neuper@37906
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(*. (c) by Richard Lang, 2003 .*)
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(* theory collecting all knowledge for LinearEquations
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created by: rlang
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date: 02.10
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changed by: rlang
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last change by: rlang
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date: 02.10.20
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*)
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theory LinEq imports Poly Equation begin
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consts
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Solve'_lineq'_equation
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:: "[bool,real,
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bool list] => bool list"
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("((Script Solve'_lineq'_equation (_ _ =))//
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(_))" 9)
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axioms
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(*-- normalize --*)
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(*WN0509 compare PolyEq.all_left "[|Not(b=!=0)|] ==> (a = b) = (a - b = 0)"*)
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all_left "[|Not(b=!=0)|] ==> (a=b) = (a+(-1)*b=0)"
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makex1_x "a^^^1 = a"
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real_assoc_1 "a+(b+c) = a+b+c"
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real_assoc_2 "a*(b*c) = a*b*c"
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(*-- solve --*)
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lin_isolate_add1 "(a + b*bdv = 0) = (b*bdv = (-1)*a)"
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lin_isolate_add2 "(a + bdv = 0) = ( bdv = (-1)*a)"
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lin_isolate_div "[|Not(b=0)|] ==> (b*bdv = c) = (bdv = c / b)"
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ML {*
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val LinEq_prls = (*3.10.02:just the following order due to subterm evaluation*)
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append_rls "LinEq_prls" e_rls
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[Calc ("op =",eval_equal "#equal_"),
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Calc ("Tools.matches",eval_matches ""),
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Calc ("Tools.lhs" ,eval_lhs ""),
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Calc ("Tools.rhs" ,eval_rhs ""),
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Calc ("Poly.has'_degree'_in",eval_has_degree_in ""),
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Calc ("Poly.is'_polyrat'_in",eval_is_polyrat_in ""),
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Calc ("Atools.occurs'_in",eval_occurs_in ""),
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Calc ("Atools.ident",eval_ident "#ident_"),
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Thm ("not_true",num_str @{not_true),
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Thm ("not_false",num_str @{not_false),
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Thm ("and_true",num_str @{and_true),
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Thm ("and_false",num_str @{and_false),
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Thm ("or_true",num_str @{or_true),
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Thm ("or_false",num_str @{or_false)
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];
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(* ----- erls ----- *)
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val LinEq_crls =
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append_rls "LinEq_crls" poly_crls
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[Thm ("real_assoc_1",num_str @{real_assoc_1)
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(*
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Don't use
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Calc ("HOL.divide", eval_cancel "#divide_"),
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Calc ("Atools.pow" ,eval_binop "#power_"),
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*)
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];
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(* ----- crls ----- *)
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val LinEq_erls =
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append_rls "LinEq_erls" Poly_erls
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[Thm ("real_assoc_1",num_str @{real_assoc_1)
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(*
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Don't use
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Calc ("HOL.divide", eval_cancel "#divide_"),
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Calc ("Atools.pow" ,eval_binop "#power_"),
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*)
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];
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ruleset' := overwritelthy thy (!ruleset',
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[("LinEq_erls",LinEq_erls)(*FIXXXME:del with rls.rls'*)
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]);
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val LinPoly_simplify = prep_rls(
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Rls {id = "LinPoly_simplify", preconds = [],
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rew_ord = ("termlessI",termlessI),
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erls = LinEq_erls,
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srls = Erls,
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calc = [],
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(*asm_thm = [],*)
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rules = [
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Thm ("real_assoc_1",num_str @{real_assoc_1),
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Calc ("op +",eval_binop "#add_"),
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Calc ("op -",eval_binop "#sub_"),
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Calc ("op *",eval_binop "#mult_"),
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(* Dont use
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Calc ("HOL.divide", eval_cancel "#divide_"),
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Calc ("Root.sqrt",eval_sqrt "#sqrt_"),
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*)
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Calc ("Atools.pow" ,eval_binop "#power_")
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],
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scr = Script ((term_of o the o (parse thy)) "empty_script")
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}:rls);
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ruleset' := overwritelthy thy (!ruleset',
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[("LinPoly_simplify",LinPoly_simplify)]);
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(*isolate the bound variable in an linear equation; 'bdv' is a meta-constant*)
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val LinEq_simplify = prep_rls(
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Rls {id = "LinEq_simplify", preconds = [],
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rew_ord = ("e_rew_ord",e_rew_ord),
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erls = LinEq_erls,
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srls = Erls,
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calc = [],
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(*asm_thm = [("lin_isolate_div","")],*)
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rules = [
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Thm("lin_isolate_add1",num_str @{lin_isolate_add1),
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(* a+bx=0 -> bx=-a *)
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Thm("lin_isolate_add2",num_str @{lin_isolate_add2),
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(* a+ x=0 -> x=-a *)
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Thm("lin_isolate_div",num_str @{lin_isolate_div)
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(* bx=c -> x=c/b *)
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],
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scr = Script ((term_of o the o (parse thy)) "empty_script")
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}:rls);
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ruleset' := overwritelthy thy (!ruleset',
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[("LinEq_simplify",LinEq_simplify)]);
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(*----------------------------- problem types --------------------------------*)
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(*
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show_ptyps();
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(get_pbt ["linear","univariate","equation"]);
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*)
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(* ---------linear----------- *)
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store_pbt
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(prep_pbt (theory "LinEq") "pbl_equ_univ_lin" [] e_pblID
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(["linear","univariate","equation"],
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[("#Given" ,["equality e_","solveFor v_"]),
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("#Where" ,["False", (*WN0509 just detected: this pbl can never be used?!?*)
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"Not( (lhs e_) is_polyrat_in v_)",
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"Not( (rhs e_) is_polyrat_in v_)",
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"((lhs e_) has_degree_in v_)=1",
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"((rhs e_) has_degree_in v_)=1"]),
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("#Find" ,["solutions v_i_"])
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],
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LinEq_prls, SOME "solve (e_::bool, v_)",
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[["LinEq","solve_lineq_equation"]]));
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(*-------------- methods------------------------------------------------------*)
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store_met
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(prep_met (theory "LinEq") "met_eqlin" [] e_metID
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(["LinEq"],
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[],
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{rew_ord'="tless_true",rls'=Atools_erls,calc = [], srls = e_rls, prls=e_rls,
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crls=LinEq_crls, nrls=norm_Poly
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(*, asm_rls=[],asm_thm=[]*)}, "empty_script"));
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(* ansprechen mit ["LinEq","solve_univar_equation"] *)
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store_met
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(prep_met (theory "LinEq") "met_eq_lin" [] e_metID
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(["LinEq","solve_lineq_equation"],
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[("#Given" ,["equality e_","solveFor v_"]),
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("#Where" ,["Not( (lhs e_) is_polyrat_in v_)",
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"( (lhs e_) has_degree_in v_)=1"]),
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("#Find" ,["solutions v_i_"])
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],
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{rew_ord'="termlessI",
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rls'=LinEq_erls,
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srls=e_rls,
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prls=LinEq_prls,
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calc=[],
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crls=LinEq_crls, nrls=norm_Poly(*,
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asm_rls=[],
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asm_thm=[("lin_isolate_div","")]*)},
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"Script Solve_lineq_equation (e_::bool) (v_::real) = " ^
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"(let e_ =((Try (Rewrite all_left False)) @@ " ^
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" (Try (Repeat (Rewrite makex1_x False))) @@ " ^
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" (Try (Rewrite_Set expand_binoms False)) @@ " ^
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" (Try (Repeat (Rewrite_Set_Inst [(bdv,v_::real)] " ^
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" make_ratpoly_in False))) @@ " ^
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" (Try (Repeat (Rewrite_Set LinPoly_simplify False)))) e_;" ^
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" e_ = ((Try (Rewrite_Set_Inst [(bdv,v_::real)] " ^
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" LinEq_simplify True)) @@ " ^
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" (Repeat(Try (Rewrite_Set LinPoly_simplify False)))) e_ " ^
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" in ((Or_to_List e_)::bool list))"
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));
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"******* LinEq.ML end *******";
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get_met ["LinEq","solve_lineq_equation"];
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*}
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end
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