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 (_ _ =))//
21 (*WN0509 compare PolyEq.all_left "[|Not(b=!=0)|] ==> (a = b) = (a - b = 0)"*)
22 all_left: "[|Not(b=!=0)|] ==> (a=b) = (a+(-1)*b=0)" and
23 makex1_x: "a^^^1 = a" and
24 real_assoc_1: "a+(b+c) = a+b+c" and
25 real_assoc_2: "a*(b*c) = a*b*c" and
28 lin_isolate_add1: "(a + b*bdv = 0) = (b*bdv = (-1)*a)" and
29 lin_isolate_add2: "(a + bdv = 0) = ( bdv = (-1)*a)" and
30 lin_isolate_div: "[|Not(b=0)|] ==> (b*bdv = c) = (bdv = c / b)"
35 val LinEq_prls = (*3.10.02:just the following order due to subterm evaluation*)
36 append_rls "LinEq_prls" e_rls
37 [Calc ("HOL.eq",eval_equal "#equal_"),
38 Calc ("Tools.matches",eval_matches ""),
39 Calc ("Tools.lhs" ,eval_lhs ""),
40 Calc ("Tools.rhs" ,eval_rhs ""),
41 Calc ("Poly.has'_degree'_in",eval_has_degree_in ""),
42 Calc ("Poly.is'_polyrat'_in",eval_is_polyrat_in ""),
43 Calc ("Atools.occurs'_in",eval_occurs_in ""),
44 Calc ("Atools.ident",eval_ident "#ident_"),
45 Thm ("not_true",num_str @{thm not_true}),
46 Thm ("not_false",num_str @{thm not_false}),
47 Thm ("and_true",num_str @{thm and_true}),
48 Thm ("and_false",num_str @{thm and_false}),
49 Thm ("or_true",num_str @{thm or_true}),
50 Thm ("or_false",num_str @{thm or_false})
52 (* ----- erls ----- *)
54 append_rls "LinEq_crls" poly_crls
55 [Thm ("real_assoc_1",num_str @{thm real_assoc_1})
58 Calc ("Fields.inverse_class.divide", eval_cancel "#divide_e"),
59 Calc ("Atools.pow" ,eval_binop "#power_"),
63 (* ----- crls ----- *)
65 append_rls "LinEq_erls" Poly_erls
66 [Thm ("real_assoc_1",num_str @{thm real_assoc_1})
69 Calc ("Fields.inverse_class.divide", eval_cancel "#divide_e"),
70 Calc ("Atools.pow" ,eval_binop "#power_"),
74 setup {* KEStore_Elems.add_rlss
75 [("LinEq_erls", (Context.theory_name @{theory}, LinEq_erls))] *}
78 val LinPoly_simplify = prep_rls(
79 Rls {id = "LinPoly_simplify", preconds = [],
80 rew_ord = ("termlessI",termlessI),
83 calc = [], errpatts = [],
85 Thm ("real_assoc_1",num_str @{thm real_assoc_1}),
86 Calc ("Groups.plus_class.plus",eval_binop "#add_"),
87 Calc ("Groups.minus_class.minus",eval_binop "#sub_"),
88 Calc ("Groups.times_class.times",eval_binop "#mult_"),
90 Calc ("Fields.inverse_class.divide", eval_cancel "#divide_e"),
91 Calc ("NthRoot.sqrt",eval_sqrt "#sqrt_"),
93 Calc ("Atools.pow" ,eval_binop "#power_")
97 setup {* KEStore_Elems.add_rlss
98 [("LinPoly_simplify", (Context.theory_name @{theory}, LinPoly_simplify))] *}
101 (*isolate the bound variable in an linear equation; 'bdv' is a meta-constant*)
102 val LinEq_simplify = prep_rls(
103 Rls {id = "LinEq_simplify", preconds = [],
104 rew_ord = ("e_rew_ord",e_rew_ord),
107 calc = [], errpatts = [],
109 Thm("lin_isolate_add1",num_str @{thm lin_isolate_add1}),
110 (* a+bx=0 -> bx=-a *)
111 Thm("lin_isolate_add2",num_str @{thm lin_isolate_add2}),
113 Thm("lin_isolate_div",num_str @{thm lin_isolate_div})
116 scr = EmptyScr}:rls);
118 setup {* KEStore_Elems.add_rlss
119 [("LinEq_simplify", (Context.theory_name @{theory}, LinEq_simplify))] *}
122 (*----------------------------- problem types --------------------------------*)
125 (get_pbt ["LINEAR","univariate","equation"]);
128 (* ---------linear----------- *)
130 (prep_pbt thy "pbl_equ_univ_lin" [] e_pblID
131 (["LINEAR","univariate","equation"],
132 [("#Given" ,["equality e_e","solveFor v_v"]),
133 ("#Where" ,["HOL.False", (*WN0509 just detected: this pbl can never be used?!?*)
134 "Not( (lhs e_e) is_polyrat_in v_v)",
135 "Not( (rhs e_e) is_polyrat_in v_v)",
136 "((lhs e_e) has_degree_in v_v)=1",
137 "((rhs e_e) has_degree_in v_v)=1"]),
138 ("#Find" ,["solutions v_v'i'"])
140 LinEq_prls, SOME "solve (e_e::bool, v_v)",
141 [["LinEq","solve_lineq_equation"]]));
143 (*-------------- methods------------------------------------------------------*)
145 (prep_met thy "met_eqlin" [] e_metID
148 {rew_ord'="tless_true",rls'=Atools_erls,calc = [], srls = e_rls, prls=e_rls,
149 crls=LinEq_crls, errpats = [], nrls = norm_Poly}, "empty_script"));
151 (* ansprechen mit ["LinEq","solve_univar_equation"] *)
153 (prep_met thy "met_eq_lin" [] e_metID
154 (["LinEq","solve_lineq_equation"],
155 [("#Given", ["equality e_e", "solveFor v_v"]),
156 ("#Where", ["Not ((lhs e_e) is_polyrat_in v_v)",
157 "((lhs e_e) has_degree_in v_v) = 1"]),
158 ("#Find", ["solutions v_v'i'"])
160 {rew_ord'="termlessI", rls'=LinEq_erls, srls=e_rls, prls=LinEq_prls,
161 calc=[], crls=LinEq_crls, errpats = [], nrls = norm_Poly},
162 "Script Solve_lineq_equation (e_e::bool) (v_v::real) = " ^
163 "(let e_e =((Try (Rewrite all_left False)) @@ " ^
164 " (Try (Repeat (Rewrite makex1_x False))) @@ " ^
165 " (Try (Rewrite_Set expand_binoms False)) @@ " ^
166 " (Try (Repeat (Rewrite_Set_Inst [(bdv, v_v::real)] " ^
167 " make_ratpoly_in False))) @@ " ^
168 " (Try (Repeat (Rewrite_Set LinPoly_simplify False))))e_e;" ^
169 " e_e = ((Try (Rewrite_Set_Inst [(bdv, v_v::real)] " ^
170 " LinEq_simplify True)) @@ " ^
171 " (Repeat(Try (Rewrite_Set LinPoly_simplify False)))) e_e " ^
172 " in ((Or_to_List e_e)::bool list))"
174 get_met ["LinEq","solve_lineq_equation"];