1 Ptyp ("Berechnung", [ |
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2 {cas = NONE, guh = "pbl_algein", init = ["e_pblID"], mathauthors = "[]", met = [], ppc = [], prls = "e_rls", thy = {AlgEin}, where_ = []}], [ |
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3 Ptyp ("numerischSymbolische", [ |
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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 |
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5 |
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6 Ptyp ("Biegelinien", [ |
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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_ = []}], [ |
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8 Ptyp ("MomentBestimmte", [ |
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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_ = []}], []), |
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10 Ptyp ("MomentGegebene", [ |
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11 {cas = NONE, guh = "pbl_bieg_momg", init = ["e_pblID"], mathauthors = "[]", met = [["IntegrierenUndKonstanteBestimmen","2xIntegrieren"]], ppc = [], prls = "e_rls", thy = {Biegelinie}, where_ = []}], []), |
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12 Ptyp ("QuerkraftUndMomentBestimmte", [ |
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13 {cas = NONE, guh = "pbl_bieg_momquer", init = ["e_pblID"], mathauthors = "[]", met = [["IntegrierenUndKonstanteBestimmen","1xIntegrieren"]], ppc = [], prls = "e_rls", thy = {Biegelinie}, where_ = []}], []), |
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14 Ptyp ("einfache", [ |
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15 {cas = NONE, guh = "pbl_bieg_einf", init = ["e_pblID"], mathauthors = "[]", met = [["IntegrierenUndKonstanteBestimmen","4x4System"]], ppc = [], prls = "e_rls", thy = {Biegelinie}, where_ = []}], []), |
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16 Ptyp ("setzeRandbedingungen", [ |
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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_ = []}], []), |
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18 Ptyp ("vonBelastungZu", [ |
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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 |
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20 |
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21 Ptyp ("SignalProcessing", [ |
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22 {cas = NONE, guh = "pbl_SP", init = ["e_pblID"], mathauthors = "[]", met = [], ppc = [], prls = "e_rls", thy = {Inverse_Z_Transform}, where_ = []}], [ |
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23 Ptyp ("Z_Transform", [ |
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24 {cas = NONE, guh = "pbl_SP_Ztrans", init = ["e_pblID"], mathauthors = "[]", met = [], ppc = [], prls = "e_rls", thy = {Inverse_Z_Transform}, where_ = []}], [ |
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25 Ptyp ("Inverse", [ |
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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 |
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27 |
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28 Ptyp ("e_pblID", [ |
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29 {cas = NONE, guh = "pbl_empty", init = ["e_pblID"], mathauthors = "[]", met = [], ppc = [], prls = "e_rls", thy = {Pure}, where_ = []}], [])--4 |
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30 |
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31 Ptyp ("equation", [ |
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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"]}], [ |
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33 Ptyp ("diophantine", [ |
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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_ = []}], []), |
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35 Ptyp ("makeFunctionTo", [ |
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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_ = []}], []), |
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37 Ptyp ("univariate", [ |
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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"]}], [ |
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39 Ptyp ("LINEAR", [ |
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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"]}], []), |
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41 Ptyp ("expanded", [ |
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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"]}], [ |
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43 Ptyp ("degree_2", [ |
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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"]}], [])]), |
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45 Ptyp ("logarithmic", [ |
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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"]}], []), |
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47 Ptyp ("polynomial", [ |
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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"]}], [ |
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49 Ptyp ("degree_0", [ |
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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"]}], []), |
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51 Ptyp ("degree_1", [ |
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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"]}], []), |
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53 Ptyp ("degree_2", [ |
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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"]}], [ |
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55 Ptyp ("abcFormula", [ |
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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"]}], []), |
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57 Ptyp ("bdv_only", [ |
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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 | |
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59 matches (?v_ + ?v_ ^^^ 2 = 0) e_e | |
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60 matches (?v_ + ?b * ?v_ ^^^ 2 = 0) e_e | |
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61 matches (?a * ?v_ + ?b * ?v_ ^^^ 2 = 0) e_e | |
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62 matches (?v_ ^^^ 2 = 0) e_e | matches (?b * ?v_ ^^^ 2 = 0) e_e"]}], []), |
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63 Ptyp ("pqFormula", [ |
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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"]}], []), |
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65 Ptyp ("sq_only", [ |
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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 | |
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67 matches (?a + ?b * ?v_ ^^^ 2 = 0) e_e | |
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68 matches (?v_ ^^^ 2 = 0) e_e | matches (?b * ?v_ ^^^ 2 = 0) e_e","~ matches (?a + ?v_ + ?v_ ^^^ 2 = 0) e_e & |
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69 ~ matches (?a + ?b * ?v_ + ?v_ ^^^ 2 = 0) e_e & |
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70 ~ matches (?a + ?v_ + ?c * ?v_ ^^^ 2 = 0) e_e & |
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71 ~ matches (?a + ?b * ?v_ + ?c * ?v_ ^^^ 2 = 0) e_e & |
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72 ~ matches (?v_ + ?v_ ^^^ 2 = 0) e_e & |
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73 ~ matches (?b * ?v_ + ?v_ ^^^ 2 = 0) e_e & |
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74 ~ matches (?v_ + ?c * ?v_ ^^^ 2 = 0) e_e & |
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75 ~ matches (?b * ?v_ + ?c * ?v_ ^^^ 2 = 0) e_e"]}], [])]), |
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76 Ptyp ("degree_3", [ |
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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"]}], []), |
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78 Ptyp ("degree_4", [ |
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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"]}], []), |
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80 Ptyp ("normalize", [ |
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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"]}], [])]), |
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82 Ptyp ("rational", [ |
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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"]}], []), |
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84 Ptyp ("root'", [ |
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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"]}], [ |
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86 Ptyp ("normalize", [ |
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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 | |
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88 rhs e_e is_sqrtTerm_in v_v & ~ rhs e_e is_normSqrtTerm_in v_v"]}], []), |
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89 Ptyp ("sq", [ |
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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 | |
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91 rhs e_e is_sqrtTerm_in v_v & rhs e_e is_normSqrtTerm_in v_v"]}], [ |
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92 Ptyp ("rat", [ |
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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 |
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94 |
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95 Ptyp ("function", [ |
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96 {cas = NONE, guh = "pbl_fun", init = ["e_pblID"], mathauthors = "[]", met = [], ppc = [], prls = "e_rls", thy = {Diff}, where_ = []}], [ |
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97 Ptyp ("derivative_of", [ |
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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_ = []}], [ |
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99 Ptyp ("named", [ |
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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_ = []}], [])]), |
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101 Ptyp ("integrate", [ |
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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_ = []}], [ |
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103 Ptyp ("named", [ |
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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_ = []}], [])]), |
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105 Ptyp ("make", [ |
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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_ = []}], [ |
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107 Ptyp ("by_explicit", [ |
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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_ = []}], []), |
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109 Ptyp ("by_new_variable", [ |
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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_ = []}], [])]), |
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111 Ptyp ("maximum_of", [ |
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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_ = []}], [ |
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113 Ptyp ("on_interval", [ |
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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 |
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115 |
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116 Ptyp ("probe", [ |
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117 {cas = NONE, guh = "pbl_probe", init = ["e_pblID"], mathauthors = "[]", met = [], ppc = [], prls = "e_rls", thy = {PolyMinus}, where_ = []}], [ |
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118 Ptyp ("bruch", [ |
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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"]}], []), |
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120 Ptyp ("polynom", [ |
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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 |
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122 |
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123 Ptyp ("simplification", [ |
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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_ = []}], [ |
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125 Ptyp ("polynomial", [ |
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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"]}], []), |
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127 Ptyp ("rational", [ |
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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"]}], [ |
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129 Ptyp ("partial_fraction", [ |
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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 |
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131 |
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132 Ptyp ("system", [ |
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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_ = []}], [ |
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134 Ptyp ("LINEAR", [ |
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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_ = []}], [ |
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136 Ptyp ("2x2", [ |
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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"]}], [ |
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138 Ptyp ("normalize", [ |
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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_ = []}], []), |
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140 Ptyp ("triangular", [ |
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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"]}], [])]), |
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142 Ptyp ("3x3", [ |
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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"]}], []), |
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144 Ptyp ("4x4", [ |
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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"]}], [ |
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146 Ptyp ("normalize", [ |
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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_ = []}], []), |
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148 Ptyp ("triangular", [ |
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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 |
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150 |
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151 Ptyp ("test", [ |
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152 {cas = NONE, guh = "pbl_test", init = ["e_pblID"], mathauthors = "[]", met = [], ppc = [], prls = "e_rls", thy = {Test}, where_ = []}], [ |
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153 Ptyp ("equation", [ |
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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"]}], [ |
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155 Ptyp ("univariate", [ |
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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"]}], [ |
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157 Ptyp ("LINEAR", [ |
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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 | |
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159 matches (?b * v_v = 0) e_e | |
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160 matches (?a + v_v = 0) e_e | matches (?a + ?b * v_v = 0) e_e"]}], []), |
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161 Ptyp ("normalize", [ |
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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_ = []}], []), |
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163 Ptyp ("plain_square", [ |
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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 | |
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165 matches (?b * v_v ^^^ 2 = 0) e_e | |
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166 matches (?a + v_v ^^^ 2 = 0) e_e | matches (v_v ^^^ 2 = 0) e_e"]}], []), |
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167 Ptyp ("polynomial", [ |
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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"]}], [ |
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169 Ptyp ("degree_two", [ |
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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_ = []}], [ |
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171 Ptyp ("abc_formula", [ |
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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_ = []}], []), |
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173 Ptyp ("pq_formula", [ |
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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_ = []}], [])])]), |
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175 Ptyp ("sqroot-test", [ |
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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"]}], []), |
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177 Ptyp ("squareroot", [ |
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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"]}], [])])]), |
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179 Ptyp ("inttype", [ |
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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 |
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181 |
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182 Ptyp ("tool", [ |
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183 {cas = NONE, guh = "pbl_tool", init = ["e_pblID"], mathauthors = "[]", met = [], ppc = [], prls = "e_rls", thy = {DiffApp}, where_ = []}], [ |
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184 Ptyp ("find_values", [ |
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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 |
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186 |
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187 Ptyp ("vereinfachen", [ |
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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_ = []}], [ |
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189 Ptyp ("polynom", [ |
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190 {cas = NONE, guh = "pbl_vereinf_poly", init = ["e_pblID"], mathauthors = "[]", met = [], ppc = [], prls = "e_rls", thy = {PolyMinus}, where_ = []}], [ |
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191 Ptyp ("binom_klammer", [ |
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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"]}], []), |
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193 Ptyp ("klammer", [ |
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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 | |
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195 matchsub (?a * (?b - ?c)) t_t | |
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196 matchsub ((?b + ?c) * ?a) t_t | matchsub ((?b - ?c) * ?a) t_t)"]}], []), |
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197 Ptyp ("plus_minus", [ |
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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 | |
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199 matchsub (?a + (?b - ?c)) t_t | |
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200 matchsub (?a - (?b + ?c)) t_t | matchsub (?a + (?b - ?c)) t_t)","~ (matchsub (?a * (?b + ?c)) t_t | |
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201 matchsub (?a * (?b - ?c)) t_t | |
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202 matchsub ((?b + ?c) * ?a) t_t | matchsub ((?b - ?c) * ?a) t_t)"]}], [])])])--12 |
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