} +\newcommand{\isasymi}{\isamath{\mathrm{i}}} +\newcommand{\isasymj}{\isamath{\mathrm{j}}} +\newcommand{\isasymk}{\isamath{\mathrm{k}}} +\newcommand{\isasyml}{\isamath{\mathrm{l}}} +\newcommand{\isasymm}{\isamath{\mathrm{m}}} +\newcommand{\isasymn}{\isamath{\mathrm{n}}} +\newcommand{\isasymo}{\isamath{\mathrm{o}}} +\newcommand{\isasymp}{\isamath{\mathrm{p}}} +\newcommand{\isasymq}{\isamath{\mathrm{q}}} +\newcommand{\isasymr}{\isamath{\mathrm{r}}} +\newcommand{\isasyms}{\isamath{\mathrm{s}}} +\newcommand{\isasymt}{\isamath{\mathrm{t}}} +\newcommand{\isasymu}{\isamath{\mathrm{u}}} +\newcommand{\isasymv}{\isamath{\mathrm{v}}} +\newcommand{\isasymw}{\isamath{\mathrm{w}}} +\newcommand{\isasymx}{\isamath{\mathrm{x}}} +\newcommand{\isasymy}{\isamath{\mathrm{y}}} +\newcommand{\isasymz}{\isamath{\mathrm{z}}} +\newcommand{\isasymAA}{\isamath{\mathfrak{A}}} %requires eufrak +\newcommand{\isasymBB}{\isamath{\mathfrak{B}}} %requires eufrak +\newcommand{\isasymCC}{\isamath{\mathfrak{C}}} %requires eufrak +\newcommand{\isasymDD}{\isamath{\mathfrak{D}}} %requires eufrak +\newcommand{\isasymEE}{\isamath{\mathfrak{E}}} %requires eufrak +\newcommand{\isasymFF}{\isamath{\mathfrak{F}}} %requires eufrak +\newcommand{\isasymGG}{\isamath{\mathfrak{G}}} %requires eufrak +\newcommand{\isasymHH}{\isamath{\mathfrak{H}}} %requires eufrak +\newcommand{\isasymII}{\isamath{\mathfrak{I}}} %requires eufrak +\newcommand{\isasymJJ}{\isamath{\mathfrak{J}}} %requires eufrak +\newcommand{\isasymKK}{\isamath{\mathfrak{K}}} %requires eufrak +\newcommand{\isasymLL}{\isamath{\mathfrak{L}}} %requires eufrak +\newcommand{\isasymMM}{\isamath{\mathfrak{M}}} %requires eufrak +\newcommand{\isasymNN}{\isamath{\mathfrak{N}}} %requires eufrak +\newcommand{\isasymOO}{\isamath{\mathfrak{O}}} %requires eufrak +\newcommand{\isasymPP}{\isamath{\mathfrak{P}}} %requires eufrak +\newcommand{\isasymQQ}{\isamath{\mathfrak{Q}}} %requires eufrak +\newcommand{\isasymRR}{\isamath{\mathfrak{R}}} %requires eufrak +\newcommand{\isasymSS}{\isamath{\mathfrak{S}}} %requires eufrak +\newcommand{\isasymTT}{\isamath{\mathfrak{T}}} %requires eufrak +\newcommand{\isasymUU}{\isamath{\mathfrak{U}}} %requires eufrak +\newcommand{\isasymVV}{\isamath{\mathfrak{V}}} %requires eufrak +\newcommand{\isasymWW}{\isamath{\mathfrak{W}}} %requires eufrak +\newcommand{\isasymXX}{\isamath{\mathfrak{X}}} %requires eufrak +\newcommand{\isasymYY}{\isamath{\mathfrak{Y}}} %requires eufrak +\newcommand{\isasymZZ}{\isamath{\mathfrak{Z}}} %requires eufrak +\newcommand{\isasymaa}{\isamath{\mathfrak{a}}} %requires eufrak +\newcommand{\isasymbb}{\isamath{\mathfrak{b}}} %requires eufrak +\newcommand{\isasymcc}{\isamath{\mathfrak{c}}} %requires eufrak +\newcommand{\isasymdd}{\isamath{\mathfrak{d}}} %requires eufrak +\newcommand{\isasymee}{\isamath{\mathfrak{e}}} %requires eufrak +\newcommand{\isasymff}{\isamath{\mathfrak{f}}} %requires eufrak +\newcommand{\isasymgg}{\isamath{\mathfrak{g}}} %requires eufrak +\newcommand{\isasymhh}{\isamath{\mathfrak{h}}} %requires eufrak +\newcommand{\isasymii}{\isamath{\mathfrak{i}}} %requires eufrak +\newcommand{\isasymjj}{\isamath{\mathfrak{j}}} %requires eufrak +\newcommand{\isasymkk}{\isamath{\mathfrak{k}}} %requires eufrak +\newcommand{\isasymll}{\isamath{\mathfrak{l}}} %requires eufrak +\newcommand{\isasymmm}{\isamath{\mathfrak{m}}} %requires eufrak +\newcommand{\isasymnn}{\isamath{\mathfrak{n}}} %requires eufrak +\newcommand{\isasymoo}{\isamath{\mathfrak{o}}} %requires eufrak +\newcommand{\isasympp}{\isamath{\mathfrak{p}}} %requires eufrak +\newcommand{\isasymqq}{\isamath{\mathfrak{q}}} %requires eufrak +\newcommand{\isasymrr}{\isamath{\mathfrak{r}}} %requires eufrak +\newcommand{\isasymss}{\isamath{\mathfrak{s}}} %requires eufrak +\newcommand{\isasymtt}{\isamath{\mathfrak{t}}} %requires eufrak +\newcommand{\isasymuu}{\isamath{\mathfrak{u}}} %requires eufrak +\newcommand{\isasymvv}{\isamath{\mathfrak{v}}} %requires eufrak +\newcommand{\isasymww}{\isamath{\mathfrak{w}}} %requires eufrak +\newcommand{\isasymxx}{\isamath{\mathfrak{x}}} %requires eufrak +\newcommand{\isasymyy}{\isamath{\mathfrak{y}}} %requires eufrak +\newcommand{\isasymzz}{\isamath{\mathfrak{z}}} %requires eufrak +\newcommand{\isasymalpha}{\isamath{\alpha}} +\newcommand{\isasymbeta}{\isamath{\beta}} +\newcommand{\isasymgamma}{\isamath{\gamma}} +\newcommand{\isasymdelta}{\isamath{\delta}} +\newcommand{\isasymepsilon}{\isamath{\varepsilon}} +\newcommand{\isasymzeta}{\isamath{\zeta}} +\newcommand{\isasymeta}{\isamath{\eta}} +\newcommand{\isasymtheta}{\isamath{\vartheta}} +\newcommand{\isasymiota}{\isamath{\iota}} +\newcommand{\isasymkappa}{\isamath{\kappa}} +\newcommand{\isasymlambda}{\isamath{\lambda}} +\newcommand{\isasymmu}{\isamath{\mu}} +\newcommand{\isasymnu}{\isamath{\nu}} +\newcommand{\isasymxi}{\isamath{\xi}} +\newcommand{\isasympi}{\isamath{\pi}} +\newcommand{\isasymrho}{\isamath{\varrho}} +\newcommand{\isasymsigma}{\isamath{\sigma}} +\newcommand{\isasymtau}{\isamath{\tau}} +\newcommand{\isasymupsilon}{\isamath{\upsilon}} +\newcommand{\isasymphi}{\isamath{\varphi}} +\newcommand{\isasymchi}{\isamath{\chi}} +\newcommand{\isasympsi}{\isamath{\psi}} +\newcommand{\isasymomega}{\isamath{\omega}} +\newcommand{\isasymGamma}{\isamath{\Gamma}} +\newcommand{\isasymDelta}{\isamath{\Delta}} +\newcommand{\isasymTheta}{\isamath{\Theta}} +\newcommand{\isasymLambda}{\isamath{\Lambda}} +\newcommand{\isasymXi}{\isamath{\Xi}} +\newcommand{\isasymPi}{\isamath{\Pi}} +\newcommand{\isasymSigma}{\isamath{\Sigma}} +\newcommand{\isasymUpsilon}{\isamath{\Upsilon}} +\newcommand{\isasymPhi}{\isamath{\Phi}} +\newcommand{\isasymPsi}{\isamath{\Psi}} +\newcommand{\isasymOmega}{\isamath{\Omega}} +\newcommand{\isasymbool}{\isamath{\mathrm{I}\mkern-3.8mu\mathrm{B}}} +\newcommand{\isasymcomplex}{\isamath{\mathrm{C}\mkern-15mu{\phantom{\mathrm{t}}\vrule}\mkern9mu}} +\newcommand{\isasymnat}{\isamath{\mathrm{I}\mkern-3.8mu\mathrm{N}}} +\newcommand{\isasymrat}{\isamath{\mathrm{Q}\mkern-16mu{\phantom{\mathrm{t}}\vrule}\mkern10mu}} +\newcommand{\isasymreal}{\isamath{\mathrm{I}\mkern-3.8mu\mathrm{R}}} +\newcommand{\isasymint}{\isamath{\mathsf{Z}\mkern-7.5mu\mathsf{Z}}} +\newcommand{\isasymleftarrow}{\isamath{\leftarrow}} +\newcommand{\isasymlongleftarrow}{\isamath{\longleftarrow}} +\newcommand{\isasymrightarrow}{\isamath{\rightarrow}} +\newcommand{\isasymlongrightarrow}{\isamath{\longrightarrow}} +\newcommand{\isasymLeftarrow}{\isamath{\Leftarrow}} +\newcommand{\isasymLongleftarrow}{\isamath{\Longleftarrow}} +\newcommand{\isasymRightarrow}{\isamath{\Rightarrow}} +\newcommand{\isasymLongrightarrow}{\isamath{\Longrightarrow}} +\newcommand{\isasymleftrightarrow}{\isamath{\leftrightarrow}} +\newcommand{\isasymlongleftrightarrow}{\isamath{\longleftrightarrow}} +\newcommand{\isasymLeftrightarrow}{\isamath{\Leftrightarrow}} +\newcommand{\isasymLongleftrightarrow}{\isamath{\Longleftrightarrow}} +\newcommand{\isasymmapsto}{\isamath{\mapsto}} +\newcommand{\isasymlongmapsto}{\isamath{\longmapsto}} +\newcommand{\isasymmidarrow}{\isamath{\relbar}} +\newcommand{\isasymMidarrow}{\isamath{\Relbar}} +\newcommand{\isasymhookleftarrow}{\isamath{\hookleftarrow}} +\newcommand{\isasymhookrightarrow}{\isamath{\hookrightarrow}} +\newcommand{\isasymleftharpoondown}{\isamath{\leftharpoondown}} +\newcommand{\isasymrightharpoondown}{\isamath{\rightharpoondown}} +\newcommand{\isasymleftharpoonup}{\isamath{\leftharpoonup}} +\newcommand{\isasymrightharpoonup}{\isamath{\rightharpoonup}} +\newcommand{\isasymrightleftharpoons}{\isamath{\rightleftharpoons}} +\newcommand{\isasymleadsto}{\isamath{\leadsto}} %requires amssymb +\newcommand{\isasymdownharpoonleft}{\isamath{\downharpoonleft}} %requires amssymb +\newcommand{\isasymdownharpoonright}{\isamath{\downharpoonright}} %requires amssymb +\newcommand{\isasymupharpoonleft}{\isamath{\upharpoonleft}} %requires amssymb +\newcommand{\isasymupharpoonright}{\isamath{\upharpoonright}} %requires amssymb +\newcommand{\isasymrestriction}{\isamath{\restriction}} %requires amssymb +\newcommand{\isasymColon}{\isamath{\mathrel{::}}} +\newcommand{\isasymup}{\isamath{\uparrow}} +\newcommand{\isasymUp}{\isamath{\Uparrow}} +\newcommand{\isasymdown}{\isamath{\downarrow}} +\newcommand{\isasymDown}{\isamath{\Downarrow}} +\newcommand{\isasymupdown}{\isamath{\updownarrow}} +\newcommand{\isasymUpdown}{\isamath{\Updownarrow}} +\newcommand{\isasymlangle}{\isamath{\langle}} +\newcommand{\isasymrangle}{\isamath{\rangle}} +\newcommand{\isasymlceil}{\isamath{\lceil}} +\newcommand{\isasymrceil}{\isamath{\rceil}} +\newcommand{\isasymlfloor}{\isamath{\lfloor}} +\newcommand{\isasymrfloor}{\isamath{\rfloor}} +\newcommand{\isasymlparr}{\isamath{\mathopen{(\mkern-3mu\mid}}} +\newcommand{\isasymrparr}{\isamath{\mathclose{\mid\mkern-3mu)}}} +\newcommand{\isasymlbrakk}{\isamath{\mathopen{\lbrack\mkern-3mu\lbrack}}} +\newcommand{\isasymrbrakk}{\isamath{\mathclose{\rbrack\mkern-3mu\rbrack}}} +\newcommand{\isasymlbrace}{\isamath{\mathopen{\lbrace\mkern-4.5mu\mid}}} +\newcommand{\isasymrbrace}{\isamath{\mathclose{\mid\mkern-4.5mu\rbrace}}} +\newcommand{\isasymguillemotleft}{\isatext{\flqq}} %requires babel +\newcommand{\isasymguillemotright}{\isatext{\frqq}} %requires babel +\newcommand{\isasymbottom}{\isamath{\bot}} +\newcommand{\isasymtop}{\isamath{\top}} +\newcommand{\isasymand}{\isamath{\wedge}} +\newcommand{\isasymAnd}{\isamath{\bigwedge}} +\newcommand{\isasymor}{\isamath{\vee}} +\newcommand{\isasymOr}{\isamath{\bigvee}} +\newcommand{\isasymforall}{\isamath{\forall\,}} +\newcommand{\isasymexists}{\isamath{\exists\,}} +\newcommand{\isasymnexists}{\isamath{\nexists\,}} %requires amssymb +\newcommand{\isasymnot}{\isamath{\neg}} +\newcommand{\isasymbox}{\isamath{\Box}} %requires amssymb +\newcommand{\isasymdiamond}{\isamath{\Diamond}} %requires amssymb +\newcommand{\isasymturnstile}{\isamath{\vdash}} +\newcommand{\isasymTurnstile}{\isamath{\models}} +\newcommand{\isasymtturnstile}{\isamath{\vdash\!\!\!\vdash}} +\newcommand{\isasymTTurnstile}{\isamath{\mid\!\models}} +\newcommand{\isasymstileturn}{\isamath{\dashv}} +\newcommand{\isasymsurd}{\isamath{\surd}} +\newcommand{\isasymle}{\isamath{\le}} +\newcommand{\isasymge}{\isamath{\ge}} +\newcommand{\isasymlless}{\isamath{\ll}} +\newcommand{\isasymggreater}{\isamath{\gg}} +\newcommand{\isasymlesssim}{\isamath{\lesssim}} %requires amssymb +\newcommand{\isasymgreatersim}{\isamath{\gtrsim}} %requires amssymb +\newcommand{\isasymlessapprox}{\isamath{\lessapprox}} %requires amssymb +\newcommand{\isasymgreaterapprox}{\isamath{\gtrapprox}} %requires amssymb +\newcommand{\isasymin}{\isamath{\in}} +\newcommand{\isasymnotin}{\isamath{\notin}} +\newcommand{\isasymsubset}{\isamath{\subset}} +\newcommand{\isasymsupset}{\isamath{\supset}} +\newcommand{\isasymsubseteq}{\isamath{\subseteq}} +\newcommand{\isasymsupseteq}{\isamath{\supseteq}} +\newcommand{\isasymsqsubset}{\isamath{\sqsubset}} %requires amssymb +\newcommand{\isasymsqsupset}{\isamath{\sqsupset}} %requires amssymb +\newcommand{\isasymsqsubseteq}{\isamath{\sqsubseteq}} +\newcommand{\isasymsqsupseteq}{\isamath{\sqsupseteq}} +\newcommand{\isasyminter}{\isamath{\cap}} +\newcommand{\isasymInter}{\isamath{\bigcap\,}} +\newcommand{\isasymunion}{\isamath{\cup}} +\newcommand{\isasymUnion}{\isamath{\bigcup\,}} +\newcommand{\isasymsqunion}{\isamath{\sqcup}} +\newcommand{\isasymSqunion}{\isamath{\bigsqcup\,}} +\newcommand{\isasymsqinter}{\isamath{\sqcap}} +\newcommand{\isasymSqinter}{\isamath{\bigsqcap\,}} %requires stmaryrd +\newcommand{\isasymsetminus}{\isamath{\setminus}} +\newcommand{\isasympropto}{\isamath{\propto}} +\newcommand{\isasymuplus}{\isamath{\uplus}} +\newcommand{\isasymUplus}{\isamath{\biguplus\,}} +\newcommand{\isasymnoteq}{\isamath{\not=}} +\newcommand{\isasymsim}{\isamath{\sim}} +\newcommand{\isasymdoteq}{\isamath{\doteq}} +\newcommand{\isasymsimeq}{\isamath{\simeq}} +\newcommand{\isasymapprox}{\isamath{\approx}} +\newcommand{\isasymasymp}{\isamath{\asymp}} +\newcommand{\isasymcong}{\isamath{\cong}} +\newcommand{\isasymsmile}{\isamath{\smile}} +\newcommand{\isasymequiv}{\isamath{\equiv}} +\newcommand{\isasymfrown}{\isamath{\frown}} +\newcommand{\isasymJoin}{\isamath{\Join}} %requires amssymb +\newcommand{\isasymbowtie}{\isamath{\bowtie}} +\newcommand{\isasymprec}{\isamath{\prec}} +\newcommand{\isasymsucc}{\isamath{\succ}} +\newcommand{\isasympreceq}{\isamath{\preceq}} +\newcommand{\isasymsucceq}{\isamath{\succeq}} +\newcommand{\isasymparallel}{\isamath{\parallel}} +\newcommand{\isasymbar}{\isamath{\mid}} +\newcommand{\isasymplusminus}{\isamath{\pm}} +\newcommand{\isasymminusplus}{\isamath{\mp}} +\newcommand{\isasymtimes}{\isamath{\times}} +\newcommand{\isasymdiv}{\isamath{\div}} +\newcommand{\isasymcdot}{\isamath{\cdot}} +\newcommand{\isasymstar}{\isamath{\star}} +\newcommand{\isasymbullet}{\boldmath\isamath{\mathchoice{\displaystyle{\cdot}}{\textstyle{\cdot}}{\scriptstyle{\bullet}}{\scriptscriptstyle{\bullet}}}} +\newcommand{\isasymcirc}{\isamath{\circ}} +\newcommand{\isasymdagger}{\isamath{\dagger}} +\newcommand{\isasymddagger}{\isamath{\ddagger}} +\newcommand{\isasymlhd}{\isamath{\lhd}} %requires amssymb +\newcommand{\isasymrhd}{\isamath{\rhd}} %requires amssymb +\newcommand{\isasymunlhd}{\isamath{\unlhd}} %requires amssymb +\newcommand{\isasymunrhd}{\isamath{\unrhd}} %requires amssymb +\newcommand{\isasymtriangleleft}{\isamath{\triangleleft}} +\newcommand{\isasymtriangleright}{\isamath{\triangleright}} +\newcommand{\isasymtriangle}{\isamath{\triangle}} +\newcommand{\isasymtriangleq}{\isamath{\triangleq}} %requires amssymb +\newcommand{\isasymoplus}{\isamath{\oplus}} +\newcommand{\isasymOplus}{\isamath{\bigoplus\,}} +\newcommand{\isasymotimes}{\isamath{\otimes}} +\newcommand{\isasymOtimes}{\isamath{\bigotimes\,}} +\newcommand{\isasymodot}{\isamath{\odot}} +\newcommand{\isasymOdot}{\isamath{\bigodot\,}} +\newcommand{\isasymominus}{\isamath{\ominus}} +\newcommand{\isasymoslash}{\isamath{\oslash}} +\newcommand{\isasymdots}{\isamath{\dots}} +\newcommand{\isasymcdots}{\isamath{\cdots}} +\newcommand{\isasymSum}{\isamath{\sum\,}} +\newcommand{\isasymProd}{\isamath{\prod\,}} +\newcommand{\isasymCoprod}{\isamath{\coprod\,}} +\newcommand{\isasyminfinity}{\isamath{\infty}} +\newcommand{\isasymintegral}{\isamath{\int\,}} +\newcommand{\isasymointegral}{\isamath{\oint\,}} +\newcommand{\isasymclubsuit}{\isamath{\clubsuit}} +\newcommand{\isasymdiamondsuit}{\isamath{\diamondsuit}} +\newcommand{\isasymheartsuit}{\isamath{\heartsuit}} +\newcommand{\isasymspadesuit}{\isamath{\spadesuit}} +\newcommand{\isasymaleph}{\isamath{\aleph}} +\newcommand{\isasymemptyset}{\isamath{\emptyset}} +\newcommand{\isasymnabla}{\isamath{\nabla}} +\newcommand{\isasympartial}{\isamath{\partial}} +\newcommand{\isasymRe}{\isamath{\Re}} +\newcommand{\isasymIm}{\isamath{\Im}} +\newcommand{\isasymflat}{\isamath{\flat}} +\newcommand{\isasymnatural}{\isamath{\natural}} +\newcommand{\isasymsharp}{\isamath{\sharp}} +\newcommand{\isasymangle}{\isamath{\angle}} +\newcommand{\isasymcopyright}{\isatext{\rm\copyright}} +\newcommand{\isasymregistered}{\isatext{\rm\textregistered}} +\newcommand{\isasymhyphen}{\isatext{\rm-}} +\newcommand{\isasyminverse}{\isamath{{}^{-1}}} +\newcommand{\isasymonesuperior}{\isamath{{}^1}} +\newcommand{\isasymonequarter}{\isatext{\rm\textonequarter}} %requires textcomp +\newcommand{\isasymtwosuperior}{\isamath{{}^2}} +\newcommand{\isasymonehalf}{\isatext{\rm\textonehalf}} %requires textcomp +\newcommand{\isasymthreesuperior}{\isamath{{}^3}} +\newcommand{\isasymthreequarters}{\isatext{\rm\textthreequarters}} %requires textcomp +\newcommand{\isasymordfeminine}{\isatext{\rm\textordfeminine}} +\newcommand{\isasymordmasculine}{\isatext{\rm\textordmasculine}} +\newcommand{\isasymsection}{\isatext{\rm\S}} +\newcommand{\isasymparagraph}{\isatext{\rm\P}} +\newcommand{\isasymexclamdown}{\isatext{\rm\textexclamdown}} +\newcommand{\isasymquestiondown}{\isatext{\rm\textquestiondown}} +\newcommand{\isasymeuro}{\isatext{\textgreek{\euro}}} %requires greek babel +\newcommand{\isasympounds}{\isamath{\pounds}} +\newcommand{\isasymyen}{\isatext{\yen}} %requires amssymb +\newcommand{\isasymcent}{\isatext{\textcent}} %requires textcomp +\newcommand{\isasymcurrency}{\isatext{\textcurrency}} %requires textcomp +\newcommand{\isasymdegree}{\isatext{\rm\textdegree}} %requires textcomp +\newcommand{\isasymamalg}{\isamath{\amalg}} +\newcommand{\isasymmho}{\isamath{\mho}} %requires amssymb +\newcommand{\isasymlozenge}{\isamath{\lozenge}} %requires amssymb +\newcommand{\isasymwp}{\isamath{\wp}} +\newcommand{\isasymwrong}{\isamath{\wr}} +\newcommand{\isasymstruct}{\isamath{\diamond}} +\newcommand{\isasymacute}{\isatext{\'\relax}} +\newcommand{\isasymindex}{\isatext{\i}} +\newcommand{\isasymdieresis}{\isatext{\"\relax}} +\newcommand{\isasymcedilla}{\isatext{\c\relax}} +\newcommand{\isasymhungarumlaut}{\isatext{\H\relax}} +\newcommand{\isasymspacespace}{\isamath{~~}} +\newcommand{\isasymmodule}{\isamath{\langle}\isakeyword{module}\isamath{\rangle}} +\newcommand{\isasymsome}{\isamath{\epsilon\,}} diff -r e41d91e86fa9 -r e633bb41ea42 doc-src/isac/jrocnik/Inverse_Z_Transform/document/pdfsetup.sty --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/doc-src/isac/jrocnik/Inverse_Z_Transform/document/pdfsetup.sty Thu Sep 08 23:17:35 2011 +0200 @@ -0,0 +1,7 @@ +%% +%% default hyperref setup (both for pdf and dvi output) +%% + +\usepackage{color} +\definecolor{linkcolor}{rgb}{0,0,0.5} +\usepackage[colorlinks=true,linkcolor=linkcolor,citecolor=linkcolor,filecolor=linkcolor,pagecolor=linkcolor,urlcolor=linkcolor]{hyperref} diff -r e41d91e86fa9 -r e633bb41ea42 doc-src/isac/jrocnik/Inverse_Z_Transform/document/root.tex --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/doc-src/isac/jrocnik/Inverse_Z_Transform/document/root.tex Thu Sep 08 23:17:35 2011 +0200 @@ -0,0 +1,60 @@ +\documentclass[11pt,a4paper]{article} +\usepackage{isabelle,isabellesym} + +% further packages required for unusual symbols (see also +% isabellesym.sty), use only when needed + +%\usepackage{amssymb} + %for \, \, \, \, \, \, + %\, \, \, \, \, + %\, \, \ + +%\usepackage[greek,english]{babel} + %option greek for \ + %option english (default language) for \, \ + +%\usepackage[only,bigsqcap]{stmaryrd} + %for \ + +%\usepackage{eufrak} + %for \ ... \, \ ... \ (also included in amssymb) + +%\usepackage{textcomp} + %for \, \, \, \, \, + %\ + +% this should be the last package used +\usepackage{pdfsetup} + +% urls in roman style, theory text in math-similar italics +\urlstyle{rm} +\isabellestyle{it} + +% for uniform font size +%\renewcommand{\isastyle}{\isastyleminor} + + +\begin{document} + +\title{Inverse-Z-Transform} +\author{By jan} +\maketitle + +\tableofcontents + +% sane default for proof documents +\parindent 0pt\parskip 0.5ex + +% generated text of all theories +\input{session} + +% optional bibliography +%\bibliographystyle{abbrv} +%\bibliography{root} + +\end{document} + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: t +%%% End: diff -r e41d91e86fa9 -r e633bb41ea42 doc-src/isac/jrocnik/Inverse_Z_Transform/document/session.tex --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/doc-src/isac/jrocnik/Inverse_Z_Transform/document/session.tex Thu Sep 08 23:17:35 2011 +0200 @@ -0,0 +1,6 @@ +\input{Inverse_Z_Transform.tex} + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: "root" +%%% End: diff -r e41d91e86fa9 -r e633bb41ea42 doc-src/isac/jrocnik/IsaMakefile --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/doc-src/isac/jrocnik/IsaMakefile Thu Sep 08 23:17:35 2011 +0200 @@ -0,0 +1,31 @@ + +## targets + +default: Inverse_Z_Transform +images: +test: Inverse_Z_Transform + +all: images test + + +## global settings + +SRC = $(ISABELLE_HOME)/src +OUT = $(ISABELLE_OUTPUT) +LOG = $(OUT)/log + +USEDIR = $(ISABELLE_TOOL) usedir -v true -i false -d false -C false -D document + + +## Inverse_Z_Transform + +Inverse_Z_Transform: $(LOG)/Isac-Inverse_Z_Transform.gz + +$(LOG)/Isac-Inverse_Z_Transform.gz: ## Inverse_Z_Transform/ROOT.ML Inverse_Z_Transform/document/root.tex Inverse_Z_Transform/*.thy + @$(USEDIR) Isac Inverse_Z_Transform + + +## clean + +clean: + @rm -f $(LOG)/Isac-Inverse_Z_Transform.gz diff -r e41d91e86fa9 -r e633bb41ea42 doc-src/isac/jrocnik/bakkarbeit_jrocnik.tex --- a/doc-src/isac/jrocnik/bakkarbeit_jrocnik.tex Thu Sep 08 23:06:39 2011 +0200 +++ b/doc-src/isac/jrocnik/bakkarbeit_jrocnik.tex Thu Sep 08 23:17:35 2011 +0200 @@ -174,7 +174,7 @@ %\section*{Anhang} \section{Demobeispiel} -\input{./Inverse_Z-Transform/document/Inverse_Z_Transform.tex} +\input{./Inverse_Z_Transform/document/Inverse_Z_Transform.tex} \begin{verbatim} diff -r e41d91e86fa9 -r e633bb41ea42 doc-src/isac/jrocnik/isabelle.sty --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/doc-src/isac/jrocnik/isabelle.sty Thu Sep 08 23:17:35 2011 +0200 @@ -0,0 +1,218 @@ +%% +%% macros for Isabelle generated LaTeX output +%% + +%%% Simple document preparation (based on theory token language and symbols) + +% isabelle environments + +\newcommand{\isabellecontext}{UNKNOWN} + +\newcommand{\isastyle}{\UNDEF} +\newcommand{\isastyleminor}{\UNDEF} +\newcommand{\isastylescript}{\UNDEF} +\newcommand{\isastyletext}{\normalsize\rm} +\newcommand{\isastyletxt}{\rm} +\newcommand{\isastylecmt}{\rm} + +%symbol markup -- \emph achieves decent spacing via italic corrections +\newcommand{\isamath}[1]{\emph{$#1$}} +\newcommand{\isatext}[1]{\emph{#1}} +\DeclareRobustCommand{\isascriptstyle}{\def\isamath##1{##1}\def\isatext##1{\mbox{\isastylescript##1}}} +\newcommand{\isactrlsub}[1]{\emph{\isascriptstyle${}\sb{#1}$}} +\newcommand{\isactrlsup}[1]{\emph{\isascriptstyle${}\sp{#1}$}} +\newcommand{\isactrlisub}[1]{\emph{\isascriptstyle${}\sb{#1}$}} +\newcommand{\isactrlisup}[1]{\emph{\isascriptstyle${}\sp{#1}$}} +\DeclareRobustCommand{\isactrlbsub}{\emph\bgroup\math{}\sb\bgroup\mbox\bgroup\isastylescript} +\DeclareRobustCommand{\isactrlesub}{\egroup\egroup\endmath\egroup} +\DeclareRobustCommand{\isactrlbsup}{\emph\bgroup\math{}\sp\bgroup\mbox\bgroup\isastylescript} +\DeclareRobustCommand{\isactrlesup}{\egroup\egroup\endmath\egroup} +\newcommand{\isactrlbold}[1]{{\bfseries\upshape\boldmath#1}} +\newcommand{\isactrlloc}[1]{{\bfseries\upshape\boldmath#1}} + +\newenvironment{isaantiq}{{\isacharat\isacharbraceleft}}{{\isacharbraceright}} +\newcommand{\isaantiqopen}{\isakeyword{\isacharbraceleft}} +\newcommand{\isaantiqclose}{\isakeyword{\isacharbraceright}} + +\newdimen\isa@parindent\newdimen\isa@parskip + +\newenvironment{isabellebody}{% +\isamarkuptrue\par% +\isa@parindent\parindent\parindent0pt% +\isa@parskip\parskip\parskip0pt% +\isastyle}{\par} + +\newenvironment{isabelle} +{\begin{trivlist}\begin{isabellebody}\item\relax} +{\end{isabellebody}\end{trivlist}} + +\newcommand{\isa}[1]{\emph{\isastyleminor #1}} + +\newcommand{\isaindent}[1]{\hphantom{#1}} +\newcommand{\isanewline}{\mbox{}\par\mbox{}} +\newcommand{\isasep}{} +\newcommand{\isadigit}[1]{#1} + +\newcommand{\isachardefaults}{% +\chardef\isacharbang=`\!% +\chardef\isachardoublequote=`\"% +\chardef\isachardoublequoteopen=`\"% +\chardef\isachardoublequoteclose=`\"% +\chardef\isacharhash=`\#% +\chardef\isachardollar=`\$% +\chardef\isacharpercent=`\%% +\chardef\isacharampersand=`\&% +\chardef\isacharprime=`\'% +\chardef\isacharparenleft=`\(% +\chardef\isacharparenright=`\)% +\chardef\isacharasterisk=`\*% +\chardef\isacharplus=`\+% +\chardef\isacharcomma=`\,% +\chardef\isacharminus=`\-% +\chardef\isachardot=`\.% +\chardef\isacharslash=`\/% +\chardef\isacharcolon=`\:% +\chardef\isacharsemicolon=`\;% +\chardef\isacharless=`\<% +\chardef\isacharequal=`\=% +\chardef\isachargreater=`\>% +\chardef\isacharquery=`\?% +\chardef\isacharat=`\@% +\chardef\isacharbrackleft=`\[% +\chardef\isacharbackslash=`\\% +\chardef\isacharbrackright=`\]% +\chardef\isacharcircum=`\^% +\chardef\isacharunderscore=`\_% +\def\isacharunderscorekeyword{\_}% +\chardef\isacharbackquote=`\`% +\chardef\isacharbackquoteopen=`\`% +\chardef\isacharbackquoteclose=`\`% +\chardef\isacharbraceleft=`\{% +\chardef\isacharbar=`\|% +\chardef\isacharbraceright=`\}% +\chardef\isachartilde=`\~% +\def\isacharverbatimopen{\isacharbraceleft\isacharasterisk}% +\def\isacharverbatimclose{\isacharasterisk\isacharbraceright}% +} + +\newcommand{\isaliteral}[2]{#2} +\newcommand{\isanil}{} + + +% keyword and section markup + +\newcommand{\isakeyword}[1] +{\emph{\bf\def\isachardot{.}\def\isacharunderscore{\isacharunderscorekeyword}% +\def\isacharbraceleft{\{}\def\isacharbraceright{\}}#1}} +\newcommand{\isacommand}[1]{\isakeyword{#1}} + +\newcommand{\isamarkupheader}[1]{\section{#1}} +\newcommand{\isamarkupchapter}[1]{\chapter{#1}} +\newcommand{\isamarkupsection}[1]{\section{#1}} +\newcommand{\isamarkupsubsection}[1]{\subsection{#1}} +\newcommand{\isamarkupsubsubsection}[1]{\subsubsection{#1}} +\newcommand{\isamarkupsect}[1]{\section{#1}} +\newcommand{\isamarkupsubsect}[1]{\subsection{#1}} +\newcommand{\isamarkupsubsubsect}[1]{\subsubsection{#1}} + +\newif\ifisamarkup +\newcommand{\isabeginpar}{\par\ifisamarkup\relax\else\medskip\fi} +\newcommand{\isaendpar}{\par\medskip} +\newenvironment{isapar}{\parindent\isa@parindent\parskip\isa@parskip\isabeginpar}{\isaendpar} +\newenvironment{isamarkuptext}{\par\isastyletext\begin{isapar}}{\end{isapar}} +\newenvironment{isamarkuptxt}{\par\isastyletxt\begin{isapar}}{\end{isapar}} +\newcommand{\isamarkupcmt}[1]{{\isastylecmt--- #1}} + + +% styles + +\def\isabellestyle#1{\csname isabellestyle#1\endcsname} + +\newcommand{\isabellestyledefault}{% +\renewcommand{\isastyle}{\small\tt\slshape}% +\renewcommand{\isastyleminor}{\small\tt\slshape}% +\renewcommand{\isastylescript}{\footnotesize\tt\slshape}% +\isachardefaults% +} +\isabellestyledefault + +\newcommand{\isabellestylett}{% +\renewcommand{\isastyle}{\small\tt}% +\renewcommand{\isastyleminor}{\small\tt}% +\renewcommand{\isastylescript}{\footnotesize\tt}% +\isachardefaults% +} + +\newcommand{\isabellestyleit}{% +\renewcommand{\isastyle}{\small\it}% +\renewcommand{\isastyleminor}{\it}% +\renewcommand{\isastylescript}{\footnotesize\it}% +\renewcommand{\isacharunderscorekeyword}{\mbox{-}}% +\renewcommand{\isacharbang}{\isamath{!}}% +\renewcommand{\isachardoublequote}{\isanil}% +\renewcommand{\isachardoublequoteopen}{\isanil}% +\renewcommand{\isachardoublequoteclose}{\isanil}% +\renewcommand{\isacharhash}{\isamath{\#}}% +\renewcommand{\isachardollar}{\isamath{\$}}% +\renewcommand{\isacharpercent}{\isamath{\%}}% +\renewcommand{\isacharampersand}{\isamath{\&}}% +\renewcommand{\isacharprime}{\isamath{\mskip2mu{'}\mskip-2mu}}% +\renewcommand{\isacharparenleft}{\isamath{(}}% +\renewcommand{\isacharparenright}{\isamath{)}}% +\renewcommand{\isacharasterisk}{\isamath{*}}% +\renewcommand{\isacharplus}{\isamath{+}}% +\renewcommand{\isacharcomma}{\isamath{\mathord,}}% +\renewcommand{\isacharminus}{\isamath{-}}% +\renewcommand{\isachardot}{\isamath{\mathord.}}% +\renewcommand{\isacharslash}{\isamath{/}}% +\renewcommand{\isacharcolon}{\isamath{\mathord:}}% +\renewcommand{\isacharsemicolon}{\isamath{\mathord;}}% +\renewcommand{\isacharless}{\isamath{<}}% +\renewcommand{\isacharequal}{\isamath{=}}% +\renewcommand{\isachargreater}{\isamath{>}}% +\renewcommand{\isacharat}{\isamath{@}}% +\renewcommand{\isacharbrackleft}{\isamath{[}}% +\renewcommand{\isacharbackslash}{\isamath{\backslash}}% +\renewcommand{\isacharbrackright}{\isamath{]}}% +\renewcommand{\isacharunderscore}{\mbox{-}}% +\renewcommand{\isacharbraceleft}{\isamath{\{}}% +\renewcommand{\isacharbar}{\isamath{\mid}}% +\renewcommand{\isacharbraceright}{\isamath{\}}}% +\renewcommand{\isachartilde}{\isamath{{}\sp{\sim}}}% +\renewcommand{\isacharbackquoteopen}{\isatext{\raise.3ex\hbox{$\scriptscriptstyle\langle$}}}% +\renewcommand{\isacharbackquoteclose}{\isatext{\raise.3ex\hbox{$\scriptscriptstyle\rangle$}}}% +\renewcommand{\isacharverbatimopen}{\isamath{\langle\!\langle}}% +\renewcommand{\isacharverbatimclose}{\isamath{\rangle\!\rangle}}% +} + +\newcommand{\isabellestylesl}{% +\isabellestyleit% +\renewcommand{\isastyle}{\small\sl}% +\renewcommand{\isastyleminor}{\sl}% +\renewcommand{\isastylescript}{\footnotesize\sl}% +} + + +% tagged regions + +%plain TeX version of comment package -- much faster! +\let\isafmtname\fmtname\def\fmtname{plain} +\usepackage{comment} +\let\fmtname\isafmtname + +\newcommand{\isafold}[1]{\emph{$\langle\mathord{\mathit{#1}}\rangle$}} + +\newcommand{\isakeeptag}[1]% +{\includecomment{isadelim#1}\includecomment{isatag#1}\csarg\def{isafold#1}{}} +\newcommand{\isadroptag}[1]% +{\excludecomment{isadelim#1}\excludecomment{isatag#1}\csarg\def{isafold#1}{}} +\newcommand{\isafoldtag}[1]% +{\includecomment{isadelim#1}\excludecomment{isatag#1}\csarg\def{isafold#1}{\isafold{#1}}} + +\isakeeptag{theory} +\isakeeptag{proof} +\isakeeptag{ML} +\isakeeptag{visible} +\isadroptag{invisible} + +\IfFileExists{isabelletags.sty}{\usepackage{isabelletags}}{} diff -r e41d91e86fa9 -r e633bb41ea42 doc-src/isac/jrocnik/isabellesym.sty --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/doc-src/isac/jrocnik/isabellesym.sty Thu Sep 08 23:17:35 2011 +0200 @@ -0,0 +1,358 @@ +%% +%% definitions of standard Isabelle symbols +%% + +\newcommand{\isasymzero}{\isamath{\mathbf{0}}} %requires amssymb +\newcommand{\isasymone}{\isamath{\mathbf{1}}} %requires amssymb +\newcommand{\isasymtwo}{\isamath{\mathbf{2}}} %requires amssymb +\newcommand{\isasymthree}{\isamath{\mathbf{3}}} %requires amssymb +\newcommand{\isasymfour}{\isamath{\mathbf{4}}} %requires amssymb +\newcommand{\isasymfive}{\isamath{\mathbf{5}}} %requires amssymb +\newcommand{\isasymsix}{\isamath{\mathbf{6}}} %requires amssymb +\newcommand{\isasymseven}{\isamath{\mathbf{7}}} %requires amssymb +\newcommand{\isasymeight}{\isamath{\mathbf{8}}} %requires amssymb +\newcommand{\isasymnine}{\isamath{\mathbf{9}}} %requires amssymb +\newcommand{\isasymA}{\isamath{\mathcal{A}}} +\newcommand{\isasymB}{\isamath{\mathcal{B}}} +\newcommand{\isasymC}{\isamath{\mathcal{C}}} +\newcommand{\isasymD}{\isamath{\mathcal{D}}} +\newcommand{\isasymE}{\isamath{\mathcal{E}}} +\newcommand{\isasymF}{\isamath{\mathcal{F}}} +\newcommand{\isasymG}{\isamath{\mathcal{G}}} +\newcommand{\isasymH}{\isamath{\mathcal{H}}} +\newcommand{\isasymI}{\isamath{\mathcal{I}}} +\newcommand{\isasymJ}{\isamath{\mathcal{J}}} +\newcommand{\isasymK}{\isamath{\mathcal{K}}} +\newcommand{\isasymL}{\isamath{\mathcal{L}}} +\newcommand{\isasymM}{\isamath{\mathcal{M}}} +\newcommand{\isasymN}{\isamath{\mathcal{N}}} +\newcommand{\isasymO}{\isamath{\mathcal{O}}} +\newcommand{\isasymP}{\isamath{\mathcal{P}}} +\newcommand{\isasymQ}{\isamath{\mathcal{Q}}} +\newcommand{\isasymR}{\isamath{\mathcal{R}}} +\newcommand{\isasymS}{\isamath{\mathcal{S}}} +\newcommand{\isasymT}{\isamath{\mathcal{T}}} +\newcommand{\isasymU}{\isamath{\mathcal{U}}} +\newcommand{\isasymV}{\isamath{\mathcal{V}}} +\newcommand{\isasymW}{\isamath{\mathcal{W}}} +\newcommand{\isasymX}{\isamath{\mathcal{X}}} +\newcommand{\isasymY}{\isamath{\mathcal{Y}}} +\newcommand{\isasymZ}{\isamath{\mathcal{Z}}} +\newcommand{\isasyma}{\isamath{\mathrm{a}}} +\newcommand{\isasymb}{\isamath{\mathrm{b}}} +\newcommand{\isasymc}{\isamath{\mathrm{c}}} +\newcommand{\isasymd}{\isamath{\mathrm{d}}} +\newcommand{\isasyme}{\isamath{\mathrm{e}}} +\newcommand{\isasymf}{\isamath{\mathrm{f}}} +\newcommand{\isasymg}{\isamath{\mathrm{g}}} +\newcommand{\isasymh}{\isamath{\mathrm{h}}} +\newcommand{\isasymi}{\isamath{\mathrm{i}}} +\newcommand{\isasymj}{\isamath{\mathrm{j}}} +\newcommand{\isasymk}{\isamath{\mathrm{k}}} +\newcommand{\isasyml}{\isamath{\mathrm{l}}} +\newcommand{\isasymm}{\isamath{\mathrm{m}}} +\newcommand{\isasymn}{\isamath{\mathrm{n}}} +\newcommand{\isasymo}{\isamath{\mathrm{o}}} +\newcommand{\isasymp}{\isamath{\mathrm{p}}} +\newcommand{\isasymq}{\isamath{\mathrm{q}}} +\newcommand{\isasymr}{\isamath{\mathrm{r}}} +\newcommand{\isasyms}{\isamath{\mathrm{s}}} +\newcommand{\isasymt}{\isamath{\mathrm{t}}} +\newcommand{\isasymu}{\isamath{\mathrm{u}}} +\newcommand{\isasymv}{\isamath{\mathrm{v}}} +\newcommand{\isasymw}{\isamath{\mathrm{w}}} +\newcommand{\isasymx}{\isamath{\mathrm{x}}} +\newcommand{\isasymy}{\isamath{\mathrm{y}}} +\newcommand{\isasymz}{\isamath{\mathrm{z}}} +\newcommand{\isasymAA}{\isamath{\mathfrak{A}}} %requires eufrak +\newcommand{\isasymBB}{\isamath{\mathfrak{B}}} %requires eufrak +\newcommand{\isasymCC}{\isamath{\mathfrak{C}}} %requires eufrak +\newcommand{\isasymDD}{\isamath{\mathfrak{D}}} %requires eufrak +\newcommand{\isasymEE}{\isamath{\mathfrak{E}}} %requires eufrak +\newcommand{\isasymFF}{\isamath{\mathfrak{F}}} %requires eufrak +\newcommand{\isasymGG}{\isamath{\mathfrak{G}}} %requires eufrak +\newcommand{\isasymHH}{\isamath{\mathfrak{H}}} %requires eufrak +\newcommand{\isasymII}{\isamath{\mathfrak{I}}} %requires eufrak +\newcommand{\isasymJJ}{\isamath{\mathfrak{J}}} %requires eufrak +\newcommand{\isasymKK}{\isamath{\mathfrak{K}}} %requires eufrak +\newcommand{\isasymLL}{\isamath{\mathfrak{L}}} %requires eufrak +\newcommand{\isasymMM}{\isamath{\mathfrak{M}}} %requires eufrak +\newcommand{\isasymNN}{\isamath{\mathfrak{N}}} %requires eufrak +\newcommand{\isasymOO}{\isamath{\mathfrak{O}}} %requires eufrak +\newcommand{\isasymPP}{\isamath{\mathfrak{P}}} %requires eufrak +\newcommand{\isasymQQ}{\isamath{\mathfrak{Q}}} %requires eufrak +\newcommand{\isasymRR}{\isamath{\mathfrak{R}}} %requires eufrak +\newcommand{\isasymSS}{\isamath{\mathfrak{S}}} %requires eufrak +\newcommand{\isasymTT}{\isamath{\mathfrak{T}}} %requires eufrak +\newcommand{\isasymUU}{\isamath{\mathfrak{U}}} %requires eufrak +\newcommand{\isasymVV}{\isamath{\mathfrak{V}}} %requires eufrak +\newcommand{\isasymWW}{\isamath{\mathfrak{W}}} %requires eufrak +\newcommand{\isasymXX}{\isamath{\mathfrak{X}}} %requires eufrak +\newcommand{\isasymYY}{\isamath{\mathfrak{Y}}} %requires eufrak +\newcommand{\isasymZZ}{\isamath{\mathfrak{Z}}} %requires eufrak +\newcommand{\isasymaa}{\isamath{\mathfrak{a}}} %requires eufrak +\newcommand{\isasymbb}{\isamath{\mathfrak{b}}} %requires eufrak +\newcommand{\isasymcc}{\isamath{\mathfrak{c}}} %requires eufrak +\newcommand{\isasymdd}{\isamath{\mathfrak{d}}} %requires eufrak +\newcommand{\isasymee}{\isamath{\mathfrak{e}}} %requires eufrak +\newcommand{\isasymff}{\isamath{\mathfrak{f}}} %requires eufrak +\newcommand{\isasymgg}{\isamath{\mathfrak{g}}} %requires eufrak +\newcommand{\isasymhh}{\isamath{\mathfrak{h}}} %requires eufrak +\newcommand{\isasymii}{\isamath{\mathfrak{i}}} %requires eufrak +\newcommand{\isasymjj}{\isamath{\mathfrak{j}}} %requires eufrak +\newcommand{\isasymkk}{\isamath{\mathfrak{k}}} %requires eufrak +\newcommand{\isasymll}{\isamath{\mathfrak{l}}} %requires eufrak +\newcommand{\isasymmm}{\isamath{\mathfrak{m}}} %requires eufrak +\newcommand{\isasymnn}{\isamath{\mathfrak{n}}} %requires eufrak +\newcommand{\isasymoo}{\isamath{\mathfrak{o}}} %requires eufrak +\newcommand{\isasympp}{\isamath{\mathfrak{p}}} %requires eufrak +\newcommand{\isasymqq}{\isamath{\mathfrak{q}}} %requires eufrak +\newcommand{\isasymrr}{\isamath{\mathfrak{r}}} %requires eufrak +\newcommand{\isasymss}{\isamath{\mathfrak{s}}} %requires eufrak +\newcommand{\isasymtt}{\isamath{\mathfrak{t}}} %requires eufrak +\newcommand{\isasymuu}{\isamath{\mathfrak{u}}} %requires eufrak +\newcommand{\isasymvv}{\isamath{\mathfrak{v}}} %requires eufrak +\newcommand{\isasymww}{\isamath{\mathfrak{w}}} %requires eufrak +\newcommand{\isasymxx}{\isamath{\mathfrak{x}}} %requires eufrak +\newcommand{\isasymyy}{\isamath{\mathfrak{y}}} %requires eufrak +\newcommand{\isasymzz}{\isamath{\mathfrak{z}}} %requires eufrak +\newcommand{\isasymalpha}{\isamath{\alpha}} +\newcommand{\isasymbeta}{\isamath{\beta}} +\newcommand{\isasymgamma}{\isamath{\gamma}} +\newcommand{\isasymdelta}{\isamath{\delta}} +\newcommand{\isasymepsilon}{\isamath{\varepsilon}} +\newcommand{\isasymzeta}{\isamath{\zeta}} +\newcommand{\isasymeta}{\isamath{\eta}} +\newcommand{\isasymtheta}{\isamath{\vartheta}} +\newcommand{\isasymiota}{\isamath{\iota}} +\newcommand{\isasymkappa}{\isamath{\kappa}} +\newcommand{\isasymlambda}{\isamath{\lambda}} +\newcommand{\isasymmu}{\isamath{\mu}} +\newcommand{\isasymnu}{\isamath{\nu}} +\newcommand{\isasymxi}{\isamath{\xi}} +\newcommand{\isasympi}{\isamath{\pi}} +\newcommand{\isasymrho}{\isamath{\varrho}} +\newcommand{\isasymsigma}{\isamath{\sigma}} +\newcommand{\isasymtau}{\isamath{\tau}} +\newcommand{\isasymupsilon}{\isamath{\upsilon}} +\newcommand{\isasymphi}{\isamath{\varphi}} +\newcommand{\isasymchi}{\isamath{\chi}} +\newcommand{\isasympsi}{\isamath{\psi}} +\newcommand{\isasymomega}{\isamath{\omega}} +\newcommand{\isasymGamma}{\isamath{\Gamma}} +\newcommand{\isasymDelta}{\isamath{\Delta}} +\newcommand{\isasymTheta}{\isamath{\Theta}} +\newcommand{\isasymLambda}{\isamath{\Lambda}} +\newcommand{\isasymXi}{\isamath{\Xi}} +\newcommand{\isasymPi}{\isamath{\Pi}} +\newcommand{\isasymSigma}{\isamath{\Sigma}} +\newcommand{\isasymUpsilon}{\isamath{\Upsilon}} +\newcommand{\isasymPhi}{\isamath{\Phi}} +\newcommand{\isasymPsi}{\isamath{\Psi}} +\newcommand{\isasymOmega}{\isamath{\Omega}} +\newcommand{\isasymbool}{\isamath{\mathrm{I}\mkern-3.8mu\mathrm{B}}} +\newcommand{\isasymcomplex}{\isamath{\mathrm{C}\mkern-15mu{\phantom{\mathrm{t}}\vrule}\mkern9mu}} +\newcommand{\isasymnat}{\isamath{\mathrm{I}\mkern-3.8mu\mathrm{N}}} +\newcommand{\isasymrat}{\isamath{\mathrm{Q}\mkern-16mu{\phantom{\mathrm{t}}\vrule}\mkern10mu}} +\newcommand{\isasymreal}{\isamath{\mathrm{I}\mkern-3.8mu\mathrm{R}}} +\newcommand{\isasymint}{\isamath{\mathsf{Z}\mkern-7.5mu\mathsf{Z}}} +\newcommand{\isasymleftarrow}{\isamath{\leftarrow}} +\newcommand{\isasymlongleftarrow}{\isamath{\longleftarrow}} +\newcommand{\isasymrightarrow}{\isamath{\rightarrow}} +\newcommand{\isasymlongrightarrow}{\isamath{\longrightarrow}} +\newcommand{\isasymLeftarrow}{\isamath{\Leftarrow}} +\newcommand{\isasymLongleftarrow}{\isamath{\Longleftarrow}} +\newcommand{\isasymRightarrow}{\isamath{\Rightarrow}} +\newcommand{\isasymLongrightarrow}{\isamath{\Longrightarrow}} +\newcommand{\isasymleftrightarrow}{\isamath{\leftrightarrow}} +\newcommand{\isasymlongleftrightarrow}{\isamath{\longleftrightarrow}} +\newcommand{\isasymLeftrightarrow}{\isamath{\Leftrightarrow}} +\newcommand{\isasymLongleftrightarrow}{\isamath{\Longleftrightarrow}} +\newcommand{\isasymmapsto}{\isamath{\mapsto}} +\newcommand{\isasymlongmapsto}{\isamath{\longmapsto}} +\newcommand{\isasymmidarrow}{\isamath{\relbar}} +\newcommand{\isasymMidarrow}{\isamath{\Relbar}} +\newcommand{\isasymhookleftarrow}{\isamath{\hookleftarrow}} +\newcommand{\isasymhookrightarrow}{\isamath{\hookrightarrow}} +\newcommand{\isasymleftharpoondown}{\isamath{\leftharpoondown}} +\newcommand{\isasymrightharpoondown}{\isamath{\rightharpoondown}} +\newcommand{\isasymleftharpoonup}{\isamath{\leftharpoonup}} +\newcommand{\isasymrightharpoonup}{\isamath{\rightharpoonup}} +\newcommand{\isasymrightleftharpoons}{\isamath{\rightleftharpoons}} +\newcommand{\isasymleadsto}{\isamath{\leadsto}} %requires amssymb +\newcommand{\isasymdownharpoonleft}{\isamath{\downharpoonleft}} %requires amssymb +\newcommand{\isasymdownharpoonright}{\isamath{\downharpoonright}} %requires amssymb +\newcommand{\isasymupharpoonleft}{\isamath{\upharpoonleft}} %requires amssymb +\newcommand{\isasymupharpoonright}{\isamath{\upharpoonright}} %requires amssymb +\newcommand{\isasymrestriction}{\isamath{\restriction}} %requires amssymb +\newcommand{\isasymColon}{\isamath{\mathrel{::}}} +\newcommand{\isasymup}{\isamath{\uparrow}} +\newcommand{\isasymUp}{\isamath{\Uparrow}} +\newcommand{\isasymdown}{\isamath{\downarrow}} +\newcommand{\isasymDown}{\isamath{\Downarrow}} +\newcommand{\isasymupdown}{\isamath{\updownarrow}} +\newcommand{\isasymUpdown}{\isamath{\Updownarrow}} +\newcommand{\isasymlangle}{\isamath{\langle}} +\newcommand{\isasymrangle}{\isamath{\rangle}} +\newcommand{\isasymlceil}{\isamath{\lceil}} +\newcommand{\isasymrceil}{\isamath{\rceil}} +\newcommand{\isasymlfloor}{\isamath{\lfloor}} +\newcommand{\isasymrfloor}{\isamath{\rfloor}} +\newcommand{\isasymlparr}{\isamath{\mathopen{(\mkern-3mu\mid}}} +\newcommand{\isasymrparr}{\isamath{\mathclose{\mid\mkern-3mu)}}} +\newcommand{\isasymlbrakk}{\isamath{\mathopen{\lbrack\mkern-3mu\lbrack}}} +\newcommand{\isasymrbrakk}{\isamath{\mathclose{\rbrack\mkern-3mu\rbrack}}} +\newcommand{\isasymlbrace}{\isamath{\mathopen{\lbrace\mkern-4.5mu\mid}}} +\newcommand{\isasymrbrace}{\isamath{\mathclose{\mid\mkern-4.5mu\rbrace}}} +\newcommand{\isasymguillemotleft}{\isatext{\flqq}} %requires babel +\newcommand{\isasymguillemotright}{\isatext{\frqq}} %requires babel +\newcommand{\isasymbottom}{\isamath{\bot}} +\newcommand{\isasymtop}{\isamath{\top}} +\newcommand{\isasymand}{\isamath{\wedge}} +\newcommand{\isasymAnd}{\isamath{\bigwedge}} +\newcommand{\isasymor}{\isamath{\vee}} +\newcommand{\isasymOr}{\isamath{\bigvee}} +\newcommand{\isasymforall}{\isamath{\forall\,}} +\newcommand{\isasymexists}{\isamath{\exists\,}} +\newcommand{\isasymnexists}{\isamath{\nexists\,}} %requires amssymb +\newcommand{\isasymnot}{\isamath{\neg}} +\newcommand{\isasymbox}{\isamath{\Box}} %requires amssymb +\newcommand{\isasymdiamond}{\isamath{\Diamond}} %requires amssymb +\newcommand{\isasymturnstile}{\isamath{\vdash}} +\newcommand{\isasymTurnstile}{\isamath{\models}} +\newcommand{\isasymtturnstile}{\isamath{\vdash\!\!\!\vdash}} +\newcommand{\isasymTTurnstile}{\isamath{\mid\!\models}} +\newcommand{\isasymstileturn}{\isamath{\dashv}} +\newcommand{\isasymsurd}{\isamath{\surd}} +\newcommand{\isasymle}{\isamath{\le}} +\newcommand{\isasymge}{\isamath{\ge}} +\newcommand{\isasymlless}{\isamath{\ll}} +\newcommand{\isasymggreater}{\isamath{\gg}} +\newcommand{\isasymlesssim}{\isamath{\lesssim}} %requires amssymb +\newcommand{\isasymgreatersim}{\isamath{\gtrsim}} %requires amssymb +\newcommand{\isasymlessapprox}{\isamath{\lessapprox}} %requires amssymb +\newcommand{\isasymgreaterapprox}{\isamath{\gtrapprox}} %requires amssymb +\newcommand{\isasymin}{\isamath{\in}} +\newcommand{\isasymnotin}{\isamath{\notin}} +\newcommand{\isasymsubset}{\isamath{\subset}} +\newcommand{\isasymsupset}{\isamath{\supset}} +\newcommand{\isasymsubseteq}{\isamath{\subseteq}} +\newcommand{\isasymsupseteq}{\isamath{\supseteq}} +\newcommand{\isasymsqsubset}{\isamath{\sqsubset}} %requires amssymb +\newcommand{\isasymsqsupset}{\isamath{\sqsupset}} %requires amssymb +\newcommand{\isasymsqsubseteq}{\isamath{\sqsubseteq}} +\newcommand{\isasymsqsupseteq}{\isamath{\sqsupseteq}} +\newcommand{\isasyminter}{\isamath{\cap}} +\newcommand{\isasymInter}{\isamath{\bigcap\,}} +\newcommand{\isasymunion}{\isamath{\cup}} +\newcommand{\isasymUnion}{\isamath{\bigcup\,}} +\newcommand{\isasymsqunion}{\isamath{\sqcup}} +\newcommand{\isasymSqunion}{\isamath{\bigsqcup\,}} +\newcommand{\isasymsqinter}{\isamath{\sqcap}} +\newcommand{\isasymSqinter}{\isamath{\bigsqcap\,}} %requires stmaryrd +\newcommand{\isasymsetminus}{\isamath{\setminus}} +\newcommand{\isasympropto}{\isamath{\propto}} +\newcommand{\isasymuplus}{\isamath{\uplus}} +\newcommand{\isasymUplus}{\isamath{\biguplus\,}} +\newcommand{\isasymnoteq}{\isamath{\not=}} +\newcommand{\isasymsim}{\isamath{\sim}} +\newcommand{\isasymdoteq}{\isamath{\doteq}} +\newcommand{\isasymsimeq}{\isamath{\simeq}} +\newcommand{\isasymapprox}{\isamath{\approx}} +\newcommand{\isasymasymp}{\isamath{\asymp}} +\newcommand{\isasymcong}{\isamath{\cong}} +\newcommand{\isasymsmile}{\isamath{\smile}} +\newcommand{\isasymequiv}{\isamath{\equiv}} +\newcommand{\isasymfrown}{\isamath{\frown}} +\newcommand{\isasymJoin}{\isamath{\Join}} %requires amssymb +\newcommand{\isasymbowtie}{\isamath{\bowtie}} +\newcommand{\isasymprec}{\isamath{\prec}} +\newcommand{\isasymsucc}{\isamath{\succ}} +\newcommand{\isasympreceq}{\isamath{\preceq}} +\newcommand{\isasymsucceq}{\isamath{\succeq}} +\newcommand{\isasymparallel}{\isamath{\parallel}} +\newcommand{\isasymbar}{\isamath{\mid}} +\newcommand{\isasymplusminus}{\isamath{\pm}} +\newcommand{\isasymminusplus}{\isamath{\mp}} +\newcommand{\isasymtimes}{\isamath{\times}} +\newcommand{\isasymdiv}{\isamath{\div}} +\newcommand{\isasymcdot}{\isamath{\cdot}} +\newcommand{\isasymstar}{\isamath{\star}} +\newcommand{\isasymbullet}{\boldmath\isamath{\mathchoice{\displaystyle{\cdot}}{\textstyle{\cdot}}{\scriptstyle{\bullet}}{\scriptscriptstyle{\bullet}}}} +\newcommand{\isasymcirc}{\isamath{\circ}} +\newcommand{\isasymdagger}{\isamath{\dagger}} +\newcommand{\isasymddagger}{\isamath{\ddagger}} +\newcommand{\isasymlhd}{\isamath{\lhd}} %requires amssymb +\newcommand{\isasymrhd}{\isamath{\rhd}} %requires amssymb +\newcommand{\isasymunlhd}{\isamath{\unlhd}} %requires amssymb +\newcommand{\isasymunrhd}{\isamath{\unrhd}} %requires amssymb +\newcommand{\isasymtriangleleft}{\isamath{\triangleleft}} +\newcommand{\isasymtriangleright}{\isamath{\triangleright}} +\newcommand{\isasymtriangle}{\isamath{\triangle}} +\newcommand{\isasymtriangleq}{\isamath{\triangleq}} %requires amssymb +\newcommand{\isasymoplus}{\isamath{\oplus}} +\newcommand{\isasymOplus}{\isamath{\bigoplus\,}} +\newcommand{\isasymotimes}{\isamath{\otimes}} +\newcommand{\isasymOtimes}{\isamath{\bigotimes\,}} +\newcommand{\isasymodot}{\isamath{\odot}} +\newcommand{\isasymOdot}{\isamath{\bigodot\,}} +\newcommand{\isasymominus}{\isamath{\ominus}} +\newcommand{\isasymoslash}{\isamath{\oslash}} +\newcommand{\isasymdots}{\isamath{\dots}} +\newcommand{\isasymcdots}{\isamath{\cdots}} +\newcommand{\isasymSum}{\isamath{\sum\,}} +\newcommand{\isasymProd}{\isamath{\prod\,}} +\newcommand{\isasymCoprod}{\isamath{\coprod\,}} +\newcommand{\isasyminfinity}{\isamath{\infty}} +\newcommand{\isasymintegral}{\isamath{\int\,}} +\newcommand{\isasymointegral}{\isamath{\oint\,}} +\newcommand{\isasymclubsuit}{\isamath{\clubsuit}} +\newcommand{\isasymdiamondsuit}{\isamath{\diamondsuit}} +\newcommand{\isasymheartsuit}{\isamath{\heartsuit}} +\newcommand{\isasymspadesuit}{\isamath{\spadesuit}} +\newcommand{\isasymaleph}{\isamath{\aleph}} +\newcommand{\isasymemptyset}{\isamath{\emptyset}} +\newcommand{\isasymnabla}{\isamath{\nabla}} +\newcommand{\isasympartial}{\isamath{\partial}} +\newcommand{\isasymRe}{\isamath{\Re}} +\newcommand{\isasymIm}{\isamath{\Im}} +\newcommand{\isasymflat}{\isamath{\flat}} +\newcommand{\isasymnatural}{\isamath{\natural}} +\newcommand{\isasymsharp}{\isamath{\sharp}} +\newcommand{\isasymangle}{\isamath{\angle}} +\newcommand{\isasymcopyright}{\isatext{\rm\copyright}} +\newcommand{\isasymregistered}{\isatext{\rm\textregistered}} +\newcommand{\isasymhyphen}{\isatext{\rm-}} +\newcommand{\isasyminverse}{\isamath{{}^{-1}}} +\newcommand{\isasymonesuperior}{\isamath{{}^1}} +\newcommand{\isasymonequarter}{\isatext{\rm\textonequarter}} %requires textcomp +\newcommand{\isasymtwosuperior}{\isamath{{}^2}} +\newcommand{\isasymonehalf}{\isatext{\rm\textonehalf}} %requires textcomp +\newcommand{\isasymthreesuperior}{\isamath{{}^3}} +\newcommand{\isasymthreequarters}{\isatext{\rm\textthreequarters}} %requires textcomp +\newcommand{\isasymordfeminine}{\isatext{\rm\textordfeminine}} +\newcommand{\isasymordmasculine}{\isatext{\rm\textordmasculine}} +\newcommand{\isasymsection}{\isatext{\rm\S}} +\newcommand{\isasymparagraph}{\isatext{\rm\P}} +\newcommand{\isasymexclamdown}{\isatext{\rm\textexclamdown}} +\newcommand{\isasymquestiondown}{\isatext{\rm\textquestiondown}} +\newcommand{\isasymeuro}{\isatext{\textgreek{\euro}}} %requires greek babel +\newcommand{\isasympounds}{\isamath{\pounds}} +\newcommand{\isasymyen}{\isatext{\yen}} %requires amssymb +\newcommand{\isasymcent}{\isatext{\textcent}} %requires textcomp +\newcommand{\isasymcurrency}{\isatext{\textcurrency}} %requires textcomp +\newcommand{\isasymdegree}{\isatext{\rm\textdegree}} %requires textcomp +\newcommand{\isasymamalg}{\isamath{\amalg}} +\newcommand{\isasymmho}{\isamath{\mho}} %requires amssymb +\newcommand{\isasymlozenge}{\isamath{\lozenge}} %requires amssymb +\newcommand{\isasymwp}{\isamath{\wp}} +\newcommand{\isasymwrong}{\isamath{\wr}} +\newcommand{\isasymstruct}{\isamath{\diamond}} +\newcommand{\isasymacute}{\isatext{\'\relax}} +\newcommand{\isasymindex}{\isatext{\i}} +\newcommand{\isasymdieresis}{\isatext{\"\relax}} +\newcommand{\isasymcedilla}{\isatext{\c\relax}} +\newcommand{\isasymhungarumlaut}{\isatext{\H\relax}} +\newcommand{\isasymspacespace}{\isamath{~~}} +\newcommand{\isasymmodule}{\isamath{\langle}\isakeyword{module}\isamath{\rangle}} +\newcommand{\isasymsome}{\isamath{\epsilon\,}}