neuper@37906
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(*. (c) by Richard Lang, 2003 .*)
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neuper@37906
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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 (_ _ =))// (_))" 9)
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axiomatization where
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(*-- normalise --*)
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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)" and
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makex1_x: "a^^^1 = a" and
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real_assoc_1: "a+(b+c) = a+b+c" and
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real_assoc_2: "a*(b*c) = a*b*c" and
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(*-- solve --*)
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lin_isolate_add1: "(a + b*bdv = 0) = (b*bdv = (-1)*a)" and
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lin_isolate_add2: "(a + bdv = 0) = ( bdv = (-1)*a)" and
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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 thy = @{theory};
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val LinEq_prls = (*3.10.02:just the following order due to subterm evaluation*)
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Rule.append_rls "LinEq_prls" Rule.e_rls
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[Rule.Calc ("HOL.eq",eval_equal "#equal_"),
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Rule.Calc ("Tools.matches",eval_matches ""),
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Rule.Calc ("Tools.lhs" ,eval_lhs ""),
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Rule.Calc ("Tools.rhs" ,eval_rhs ""),
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Rule.Calc ("Poly.has'_degree'_in",eval_has_degree_in ""),
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Rule.Calc ("Poly.is'_polyrat'_in",eval_is_polyrat_in ""),
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Rule.Calc ("Atools.occurs'_in",eval_occurs_in ""),
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Rule.Calc ("Atools.ident",eval_ident "#ident_"),
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Rule.Thm ("not_true",TermC.num_str @{thm not_true}),
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Rule.Thm ("not_false",TermC.num_str @{thm not_false}),
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Rule.Thm ("and_true",TermC.num_str @{thm and_true}),
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Rule.Thm ("and_false",TermC.num_str @{thm and_false}),
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Rule.Thm ("or_true",TermC.num_str @{thm or_true}),
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Rule.Thm ("or_false",TermC.num_str @{thm or_false})
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];
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(* ----- erls ----- *)
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val LinEq_crls =
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Rule.append_rls "LinEq_crls" poly_crls
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[Rule.Thm ("real_assoc_1",TermC.num_str @{thm real_assoc_1})
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(*
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Don't use
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Rule.Calc ("Rings.divide_class.divide", eval_cancel "#divide_e"),
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Rule.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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Rule.append_rls "LinEq_erls" Poly_erls
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[Rule.Thm ("real_assoc_1",TermC.num_str @{thm real_assoc_1})
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(*
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Don't use
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Rule.Calc ("Rings.divide_class.divide", eval_cancel "#divide_e"),
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Rule.Calc ("Atools.pow" ,eval_binop "#power_"),
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*)
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];
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*}
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setup {* KEStore_Elems.add_rlss
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[("LinEq_erls", (Context.theory_name @{theory}, LinEq_erls))] *}
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ML {*
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val LinPoly_simplify = prep_rls'(
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Rule.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 = Rule.Erls,
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calc = [], errpatts = [],
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rules = [
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Rule.Thm ("real_assoc_1",TermC.num_str @{thm real_assoc_1}),
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Rule.Calc ("Groups.plus_class.plus",eval_binop "#add_"),
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Rule.Calc ("Groups.minus_class.minus",eval_binop "#sub_"),
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Rule.Calc ("Groups.times_class.times",eval_binop "#mult_"),
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(* Dont use
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Rule.Calc ("Rings.divide_class.divide", eval_cancel "#divide_e"),
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Rule.Calc ("NthRoot.sqrt",eval_sqrt "#sqrt_"),
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*)
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Rule.Calc ("Atools.pow" ,eval_binop "#power_")
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],
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scr = Rule.EmptyScr});
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*}
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setup {* KEStore_Elems.add_rlss
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[("LinPoly_simplify", (Context.theory_name @{theory}, LinPoly_simplify))] *}
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ML {*
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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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Rule.Rls {id = "LinEq_simplify", preconds = [],
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rew_ord = ("e_rew_ord", Rule.e_rew_ord),
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erls = LinEq_erls,
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srls = Rule.Erls,
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calc = [], errpatts = [],
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rules = [
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Rule.Thm("lin_isolate_add1",TermC.num_str @{thm lin_isolate_add1}),
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(* a+bx=0 -> bx=-a *)
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Rule.Thm("lin_isolate_add2",TermC.num_str @{thm lin_isolate_add2}),
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(* a+ x=0 -> x=-a *)
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Rule.Thm("lin_isolate_div",TermC.num_str @{thm lin_isolate_div})
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(* bx=c -> x=c/b *)
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],
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scr = Rule.EmptyScr});
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*}
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setup {* KEStore_Elems.add_rlss
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[("LinEq_simplify", (Context.theory_name @{theory}, LinEq_simplify))] *}
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(*----------------------------- problem types --------------------------------*)
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(* ---------linear----------- *)
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setup {* KEStore_Elems.add_pbts
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[(Specify.prep_pbt thy "pbl_equ_univ_lin" [] Celem.e_pblID
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(["LINEAR", "univariate", "equation"],
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[("#Given" ,["equality e_e", "solveFor v_v"]),
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("#Where" ,["HOL.False", (*WN0509 just detected: this pbl can never be used?!?*)
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"Not( (lhs e_e) is_polyrat_in v_v)",
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"Not( (rhs e_e) is_polyrat_in v_v)",
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"((lhs e_e) has_degree_in v_v)=1",
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"((rhs e_e) has_degree_in v_v)=1"]),
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("#Find" ,["solutions v_v'i'"])],
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LinEq_prls, SOME "solve (e_e::bool, v_v)", [["LinEq", "solve_lineq_equation"]]))] *}
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(*-------------- methods------------------------------------------------------*)
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setup {* KEStore_Elems.add_mets
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[Specify.prep_met thy "met_eqlin" [] Celem.e_metID
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(["LinEq"], [],
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{rew_ord' = "tless_true",rls' = Atools_erls,calc = [], srls = Rule.e_rls, prls = Rule.e_rls,
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crls = LinEq_crls, errpats = [], nrls = norm_Poly},
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"empty_script"),
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(* ansprechen mit ["LinEq","solve_univar_equation"] *)
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Specify.prep_met thy "met_eq_lin" [] Celem.e_metID
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(["LinEq","solve_lineq_equation"],
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[("#Given", ["equality e_e", "solveFor v_v"]),
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("#Where", ["Not ((lhs e_e) is_polyrat_in v_v)", "((lhs e_e) has_degree_in v_v) = 1"]),
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("#Find", ["solutions v_v'i'"])],
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{rew_ord' = "termlessI", rls' = LinEq_erls, srls = Rule.e_rls, prls = LinEq_prls, calc = [],
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crls = LinEq_crls, errpats = [], nrls = norm_Poly},
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"Script Solve_lineq_equation (e_e::bool) (v_v::real) = " ^
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"(let e_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_v::real)] " ^
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" make_ratpoly_in False))) @@ " ^
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" (Try (Repeat (Rewrite_Set LinPoly_simplify False))))e_e;" ^
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" e_e = ((Try (Rewrite_Set_Inst [(bdv, v_v::real)] " ^
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" LinEq_simplify True)) @@ " ^
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" (Repeat(Try (Rewrite_Set LinPoly_simplify False)))) e_e " ^
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" in ((Or_to_List e_e)::bool list))")]
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*}
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ML {* Specify.get_met' @{theory} ["LinEq","solve_lineq_equation"]; *}
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end
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