[-Test_Isac] funpack: Const ("Partial_Fractions.AA",..) makes trick superfluous
1.1 --- a/src/Tools/isac/Interpret/tactic.sml Thu Mar 07 16:50:20 2019 +0100
1.2 +++ b/src/Tools/isac/Interpret/tactic.sml Thu Mar 07 17:22:20 2019 +0100
1.3 @@ -318,7 +318,6 @@
1.4 This is useful for costly results, e.g. from rewriting;
1.5 however, these results might be changed by Scripts like
1.6 " eq = (Rewrite_Set ''ansatz_rls'' False) eql;" ^
1.7 - " eq = drop_questionmarks eq;" ^
1.8 " eq = (Rewrite_Set equival_trans False) eq;" ^
1.9 TODO.WN120106 ANALOGOUSLY TO Substitute':
1.10 So tac_ contains the term t the result was calculated from
2.1 --- a/src/Tools/isac/Knowledge/Inverse_Z_Transform.thy Thu Mar 07 16:50:20 2019 +0100
2.2 +++ b/src/Tools/isac/Knowledge/Inverse_Z_Transform.thy Thu Mar 07 17:22:20 2019 +0100
2.3 @@ -150,7 +150,6 @@
2.4 (eqr::real) = (Try (Rewrite_Set ''ansatz_rls'' False)) eql; \<comment> \<open>---\<close>
2.5 (eq::bool) = Take (eql = eqr); \<comment> \<open>Maybe possible to use HOLogic.mk_eq ??\<close>
2.6 eq = (Try (Rewrite_Set ''equival_trans'' False)) eq; \<comment> \<open>---\<close>
2.7 - eq = drop_questionmarks eq;
2.8 (z1::real) = (rhs (NTH 1 L_L)); \<comment> \<open>prepare equation for a - eq_a therefor substitute z with solution 1 - z1\<close>
2.9 (z2::real) = (rhs (NTH 2 L_L)); \<comment> \<open>---\<close>
2.10 (eq_a::bool) = Take eq;
2.11 @@ -169,14 +168,11 @@
2.12 [''univariate'',''equation''],[''no_met''])
2.13 [BOOL eq_b, REAL (B::real)]);
2.14 (b::real) = (rhs(NTH 1 sol_b)); \<comment> \<open>---\<close>
2.15 - eqr = drop_questionmarks eqr;
2.16 (pbz::real) = Take eqr;
2.17 pbz = ((Substitute [A=a, B=b]) pbz); \<comment> \<open>---\<close>
2.18 pbz = Rewrite ''ruleYZ'' False pbz;
2.19 - pbz = drop_questionmarks pbz; \<comment> \<open>---\<close>
2.20 (X_z::bool) = Take (X_z = pbz);
2.21 - (n_eq::bool) = (Rewrite_Set ''inverse_z'' False) X_z;
2.22 - n_eq = drop_questionmarks n_eq
2.23 + (n_eq::bool) = (Rewrite_Set ''inverse_z'' False) X_z
2.24 in n_eq)"
2.25 *)
2.26 setup \<open>KEStore_Elems.add_mets
2.27 @@ -216,7 +212,6 @@
2.28 (*Maybe possible to use HOLogic.mk_eq ??*)
2.29 " eq = (Try (Rewrite_Set ''equival_trans'' False)) eq; "^
2.30
2.31 - " eq = drop_questionmarks eq; "^
2.32 " (z1::real) = (rhs (NTH 1 L_L)); "^
2.33 (*
2.34 * prepare equation for a - eq_a
2.35 @@ -242,16 +237,13 @@
2.36 " [BOOL eq_b, REAL (B::real)]); "^
2.37 " (b::real) = (rhs(NTH 1 sol_b)); "^
2.38
2.39 - " eqr = drop_questionmarks eqr; "^
2.40 " (pbz::real) = Take eqr; "^
2.41 " pbz = ((Substitute [A=a, B=b]) pbz); "^
2.42
2.43 " pbz = Rewrite ''ruleYZ'' False pbz; "^
2.44 - " pbz = drop_questionmarks pbz; "^
2.45
2.46 " (X_z::bool) = Take (X_z = pbz); "^
2.47 - " (n_eq::bool) = (Rewrite_Set ''inverse_z'' False) X_z; "^
2.48 - " n_eq = drop_questionmarks n_eq "^
2.49 + " (n_eq::bool) = (Rewrite_Set ''inverse_z'' False) X_z "^
2.50 "in n_eq)")]
2.51 \<close>
2.52 (* same error as in inverse_ztransform2
2.53 @@ -280,14 +272,11 @@
2.54 (*([3], Res), ?X' z = 4 * (?z / (z - 1 / 2)) + -4 * (?z / (z - -1 / 4))*)
2.55 pbz_eq = Rewrite ''ruleYZ'' False pbz_eq;
2.56 (* 4 * (z / (z - 1 / 2)) + -4 * (z / (z - -1 / 4))*)
2.57 - pbz_eq = drop_questionmarks pbz_eq;
2.58 (*([4], Frm), X_z = 4 * (z / (z - 1 / 2)) + -4 * (z / (z - -1 / 4))*)
2.59 (X_zeq::bool) = Take (X_z = rhs pbz_eq);
2.60 (*([4], Res), X_z = 4 * (1 / 2) ^^^ ?n * ?u [?n] + -4 * (-1 / 4) ^^^ ?n * ?u [?n]*)
2.61 - n_eq = (Rewrite_Set ''inverse_z'' False) X_zeq;
2.62 + n_eq = (Rewrite_Set ''inverse_z'' False) X_zeq
2.63 (* X_z = 4 * (1 / 2) ^^^ n * u [n] + -4 * (-1 / 4) ^^^ n * u [n]*)
2.64 - n_eq = drop_questionmarks n_eq
2.65 -(*([], Res), X_z = 4 * (1 / 2) ^^^ n * u [n] + -4 * (-1 / 4) ^^^ n * u [n]*)
2.66 in n_eq) "
2.67 *)
2.68 setup \<open>KEStore_Elems.add_mets
2.69 @@ -313,9 +302,8 @@
2.70 Rule.Calc ("Rational.get_denominator", eval_get_denominator "#get_denominator"),
2.71 Rule.Calc ("Rational.get_numerator", eval_get_numerator "#get_numerator"),
2.72 Rule.Calc ("Partial_Fractions.factors_from_solution",
2.73 - eval_factors_from_solution "#factors_from_solution"),
2.74 - Rule.Calc("Partial_Fractions.drop_questionmarks", eval_drop_questionmarks "#drop_?")],
2.75 - scr = Rule.EmptyScr},
2.76 + eval_factors_from_solution "#factors_from_solution")
2.77 + ], scr = Rule.EmptyScr},
2.78 prls = Rule.e_rls, crls = Rule.e_rls, errpats = [], nrls = norm_Rational},
2.79 (*([], Frm), Problem (Isac, [Inverse, Z_Transform, SignalProcessing])*)
2.80 "Script InverseZTransform (X_eq::bool) = "^
2.81 @@ -341,13 +329,11 @@
2.82 (*([3], Res), ?X' z = 4 * (?z / (z - 1 / 2)) + -4 * (?z / (z - -1 / 4))*)
2.83 " pbz_eq = Rewrite ''ruleYZ'' False pbz_eq; "^
2.84 (* 4 * (z / (z - 1 / 2)) + -4 * (z / (z - -1 / 4))*)
2.85 - " pbz_eq = drop_questionmarks pbz_eq; "^
2.86 (*([4], Frm), X_z = 4 * (z / (z - 1 / 2)) + -4 * (z / (z - -1 / 4))*)
2.87 " (X_zeq::bool) = Take (X_z = rhs pbz_eq); "^
2.88 (*([4], Res), X_z = 4 * (1 / 2) ^^^ ?n * ?u [?n] + -4 * (-1 / 4) ^^^ ?n * ?u [?n]*)
2.89 - " n_eq = (Rewrite_Set ''inverse_z'' False) X_zeq; "^
2.90 + " n_eq = (Rewrite_Set ''inverse_z'' False) X_zeq "^
2.91 (* X_z = 4 * (1 / 2) ^^^ n * u [n] + -4 * (-1 / 4) ^^^ n * u [n]*)
2.92 - " n_eq = drop_questionmarks n_eq "^
2.93 (*([], Res), X_z = 4 * (1 / 2) ^^^ n * u [n] + -4 * (-1 / 4) ^^^ n * u [n]*)
2.94 "in n_eq)")]
2.95 \<close>
3.1 --- a/src/Tools/isac/Knowledge/Partial_Fractions.thy Thu Mar 07 16:50:20 2019 +0100
3.2 +++ b/src/Tools/isac/Knowledge/Partial_Fractions.thy Thu Mar 07 17:22:20 2019 +0100
3.3 @@ -21,11 +21,8 @@
3.4 subsection \<open>eval_ functions\<close>
3.5 consts
3.6 factors_from_solution :: "bool list => real"
3.7 - drop_questionmarks :: "'a => 'a"
3.8 -(* version for later switch to partial_function
3.9 - A :: real \<comment> \<open>PROG redesign (Substitute [A = a, B = b]) pbz ?\<close>
3.10 - B :: real \<comment> \<open>PROG redesign (Substitute [A = a, B = b]) pbz ?\<close>
3.11 -*)
3.12 + AA :: real
3.13 + BB :: real
3.14
3.15 text \<open>these might be used for variants of fac_from_sol\<close>
3.16 ML \<open>
3.17 @@ -70,56 +67,36 @@
3.18 | eval_factors_from_solution _ _ _ _ = NONE;
3.19 \<close>
3.20
3.21 -text \<open>'ansatz' introduces '?Vars' (questionable design); drop these again\<close>
3.22 -ML \<open>
3.23 -(*("drop_questionmarks", ("Partial_Fractions.drop_questionmarks", eval_drop_questionmarks ""))*)
3.24 -fun eval_drop_questionmarks (thmid:string) _
3.25 - (t as Const ("Partial_Fractions.drop_questionmarks", _) $ tm) thy =
3.26 - if TermC.contains_Var tm
3.27 - then
3.28 - let
3.29 - val tm' = TermC.var2free tm
3.30 - in SOME (TermC.mk_thmid thmid (Rule.term_to_string''' thy tm') "",
3.31 - HOLogic.Trueprop $ (TermC.mk_equality (t, tm')))
3.32 - end
3.33 - else NONE
3.34 - | eval_drop_questionmarks _ _ _ _ = NONE;
3.35 -\<close>
3.36 -
3.37 -text \<open>store eval_ functions for calls from Scripts\<close>
3.38 -setup \<open>KEStore_Elems.add_calcs
3.39 - [("drop_questionmarks", ("Partial_Fractions.drop'_questionmarks", eval_drop_questionmarks ""))]\<close>
3.40 -
3.41 subsection \<open>'ansatz' for partial fractions\<close>
3.42 axiomatization where
3.43 - ansatz_2nd_order: "n / (a*b) = A/a + B/b" and
3.44 - ansatz_3rd_order: "n / (a*b*c) = A/a + B/b + C/c" and
3.45 - ansatz_4th_order: "n / (a*b*c*d) = A/a + B/b + C/c + D/d" and
3.46 + ansatz_2nd_order: "n / (a*b) = AA/a + BB/b" and
3.47 + ansatz_3rd_order: "n / (a*b*c) = AA/a + BB/b + C/c" and
3.48 + ansatz_4th_order: "n / (a*b*c*d) = AA/a + BB/b + C/c + D/d" and
3.49 (*version 1*)
3.50 - equival_trans_2nd_order: "(n/(a*b) = A/a + B/b) = (n = A*b + B*a)" and
3.51 - equival_trans_3rd_order: "(n/(a*b*c) = A/a + B/b + C/c) = (n = A*b*c + B*a*c + C*a*b)" and
3.52 - equival_trans_4th_order: "(n/(a*b*c*d) = A/a + B/b + C/c + D/d) =
3.53 - (n = A*b*c*d + B*a*c*d + C*a*b*d + D*a*b*c)" and
3.54 + equival_trans_2nd_order: "(n/(a*b) = AA/a + BB/b) = (n = AA*b + BB*a)" and
3.55 + equival_trans_3rd_order: "(n/(a*b*c) = AA/a + BB/b + C/c) = (n = AA*b*c + BB*a*c + C*a*b)" and
3.56 + equival_trans_4th_order: "(n/(a*b*c*d) = AA/a + BB/b + C/c + D/d) =
3.57 + (n = AA*b*c*d + BB*a*c*d + C*a*b*d + D*a*b*c)" and
3.58 (*version 2: not yet used, see partial_fractions.sml*)
3.59 - multiply_2nd_order: "(n/x = A/a + B/b) = (a*b*n/x = A*b + B*a)" and
3.60 - multiply_3rd_order: "(n/x = A/a + B/b + C/c) = (a*b*c*n/x = A*b*c + B*a*c + C*a*b)" and
3.61 + multiply_2nd_order: "(n/x = AA/a + BB/b) = (a*b*n/x = AA*b + BB*a)" and
3.62 + multiply_3rd_order: "(n/x = AA/a + BB/b + C/c) = (a*b*c*n/x = AA*b*c + BB*a*c + C*a*b)" and
3.63 multiply_4th_order:
3.64 - "(n/x = A/a + B/b + C/c + D/d) = (a*b*c*d*n/x = A*b*c*d + B*a*c*d + C*a*b*d + D*a*b*c)"
3.65 + "(n/x = AA/a + BB/b + C/c + D/d) = (a*b*c*d*n/x = AA*b*c*d + BB*a*c*d + C*a*b*d + D*a*b*c)"
3.66
3.67 text \<open>Probably the optimal formalization woudl be ...
3.68
3.69 - multiply_2nd_order: "x = a*b ==> (n/x = A/a + B/b) = (a*b*n/x = A*b + B*a)" and
3.70 + multiply_2nd_order: "x = a*b ==> (n/x = AA/a + BB/b) = (a*b*n/x = AA*b + BB*a)" and
3.71 multiply_3rd_order: "x = a*b*c ==>
3.72 - (n/x = A/a + B/b + C/c) = (a*b*c*n/x = A*b*c + B*a*c + C*a*b)" and
3.73 + (n/x = AA/a + BB/b + C/c) = (a*b*c*n/x = AA*b*c + BB*a*c + C*a*b)" and
3.74 multiply_4th_order: "x = a*b*c*d ==>
3.75 - (n/x = A/a + B/b + C/c + D/d) = (a*b*c*d*n/x = A*b*c*d + B*a*c*d + C*a*b*d + D*a*b*c)"
3.76 + (n/x = AA/a + BB/b + C/c + D/d) = (a*b*c*d*n/x = AA*b*c*d + BB*a*c*d + C*a*b*d + D*a*b*c)"
3.77
3.78 ... because it would allow to start the ansatz as follows
3.79 (1) 3 / (z * (z - 1 / 4 + -1 / 8 * (1 / z))) = 3 / (z * (z - 1 / 4 + -1 / 8 * (1 / z)))
3.80 (2) 3 / (z * (z - 1 / 4 + -1 / 8 * (1 / z))) = AA / (z - 1 / 2) + BB / (z - -1 / 4)
3.81 (3) (z - 1 / 2) * (z - -1 / 4) * 3 / (z * (z - 1 / 4 + -1 / 8 * (1 / z))) =
3.82 (z - 1 / 2) * (z - -1 / 4) * AA / (z - 1 / 2) + BB / (z - -1 / 4)
3.83 -(4) 3 = A * (z - -1 / 4) + B * (z - 1 / 2)
3.84 +(4) 3 = AA * (z - -1 / 4) + BB * (z - 1 / 2)
3.85
3.86 ... (1==>2) ansatz
3.87 (2==>3) multiply_*
3.88 @@ -209,21 +186,10 @@
3.89 Rule.Calc("Rational.get_denominator", eval_get_denominator "#get_denominator"),
3.90 Rule.Calc("Rational.get_numerator", eval_get_numerator "#get_numerator"),
3.91 Rule.Calc("Partial_Fractions.factors_from_solution",
3.92 - eval_factors_from_solution "#factors_from_solution"),
3.93 - Rule.Calc("Partial_Fractions.drop_questionmarks", eval_drop_questionmarks "#drop_?")],
3.94 + eval_factors_from_solution "#factors_from_solution")
3.95 + ],
3.96 scr = Rule.EmptyScr};
3.97 \<close>
3.98 -ML \<open>
3.99 -eval_drop_questionmarks;
3.100 -\<close>
3.101 -ML \<open>
3.102 -val ctxt = Proof_Context.init_global @{theory};
3.103 -val SOME t = TermC.parseNEW ctxt "eqr = drop_questionmarks eqr";
3.104 -\<close>
3.105 -ML \<open>
3.106 -TermC.parseNEW ctxt "decomposedFunction p_p'''";
3.107 -TermC.parseNEW ctxt "decomposedFunction";
3.108 -\<close>
3.109
3.110 (* current version, error outcommented *)
3.111 (*ok
3.112 @@ -245,28 +211,26 @@
3.113 \<comment> \<open>([4], Frm), 3 / ((z - 1 / 2) * (z - -1 / 4)) = ?A / (z - 1 / 2) + ?B / (z - -1 / 4)\<close>
3.114 eq = Take (eql = eqr); \<comment> \<open>([4], Res), 3 = ?A * (z - -1 / 4) + ?B * (z - 1 / 2)\<close>
3.115 eq = (Try (Rewrite_Set ''equival_trans'' False)) eq;
3.116 - \<comment> \<open>eq = 3 = A * (z - -1 / 4) + B * (z - 1 / 2)\<close>
3.117 - eq = drop_questionmarks eq; \<comment> \<open>z1 = 1 / 2)\<close>
3.118 + \<comment> \<open>eq = 3 = AA * (z - -1 / 4) + BB * (z - 1 / 2)\<close>
3.119 z1 = rhs (NTH 1 L_L); \<comment> \<open>z2 = -1 / 4\<close>
3.120 - z2 = rhs (NTH 2 L_L); \<comment> \<open>([5], Frm), 3 = A * (z - -1 / 4) + B * (z - 1 / 2)\<close>
3.121 - eq_a = Take eq; \<comment> \<open>([5], Res), 3 = A * (1 / 2 - -1 / 4) + B * (1 / 2 - 1 / 2)\<close>
3.122 - eq_a = Substitute [zzz = z1] eq; \<comment> \<open>([6], Res), 3 = 3 * A / 4\<close>
3.123 + z2 = rhs (NTH 2 L_L); \<comment> \<open>([5], Frm), 3 = AA * (z - -1 / 4) + BB * (z - 1 / 2)\<close>
3.124 + eq_a = Take eq; \<comment> \<open>([5], Res), 3 = AA * (1 / 2 - -1 / 4) + BB * (1 / 2 - 1 / 2)\<close>
3.125 + eq_a = Substitute [zzz = z1] eq; \<comment> \<open>([6], Res), 3 = 3 * AA / 4\<close>
3.126 eq_a = (Rewrite_Set ''norm_Rational'' False) eq_a;
3.127 -\<comment> \<open>----- ([7], Pbl), solve (3 = 3 * A / 4, A)\<close>
3.128 - \<comment> \<open>([7], Res), [A = 4]\<close>
3.129 +\<comment> \<open>----- ([7], Pbl), solve (3 = 3 * AA / 4, AA)\<close>
3.130 + \<comment> \<open>([7], Res), [AA = 4]\<close>
3.131 sol_a = SubProblem (''Isac'', [''univariate'',''equation''], [''no_met''])
3.132 - [BOOL eq_a, REAL (A::real)] ; \<comment> \<open>a = 4\<close>
3.133 - a = rhs (NTH 1 sol_a); \<comment> \<open>([8], Frm), 3 = A * (z - -1 / 4) + B * (z - 1 / 2)\<close>
3.134 - eq_b = Take eq; \<comment> \<open>([8], Res), 3 = A * (-1 / 4 - -1 / 4) + B * (-1 / 4 - 1 / 2)\<close>
3.135 - eq_b = Substitute [zzz = z2] eq_b; \<comment> \<open>([9], Res), 3 = -3 * B / 4\<close>
3.136 - eq_b = (Rewrite_Set ''norm_Rational'' False) eq_b; \<comment> \<open>([10], Pbl), solve (3 = -3 * B / 4, B)\<close>
3.137 - sol_b = SubProblem (''Isac'', \<comment> \<open>([10], Res), [B = -4]\<close>
3.138 + [BOOL eq_a, REAL (AA::real)] ; \<comment> \<open>a = 4\<close>
3.139 + a = rhs (NTH 1 sol_a); \<comment> \<open>([8], Frm), 3 = AA * (z - -1 / 4) + BB * (z - 1 / 2)\<close>
3.140 + eq_b = Take eq; \<comment> \<open>([8], Res), 3 = AA * (-1 / 4 - -1 / 4) + BB * (-1 / 4 - 1 / 2)\<close>
3.141 + eq_b = Substitute [zzz = z2] eq_b; \<comment> \<open>([9], Res), 3 = -3 * BB / 4\<close>
3.142 + eq_b = (Rewrite_Set ''norm_Rational'' False) eq_b; \<comment> \<open>([10], Pbl), solve (3 = -3 * BB / 4, BB)\<close>
3.143 + sol_b = SubProblem (''Isac'', \<comment> \<open>([10], Res), [BB = -4]\<close>
3.144 [''univariate'',''equation''], [''no_met''])
3.145 - [BOOL eq_b, REAL (B::real)]; \<comment> \<open>b = -4\<close>
3.146 - b = rhs (NTH 1 sol_b); \<comment> \<open>eqr = A / (z - 1 / 2) + B / (z - -1 / 4)\<close>
3.147 - eqr = drop_questionmarks eqr; \<comment> \<open>([11], Frm), A / (z - 1 / 2) + B / (z - -1 / 4)\<close>
3.148 + [BOOL eq_b, REAL (BB::real)]; \<comment> \<open>b = -4\<close>
3.149 + b = rhs (NTH 1 sol_b); \<comment> \<open>eqr = AA / (z - 1 / 2) + BB / (z - -1 / 4)\<close>
3.150 pbz = Take eqr; \<comment> \<open>([11], Res), 4 / (z - 1 / 2) + -4 / (z - -1 / 4)\<close>
3.151 - pbz = Substitute [A = a, B = b] pbz \<comment> \<open>([], Res), 4 / (z - 1 / 2) + -4 / (z - -1 / 4)\<close>
3.152 + pbz = Substitute [AA = a, BB = b] pbz \<comment> \<open>([], Res), 4 / (z - 1 / 2) + -4 / (z - -1 / 4)\<close>
3.153 in pbz) "
3.154 *)
3.155 setup \<open>KEStore_Elems.add_mets
3.156 @@ -307,45 +271,43 @@
3.157 " (eq::bool) = Take (eql = eqr); " ^
3.158 (*([4], Res), 3 = ?A * (z - -1 / 4) + ?B * (z - 1 / 2)*)
3.159 " eq = (Try (Rewrite_Set ''equival_trans'' False)) eq;" ^
3.160 - (* eq = 3 = A * (z - -1 / 4) + B * (z - 1 / 2)*)
3.161 - " eq = drop_questionmarks eq; " ^
3.162 + (* eq = 3 = AA * (z - -1 / 4) + BB * (z - 1 / 2)*)
3.163 (* z1 = 1 / 2*)
3.164 " (z1::real) = (rhs (NTH 1 L_L)); " ^
3.165 (* z2 = -1 / 4*)
3.166 " (z2::real) = (rhs (NTH 2 L_L)); " ^
3.167 - (*([5], Frm), 3 = A * (z - -1 / 4) + B * (z - 1 / 2)*)
3.168 + (*([5], Frm), 3 = AA * (z - -1 / 4) + BB * (z - 1 / 2)*)
3.169 " (eq_a::bool) = Take eq; " ^
3.170 - (*([5], Res), 3 = A * (1 / 2 - -1 / 4) + B * (1 / 2 - 1 / 2)*)
3.171 + (*([5], Res), 3 = AA * (1 / 2 - -1 / 4) + BB * (1 / 2 - 1 / 2)*)
3.172 " eq_a = (Substitute [zzz = z1]) eq; " ^
3.173 - (*([6], Res), 3 = 3 * A / 4*)
3.174 + (*([6], Res), 3 = 3 * AA / 4*)
3.175 " eq_a = (Rewrite_Set ''norm_Rational'' False) eq_a; " ^
3.176
3.177 - (*([7], Pbl), solve (3 = 3 * A / 4, A)*)
3.178 + (*([7], Pbl), solve (3 = 3 * AA / 4, AA)*)
3.179 " (sol_a::bool list) = " ^
3.180 " (SubProblem (''Isac'', [''univariate'',''equation''], [''no_met'']) " ^
3.181 - (*([7], Res), [A = 4]*)
3.182 - " [BOOL eq_a, REAL (A::real)]); " ^
3.183 + (*([7], Res), [AA = 4]*)
3.184 + " [BOOL eq_a, REAL (AA::real)]); " ^
3.185 (* a = 4*)
3.186 " (a::real) = (rhs (NTH 1 sol_a)); " ^
3.187 - (*([8], Frm), 3 = A * (z - -1 / 4) + B * (z - 1 / 2)*)
3.188 + (*([8], Frm), 3 = AA * (z - -1 / 4) + BB * (z - 1 / 2)*)
3.189 " (eq_b::bool) = Take eq; " ^
3.190 - (*([8], Res), 3 = A * (-1 / 4 - -1 / 4) + B * (-1 / 4 - 1 / 2)*)
3.191 + (*([8], Res), 3 = AA * (-1 / 4 - -1 / 4) + BB * (-1 / 4 - 1 / 2)*)
3.192 " eq_b = (Substitute [zzz = z2]) eq_b; " ^
3.193 - (*([9], Res), 3 = -3 * B / 4*)
3.194 + (*([9], Res), 3 = -3 * BB / 4*)
3.195 " eq_b = (Rewrite_Set ''norm_Rational'' False) eq_b; " ^
3.196 - (*([10], Pbl), solve (3 = -3 * B / 4, B)*)
3.197 + (*([10], Pbl), solve (3 = -3 * BB / 4, BB)*)
3.198 " (sol_b::bool list) = " ^
3.199 " (SubProblem (''Isac'', [''univariate'',''equation''], [''no_met'']) " ^
3.200 - (*([10], Res), [B = -4]*)
3.201 - " [BOOL eq_b, REAL (B::real)]); " ^
3.202 + (*([10], Res), [BB = -4]*)
3.203 + " [BOOL eq_b, REAL (BB::real)]); " ^
3.204 (* b = -4*)
3.205 " (b::real) = (rhs (NTH 1 sol_b)); " ^
3.206 - (* eqr = A / (z - 1 / 2) + B / (z - -1 / 4)*)
3.207 - " eqr = drop_questionmarks eqr; " ^
3.208 - (*([11], Frm), A / (z - 1 / 2) + B / (z - -1 / 4)*)
3.209 + (* eqr = AA / (z - 1 / 2) + BB / (z - -1 / 4)*)
3.210 + (*([11], Frm), AA / (z - 1 / 2) + BB / (z - -1 / 4)*)
3.211 " (pbz::real) = Take eqr; " ^
3.212 (*([11], Res), 4 / (z - 1 / 2) + -4 / (z - -1 / 4)*)
3.213 - " pbz = ((Substitute [A = a, B = b]) pbz) " ^
3.214 + " pbz = ((Substitute [AA = a, BB = b]) pbz) " ^
3.215 (*([], Res), 4 / (z - 1 / 2) + -4 / (z - -1 / 4)*)
3.216 "in pbz)"
3.217 )]