doc-isac/mlehnfeld/master/ordered-KEStore_Elems.get_ptyps
changeset 55467 2e9db65faf65
parent 55346 000eb2d7f608
equal deleted inserted replaced
55466:55c2d2ee3f92 55467:2e9db65faf65
     1 Ptyp ("Berechnung", [
       
     2 {cas = NONE, guh = "pbl_algein", init = ["e_pblID"], mathauthors = "[]", met = [], ppc = [], prls = "e_rls", thy = {AlgEin}, where_ = []}], [
       
     3 Ptyp ("numerischSymbolische", [
       
     4 {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 
       
     5 
       
     6 Ptyp ("Biegelinien", [
       
     7 {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_ = []}], [
       
     8 Ptyp ("MomentBestimmte", [
       
     9 {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_ = []}], []),
       
    10 Ptyp ("MomentGegebene", [
       
    11 {cas = NONE, guh = "pbl_bieg_momg", init = ["e_pblID"], mathauthors = "[]", met = [["IntegrierenUndKonstanteBestimmen","2xIntegrieren"]], ppc = [], prls = "e_rls", thy = {Biegelinie}, where_ = []}], []),
       
    12 Ptyp ("QuerkraftUndMomentBestimmte", [
       
    13 {cas = NONE, guh = "pbl_bieg_momquer", init = ["e_pblID"], mathauthors = "[]", met = [["IntegrierenUndKonstanteBestimmen","1xIntegrieren"]], ppc = [], prls = "e_rls", thy = {Biegelinie}, where_ = []}], []),
       
    14 Ptyp ("einfache", [
       
    15 {cas = NONE, guh = "pbl_bieg_einf", init = ["e_pblID"], mathauthors = "[]", met = [["IntegrierenUndKonstanteBestimmen","4x4System"]], ppc = [], prls = "e_rls", thy = {Biegelinie}, where_ = []}], []),
       
    16 Ptyp ("setzeRandbedingungen", [
       
    17 {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_ = []}], []),
       
    18 Ptyp ("vonBelastungZu", [
       
    19 {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 
       
    20 
       
    21 Ptyp ("SignalProcessing", [
       
    22 {cas = NONE, guh = "pbl_SP", init = ["e_pblID"], mathauthors = "[]", met = [], ppc = [], prls = "e_rls", thy = {Inverse_Z_Transform}, where_ = []}], [
       
    23 Ptyp ("Z_Transform", [
       
    24 {cas = NONE, guh = "pbl_SP_Ztrans", init = ["e_pblID"], mathauthors = "[]", met = [], ppc = [], prls = "e_rls", thy = {Inverse_Z_Transform}, where_ = []}], [
       
    25 Ptyp ("Inverse", [
       
    26 {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 
       
    27 
       
    28 Ptyp ("e_pblID", [
       
    29 {cas = NONE, guh = "pbl_empty", init = ["e_pblID"], mathauthors = "[]", met = [], ppc = [], prls = "e_rls", thy = {Pure}, where_ = []}], [])--4 
       
    30 
       
    31 Ptyp ("equation", [
       
    32 {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"]}], [
       
    33 Ptyp ("diophantine", [
       
    34 {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_ = []}], []),
       
    35 Ptyp ("makeFunctionTo", [
       
    36 {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_ = []}], []),
       
    37 Ptyp ("univariate", [
       
    38 {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"]}], [
       
    39 Ptyp ("LINEAR", [
       
    40 {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"]}], []),
       
    41 Ptyp ("expanded", [
       
    42 {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"]}], [
       
    43 Ptyp ("degree_2", [
       
    44 {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"]}], [])]),
       
    45 Ptyp ("logarithmic", [
       
    46 {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"]}], []),
       
    47 Ptyp ("polynomial", [
       
    48 {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"]}], [
       
    49 Ptyp ("degree_0", [
       
    50 {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"]}], []),
       
    51 Ptyp ("degree_1", [
       
    52 {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"]}], []),
       
    53 Ptyp ("degree_2", [
       
    54 {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"]}], [
       
    55 Ptyp ("abcFormula", [
       
    56 {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"]}], []),
       
    57 Ptyp ("bdv_only", [
       
    58 {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 |
       
    59 matches (?v_ + ?v_ ^^^ 2 = 0) e_e |
       
    60 matches (?v_ + ?b * ?v_ ^^^ 2 = 0) e_e |
       
    61 matches (?a * ?v_ + ?b * ?v_ ^^^ 2 = 0) e_e |
       
    62 matches (?v_ ^^^ 2 = 0) e_e | matches (?b * ?v_ ^^^ 2 = 0) e_e"]}], []),
       
    63 Ptyp ("pqFormula", [
       
    64 {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"]}], []),
       
    65 Ptyp ("sq_only", [
       
    66 {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 |
       
    67 matches (?a + ?b * ?v_ ^^^ 2 = 0) e_e |
       
    68 matches (?v_ ^^^ 2 = 0) e_e | matches (?b * ?v_ ^^^ 2 = 0) e_e","~ matches (?a + ?v_ + ?v_ ^^^ 2 = 0) e_e &
       
    69 ~ matches (?a + ?b * ?v_ + ?v_ ^^^ 2 = 0) e_e &
       
    70 ~ matches (?a + ?v_ + ?c * ?v_ ^^^ 2 = 0) e_e &
       
    71 ~ matches (?a + ?b * ?v_ + ?c * ?v_ ^^^ 2 = 0) e_e &
       
    72 ~ matches (?v_ + ?v_ ^^^ 2 = 0) e_e &
       
    73 ~ matches (?b * ?v_ + ?v_ ^^^ 2 = 0) e_e &
       
    74 ~ matches (?v_ + ?c * ?v_ ^^^ 2 = 0) e_e &
       
    75 ~ matches (?b * ?v_ + ?c * ?v_ ^^^ 2 = 0) e_e"]}], [])]),
       
    76 Ptyp ("degree_3", [
       
    77 {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"]}], []),
       
    78 Ptyp ("degree_4", [
       
    79 {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"]}], []),
       
    80 Ptyp ("normalize", [
       
    81 {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"]}], [])]),
       
    82 Ptyp ("rational", [
       
    83 {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"]}], []),
       
    84 Ptyp ("root'", [
       
    85 {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"]}], [
       
    86 Ptyp ("normalize", [
       
    87 {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 |
       
    88 rhs e_e is_sqrtTerm_in v_v & ~ rhs e_e is_normSqrtTerm_in v_v"]}], []),
       
    89 Ptyp ("sq", [
       
    90 {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 |
       
    91 rhs e_e is_sqrtTerm_in v_v & rhs e_e is_normSqrtTerm_in v_v"]}], [
       
    92 Ptyp ("rat", [
       
    93 {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 
       
    94 
       
    95 Ptyp ("function", [
       
    96 {cas = NONE, guh = "pbl_fun", init = ["e_pblID"], mathauthors = "[]", met = [], ppc = [], prls = "e_rls", thy = {Diff}, where_ = []}], [
       
    97 Ptyp ("derivative_of", [
       
    98 {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_ = []}], [
       
    99 Ptyp ("named", [
       
   100 {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_ = []}], [])]),
       
   101 Ptyp ("integrate", [
       
   102 {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_ = []}], [
       
   103 Ptyp ("named", [
       
   104 {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_ = []}], [])]),
       
   105 Ptyp ("make", [
       
   106 {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_ = []}], [
       
   107 Ptyp ("by_explicit", [
       
   108 {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_ = []}], []),
       
   109 Ptyp ("by_new_variable", [
       
   110 {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_ = []}], [])]),
       
   111 Ptyp ("maximum_of", [
       
   112 {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_ = []}], [
       
   113 Ptyp ("on_interval", [
       
   114 {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 
       
   115 
       
   116 Ptyp ("probe", [
       
   117 {cas = NONE, guh = "pbl_probe", init = ["e_pblID"], mathauthors = "[]", met = [], ppc = [], prls = "e_rls", thy = {PolyMinus}, where_ = []}], [
       
   118 Ptyp ("bruch", [
       
   119 {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"]}], []),
       
   120 Ptyp ("polynom", [
       
   121 {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 
       
   122 
       
   123 Ptyp ("simplification", [
       
   124 {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_ = []}], [
       
   125 Ptyp ("polynomial", [
       
   126 {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"]}], []),
       
   127 Ptyp ("rational", [
       
   128 {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"]}], [
       
   129 Ptyp ("partial_fraction", [
       
   130 {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 
       
   131 
       
   132 Ptyp ("system", [
       
   133 {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_ = []}], [
       
   134 Ptyp ("LINEAR", [
       
   135 {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_ = []}], [
       
   136 Ptyp ("2x2", [
       
   137 {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"]}], [
       
   138 Ptyp ("normalize", [
       
   139 {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_ = []}], []),
       
   140 Ptyp ("triangular", [
       
   141 {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"]}], [])]),
       
   142 Ptyp ("3x3", [
       
   143 {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"]}], []),
       
   144 Ptyp ("4x4", [
       
   145 {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"]}], [
       
   146 Ptyp ("normalize", [
       
   147 {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_ = []}], []),
       
   148 Ptyp ("triangular", [
       
   149 {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 
       
   150 
       
   151 Ptyp ("test", [
       
   152 {cas = NONE, guh = "pbl_test", init = ["e_pblID"], mathauthors = "[]", met = [], ppc = [], prls = "e_rls", thy = {Test}, where_ = []}], [
       
   153 Ptyp ("equation", [
       
   154 {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"]}], [
       
   155 Ptyp ("univariate", [
       
   156 {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"]}], [
       
   157 Ptyp ("LINEAR", [
       
   158 {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 |
       
   159 matches (?b * v_v = 0) e_e |
       
   160 matches (?a + v_v = 0) e_e | matches (?a + ?b * v_v = 0) e_e"]}], []),
       
   161 Ptyp ("normalize", [
       
   162 {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_ = []}], []),
       
   163 Ptyp ("plain_square", [
       
   164 {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 |
       
   165 matches (?b * v_v ^^^ 2 = 0) e_e |
       
   166 matches (?a + v_v ^^^ 2 = 0) e_e | matches (v_v ^^^ 2 = 0) e_e"]}], []),
       
   167 Ptyp ("polynomial", [
       
   168 {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"]}], [
       
   169 Ptyp ("degree_two", [
       
   170 {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_ = []}], [
       
   171 Ptyp ("abc_formula", [
       
   172 {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_ = []}], []),
       
   173 Ptyp ("pq_formula", [
       
   174 {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_ = []}], [])])]),
       
   175 Ptyp ("sqroot-test", [
       
   176 {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"]}], []),
       
   177 Ptyp ("squareroot", [
       
   178 {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"]}], [])])]),
       
   179 Ptyp ("inttype", [
       
   180 {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 
       
   181 
       
   182 Ptyp ("tool", [
       
   183 {cas = NONE, guh = "pbl_tool", init = ["e_pblID"], mathauthors = "[]", met = [], ppc = [], prls = "e_rls", thy = {DiffApp}, where_ = []}], [
       
   184 Ptyp ("find_values", [
       
   185 {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 
       
   186 
       
   187 Ptyp ("vereinfachen", [
       
   188 {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_ = []}], [
       
   189 Ptyp ("polynom", [
       
   190 {cas = NONE, guh = "pbl_vereinf_poly", init = ["e_pblID"], mathauthors = "[]", met = [], ppc = [], prls = "e_rls", thy = {PolyMinus}, where_ = []}], [
       
   191 Ptyp ("binom_klammer", [
       
   192 {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"]}], []),
       
   193 Ptyp ("klammer", [
       
   194 {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 |
       
   195    matchsub (?a * (?b - ?c)) t_t |
       
   196    matchsub ((?b + ?c) * ?a) t_t | matchsub ((?b - ?c) * ?a) t_t)"]}], []),
       
   197 Ptyp ("plus_minus", [
       
   198 {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 |
       
   199    matchsub (?a + (?b - ?c)) t_t |
       
   200    matchsub (?a - (?b + ?c)) t_t | matchsub (?a + (?b - ?c)) t_t)","~ (matchsub (?a * (?b + ?c)) t_t |
       
   201    matchsub (?a * (?b - ?c)) t_t |
       
   202    matchsub ((?b + ?c) * ?a) t_t | matchsub ((?b - ?c) * ?a) t_t)"]}], [])])])--12