1 (*. (c) by Richard Lang, 2003 .*)
2 (* theory collecting all knowledge for LinearEquations
10 theory LinEq imports Poly Equation begin
13 Solve'_lineq'_equation
15 bool list] => bool list"
16 ("((Script Solve'_lineq'_equation (_ _ =))// (_))" 9)
20 (*WN0509 compare PolyEq.all_left "[|Not(b=!=0)|] ==> (a = b) = (a - b = 0)"*)
21 all_left: "[|Not(b=!=0)|] ==> (a=b) = (a+(-1)*b=0)" and
22 makex1_x: "a^^^1 = a" and
23 real_assoc_1: "a+(b+c) = a+b+c" and
24 real_assoc_2: "a*(b*c) = a*b*c" and
27 lin_isolate_add1: "(a + b*bdv = 0) = (b*bdv = (-1)*a)" and
28 lin_isolate_add2: "(a + bdv = 0) = ( bdv = (-1)*a)" and
29 lin_isolate_div: "[|Not(b=0)|] ==> (b*bdv = c) = (bdv = c / b)"
34 val LinEq_prls = (*3.10.02:just the following order due to subterm evaluation*)
35 Rule.append_rls "LinEq_prls" Rule.e_rls
36 [Rule.Calc ("HOL.eq",eval_equal "#equal_"),
37 Rule.Calc ("Tools.matches", Tools.eval_matches ""),
38 Rule.Calc ("Tools.lhs" , Tools.eval_lhs ""),
39 Rule.Calc ("Tools.rhs" , Tools.eval_rhs ""),
40 Rule.Calc ("Poly.has'_degree'_in",eval_has_degree_in ""),
41 Rule.Calc ("Poly.is'_polyrat'_in",eval_is_polyrat_in ""),
42 Rule.Calc ("Atools.occurs'_in",eval_occurs_in ""),
43 Rule.Calc ("Atools.ident",eval_ident "#ident_"),
44 Rule.Thm ("not_true",TermC.num_str @{thm not_true}),
45 Rule.Thm ("not_false",TermC.num_str @{thm not_false}),
46 Rule.Thm ("and_true",TermC.num_str @{thm and_true}),
47 Rule.Thm ("and_false",TermC.num_str @{thm and_false}),
48 Rule.Thm ("or_true",TermC.num_str @{thm or_true}),
49 Rule.Thm ("or_false",TermC.num_str @{thm or_false})
51 (* ----- erls ----- *)
53 Rule.append_rls "LinEq_crls" poly_crls
54 [Rule.Thm ("real_assoc_1",TermC.num_str @{thm real_assoc_1})
57 Rule.Calc ("Rings.divide_class.divide", eval_cancel "#divide_e"),
58 Rule.Calc ("Atools.pow" ,eval_binop "#power_"),
62 (* ----- crls ----- *)
64 Rule.append_rls "LinEq_erls" Poly_erls
65 [Rule.Thm ("real_assoc_1",TermC.num_str @{thm real_assoc_1})
68 Rule.Calc ("Rings.divide_class.divide", eval_cancel "#divide_e"),
69 Rule.Calc ("Atools.pow" ,eval_binop "#power_"),
73 setup \<open>KEStore_Elems.add_rlss
74 [("LinEq_erls", (Context.theory_name @{theory}, LinEq_erls))]\<close>
77 val LinPoly_simplify = prep_rls'(
78 Rule.Rls {id = "LinPoly_simplify", preconds = [],
79 rew_ord = ("termlessI",termlessI),
82 calc = [], errpatts = [],
84 Rule.Thm ("real_assoc_1",TermC.num_str @{thm real_assoc_1}),
85 Rule.Calc ("Groups.plus_class.plus",eval_binop "#add_"),
86 Rule.Calc ("Groups.minus_class.minus",eval_binop "#sub_"),
87 Rule.Calc ("Groups.times_class.times",eval_binop "#mult_"),
89 Rule.Calc ("Rings.divide_class.divide", eval_cancel "#divide_e"),
90 Rule.Calc ("NthRoot.sqrt",eval_sqrt "#sqrt_"),
92 Rule.Calc ("Atools.pow" ,eval_binop "#power_")
94 scr = Rule.EmptyScr});
96 setup \<open>KEStore_Elems.add_rlss
97 [("LinPoly_simplify", (Context.theory_name @{theory}, LinPoly_simplify))]\<close>
100 (*isolate the bound variable in an linear equation; 'bdv' is a meta-constant*)
101 val LinEq_simplify = prep_rls'(
102 Rule.Rls {id = "LinEq_simplify", preconds = [],
103 rew_ord = ("e_rew_ord", Rule.e_rew_ord),
106 calc = [], errpatts = [],
108 Rule.Thm("lin_isolate_add1",TermC.num_str @{thm lin_isolate_add1}),
109 (* a+bx=0 -> bx=-a *)
110 Rule.Thm("lin_isolate_add2",TermC.num_str @{thm lin_isolate_add2}),
112 Rule.Thm("lin_isolate_div",TermC.num_str @{thm lin_isolate_div})
115 scr = Rule.EmptyScr});
117 setup \<open>KEStore_Elems.add_rlss
118 [("LinEq_simplify", (Context.theory_name @{theory}, LinEq_simplify))]\<close>
120 (*----------------------------- problem types --------------------------------*)
121 (* ---------linear----------- *)
122 setup \<open>KEStore_Elems.add_pbts
123 [(Specify.prep_pbt thy "pbl_equ_univ_lin" [] Celem.e_pblID
124 (["LINEAR", "univariate", "equation"],
125 [("#Given" ,["equality e_e", "solveFor v_v"]),
126 ("#Where" ,["HOL.False", (*WN0509 just detected: this pbl can never be used?!?*)
127 "Not( (lhs e_e) is_polyrat_in v_v)",
128 "Not( (rhs e_e) is_polyrat_in v_v)",
129 "((lhs e_e) has_degree_in v_v)=1",
130 "((rhs e_e) has_degree_in v_v)=1"]),
131 ("#Find" ,["solutions v_v'i'"])],
132 LinEq_prls, SOME "solve (e_e::bool, v_v)", [["LinEq", "solve_lineq_equation"]]))]\<close>
134 (*-------------- methods------------------------------------------------------*)
135 setup \<open>KEStore_Elems.add_mets
136 [Specify.prep_met thy "met_eqlin" [] Celem.e_metID
138 {rew_ord' = "tless_true",rls' = Atools_erls,calc = [], srls = Rule.e_rls, prls = Rule.e_rls,
139 crls = LinEq_crls, errpats = [], nrls = norm_Poly},
142 (* ansprechen mit ["LinEq","solve_univar_equation"] *)
144 partial_function (tailrec) solve_linear_equation :: "bool \<Rightarrow> real \<Rightarrow> bool list"
146 "solve_linear_equation e_e v_v =
147 (let e_e =((Try (Rewrite ''all_left'' False)) @@
148 (Try (Repeat (Rewrite ''makex1_x'' False))) @@
149 (Try (Rewrite_Set ''expand_binoms'' False)) @@
150 (Try (Repeat (Rewrite_Set_Inst [(''bdv'', v_v)]
151 ''make_ratpoly_in'' False))) @@
152 (Try (Repeat (Rewrite_Set ''LinPoly_simplify'' False))))e_e;
153 e_e = ((Try (Rewrite_Set_Inst [(''bdv'', v_v::real)]
154 ''LinEq_simplify'' True)) @@
155 (Repeat(Try (Rewrite_Set ''LinPoly_simplify'' False)))) e_e
158 setup \<open>KEStore_Elems.add_mets
159 [Specify.prep_met thy "met_eq_lin" [] Celem.e_metID
160 (["LinEq","solve_lineq_equation"],
161 [("#Given", ["equality e_e", "solveFor v_v"]),
162 ("#Where", ["Not ((lhs e_e) is_polyrat_in v_v)", "((lhs e_e) has_degree_in v_v) = 1"]),
163 ("#Find", ["solutions v_v'i'"])],
164 {rew_ord' = "termlessI", rls' = LinEq_erls, srls = Rule.e_rls, prls = LinEq_prls, calc = [],
165 crls = LinEq_crls, errpats = [], nrls = norm_Poly},
166 "Script Solve_lineq_equation (e_e::bool) (v_v::real) = " ^
167 "(let e_e =((Try (Rewrite ''all_left'' False)) @@ " ^
168 " (Try (Repeat (Rewrite ''makex1_x'' False))) @@ " ^
169 " (Try (Rewrite_Set ''expand_binoms'' False)) @@ " ^
170 " (Try (Repeat (Rewrite_Set_Inst [(''bdv'', v_v::real)] " ^
171 " ''make_ratpoly_in'' False))) @@ " ^
172 " (Try (Repeat (Rewrite_Set ''LinPoly_simplify'' False))))e_e;" ^
173 " e_e = ((Try (Rewrite_Set_Inst [(''bdv'', v_v::real)] " ^
174 " ''LinEq_simplify'' True)) @@ " ^
175 " (Repeat(Try (Rewrite_Set ''LinPoly_simplify'' False)))) e_e " ^
176 " in ((Or_to_List e_e)::bool list))")]
178 ML \<open>Specify.get_met' @{theory} ["LinEq","solve_lineq_equation"];\<close>