neuper@37906
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(* tests on integration over the reals
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neuper@37906
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author: Walther Neuper
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neuper@37906
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050814, 08:51
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neuper@37906
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(c) due to copyright terms
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neuper@37906
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neuper@37906
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use"../smltest/IsacKnowledge/integrate.sml";
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neuper@37906
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use"integrate.sml";
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neuper@37906
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*)
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neuper@38010
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val thy = theory "Integrate";
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neuper@37906
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neuper@38013
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"--------------------------------------------------------";
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neuper@38013
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"table of contents --------------------------------------";
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neuper@38013
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"--------------------------------------------------------";
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neuper@38013
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"----------- parsing ------------------------------------";
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neuper@38013
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"----------- integrate by rewriting ---------------------";
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neuper@38013
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"----------- test add_new_c, is_f_x ---------------------";
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neuper@38013
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"----------- simplify by ruleset reducing make_ratpoly_in";
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neuper@38013
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"----------- integrate by ruleset -----------------------";
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neuper@38013
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"----------- rewrite 3rd integration in 7.27 ------------";
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neuper@38013
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"----------- check probem type --------------------------";
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neuper@38013
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"----------- check Scripts ------------------------------";
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neuper@38013
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"----------- me method [diff,integration] ---------------";
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neuper@38013
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"----------- me method [diff,integration,named] ---------";
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neuper@38013
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"----------- me met [diff,integration,named] Biegelinie.Q";
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neuper@38013
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"----------- interSteps [diff,integration] --------------";
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neuper@38013
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"----------- method analog to rls 'integration' ---------";
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neuper@38013
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"----------- Ambiguous input: Integral ?u + ?v D ?bdv = .";
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neuper@38013
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"----------- CAS input ----------------------------------";
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neuper@38013
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"--------------------------------------------------------";
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neuper@38013
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"--------------------------------------------------------";
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neuper@38013
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"--------------------------------------------------------";
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neuper@37906
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neuper@37906
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neuper@37906
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neuper@38013
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"----------- parsing ------------------------------------";
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neuper@38013
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"----------- parsing ------------------------------------";
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neuper@38013
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"----------- parsing ------------------------------------";
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neuper@38013
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fun str2term str = (term_of o the o (parse thy)) str;
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neuper@38015
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fun term2s t = Print_Mode.setmp [] (Syntax.string_of_term
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neuper@38015
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(ProofContext.init_global thy)) t;
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neuper@37906
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neuper@37924
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val t = str2term "Integral x D x";
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neuper@37924
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val t = str2term "Integral x^^^2 D x";
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neuper@38048
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case t of
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neuper@38048
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Const ("Integrate.Integral", _) $
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neuper@38048
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(Const ("Atools.pow", _) $ Free _ $ Free _) $ Free ("x", _) => ()
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neuper@38048
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| _ => error "integrate.sml: parsing: Integral x^^^2 D x";
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neuper@37906
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neuper@37924
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val t = str2term "ff x is_f_x";
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neuper@37906
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case t of Const ("Integrate.is'_f'_x", _) $ _ => ()
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neuper@38031
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| _ => error "integrate.sml: parsing: ff x is_f_x";
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neuper@37906
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neuper@37906
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neuper@38013
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"----------- integrate by rewriting ---------------------";
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neuper@38013
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"----------- integrate by rewriting ---------------------";
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neuper@38013
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"----------- integrate by rewriting ---------------------";
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neuper@37906
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val conditions_in_integration_rules =
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neuper@37906
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Rls {id="conditions_in_integration_rules",
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neuper@37906
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preconds = [],
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neuper@37906
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rew_ord = ("termlessI",termlessI),
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neuper@37906
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erls = Erls,
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neuper@37906
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srls = Erls, calc = [],
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neuper@37906
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rules = [(*for rewriting conditions in Thm's*)
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neuper@37906
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Calc ("Atools.occurs'_in",
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neuper@37906
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eval_occurs_in "#occurs_in_"),
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neuper@37970
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Thm ("not_true",num_str @{thm not_true}),
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neuper@37970
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Thm ("not_false",num_str @{thm not_false})
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neuper@37906
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],
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neuper@37906
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scr = EmptyScr};
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neuper@37924
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val subs = [(str2term "bdv", str2term "x")];
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neuper@37906
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fun rewrit thm str =
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neuper@38013
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fst (the (rewrite_inst_ thy tless_true
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neuper@37906
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conditions_in_integration_rules
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true subs thm str));
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neuper@38013
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val str = rewrit @{thm "integral_const"} (str2term "Integral 1 D x");
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neuper@38048
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if term2s str = "1 * x" then () else error "integrate.sml Integral 1 D x";
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neuper@38048
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neuper@38013
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val str = rewrit @{thm "integral_const"} (str2term "Integral M'/EJ D x");
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neuper@38013
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term2s str;
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neuper@38013
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val str = (rewrit @{thm "integral_const"} (str2term "Integral x D x"))
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neuper@37924
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handle OPTION => str2term "no_rewrite";
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neuper@37906
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neuper@38013
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val str = rewrit @{thm "integral_var"} (str2term "Integral x D x");
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neuper@38013
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term2s str;
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neuper@38013
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val str = (rewrit @{thm "integral_var"} (str2term "Integral a D x"))
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neuper@37924
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handle OPTION => str2term "no_rewrite";
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neuper@37906
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neuper@38013
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val str = rewrit @{thm "integral_add"} (str2term "Integral x + 1 D x");
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neuper@38013
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term2s str;
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neuper@37906
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neuper@38013
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val str = rewrit @{thm "integral_mult"} (str2term "Integral M'/EJ * x^^^3 D x");
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neuper@38013
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term2s str;
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neuper@38013
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val str = (rewrit @{thm "integral_mult"} (str2term "Integral x * x D x"))
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neuper@37924
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handle OPTION => str2term "no_rewrite";
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neuper@37906
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neuper@38013
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val str = rewrit @{thm "integral_pow"} (str2term "Integral x^^^3 D x");
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neuper@38048
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if term2s str = "x ^^^ (3 + 1) / (3 + 1)" then ()
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neuper@38048
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else error "integrate.sml Integral x^^^3 D x";
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neuper@37906
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neuper@37906
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neuper@38013
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"----------- test add_new_c, is_f_x ---------------------";
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neuper@38013
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"----------- test add_new_c, is_f_x ---------------------";
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neuper@38013
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"----------- test add_new_c, is_f_x ---------------------";
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neuper@38048
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val term = str2term "x^^^2 * c + c_2";
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neuper@37906
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val cc = new_c term;
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neuper@38031
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if term2str cc = "c_3" then () else error "integrate.sml: new_c ???";
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neuper@37906
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neuper@37926
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val SOME (id,t') = eval_add_new_c "" "Integrate.add'_new'_c" term thy;
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neuper@37906
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if term2str t' = "x ^^^ 2 * c + c_2 = x ^^^ 2 * c + c_2 + c_3" then ()
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neuper@38031
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else error "intergrate.sml: diff. eval_add_new_c";
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neuper@37906
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neuper@37906
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val cc = ("Integrate.add'_new'_c", eval_add_new_c "add_new_c_");
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neuper@37926
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val SOME (thmstr, thm) = get_calculation1_ thy cc term;
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neuper@37906
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neuper@37926
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val SOME (t',_) = rewrite_set_ thy true add_new_c term;
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neuper@37906
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if term2str t' = "x ^^^ 2 * c + c_2 + c_3" then ()
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neuper@38031
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else error "intergrate.sml: diff. rewrite_set add_new_c 1";
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neuper@37906
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neuper@37906
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val term = str2term "ff x = x^^^2*c + c_2";
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neuper@37926
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val SOME (t',_) = rewrite_set_ thy true add_new_c term;
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neuper@37906
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if term2str t' = "ff x = x ^^^ 2 * c + c_2 + c_3" then ()
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neuper@38031
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else error "intergrate.sml: diff. rewrite_set add_new_c 2";
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neuper@37906
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neuper@37906
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neuper@37906
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(*WN080222 replace call_new_c with add_new_c----------------------
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neuper@37924
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val term = str2term "new_c (c * x^^^2 + c_2)";
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neuper@37926
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val SOME (_,t') = eval_new_c 0 0 term 0;
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neuper@37906
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if term2s t' = "new_c c * x ^^^ 2 + c_2 = c_3" then ()
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neuper@38031
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else error "integrate.sml: eval_new_c ???";
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neuper@37906
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neuper@37924
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val t = str2term "matches (?u + new_c ?v) (x ^^^ 2 / 2)";
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neuper@37926
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val SOME (_,t') = eval_matches "" "Tools.matches" t thy; term2s t';
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neuper@37906
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if term2s t' = "matches (?u + new_c ?v) (x ^^^ 2 / 2) = False" then ()
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neuper@38031
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else error "integrate.sml: matches new_c = False";
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neuper@37906
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neuper@37924
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val t = str2term "matches (?u + new_c ?v) (x ^^^ 2 / 2 + new_c x ^^^ 2 / 2)";
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neuper@37926
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val SOME (_,t') = eval_matches "" "Tools.matches" t thy; term2s t';
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neuper@37906
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if term2s t'="matches (?u + new_c ?v) (x ^^^ 2 / 2 + new_c x ^^^ 2 / 2) = True"
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neuper@38031
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then () else error "integrate.sml: matches new_c = True";
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neuper@37906
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neuper@37924
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val t = str2term "ff x is_f_x";
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neuper@37926
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val SOME (_,t') = eval_is_f_x "" "" t thy; term2s t';
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neuper@37906
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if term2s t' = "(ff x is_f_x) = True" then ()
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neuper@38031
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else error "integrate.sml: eval_is_f_x --> true";
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neuper@37906
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neuper@37924
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val t = str2term "q_0/2 * L * x is_f_x";
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neuper@37926
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val SOME (_,t') = eval_is_f_x "" "" t thy; term2s t';
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neuper@37906
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if term2s t' = "(q_0 / 2 * L * x is_f_x) = False" then ()
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neuper@38031
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else error "integrate.sml: eval_is_f_x --> false";
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neuper@37906
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neuper@37906
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val conditions_in_integration =
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neuper@37906
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Rls {id="conditions_in_integration",
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neuper@37970
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preconds = [],
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neuper@37970
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rew_ord = ("termlessI",termlessI),
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neuper@37970
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erls = Erls,
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neuper@37970
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srls = Erls, calc = [],
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neuper@37970
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rules = [Calc ("Tools.matches",eval_matches ""),
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neuper@37970
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Calc ("Integrate.is'_f'_x",
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neuper@37970
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eval_is_f_x "is_f_x_"),
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neuper@37970
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Thm ("not_true",num_str @{thm not_true}),
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neuper@37970
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Thm ("not_false",num_str @{thm not_false})
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neuper@37970
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],
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neuper@37970
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scr = EmptyScr};
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neuper@37906
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fun rewrit thm t =
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neuper@38013
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fst (the (rewrite_inst_ thy tless_true
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neuper@37906
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conditions_in_integration true subs thm t));
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neuper@37924
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val t = rewrit call_for_new_c (str2term "x ^^^ 2 / 2"); term2s t;
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neuper@37906
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val t = (rewrit call_for_new_c t)
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neuper@37924
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handle OPTION => str2term "no_rewrite";
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neuper@37906
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neuper@37906
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val t = rewrit call_for_new_c
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neuper@37924
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(str2term "ff x = q_0/2 *L*x"); term2s t;
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neuper@37906
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val t = (rewrit call_for_new_c
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neuper@37924
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(str2term "ff x = q_0 / 2 * L * x + new_c q_0 / 2 * L * x"))
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neuper@37924
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handle OPTION => (*NOT: + new_c ..=..!!*)str2term "no_rewrite";
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neuper@37906
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--------------------------------------------------------------------*)
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neuper@37906
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neuper@37906
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neuper@38013
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"----------- simplify by ruleset reducing make_ratpoly_in";
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neuper@38013
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"----------- simplify by ruleset reducing make_ratpoly_in";
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neuper@38013
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"----------- simplify by ruleset reducing make_ratpoly_in";
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neuper@38015
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val thy = theory "Isac";
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neuper@38030
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"===== test 1";
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neuper@38015
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val subs = [(str2term "bdv", str2term "x")];
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neuper@37906
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val t = str2term "1/EI * (L * q_0 * x / 2 + -1 * q_0 * x^^^2 / 2)";
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neuper@37906
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neuper@37906
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"----- stepwise from the rulesets in simplify_Integral and below-----";
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neuper@38030
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val rls = norm_Rational_noadd_fractions;
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neuper@37906
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case rewrite_set_inst_ thy true subs rls t of
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neuper@38031
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SOME _ => error "integrate.sml simplify by ruleset norm_Rational_.#2"
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neuper@37926
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| NONE => ();
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neuper@37906
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neuper@38030
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"===== test 2";
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neuper@38030
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val rls = order_add_mult_in;
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neuper@37926
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val SOME (t,[]) = rewrite_set_ thy true rls t;
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neuper@38030
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if term2str t = "1 / EI * (L * (q_0 * x) / 2 + -1 * (q_0 * x ^^^ 2) / 2)" then()
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neuper@38031
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else error "integrate.sml simplify by ruleset order_add_mult_in #2";
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neuper@37906
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neuper@38030
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"===== test 3";
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neuper@38030
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val rls = discard_parentheses;
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neuper@37926
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val SOME (t,[]) = rewrite_set_ thy true rls t;
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neuper@37906
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if term2str t = "1 / EI * (L * q_0 * x / 2 + -1 * q_0 * x ^^^ 2 / 2)" then ()
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neuper@38031
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else error "integrate.sml simplify by ruleset discard_parenth.. #3";
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neuper@37906
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neuper@38030
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"===== test 4";
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neuper@37970
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val rls =
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neuper@37970
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(append_rls "separate_bdv"
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neuper@37970
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collect_bdv
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neuper@37970
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[Thm ("separate_bdv", num_str @{thm separate_bdv}),
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neuper@37970
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(*"?a * ?bdv / ?b = ?a / ?b * ?bdv"*)
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neuper@38030
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(*"?a * ?bdv / ?b = ?a / ?b * ?bdv"*)
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neuper@37970
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Thm ("separate_bdv_n", num_str @{thm separate_bdv_n}),
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neuper@38030
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(*"?a * ?bdv ^^^ ?n / ?b = ?a / ?b * ?bdv ^^^ ?n"*)
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neuper@37970
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Thm ("separate_1_bdv", num_str @{thm separate_1_bdv}),
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neuper@37970
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(*"?bdv / ?b = (1 / ?b) * ?bdv"*)
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neuper@38030
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(*"?bdv / ?b = (1::?'a) / ?b * ?bdv"*)
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neuper@37970
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Thm ("separate_1_bdv_n", num_str @{thm separate_1_bdv_n})
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neuper@38030
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(*"?bdv ^^^ ?n / ?b = 1 / ?b * ?bdv ^^^ ?n"*)
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neuper@37970
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]);
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neuper@38030
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(*show_types := true; --- do we need type-constraint in thms? *)
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neuper@38030
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@{thm separate_bdv}; (*::?'a does NOT rewrite here WITHOUT type constraint*)
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neuper@38030
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@{thm separate_bdv_n}; (*::real ..because of ^^^, rewrites*)
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neuper@38030
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@{thm separate_1_bdv}; (*::?'a*)
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neuper@38030
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val xxx = num_str @{thm separate_1_bdv}; (*::?'a*)
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neuper@38030
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@{thm separate_1_bdv_n}; (*::real ..because of ^^^*)
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neuper@38030
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(*show_types := false; --- do we need type-constraint in thms? YES ?!?!?!*)
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neuper@38030
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neuper@38030
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val SOME (t, []) = rewrite_set_inst_ thy true subs rls t;
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neuper@37906
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if term2str t = "1 / EI * (L * q_0 / 2 * x + -1 * q_0 / 2 * x ^^^ 2)" then ()
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neuper@38031
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else error "integrate.sml simplify by ruleset separate_bdv.. #4";
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neuper@37906
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neuper@38030
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"===== test 5";
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neuper@37906
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val t = str2term "1/EI * (L * q_0 * x / 2 + -1 * q_0 * x^^^2 / 2)";
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neuper@37906
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val rls = simplify_Integral;
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neuper@37926
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val SOME (t,[]) = rewrite_set_inst_ thy true subs rls t;
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neuper@38048
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(* given was: "1 / EI * (L * q_0 * x / 2 + -1 * q_0 * x^^^2 / 2)" *)
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neuper@37906
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if term2str t = "1 / EI * (L * q_0 / 2 * x + -1 * q_0 / 2 * x ^^^ 2)" then ()
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neuper@38031
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else error "integrate.sml, simplify_Integral #99";
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neuper@37906
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neuper@38030
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neuper@37906
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"........... 2nd integral ........................................";
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neuper@37906
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"........... 2nd integral ........................................";
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neuper@37906
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"........... 2nd integral ........................................";
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neuper@37906
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val t = str2term
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neuper@38030
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"Integral 1 / EI * (L * q_0 / 2 * (x ^^^ 2 / 2) + -1 * q_0 / 2 * (x ^^^ 3 / 3)) D x";
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neuper@37906
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246 |
val rls = simplify_Integral;
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neuper@37926
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247 |
val SOME (t,[]) = rewrite_set_inst_ thy true subs rls t;
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neuper@37906
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if term2str t =
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neuper@38048
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249 |
"Integral 1 / EI * (L * q_0 / 4 * x ^^^ 2 + -1 * q_0 / 6 * x ^^^ 3) D x"
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neuper@38048
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then () else raise error "integrate.sml, simplify_Integral #198";
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neuper@38030
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neuper@37906
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val rls = integration_rules;
|
neuper@37926
|
253 |
val SOME (t,[]) = rewrite_set_ thy true rls t;
|
neuper@37906
|
254 |
if term2str t =
|
neuper@37906
|
255 |
"1 / EI * (L * q_0 / 4 * (x ^^^ 3 / 3) + -1 * q_0 / 6 * (x ^^^ 4 / 4))"
|
neuper@38031
|
256 |
then () else error "integrate.sml, simplify_Integral #199";
|
neuper@37906
|
257 |
|
neuper@37906
|
258 |
|
neuper@38013
|
259 |
"----------- integrate by ruleset -----------------------";
|
neuper@38013
|
260 |
"----------- integrate by ruleset -----------------------";
|
neuper@38013
|
261 |
"----------- integrate by ruleset -----------------------";
|
neuper@37906
|
262 |
val rls = "integration_rules";
|
neuper@37906
|
263 |
val subs = [("bdv","x::real")];
|
neuper@37906
|
264 |
fun rewrit_sinst subs rls str =
|
neuper@37991
|
265 |
fst (the (rewrite_set_inst "Integrate" true subs rls str));
|
neuper@37906
|
266 |
(*~~~~~~~~~~~~~~~~~~~~~~~~~~~*)
|
neuper@37906
|
267 |
val str = rewrit_sinst subs rls "Integral x D x";
|
neuper@37906
|
268 |
val str = rewrit_sinst subs rls "Integral c * x ^^^ 2 + c_2 D x";
|
neuper@37906
|
269 |
if str = "c * (x ^^^ 3 / 3) + c_2 * x"
|
neuper@38031
|
270 |
then () else error "integrate.sml: diff.behav. in integration_rules";
|
neuper@37906
|
271 |
|
neuper@37906
|
272 |
val rls = "add_new_c";
|
neuper@37906
|
273 |
val str = rewrit_sinst subs rls "c * (x ^^^ 3 / 3) + c_2 * x";
|
neuper@37906
|
274 |
if str = "c * (x ^^^ 3 / 3) + c_2 * x + c_3" then ()
|
neuper@38031
|
275 |
else error "integrate.sml: diff.behav. in add_new_c simpl.";
|
neuper@37906
|
276 |
|
neuper@37906
|
277 |
val str = rewrit_sinst subs rls "F x = x ^^^ 3 / 3 + x";
|
neuper@37906
|
278 |
if str = "F x = x ^^^ 3 / 3 + x + c"(*not "F x + c =..."*) then ()
|
neuper@38031
|
279 |
else error "integrate.sml: diff.behav. in add_new_c equation";
|
neuper@37906
|
280 |
|
neuper@37906
|
281 |
val rls = "simplify_Integral";
|
neuper@37906
|
282 |
(*~~~~~~~~~~~~~~~~~~~~~~~~~~~*)
|
neuper@37906
|
283 |
val str = "ff x = c * x + -1 * q_0 * (x ^^^ 2 / 2) + c_2";
|
neuper@37906
|
284 |
val str = rewrit_sinst subs rls str;
|
neuper@37906
|
285 |
if str = "ff x = c_2 + c * x + -1 * q_0 / 2 * x ^^^ 2"
|
neuper@38031
|
286 |
then () else error "integrate.sml: diff.behav. in simplify_I #1";
|
neuper@37906
|
287 |
|
neuper@37906
|
288 |
val rls = "integration";
|
neuper@37906
|
289 |
(*~~~~~~~~~~~~~~~~~~~~~~~~~~~*)
|
neuper@37906
|
290 |
val str = rewrit_sinst subs rls "Integral c * x ^^^ 2 + c_2 D x";
|
neuper@37906
|
291 |
if str = "c_3 + c_2 * x + c / 3 * x ^^^ 3"
|
neuper@38031
|
292 |
then () else error "integrate.sml: diff.behav. in integration #1";
|
neuper@37906
|
293 |
|
neuper@37906
|
294 |
val str = rewrit_sinst subs rls "Integral 3*x^^^2 + 2*x + 1 D x";
|
neuper@37906
|
295 |
if str = "c + x + x ^^^ 2 + x ^^^ 3" then ()
|
neuper@38031
|
296 |
else error "integrate.sml: diff.behav. in integration #2";
|
neuper@37906
|
297 |
|
neuper@37906
|
298 |
val str = rewrit_sinst subs rls
|
neuper@37906
|
299 |
"Integral 1 / EI * (L * q_0 / 2 * x + -1 * q_0 / 2 * x ^^^ 2) D x";
|
neuper@37906
|
300 |
if str =
|
neuper@37906
|
301 |
"c + 1 / EI * (L * q_0 / 4 * x ^^^ 2 + -1 * q_0 / 6 * x ^^^ 3)"
|
neuper@38031
|
302 |
then () else error "integrate.sml: diff.behav. in integration #3";
|
neuper@37906
|
303 |
|
neuper@37906
|
304 |
val str = "Integral "^str^" D x";
|
neuper@37906
|
305 |
val str = rewrit_sinst subs rls str;
|
neuper@37906
|
306 |
if str =
|
neuper@37906
|
307 |
"c_2 + c * x + 1 / EI * (L * q_0 / 12 * x ^^^ 3 + -1 * q_0 / 24 * x ^^^ 4)"
|
neuper@38031
|
308 |
then () else error "integrate.sml: diff.behav. in integration #4";
|
neuper@37906
|
309 |
|
neuper@37906
|
310 |
|
neuper@38048
|
311 |
|
neuper@38013
|
312 |
"----------- rewrite 3rd integration in 7.27 ------------";
|
neuper@38013
|
313 |
"----------- rewrite 3rd integration in 7.27 ------------";
|
neuper@38013
|
314 |
"----------- rewrite 3rd integration in 7.27 ------------";
|
neuper@38048
|
315 |
val thy = theory "Isac" (*because of Undeclared constant "Biegelinie.EI*);
|
neuper@37906
|
316 |
val bdv = [(str2term"bdv", str2term"x")];
|
neuper@37906
|
317 |
val t = str2term
|
neuper@37906
|
318 |
"Integral 1 / EI * ((L * q_0 * x + -1 * q_0 * x ^^^ 2) / 2) D x";
|
neuper@37926
|
319 |
val SOME(t,_)= rewrite_set_inst_ thy true bdv simplify_Integral t;
|
neuper@37906
|
320 |
if term2str t =
|
neuper@37906
|
321 |
"Integral 1 / EI * (L * q_0 / 2 * x + -1 * q_0 / 2 * x ^^^ 2) D x" then ()
|
neuper@38031
|
322 |
else error "integrate.sml 3rd integration in 7.27, simplify_Integral";
|
neuper@37906
|
323 |
|
neuper@37926
|
324 |
val SOME(t,_)= rewrite_set_inst_ thy true bdv integration t;
|
neuper@37906
|
325 |
if term2str t = "c + 1 / EI * (L * q_0 / 4 * x ^^^ 2 + -1 * q_0 / 6 * x ^^^ 3)"
|
neuper@38031
|
326 |
then () else error "integrate.sml 3rd integration in 7.27, integration";
|
neuper@37906
|
327 |
|
neuper@37906
|
328 |
|
neuper@38013
|
329 |
"----------- check probem type --------------------------";
|
neuper@38013
|
330 |
"----------- check probem type --------------------------";
|
neuper@38013
|
331 |
"----------- check probem type --------------------------";
|
neuper@37994
|
332 |
val model = {Given =["functionTerm f_f", "integrateBy v_v"],
|
neuper@37906
|
333 |
Where =[],
|
neuper@38048
|
334 |
Find =["antiDerivative F_F"],
|
neuper@37906
|
335 |
With =[],
|
neuper@37906
|
336 |
Relate=[]}:string ppc;
|
neuper@38013
|
337 |
val chkmodel = ((map (the o (parse thy))) o ppc2list) model;
|
neuper@37906
|
338 |
val t1 = (term_of o hd) chkmodel;
|
neuper@37906
|
339 |
val t2 = (term_of o hd o tl) chkmodel;
|
neuper@37906
|
340 |
val t3 = (term_of o hd o tl o tl) chkmodel;
|
neuper@37906
|
341 |
case t3 of Const ("Integrate.antiDerivative", _) $ _ => ()
|
neuper@38031
|
342 |
| _ => error "integrate.sml: Integrate.antiDerivative ???";
|
neuper@37906
|
343 |
|
neuper@37994
|
344 |
val model = {Given =["functionTerm f_f", "integrateBy v_v"],
|
neuper@37906
|
345 |
Where =[],
|
neuper@38049
|
346 |
Find =["antiDerivativeName F_F"],
|
neuper@37906
|
347 |
With =[],
|
neuper@37906
|
348 |
Relate=[]}:string ppc;
|
neuper@38013
|
349 |
val chkmodel = ((map (the o (parse thy))) o ppc2list) model;
|
neuper@37906
|
350 |
val t1 = (term_of o hd) chkmodel;
|
neuper@37906
|
351 |
val t2 = (term_of o hd o tl) chkmodel;
|
neuper@37906
|
352 |
val t3 = (term_of o hd o tl o tl) chkmodel;
|
neuper@37906
|
353 |
case t3 of Const ("Integrate.antiDerivativeName", _) $ _ => ()
|
neuper@38031
|
354 |
| _ => error "integrate.sml: Integrate.antiDerivativeName";
|
neuper@37906
|
355 |
|
neuper@37906
|
356 |
"----- compare 'Find's from problem, script, formalization -------";
|
neuper@37906
|
357 |
val {ppc,...} = get_pbt ["named","integrate","function"];
|
neuper@37906
|
358 |
val ("#Find", (Const ("Integrate.antiDerivativeName", _),
|
neuper@38049
|
359 |
F1_ as Free ("F_F", F1_type))) = last_elem ppc;
|
neuper@37906
|
360 |
val {scr = Script sc,... } = get_met ["diff","integration","named"];
|
neuper@37906
|
361 |
val [_,_, F2_] = formal_args sc;
|
neuper@38031
|
362 |
if F1_ = F2_ then () else error "integrate.sml: unequal find's";
|
neuper@37906
|
363 |
|
neuper@37906
|
364 |
val ((dsc as Const ("Integrate.antiDerivativeName", _))
|
neuper@37924
|
365 |
$ Free ("ff", F3_type)) = str2term "antiDerivativeName ff";
|
neuper@38031
|
366 |
if is_dsc dsc then () else error "integrate.sml: no description";
|
neuper@37906
|
367 |
if F1_type = F3_type then ()
|
neuper@38031
|
368 |
else error "integrate.sml: unequal types in find's";
|
neuper@37906
|
369 |
|
neuper@37906
|
370 |
show_ptyps();
|
neuper@37906
|
371 |
val pbl = get_pbt ["integrate","function"];
|
neuper@37926
|
372 |
case #cas pbl of SOME (Const ("Integrate.Integrate",_) $ _) => ()
|
neuper@38031
|
373 |
| _ => error "integrate.sml: Integrate.Integrate ???";
|
neuper@37906
|
374 |
|
neuper@37906
|
375 |
|
neuper@38013
|
376 |
"----------- check Scripts ------------------------------";
|
neuper@38013
|
377 |
"----------- check Scripts ------------------------------";
|
neuper@38013
|
378 |
"----------- check Scripts ------------------------------";
|
neuper@37906
|
379 |
val str =
|
neuper@37994
|
380 |
"Script IntegrationScript (f_f::real) (v_v::real) = \
|
neuper@38049
|
381 |
\ (let t_t = Take (Integral f_f D v_v) \
|
neuper@38049
|
382 |
\ in (Rewrite_Set_Inst [(bdv,v_v)] integration False) (t_t::real))";
|
neuper@37906
|
383 |
val sc = ((inst_abs thy) o term_of o the o (parse thy)) str;
|
neuper@37906
|
384 |
atomty sc;
|
neuper@37906
|
385 |
|
neuper@37906
|
386 |
val str =
|
neuper@38049
|
387 |
"Script NamedIntegrationScript (f_f::real) (v_v::real) (F_F::real=>real) = \
|
neuper@38049
|
388 |
\ (let t_t = Take (F_F v_v = Integral f_f D v_v) \
|
neuper@38049
|
389 |
\ in (Rewrite_Set_Inst [(bdv,v_v)] integration False) t_t)";
|
neuper@37906
|
390 |
val sc = ((inst_abs thy) o term_of o the o (parse thy)) str;
|
neuper@37906
|
391 |
atomty sc;
|
neuper@37906
|
392 |
show_mets();
|
neuper@37906
|
393 |
|
neuper@37906
|
394 |
|
neuper@38013
|
395 |
"----------- me method [diff,integration] ---------------";
|
neuper@38013
|
396 |
"----------- me method [diff,integration] ---------------";
|
neuper@38013
|
397 |
"----------- me method [diff,integration] ---------------";
|
neuper@37906
|
398 |
(*exp_CalcInt_No-1.xml*)
|
neuper@37906
|
399 |
val fmz = ["functionTerm (x^^^2 + 1)",
|
neuper@37906
|
400 |
"integrateBy x","antiDerivative FF"];
|
neuper@37906
|
401 |
val (dI',pI',mI') =
|
neuper@37991
|
402 |
("Integrate",["integrate","function"],
|
neuper@37906
|
403 |
["diff","integration"]);
|
neuper@37906
|
404 |
val p = e_pos'; val c = [];
|
neuper@37906
|
405 |
val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
|
neuper@37906
|
406 |
val (p,_,f,nxt,_,pt) = me nxt p c pt;
|
neuper@37906
|
407 |
val (p,_,f,nxt,_,pt) = me nxt p c pt;
|
neuper@37906
|
408 |
val (p,_,f,nxt,_,pt) = me nxt p c pt;
|
neuper@37906
|
409 |
val (p,_,f,nxt,_,pt) = me nxt p c pt;
|
neuper@37906
|
410 |
val (p,_,f,nxt,_,pt) = me nxt p c pt;
|
neuper@37906
|
411 |
val (p,_,f,nxt,_,pt) = me nxt p c pt;
|
neuper@37906
|
412 |
val (p,_,f,nxt,_,pt) = me nxt p c pt(*nxt <- Apply_Method*);
|
neuper@37906
|
413 |
val (p,_,f,nxt,_,pt) = me nxt p c pt; f2str f;
|
neuper@37906
|
414 |
val (p,_,f,nxt,_,pt) = me nxt p c pt; f2str f;
|
neuper@37906
|
415 |
val (p,_,f,nxt,_,pt) = me nxt p c pt; f2str f;
|
neuper@37906
|
416 |
if f2str f = "c + x + 1 / 3 * x ^^^ 3" then ()
|
neuper@38031
|
417 |
else error "integrate.sml: method [diff,integration]";
|
neuper@37906
|
418 |
|
neuper@37906
|
419 |
|
neuper@38049
|
420 |
(*=== inhibit exn ?=============================================================
|
neuper@38013
|
421 |
"----------- me method [diff,integration,named] ---------";
|
neuper@38013
|
422 |
"----------- me method [diff,integration,named] ---------";
|
neuper@38013
|
423 |
"----------- me method [diff,integration,named] ---------";
|
neuper@37906
|
424 |
(*exp_CalcInt_No-2.xml*)
|
neuper@37906
|
425 |
val fmz = ["functionTerm (x^^^2 + 1)",
|
neuper@37906
|
426 |
"integrateBy x","antiDerivativeName F"];
|
neuper@37906
|
427 |
val (dI',pI',mI') =
|
neuper@37991
|
428 |
("Integrate",["named","integrate","function"],
|
neuper@37906
|
429 |
["diff","integration","named"]);
|
neuper@37906
|
430 |
val p = e_pos'; val c = [];
|
neuper@37906
|
431 |
val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
|
neuper@37906
|
432 |
val (p,_,f,nxt,_,pt) = me nxt p c pt;
|
neuper@37906
|
433 |
val (p,_,f,nxt,_,pt) = me nxt p c pt;
|
neuper@37906
|
434 |
val (p,_,f,nxt,_,pt) = me nxt p c pt(*nxt <- Add_Find *);
|
neuper@37906
|
435 |
val (p,_,f,nxt,_,pt) = me nxt p c pt;
|
neuper@37906
|
436 |
val (p,_,f,nxt,_,pt) = me nxt p c pt;
|
neuper@37906
|
437 |
val (p,_,f,nxt,_,pt) = me nxt p c pt;
|
neuper@37906
|
438 |
val (p,_,f,nxt,_,pt) = me nxt p c pt(*nxt <- Apply_Method*);
|
neuper@37906
|
439 |
val (p,_,f,nxt,_,pt) = me nxt p c pt;
|
neuper@37906
|
440 |
val (p,_,f,nxt,_,pt) = me nxt p c pt;
|
neuper@37906
|
441 |
val (p,_,f,nxt,_,pt) = me nxt p c pt; f2str f;
|
neuper@37906
|
442 |
if f2str f = "F x = c + x + 1 / 3 * x ^^^ 3" then()
|
neuper@38031
|
443 |
else error "integrate.sml: method [diff,integration,named]";
|
neuper@37906
|
444 |
|
neuper@37906
|
445 |
|
neuper@38013
|
446 |
"----------- me met [diff,integration,named] Biegelinie.Q";
|
neuper@38013
|
447 |
"----------- me met [diff,integration,named] Biegelinie.Q";
|
neuper@38013
|
448 |
"----------- me met [diff,integration,named] Biegelinie.Q";
|
neuper@37906
|
449 |
(*exp_CalcInt_No-3.xml*)
|
neuper@37906
|
450 |
val fmz = ["functionTerm (- q_0)",
|
neuper@37906
|
451 |
"integrateBy x","antiDerivativeName Q"];
|
neuper@37906
|
452 |
val (dI',pI',mI') =
|
neuper@37991
|
453 |
("Biegelinie",["named","integrate","function"],
|
neuper@37906
|
454 |
["diff","integration","named"]);
|
neuper@37906
|
455 |
val p = e_pos'; val c = [];
|
neuper@37906
|
456 |
val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
|
neuper@37906
|
457 |
val (p,_,f,nxt,_,pt) = me nxt p c pt;
|
neuper@37906
|
458 |
val (p,_,f,nxt,_,pt) = me nxt p c pt;
|
neuper@37906
|
459 |
(*Error Tac Q not in ...*)
|
neuper@37906
|
460 |
val (p,_,f,nxt,_,pt) = me nxt p c pt(*nxt <- Add_Find *);
|
neuper@37906
|
461 |
val (p,_,f,nxt,_,pt) = me nxt p c pt;
|
neuper@37906
|
462 |
val (p,_,f,nxt,_,pt) = me nxt p c pt;
|
neuper@37906
|
463 |
val (p,_,f,nxt,_,pt) = me nxt p c pt;
|
neuper@37906
|
464 |
val (p,_,f,nxt,_,pt) = me nxt p c pt(*nxt <- Apply_Method*);
|
neuper@37906
|
465 |
val (p,_,f,nxt,_,pt) = me nxt p c pt;
|
neuper@37906
|
466 |
val (p,_,f,nxt,_,pt) = me nxt p c pt;
|
neuper@37906
|
467 |
val (p,_,f,nxt,_,pt) = me nxt p c pt; f2str f;
|
neuper@37906
|
468 |
|
neuper@37906
|
469 |
if f2str f = "Q x = c + -1 * q_0 * x" then()
|
neuper@38031
|
470 |
else error "integrate.sml: method [diff,integration,named] .Q";
|
neuper@37906
|
471 |
|
neuper@37906
|
472 |
|
neuper@38013
|
473 |
"----------- interSteps [diff,integration] --------------";
|
neuper@38013
|
474 |
"----------- interSteps [diff,integration] --------------";
|
neuper@38013
|
475 |
"----------- interSteps [diff,integration] --------------";
|
neuper@37906
|
476 |
states:=[];
|
neuper@37906
|
477 |
CalcTree
|
neuper@37906
|
478 |
[(["functionTerm (x^2 + 1)","integrateBy x","antiDerivative FF"],
|
neuper@37991
|
479 |
("Integrate",["integrate","function"],
|
neuper@37906
|
480 |
["diff","integration"]))];
|
neuper@37906
|
481 |
Iterator 1;
|
neuper@37906
|
482 |
moveActiveRoot 1;
|
neuper@37906
|
483 |
autoCalculate 1 CompleteCalc;
|
neuper@37906
|
484 |
val ((pt,p),_) = get_calc 1; show_pt pt;
|
neuper@37906
|
485 |
|
neuper@37906
|
486 |
interSteps 1 ([1],Res);
|
neuper@37906
|
487 |
val ((pt,p),_) = get_calc 1; show_pt pt;
|
neuper@37906
|
488 |
if existpt' ([1,3], Res) pt then ()
|
neuper@38031
|
489 |
else error "integrate.sml: interSteps on Rewrite_Set_Inst 1";
|
neuper@37906
|
490 |
|
neuper@37906
|
491 |
|
neuper@38013
|
492 |
"----------- method analog to rls 'integration' ---------";
|
neuper@38013
|
493 |
"----------- method analog to rls 'integration' ---------";
|
neuper@38013
|
494 |
"----------- method analog to rls 'integration' ---------";
|
neuper@37906
|
495 |
store_met
|
neuper@38013
|
496 |
(prep_met thy "met_testint" [] e_metID
|
neuper@37906
|
497 |
(["diff","integration","test"],
|
neuper@37994
|
498 |
[("#Given" ,["functionTerm f_f", "integrateBy v_v"]),
|
neuper@38049
|
499 |
("#Find" ,["antiDerivative F_F"])
|
neuper@37906
|
500 |
],
|
neuper@37906
|
501 |
{rew_ord'="tless_true", rls'=Atools_erls, calc = [],
|
neuper@37906
|
502 |
srls = e_rls,
|
neuper@37906
|
503 |
prls=e_rls,
|
neuper@37906
|
504 |
crls = Atools_erls, nrls = e_rls},
|
neuper@37994
|
505 |
"Script IntegrationScript (f_f::real) (v_v::real) = \
|
neuper@37991
|
506 |
\ (((Rewrite_Set_Inst [(bdv,v_v)] integration_rules False) @@ \
|
neuper@37991
|
507 |
\ (Rewrite_Set_Inst [(bdv,v_v)] add_new_c False) @@ \
|
neuper@37994
|
508 |
\ (Rewrite_Set_Inst [(bdv,v_v)] simplify_Integral False)) (f_f::real))"
|
neuper@37906
|
509 |
));
|
neuper@37906
|
510 |
|
neuper@37906
|
511 |
states:=[];
|
neuper@37906
|
512 |
CalcTree
|
neuper@37906
|
513 |
[(["functionTerm (Integral x^2 + 1 D x)","integrateBy x",
|
neuper@37906
|
514 |
"antiDerivative FF"],
|
neuper@37991
|
515 |
("Integrate",["integrate","function"],
|
neuper@37906
|
516 |
["diff","integration","test"]))];
|
neuper@37906
|
517 |
Iterator 1;
|
neuper@37906
|
518 |
moveActiveRoot 1;
|
neuper@37906
|
519 |
autoCalculate 1 CompleteCalcHead;
|
neuper@37906
|
520 |
|
neuper@37906
|
521 |
fetchProposedTactic 1 (*..Apply_Method*);
|
neuper@37906
|
522 |
autoCalculate 1 (Step 1);
|
neuper@37906
|
523 |
getTactic 1 ([1], Frm) (*still empty*);
|
neuper@37906
|
524 |
|
neuper@37906
|
525 |
fetchProposedTactic 1 (*Rewrite_Set_Inst integration_rules*);
|
neuper@37906
|
526 |
autoCalculate 1 (Step 1);
|
neuper@37906
|
527 |
|
neuper@37906
|
528 |
fetchProposedTactic 1 (*Rewrite_Set_Inst add_new_c*);
|
neuper@37906
|
529 |
autoCalculate 1 (Step 1);
|
neuper@37906
|
530 |
|
neuper@37906
|
531 |
fetchProposedTactic 1 (*Rewrite_Set_Inst simplify_Integral*);
|
neuper@37906
|
532 |
autoCalculate 1 (Step 1);
|
neuper@37906
|
533 |
|
neuper@37906
|
534 |
autoCalculate 1 CompleteCalc;
|
neuper@37906
|
535 |
val ((pt,p),_) = get_calc 1; show_pt pt;
|
neuper@37906
|
536 |
if existpt' ([3], Res) pt then ()
|
neuper@38031
|
537 |
else error "integrate.sml: test-script doesnt work";
|
neuper@37906
|
538 |
|
neuper@37906
|
539 |
|
neuper@38013
|
540 |
"----------- Ambiguous input: Integral ?u + ?v D ?bdv = .";
|
neuper@38013
|
541 |
"----------- Ambiguous input: Integral ?u + ?v D ?bdv = .";
|
neuper@38013
|
542 |
"----------- Ambiguous input: Integral ?u + ?v D ?bdv = .";
|
neuper@37906
|
543 |
states:=[];
|
neuper@37906
|
544 |
CalcTree
|
neuper@37906
|
545 |
[(["functionTerm (x^2 + 1)","integrateBy x","antiDerivative FF"],
|
neuper@37991
|
546 |
("Integrate",["integrate","function"],
|
neuper@37906
|
547 |
["diff","integration"]))];
|
neuper@37906
|
548 |
Iterator 1;
|
neuper@37906
|
549 |
moveActiveRoot 1;
|
neuper@37906
|
550 |
autoCalculate 1 CompleteCalc;
|
neuper@37906
|
551 |
val ((pt,p),_) = get_calc 1; show_pt pt;
|
neuper@37906
|
552 |
|
neuper@37906
|
553 |
interSteps 1 ([1],Res);
|
neuper@37906
|
554 |
val ((pt,p),_) = get_calc 1; show_pt pt;
|
neuper@37906
|
555 |
interSteps 1 ([1,1],Res);
|
neuper@37906
|
556 |
val ((pt,p),_) = get_calc 1; show_pt pt;
|
neuper@37906
|
557 |
getTactic 1 ([1,1,1],Frm);
|
neuper@37906
|
558 |
|
neuper@37906
|
559 |
val str = (unenclose o string_of_thm) integral_add;
|
neuper@37906
|
560 |
writeln str;
|
neuper@37906
|
561 |
(*
|
neuper@37906
|
562 |
read_cterm (sign_of thy) (str,(TVar(("DUMMY",0),[])));
|
neuper@37906
|
563 |
|
neuper@37906
|
564 |
*** More than one term is type correct:
|
neuper@37906
|
565 |
*** ((Integral (?u + ?v) D ?bdv) =
|
neuper@37906
|
566 |
*** (Integral ?u D (?bdv + (Integral ?v D ?bdv))))
|
neuper@37906
|
567 |
###^^^###
|
neuper@37906
|
568 |
*** ((Integral (?u + ?v) D ?bdv) =
|
neuper@37906
|
569 |
*** ((Integral ?u D ?bdv) + (Integral ?v D ?bdv)))
|
neuper@37906
|
570 |
*)
|
neuper@37906
|
571 |
|
neuper@37906
|
572 |
if existpt' ([1,1,5], Res) pt then ()
|
neuper@38031
|
573 |
else error "integrate.sml: interSteps on Rewrite_Set_Inst 2";
|
neuper@37906
|
574 |
|
neuper@38013
|
575 |
|
neuper@38013
|
576 |
"----------- CAS input ----------------------------------";
|
neuper@38013
|
577 |
"----------- CAS input ----------------------------------";
|
neuper@38013
|
578 |
"----------- CAS input ----------------------------------";
|
neuper@37906
|
579 |
val t = str2term "Integrate (x^^^2 + x + 1, x)";
|
neuper@37906
|
580 |
case t of Const ("Integrate.Integrate", _) $ _ => ()
|
neuper@38031
|
581 |
| _ => error "diff.sml behav.changed for Integrate (..., x)";
|
neuper@37906
|
582 |
atomty t;
|
neuper@37906
|
583 |
|
neuper@37906
|
584 |
states:=[];
|
neuper@37906
|
585 |
CalcTree [([], ("e_domID", ["e_pblID"], ["e_metID"]))];
|
neuper@37906
|
586 |
Iterator 1;
|
neuper@37906
|
587 |
moveActiveRoot 1;
|
neuper@37906
|
588 |
replaceFormula 1 "Integrate (x^2 + x + 1, x)";
|
neuper@37906
|
589 |
autoCalculate 1 CompleteCalc;
|
neuper@37906
|
590 |
val ((pt,p),_) = get_calc 1;
|
neuper@37906
|
591 |
val Form res = (#1 o pt_extract) (pt, ([],Res));
|
neuper@37906
|
592 |
show_pt pt;
|
neuper@37906
|
593 |
(* WN070703 does not work like Diff due to error in next-pos
|
neuper@37906
|
594 |
if p = ([], Res) andalso term2str res = "5 * a" then ()
|
neuper@38031
|
595 |
else error "diff.sml behav.changed for Integrate (x^2 + x + 1, x)";
|
neuper@37934
|
596 |
*)
|
neuper@38022
|
597 |
|
neuper@38048
|
598 |
===== inhibit exn ?===========================================================*)
|
neuper@38048
|
599 |
|
neuper@38048
|
600 |
(*========== inhibit exn =======================================================
|
neuper@38048
|
601 |
============ inhibit exn =====================================================*)
|
neuper@38048
|
602 |
|
neuper@38048
|
603 |
(*-.-.-.-.-.-isolate response.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.
|
neuper@38048
|
604 |
-.-.-.-.-.-.-isolate response.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.*)
|