1.1 --- a/doc-isac/mlehnfeld/master/ordered-ptyps.Unsynchronized Thu Jun 26 17:19:30 2014 +0200
1.2 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000
1.3 @@ -1,202 +0,0 @@
1.4 -Ptyp ("Berechnung", [
1.5 -{cas = NONE, guh = "pbl_algein", init = ["e_pblID"], mathauthors = "[]", met = [], ppc = [], prls = "e_rls", thy = {AlgEin}, where_ = []}], [
1.6 -Ptyp ("numerischSymbolische", [
1.7 -{cas = NONE, guh = "pbl_algein_numsym", init = ["e_pblID"], mathauthors = "[]", met = [["Berechnung","erstNumerisch"],["Berechnung","erstSymbolisch"]], ppc = ["(#Given, (KantenLaenge, k_k))","(#Given, (Querschnitt, q__q))","(#Given, (KantenUnten, u_u))","(#Given, (KantenSenkrecht, s_s))","(#Given, (KantenOben, o_o))","(#Find, (GesamtLaenge, l_l))"], prls = "e_rls", thy = {AlgEin}, where_ = []}], [])])--1
1.8 -
1.9 -Ptyp ("Biegelinien", [
1.10 -{cas = NONE, guh = "pbl_bieg", init = ["e_pblID"], mathauthors = "[]", met = [["IntegrierenUndKonstanteBestimmen2"]], ppc = ["(#Given, (Traegerlaenge, l_l))","(#Given, (Streckenlast, q_q))","(#Find, (Biegelinie, b_b))","(#Relate, (Randbedingungen, r_b))"], prls = "e_rls", thy = {Biegelinie}, where_ = []}], [
1.11 -Ptyp ("MomentBestimmte", [
1.12 -{cas = NONE, guh = "pbl_bieg_mom", init = ["e_pblID"], mathauthors = "[]", met = [["IntegrierenUndKonstanteBestimmen"]], ppc = ["(#Given, (Traegerlaenge, l_l))","(#Given, (Streckenlast, q_q))","(#Find, (Biegelinie, b_b))","(#Relate, (RandbedingungenBiegung, r_b))","(#Relate, (RandbedingungenMoment, r_m))"], prls = "e_rls", thy = {Biegelinie}, where_ = []}], []),
1.13 -Ptyp ("MomentGegebene", [
1.14 -{cas = NONE, guh = "pbl_bieg_momg", init = ["e_pblID"], mathauthors = "[]", met = [["IntegrierenUndKonstanteBestimmen","2xIntegrieren"]], ppc = [], prls = "e_rls", thy = {Biegelinie}, where_ = []}], []),
1.15 -Ptyp ("QuerkraftUndMomentBestimmte", [
1.16 -{cas = NONE, guh = "pbl_bieg_momquer", init = ["e_pblID"], mathauthors = "[]", met = [["IntegrierenUndKonstanteBestimmen","1xIntegrieren"]], ppc = [], prls = "e_rls", thy = {Biegelinie}, where_ = []}], []),
1.17 -Ptyp ("einfache", [
1.18 -{cas = NONE, guh = "pbl_bieg_einf", init = ["e_pblID"], mathauthors = "[]", met = [["IntegrierenUndKonstanteBestimmen","4x4System"]], ppc = [], prls = "e_rls", thy = {Biegelinie}, where_ = []}], []),
1.19 -Ptyp ("setzeRandbedingungen", [
1.20 -{cas = NONE, guh = "pbl_bieg_randbed", init = ["e_pblID"], mathauthors = "[]", met = [["Biegelinien","setzeRandbedingungenEin"]], ppc = ["(#Given, (Funktionen, fun_s))","(#Given, (Randbedingungen, r_b))","(#Find, (Gleichungen, equs'''))"], prls = "e_rls", thy = {Biegelinie}, where_ = []}], []),
1.21 -Ptyp ("vonBelastungZu", [
1.22 -{cas = NONE, guh = "pbl_bieg_vonq", init = ["e_pblID"], mathauthors = "[]", met = [["Biegelinien","ausBelastung"]], ppc = ["(#Given, (Streckenlast, q_q))","(#Given, (FunktionsVariable, v_v))","(#Find, (Funktionen, funs'''))"], prls = "e_rls", thy = {Biegelinie}, where_ = []}], [])])--2
1.23 -
1.24 -Ptyp ("SignalProcessing", [
1.25 -{cas = NONE, guh = "pbl_SP", init = ["e_pblID"], mathauthors = "[]", met = [], ppc = [], prls = "e_rls", thy = {Inverse_Z_Transform}, where_ = []}], [
1.26 -Ptyp ("Z_Transform", [
1.27 -{cas = NONE, guh = "pbl_SP_Ztrans", init = ["e_pblID"], mathauthors = "[]", met = [], ppc = [], prls = "e_rls", thy = {Inverse_Z_Transform}, where_ = []}], [
1.28 -Ptyp ("Inverse", [
1.29 -{cas = NONE, guh = "pbl_SP_Ztrans_inv", init = ["e_pblID"], mathauthors = "[]", met = [["SignalProcessing","Z_Transform","Inverse"]], ppc = ["(#Given, (filterExpression, X_eq))","(#Find, (stepResponse, n_eq))"], prls = "e_rls", thy = {Inverse_Z_Transform}, where_ = []}], [])])])--3
1.30 -
1.31 -Ptyp ("e_pblID", [
1.32 -{cas = NONE, guh = "pbl_empty", init = ["e_pblID"], mathauthors = "[]", met = [], ppc = [], prls = "e_rls", thy = {Pure}, where_ = []}], [])--4
1.33 -
1.34 -Ptyp ("equation", [
1.35 -{cas = (SOME solve (e_e, v_v)), guh = "pbl_equ", init = ["e_pblID"], mathauthors = "[]", met = [], ppc = ["(#Given, (equality, e_e))","(#Given, (solveFor, v_v))","(#Find, (solutions, v_v'i'))"], prls = "equation_prls", thy = {Equation}, where_ = ["matches (?a = ?b) e_e"]}], [
1.36 -Ptyp ("diophantine", [
1.37 -{cas = (SOME solve (e_e, v_v)), guh = "pbl_equ_dio", init = ["e_pblID"], mathauthors = "[]", met = [["LinEq","solve_lineq_equation"]], ppc = ["(#Given, (boolTestGiven, e_e))","(#Given, (intTestGiven, v_v))","(#Find, (boolTestFind, s_s))"], prls = "e_rls", thy = {DiophantEq}, where_ = []}], []),
1.38 -Ptyp ("makeFunctionTo", [
1.39 -{cas = NONE, guh = "pbl_equ_fromfun", init = ["e_pblID"], mathauthors = "[]", met = [["Equation","fromFunction"]], ppc = ["(#Given, (functionEq, fu_n))","(#Given, (substitution, su_b))","(#Find, (equality, equ'''))"], prls = "e_rls", thy = {Biegelinie}, where_ = []}], []),
1.40 -Ptyp ("univariate", [
1.41 -{cas = (SOME solve (e_e, v_v)), guh = "pbl_equ_univ", init = ["e_pblID"], mathauthors = "[]", met = [], ppc = ["(#Given, (equality, e_e))","(#Given, (solveFor, v_v))","(#Find, (solutions, v_v'i'))"], prls = "univariate_equation_prls", thy = {Equation}, where_ = ["matches (?a = ?b) e_e"]}], [
1.42 -Ptyp ("LINEAR", [
1.43 -{cas = (SOME solve (e_e, v_v)), guh = "pbl_equ_univ_lin", init = ["e_pblID"], mathauthors = "[]", met = [["LinEq","solve_lineq_equation"]], ppc = ["(#Given, (equality, e_e))","(#Given, (solveFor, v_v))","(#Find, (solutions, v_v'i'))"], prls = "LinEq_prls", thy = {LinEq}, where_ = ["False","~ lhs e_e is_polyrat_in v_v","~ rhs e_e is_polyrat_in v_v","lhs e_e has_degree_in v_v = 1","rhs e_e has_degree_in v_v = 1"]}], []),
1.44 -Ptyp ("expanded", [
1.45 -{cas = (SOME solve (e_e, v_v)), guh = "pbl_equ_univ_expand", init = ["e_pblID"], mathauthors = "[]", met = [], ppc = ["(#Given, (equality, e_e))","(#Given, (solveFor, v_v))","(#Find, (solutions, v_v'i'))"], prls = "PolyEq_prls", thy = {PolyEq}, where_ = ["matches (?a = 0) e_e","lhs e_e is_expanded_in v_v"]}], [
1.46 -Ptyp ("degree_2", [
1.47 -{cas = (SOME solve (e_e, v_v)), guh = "pbl_equ_univ_expand_deg2", init = ["e_pblID"], mathauthors = "[]", met = [["PolyEq","complete_square"]], ppc = ["(#Given, (equality, e_e))","(#Given, (solveFor, v_v))","(#Find, (solutions, v_v'i'))"], prls = "PolyEq_prls", thy = {PolyEq}, where_ = ["lhs e_e has_degree_in v_v = 2"]}], [])]),
1.48 -Ptyp ("logarithmic", [
1.49 -{cas = (SOME solve (e_e, v_v)), guh = "pbl_test_equ_univ_log", init = ["e_pblID"], mathauthors = "[]", met = [["Equation","solve_log"]], ppc = ["(#Given, (equality, e_e))","(#Given, (solveFor, v_v))","(#Find, (solutions, v_v'i'))"], prls = "PolyEq_prls", thy = {LogExp}, where_ = ["matches (?a log ?v_v = ?b) e_e"]}], []),
1.50 -Ptyp ("polynomial", [
1.51 -{cas = (SOME solve (e_e, v_v)), guh = "pbl_equ_univ_poly", init = ["e_pblID"], mathauthors = "[]", met = [], ppc = ["(#Given, (equality, e_e))","(#Given, (solveFor, v_v))","(#Find, (solutions, v_v'i'))"], prls = "PolyEq_prls", thy = {PolyEq}, where_ = ["~ e_e is_ratequation_in v_v","~ lhs e_e is_rootTerm_in v_v","~ rhs e_e is_rootTerm_in v_v"]}], [
1.52 -Ptyp ("degree_0", [
1.53 -{cas = (SOME solve (e_e, v_v)), guh = "pbl_equ_univ_poly_deg0", init = ["e_pblID"], mathauthors = "[]", met = [["PolyEq","solve_d0_polyeq_equation"]], ppc = ["(#Given, (equality, e_e))","(#Given, (solveFor, v_v))","(#Find, (solutions, v_v'i'))"], prls = "PolyEq_prls", thy = {PolyEq}, where_ = ["matches (?a = 0) e_e","lhs e_e is_poly_in v_v","lhs e_e has_degree_in v_v = 0"]}], []),
1.54 -Ptyp ("degree_1", [
1.55 -{cas = (SOME solve (e_e, v_v)), guh = "pbl_equ_univ_poly_deg1", init = ["e_pblID"], mathauthors = "[]", met = [["PolyEq","solve_d1_polyeq_equation"]], ppc = ["(#Given, (equality, e_e))","(#Given, (solveFor, v_v))","(#Find, (solutions, v_v'i'))"], prls = "PolyEq_prls", thy = {PolyEq}, where_ = ["matches (?a = 0) e_e","lhs e_e is_poly_in v_v","lhs e_e has_degree_in v_v = 1"]}], []),
1.56 -Ptyp ("degree_2", [
1.57 -{cas = (SOME solve (e_e, v_v)), guh = "pbl_equ_univ_poly_deg2", init = ["e_pblID"], mathauthors = "[]", met = [["PolyEq","solve_d2_polyeq_equation"]], ppc = ["(#Given, (equality, e_e))","(#Given, (solveFor, v_v))","(#Find, (solutions, v_v'i'))"], prls = "PolyEq_prls", thy = {PolyEq}, where_ = ["matches (?a = 0) e_e","lhs e_e is_poly_in v_v","lhs e_e has_degree_in v_v = 2"]}], [
1.58 -Ptyp ("abcFormula", [
1.59 -{cas = (SOME solve (e_e, v_v)), guh = "pbl_equ_univ_poly_deg2_abc", init = ["e_pblID"], mathauthors = "[]", met = [["PolyEq","solve_d2_polyeq_abc_equation"]], ppc = ["(#Given, (equality, e_e))","(#Given, (solveFor, v_v))","(#Find, (solutions, v_v'i'))"], prls = "PolyEq_prls", thy = {PolyEq}, where_ = ["matches (?a + ?v_ ^^^ 2 = 0) e_e | matches (?a + ?b * ?v_ ^^^ 2 = 0) e_e"]}], []),
1.60 -Ptyp ("bdv_only", [
1.61 -{cas = (SOME solve (e_e, v_v)), guh = "pbl_equ_univ_poly_deg2_bdvonly", init = ["e_pblID"], mathauthors = "[]", met = [["PolyEq","solve_d2_polyeq_bdvonly_equation"]], ppc = ["(#Given, (equality, e_e))","(#Given, (solveFor, v_v))","(#Find, (solutions, v_v'i'))"], prls = "PolyEq_prls", thy = {PolyEq}, where_ = ["matches (?a * ?v_ + ?v_ ^^^ 2 = 0) e_e |
1.62 -matches (?v_ + ?v_ ^^^ 2 = 0) e_e |
1.63 -matches (?v_ + ?b * ?v_ ^^^ 2 = 0) e_e |
1.64 -matches (?a * ?v_ + ?b * ?v_ ^^^ 2 = 0) e_e |
1.65 -matches (?v_ ^^^ 2 = 0) e_e | matches (?b * ?v_ ^^^ 2 = 0) e_e"]}], []),
1.66 -Ptyp ("pqFormula", [
1.67 -{cas = (SOME solve (e_e, v_v)), guh = "pbl_equ_univ_poly_deg2_pq", init = ["e_pblID"], mathauthors = "[]", met = [["PolyEq","solve_d2_polyeq_pq_equation"]], ppc = ["(#Given, (equality, e_e))","(#Given, (solveFor, v_v))","(#Find, (solutions, v_v'i'))"], prls = "PolyEq_prls", thy = {PolyEq}, where_ = ["matches (?a + 1 * ?v_ ^^^ 2 = 0) e_e | matches (?a + ?v_ ^^^ 2 = 0) e_e"]}], []),
1.68 -Ptyp ("sq_only", [
1.69 -{cas = (SOME solve (e_e, v_v)), guh = "pbl_equ_univ_poly_deg2_sqonly", init = ["e_pblID"], mathauthors = "[]", met = [["PolyEq","solve_d2_polyeq_sqonly_equation"]], ppc = ["(#Given, (equality, e_e))","(#Given, (solveFor, v_v))","(#Find, (solutions, v_v'i'))"], prls = "PolyEq_prls", thy = {PolyEq}, where_ = ["matches (?a + ?v_ ^^^ 2 = 0) e_e |
1.70 -matches (?a + ?b * ?v_ ^^^ 2 = 0) e_e |
1.71 -matches (?v_ ^^^ 2 = 0) e_e | matches (?b * ?v_ ^^^ 2 = 0) e_e","~ matches (?a + ?v_ + ?v_ ^^^ 2 = 0) e_e &
1.72 -~ matches (?a + ?b * ?v_ + ?v_ ^^^ 2 = 0) e_e &
1.73 -~ matches (?a + ?v_ + ?c * ?v_ ^^^ 2 = 0) e_e &
1.74 -~ matches (?a + ?b * ?v_ + ?c * ?v_ ^^^ 2 = 0) e_e &
1.75 -~ matches (?v_ + ?v_ ^^^ 2 = 0) e_e &
1.76 -~ matches (?b * ?v_ + ?v_ ^^^ 2 = 0) e_e &
1.77 -~ matches (?v_ + ?c * ?v_ ^^^ 2 = 0) e_e &
1.78 -~ matches (?b * ?v_ + ?c * ?v_ ^^^ 2 = 0) e_e"]}], [])]),
1.79 -Ptyp ("degree_3", [
1.80 -{cas = (SOME solve (e_e, v_v)), guh = "pbl_equ_univ_poly_deg3", init = ["e_pblID"], mathauthors = "[]", met = [["PolyEq","solve_d3_polyeq_equation"]], ppc = ["(#Given, (equality, e_e))","(#Given, (solveFor, v_v))","(#Find, (solutions, v_v'i'))"], prls = "PolyEq_prls", thy = {PolyEq}, where_ = ["matches (?a = 0) e_e","lhs e_e is_poly_in v_v","lhs e_e has_degree_in v_v = 3"]}], []),
1.81 -Ptyp ("degree_4", [
1.82 -{cas = (SOME solve (e_e, v_v)), guh = "pbl_equ_univ_poly_deg4", init = ["e_pblID"], mathauthors = "[]", met = [], ppc = ["(#Given, (equality, e_e))","(#Given, (solveFor, v_v))","(#Find, (solutions, v_v'i'))"], prls = "PolyEq_prls", thy = {PolyEq}, where_ = ["matches (?a = 0) e_e","lhs e_e is_poly_in v_v","lhs e_e has_degree_in v_v = 4"]}], []),
1.83 -Ptyp ("normalize", [
1.84 -{cas = (SOME solve (e_e, v_v)), guh = "pbl_equ_univ_poly_norm", init = ["e_pblID"], mathauthors = "[]", met = [["PolyEq","normalize_poly"]], ppc = ["(#Given, (equality, e_e))","(#Given, (solveFor, v_v))","(#Find, (solutions, v_v'i'))"], prls = "PolyEq_prls", thy = {PolyEq}, where_ = ["~ matches (?a = 0) e_e | ~ lhs e_e is_poly_in v_v"]}], [])]),
1.85 -Ptyp ("rational", [
1.86 -{cas = (SOME solve (e_e, v_v)), guh = "pbl_equ_univ_rat", init = ["e_pblID"], mathauthors = "[]", met = [["RatEq","solve_rat_equation"]], ppc = ["(#Given, (equality, e_e))","(#Given, (solveFor, v_v))","(#Find, (solutions, v_v'i'))"], prls = "RatEq_prls", thy = {RatEq}, where_ = ["e_e is_ratequation_in v_v"]}], []),
1.87 -Ptyp ("root'", [
1.88 -{cas = (SOME solve (e_e, v_v)), guh = "pbl_equ_univ_root", init = ["e_pblID"], mathauthors = "[]", met = [], ppc = ["(#Given, (equality, e_e))","(#Given, (solveFor, v_v))","(#Find, (solutions, v_v'i'))"], prls = "RootEq_prls", thy = {RootEq}, where_ = ["lhs e_e is_rootTerm_in v_v | rhs e_e is_rootTerm_in v_v"]}], [
1.89 -Ptyp ("normalize", [
1.90 -{cas = (SOME solve (e_e, v_v)), guh = "pbl_equ_univ_root_norm", init = ["e_pblID"], mathauthors = "[]", met = [["RootEq","norm_sq_root_equation"]], ppc = ["(#Given, (equality, e_e))","(#Given, (solveFor, v_v))","(#Find, (solutions, v_v'i'))"], prls = "RootEq_prls", thy = {RootEq}, where_ = ["lhs e_e is_sqrtTerm_in v_v & ~ lhs e_e is_normSqrtTerm_in v_v |
1.91 -rhs e_e is_sqrtTerm_in v_v & ~ rhs e_e is_normSqrtTerm_in v_v"]}], []),
1.92 -Ptyp ("sq", [
1.93 -{cas = (SOME solve (e_e, v_v)), guh = "pbl_equ_univ_root_sq", init = ["e_pblID"], mathauthors = "[]", met = [["RootEq","solve_sq_root_equation"]], ppc = ["(#Given, (equality, e_e))","(#Given, (solveFor, v_v))","(#Find, (solutions, v_v'i'))"], prls = "RootEq_prls", thy = {RootEq}, where_ = ["lhs e_e is_sqrtTerm_in v_v & lhs e_e is_normSqrtTerm_in v_v |
1.94 -rhs e_e is_sqrtTerm_in v_v & rhs e_e is_normSqrtTerm_in v_v"]}], [
1.95 -Ptyp ("rat", [
1.96 -{cas = (SOME solve (e_e, v_v)), guh = "pbl_equ_univ_root_sq_rat", init = ["e_pblID"], mathauthors = "[]", met = [["RootRatEq","elim_rootrat_equation"]], ppc = ["(#Given, (equality, e_e))","(#Given, (solveFor, v_v))","(#Find, (solutions, v_v'i'))"], prls = "RootRatEq_prls", thy = {RootRatEq}, where_ = ["lhs e_e is_rootRatAddTerm_in v_v | rhs e_e is_rootRatAddTerm_in v_v"]}], [])])])])])--5
1.97 -
1.98 -Ptyp ("function", [
1.99 -{cas = NONE, guh = "pbl_fun", init = ["e_pblID"], mathauthors = "[]", met = [], ppc = [], prls = "e_rls", thy = {Diff}, where_ = []}], [
1.100 -Ptyp ("derivative_of", [
1.101 -{cas = (SOME Diff (f_f, v_v)), guh = "pbl_fun_deriv", init = ["e_pblID"], mathauthors = "[]", met = [["diff","differentiate_on_R"],["diff","after_simplification"]], ppc = ["(#Given, (functionTerm, f_f))","(#Given, (differentiateFor, v_v))","(#Find, (derivative, f_f'))"], prls = "e_rls", thy = {Diff}, where_ = []}], [
1.102 -Ptyp ("named", [
1.103 -{cas = (SOME Differentiate (f_f, v_v)), guh = "pbl_fun_deriv_nam", init = ["e_pblID"], mathauthors = "[]", met = [["diff","differentiate_equality"]], ppc = ["(#Given, (functionEq, f_f))","(#Given, (differentiateFor, v_v))","(#Find, (derivativeEq, f_f'))"], prls = "e_rls", thy = {Diff}, where_ = []}], [])]),
1.104 -Ptyp ("integrate", [
1.105 -{cas = (SOME Integrate (f_f, v_v)), guh = "pbl_fun_integ", init = ["e_pblID"], mathauthors = "[]", met = [["diff","integration"]], ppc = ["(#Given, (functionTerm, f_f))","(#Given, (integrateBy, v_v))","(#Find, (Integrate.antiDerivative, F_F))"], prls = "e_rls", thy = {Integrate}, where_ = []}], [
1.106 -Ptyp ("named", [
1.107 -{cas = (SOME Integrate (f_f, v_v)), guh = "pbl_fun_integ_nam", init = ["e_pblID"], mathauthors = "[]", met = [["diff","integration","named"]], ppc = ["(#Given, (functionTerm, f_f))","(#Given, (integrateBy, v_v))","(#Find, (antiDerivativeName, F_F))"], prls = "e_rls", thy = {Integrate}, where_ = []}], [])]),
1.108 -Ptyp ("make", [
1.109 -{cas = NONE, guh = "pbl_fun_make", init = ["e_pblID"], mathauthors = "[]", met = [], ppc = ["(#Given, (functionOf, f_f))","(#Given, (boundVariable, v_v))","(#Given, (equalities, eqs))","(#Find, (functionEq, f_1))"], prls = "e_rls", thy = {DiffApp}, where_ = []}], [
1.110 -Ptyp ("by_explicit", [
1.111 -{cas = NONE, guh = "pbl_fun_max_expl", init = ["e_pblID"], mathauthors = "[]", met = [["DiffApp","make_fun_by_explicit"]], ppc = ["(#Given, (functionOf, f_f))","(#Given, (boundVariable, v_v))","(#Given, (equalities, eqs))","(#Find, (functionEq, f_1))"], prls = "e_rls", thy = {DiffApp}, where_ = []}], []),
1.112 -Ptyp ("by_new_variable", [
1.113 -{cas = NONE, guh = "pbl_fun_max_newvar", init = ["e_pblID"], mathauthors = "[]", met = [["DiffApp","make_fun_by_new_variable"]], ppc = ["(#Given, (functionOf, f_f))","(#Given, (boundVariable, v_v))","(#Given, (equalities, eqs))","(#Find, (functionEq, f_1))"], prls = "e_rls", thy = {DiffApp}, where_ = []}], [])]),
1.114 -Ptyp ("maximum_of", [
1.115 -{cas = NONE, guh = "pbl_fun_max", init = ["e_pblID"], mathauthors = "[]", met = [], ppc = ["(#Given, (fixedValues, f_ix))","(#Find, (maximum, m_m))","(#Find, (valuesFor, v_s))","(#Relate, (relations, r_s))"], prls = "e_rls", thy = {DiffApp}, where_ = []}], [
1.116 -Ptyp ("on_interval", [
1.117 -{cas = NONE, guh = "pbl_fun_max_interv", init = ["e_pblID"], mathauthors = "[]", met = [], ppc = ["(#Given, (functionEq, t_t))","(#Given, (boundVariable, v_v))","(#Given, (interval, i_tv))","(#Find, (maxArgument, v_0))"], prls = "e_rls", thy = {DiffApp}, where_ = []}], [])])])--6
1.118 -
1.119 -Ptyp ("probe", [
1.120 -{cas = NONE, guh = "pbl_probe", init = ["e_pblID"], mathauthors = "[]", met = [], ppc = [], prls = "e_rls", thy = {PolyMinus}, where_ = []}], [
1.121 -Ptyp ("bruch", [
1.122 -{cas = (SOME Probe e_e w_w), guh = "pbl_probe_bruch", init = ["e_pblID"], mathauthors = "[]", met = [["probe","fuer_bruch"]], ppc = ["(#Given, (Pruefe, e_e))","(#Given, (mitWert, w_w))","(#Find, (Geprueft, p_p))"], prls = "prls_pbl_probe_bruch", thy = {PolyMinus}, where_ = ["e_e is_ratpolyexp"]}], []),
1.123 -Ptyp ("polynom", [
1.124 -{cas = (SOME Probe e_e w_w), guh = "pbl_probe_poly", init = ["e_pblID"], mathauthors = "[]", met = [["probe","fuer_polynom"]], ppc = ["(#Given, (Pruefe, e_e))","(#Given, (mitWert, w_w))","(#Find, (Geprueft, p_p))"], prls = "prls_pbl_probe_poly", thy = {PolyMinus}, where_ = ["e_e is_polyexp"]}], [])])--7
1.125 -
1.126 -Ptyp ("simplification", [
1.127 -{cas = (SOME Simplify t_t), guh = "pbl_simp", init = ["e_pblID"], mathauthors = "[]", met = [], ppc = ["(#Given, (Term, t_t))","(#Find, (normalform, n_n))"], prls = "e_rls", thy = {Simplify}, where_ = []}], [
1.128 -Ptyp ("polynomial", [
1.129 -{cas = (SOME Simplify t_t), guh = "pbl_simp_poly", init = ["e_pblID"], mathauthors = "[]", met = [["simplification","for_polynomials"]], ppc = ["(#Given, (Term, t_t))","(#Find, (normalform, n_n))"], prls = "e_rls", thy = {Poly}, where_ = ["t_t is_polyexp"]}], []),
1.130 -Ptyp ("rational", [
1.131 -{cas = (SOME Simplify t_t), guh = "pbl_simp_rat", init = ["e_pblID"], mathauthors = "[]", met = [["simplification","of_rationals"]], ppc = ["(#Given, (Term, t_t))","(#Find, (normalform, n_n))"], prls = "e_rls", thy = {Rational}, where_ = ["t_t is_ratpolyexp"]}], [
1.132 -Ptyp ("partial_fraction", [
1.133 -{cas = NONE, guh = "pbl_simp_rat_partfrac", init = ["e_pblID"], mathauthors = "[]", met = [["simplification","of_rationals","to_partial_fraction"]], ppc = ["(#Given, (functionTerm, t_t))","(#Given, (solveFor, v_v))","(#Find, (decomposedFunction, p_p'''))"], prls = "e_rls", thy = {Partial_Fractions}, where_ = []}], [])])])--8
1.134 -
1.135 -Ptyp ("system", [
1.136 -{cas = (SOME solveSystem e_s v_s), guh = "pbl_equsys", init = ["e_pblID"], mathauthors = "[]", met = [], ppc = ["(#Given, (equalities, e_s))","(#Given, (solveForVars, v_s))","(#Find, (solution, ss'''))"], prls = "e_rls", thy = {EqSystem}, where_ = []}], [
1.137 -Ptyp ("LINEAR", [
1.138 -{cas = (SOME solveSystem e_s v_s), guh = "pbl_equsys_lin", init = ["e_pblID"], mathauthors = "[]", met = [], ppc = ["(#Given, (equalities, e_s))","(#Given, (solveForVars, v_s))","(#Find, (solution, ss'''))"], prls = "e_rls", thy = {EqSystem}, where_ = []}], [
1.139 -Ptyp ("2x2", [
1.140 -{cas = (SOME solveSystem e_s v_s), guh = "pbl_equsys_lin_2x2", init = ["e_pblID"], mathauthors = "[]", met = [], ppc = ["(#Given, (equalities, e_s))","(#Given, (solveForVars, v_s))","(#Find, (solution, ss'''))"], prls = "prls_2x2_linear_system", thy = {EqSystem}, where_ = ["LENGTH e_s = 2","LENGTH v_s = 2"]}], [
1.141 -Ptyp ("normalize", [
1.142 -{cas = (SOME solveSystem e_s v_s), guh = "pbl_equsys_lin_2x2_norm", init = ["e_pblID"], mathauthors = "[]", met = [["EqSystem","normalize","2x2"]], ppc = ["(#Given, (equalities, e_s))","(#Given, (solveForVars, v_s))","(#Find, (solution, ss'''))"], prls = "e_rls", thy = {EqSystem}, where_ = []}], []),
1.143 -Ptyp ("triangular", [
1.144 -{cas = (SOME solveSystem e_s v_s), guh = "pbl_equsys_lin_2x2_tri", init = ["e_pblID"], mathauthors = "[]", met = [["EqSystem","top_down_substitution","2x2"]], ppc = ["(#Given, (equalities, e_s))","(#Given, (solveForVars, v_s))","(#Find, (solution, ss'''))"], prls = "prls_triangular", thy = {EqSystem}, where_ = ["tl v_s from v_s occur_exactly_in NTH 1 e_s","v_s from v_s occur_exactly_in NTH 2 e_s"]}], [])]),
1.145 -Ptyp ("3x3", [
1.146 -{cas = (SOME solveSystem e_s v_s), guh = "pbl_equsys_lin_3x3", init = ["e_pblID"], mathauthors = "[]", met = [], ppc = ["(#Given, (equalities, e_s))","(#Given, (solveForVars, v_s))","(#Find, (solution, ss'''))"], prls = "prls_3x3_linear_system", thy = {EqSystem}, where_ = ["LENGTH e_s = 3","LENGTH v_s = 3"]}], []),
1.147 -Ptyp ("4x4", [
1.148 -{cas = (SOME solveSystem e_s v_s), guh = "pbl_equsys_lin_4x4", init = ["e_pblID"], mathauthors = "[]", met = [], ppc = ["(#Given, (equalities, e_s))","(#Given, (solveForVars, v_s))","(#Find, (solution, ss'''))"], prls = "prls_4x4_linear_system", thy = {EqSystem}, where_ = ["LENGTH e_s = 4","LENGTH v_s = 4"]}], [
1.149 -Ptyp ("normalize", [
1.150 -{cas = (SOME solveSystem e_s v_s), guh = "pbl_equsys_lin_4x4_norm", init = ["e_pblID"], mathauthors = "[]", met = [["EqSystem","normalize","4x4"]], ppc = ["(#Given, (equalities, e_s))","(#Given, (solveForVars, v_s))","(#Find, (solution, ss'''))"], prls = "e_rls", thy = {EqSystem}, where_ = []}], []),
1.151 -Ptyp ("triangular", [
1.152 -{cas = (SOME solveSystem e_s v_s), guh = "pbl_equsys_lin_4x4_tri", init = ["e_pblID"], mathauthors = "[]", met = [["EqSystem","top_down_substitution","4x4"]], ppc = ["(#Given, (equalities, e_s))","(#Given, (solveForVars, v_s))","(#Find, (solution, ss'''))"], prls = "prls_tri_4x4_lin_sys", thy = {EqSystem}, where_ = ["NTH 1 v_s occurs_in NTH 1 e_s","NTH 2 v_s occurs_in NTH 2 e_s","NTH 3 v_s occurs_in NTH 3 e_s","NTH 4 v_s occurs_in NTH 4 e_s"]}], [])])])])--9
1.153 -
1.154 -Ptyp ("test", [
1.155 -{cas = NONE, guh = "pbl_test", init = ["e_pblID"], mathauthors = "[]", met = [], ppc = [], prls = "e_rls", thy = {Test}, where_ = []}], [
1.156 -Ptyp ("equation", [
1.157 -{cas = (SOME solve (e_e, v_v)), guh = "pbl_test_equ", init = ["e_pblID"], mathauthors = "[]", met = [], ppc = ["(#Given, (equality, e_e))","(#Given, (solveFor, v_v))","(#Find, (solutions, v_v'i'))"], prls = "matches", thy = {Test}, where_ = ["matches (?a = ?b) e_e"]}], [
1.158 -Ptyp ("univariate", [
1.159 -{cas = (SOME solve (e_e, v_v)), guh = "pbl_test_uni", init = ["e_pblID"], mathauthors = "[]", met = [], ppc = ["(#Given, (equality, e_e))","(#Given, (solveFor, v_v))","(#Find, (solutions, v_v'i'))"], prls = "matches", thy = {Test}, where_ = ["matches (?a = ?b) e_e"]}], [
1.160 -Ptyp ("LINEAR", [
1.161 -{cas = (SOME solve (e_e, v_v)), guh = "pbl_test_uni_lin", init = ["e_pblID"], mathauthors = "[]", met = [["Test","solve_linear"]], ppc = ["(#Given, (equality, e_e))","(#Given, (solveFor, v_v))","(#Find, (solutions, v_v'i'))"], prls = "matches", thy = {Test}, where_ = ["matches (v_v = 0) e_e |
1.162 -matches (?b * v_v = 0) e_e |
1.163 -matches (?a + v_v = 0) e_e | matches (?a + ?b * v_v = 0) e_e"]}], []),
1.164 -Ptyp ("normalize", [
1.165 -{cas = (SOME solve (e_e, v_v)), guh = "pbl_test_uni_norm", init = ["e_pblID"], mathauthors = "[]", met = [["Test","norm_univar_equation"]], ppc = ["(#Given, (equality, e_e))","(#Given, (solveFor, v_v))","(#Find, (solutions, v_v'i'))"], prls = "e_rls", thy = {Test}, where_ = []}], []),
1.166 -Ptyp ("plain_square", [
1.167 -{cas = (SOME solve (e_e, v_v)), guh = "pbl_test_uni_plain2", init = ["e_pblID"], mathauthors = "[]", met = [["Test","solve_plain_square"]], ppc = ["(#Given, (equality, e_e))","(#Given, (solveFor, v_v))","(#Find, (solutions, v_v'i'))"], prls = "matches", thy = {Test}, where_ = ["matches (?a + ?b * v_v ^^^ 2 = 0) e_e |
1.168 -matches (?b * v_v ^^^ 2 = 0) e_e |
1.169 -matches (?a + v_v ^^^ 2 = 0) e_e | matches (v_v ^^^ 2 = 0) e_e"]}], []),
1.170 -Ptyp ("polynomial", [
1.171 -{cas = (SOME solve (e_e, v_v)), guh = "pbl_test_uni_poly", init = ["e_pblID"], mathauthors = "[]", met = [], ppc = ["(#Given, (equality, v_v ^^^ 2 + p_p * v_v + q__q = 0))","(#Given, (solveFor, v_v))","(#Find, (solutions, v_v'i'))"], prls = "e_rls", thy = {Test}, where_ = ["False"]}], [
1.172 -Ptyp ("degree_two", [
1.173 -{cas = (SOME solve (v_v ^^^ 2 + p_p * v_v + q__q = 0, v_v)), guh = "pbl_test_uni_poly_deg2", init = ["e_pblID"], mathauthors = "[]", met = [], ppc = ["(#Given, (equality, v_v ^^^ 2 + p_p * v_v + q__q = 0))","(#Given, (solveFor, v_v))","(#Find, (solutions, v_v'i'))"], prls = "e_rls", thy = {Test}, where_ = []}], [
1.174 -Ptyp ("abc_formula", [
1.175 -{cas = (SOME solve (a_a * x ^^^ 2 + b_b * x + c_c = 0, v_v)), guh = "pbl_test_uni_poly_deg2_abc", init = ["e_pblID"], mathauthors = "[]", met = [], ppc = ["(#Given, (equality, a_a * x ^^^ 2 + b_b * x + c_c = 0))","(#Given, (solveFor, v_v))","(#Find, (solutions, v_v'i'))"], prls = "e_rls", thy = {Test}, where_ = []}], []),
1.176 -Ptyp ("pq_formula", [
1.177 -{cas = (SOME solve (v_v ^^^ 2 + p_p * v_v + q__q = 0, v_v)), guh = "pbl_test_uni_poly_deg2_pq", init = ["e_pblID"], mathauthors = "[]", met = [], ppc = ["(#Given, (equality, v_v ^^^ 2 + p_p * v_v + q__q = 0))","(#Given, (solveFor, v_v))","(#Find, (solutions, v_v'i'))"], prls = "e_rls", thy = {Test}, where_ = []}], [])])]),
1.178 -Ptyp ("sqroot-test", [
1.179 -{cas = (SOME solve (e_e, v_v)), guh = "pbl_test_uni_roottest", init = ["e_pblID"], mathauthors = "[]", met = [], ppc = ["(#Given, (equality, e_e))","(#Given, (solveFor, v_v))","(#Find, (solutions, v_v'i'))"], prls = "e_rls", thy = {Test}, where_ = ["precond_rootpbl v_v"]}], []),
1.180 -Ptyp ("squareroot", [
1.181 -{cas = (SOME solve (e_e, v_v)), guh = "pbl_test_uni_root", init = ["e_pblID"], mathauthors = "[]", met = [["Test","square_equation"]], ppc = ["(#Given, (equality, e_e))","(#Given, (solveFor, v_v))","(#Find, (solutions, v_v'i'))"], prls = "contains_root", thy = {Test}, where_ = ["precond_rootpbl v_v"]}], [])])]),
1.182 -Ptyp ("inttype", [
1.183 -{cas = NONE, guh = "pbl_test_intsimp", init = ["e_pblID"], mathauthors = "[]", met = [["Test","intsimp"]], ppc = ["(#Given, (intTestGiven, t_t))","(#Find, (intTestFind, s_s))"], prls = "e_rls", thy = {Test}, where_ = []}], [])])--10
1.184 -
1.185 -Ptyp ("tool", [
1.186 -{cas = NONE, guh = "pbl_tool", init = ["e_pblID"], mathauthors = "[]", met = [], ppc = [], prls = "e_rls", thy = {DiffApp}, where_ = []}], [
1.187 -Ptyp ("find_values", [
1.188 -{cas = NONE, guh = "pbl_tool_findvals", init = ["e_pblID"], mathauthors = "[]", met = [], ppc = ["(#Given, (maxArgument, m_ax))","(#Given, (functionEq, f_f))","(#Given, (boundVariable, v_v))","(#Find, (valuesFor, v_ls))","(#Relate, (additionalRels, r_s))"], prls = "e_rls", thy = {DiffApp}, where_ = []}], [])])--11
1.189 -
1.190 -Ptyp ("vereinfachen", [
1.191 -{cas = (SOME Vereinfache t_t), guh = "pbl_vereinfache", init = ["e_pblID"], mathauthors = "[]", met = [], ppc = ["(#Given, (Term, t_t))","(#Find, (normalform, n_n))"], prls = "e_rls", thy = {Simplify}, where_ = []}], [
1.192 -Ptyp ("polynom", [
1.193 -{cas = NONE, guh = "pbl_vereinf_poly", init = ["e_pblID"], mathauthors = "[]", met = [], ppc = [], prls = "e_rls", thy = {PolyMinus}, where_ = []}], [
1.194 -Ptyp ("binom_klammer", [
1.195 -{cas = (SOME Vereinfache t_t), guh = "pbl_vereinf_poly_klammer_mal", init = ["e_pblID"], mathauthors = "[]", met = [["simplification","for_polynomials","with_parentheses_mult"]], ppc = ["(#Given, (Term, t_t))","(#Find, (normalform, n_n))"], prls = "e_rls", thy = {PolyMinus}, where_ = ["t_t is_polyexp"]}], []),
1.196 -Ptyp ("klammer", [
1.197 -{cas = (SOME Vereinfache t_t), guh = "pbl_vereinf_poly_klammer", init = ["e_pblID"], mathauthors = "[]", met = [["simplification","for_polynomials","with_parentheses"]], ppc = ["(#Given, (Term, t_t))","(#Find, (normalform, n_n))"], prls = "prls_pbl_vereinf_poly_klammer", thy = {PolyMinus}, where_ = ["t_t is_polyexp","~ (matchsub (?a * (?b + ?c)) t_t |
1.198 - matchsub (?a * (?b - ?c)) t_t |
1.199 - matchsub ((?b + ?c) * ?a) t_t | matchsub ((?b - ?c) * ?a) t_t)"]}], []),
1.200 -Ptyp ("plus_minus", [
1.201 -{cas = (SOME Vereinfache t_t), guh = "pbl_vereinf_poly_minus", init = ["e_pblID"], mathauthors = "[]", met = [["simplification","for_polynomials","with_minus"]], ppc = ["(#Given, (Term, t_t))","(#Find, (normalform, n_n))"], prls = "prls_pbl_vereinf_poly", thy = {PolyMinus}, where_ = ["t_t is_polyexp","~ (matchsub (?a + (?b + ?c)) t_t |
1.202 - matchsub (?a + (?b - ?c)) t_t |
1.203 - matchsub (?a - (?b + ?c)) t_t | matchsub (?a + (?b - ?c)) t_t)","~ (matchsub (?a * (?b + ?c)) t_t |
1.204 - matchsub (?a * (?b - ?c)) t_t |
1.205 - matchsub ((?b + ?c) * ?a) t_t | matchsub ((?b - ?c) * ?a) t_t)"]}], [])])])--12