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(*.(c) by Richard Lang, 2003 .*)
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(* collecting all knowledge for Root and Rational Equations
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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: 02.11.04
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*)
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(* use"knowledge/RootRatEq.ML";
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use"RootRatEq.ML";
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use"ROOT.ML";
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cd"knowledge";
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remove_thy"RootRatEq";
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use_thy"Isac";
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*)
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"******* RootRatEq.ML begin *******";
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theory' := overwritel (!theory', [("RootRatEq.thy",RootRatEq.thy)]);
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(*-------------------------functions---------------------*)
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(* true if denominator contains (sq)root in + or - term
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1/(sqrt(x+3)*(x+4)) -> false; 1/(sqrt(x)+2) -> true
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if false then (term)^2 contains no (sq)root *)
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fun is_rootRatAddTerm_in t v =
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let
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fun coeff_in c v = member op = v (vars c);
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fun rootadd (t as (Const ("op +",_) $ t2 $ t3)) v = (is_rootTerm_in t2 v) orelse
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(is_rootTerm_in t3 v)
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| rootadd (t as (Const ("op -",_) $ t2 $ t3)) v = (is_rootTerm_in t2 v) orelse
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(is_rootTerm_in t3 v)
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| rootadd _ _ = false;
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fun findrootrat (_ $ _ $ _ $ _) v = raise error("is_rootRatAddTerm_in:")
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(* at the moment there is no term like this, but ....*)
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| findrootrat (t as (Const ("HOL.divide",_) $ _ $ t3)) v =
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if (is_rootTerm_in t3 v) then rootadd t3 v else false
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| findrootrat (_ $ t1 $ t2) v = (findrootrat t1 v) orelse (findrootrat t2 v)
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| findrootrat (_ $ t1) v = (findrootrat t1 v)
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| findrootrat _ _ = false;
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in
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findrootrat t v
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end;
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fun eval_is_rootRatAddTerm_in _ _ (p as (Const ("RootRatEq.is'_rootRatAddTerm'_in",_) $ t $ v)) _ =
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if is_rootRatAddTerm_in t v then
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SOME ((term2str p) ^ " = True",
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Trueprop $ (mk_equality (p, HOLogic.true_const)))
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else SOME ((term2str p) ^ " = True",
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Trueprop $ (mk_equality (p, HOLogic.false_const)))
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| eval_is_rootRatAddTerm_in _ _ _ _ = ((*writeln"### nichts matcht";*) NONE);
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(*-------------------------rulse-------------------------*)
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val RootRatEq_prls =
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append_rls "RootRatEq_prls" e_rls
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[Calc ("Atools.ident",eval_ident "#ident_"),
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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 ("RootEq.is'_rootTerm'_in",eval_is_rootTerm_in ""),
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Calc ("RootRatEq.is'_rootRatAddTerm'_in", eval_is_rootRatAddTerm_in ""),
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Calc ("op =",eval_equal "#equal_"),
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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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val RooRatEq_erls =
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merge_rls "RooRatEq_erls" rootrat_erls
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(merge_rls "" RootEq_erls
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(merge_rls "" rateq_erls
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(append_rls "" e_rls
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[])));
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val RootRatEq_crls =
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merge_rls "RootRatEq_crls" rootrat_erls
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(merge_rls "" RootEq_erls
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(merge_rls "" rateq_erls
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(append_rls "" e_rls
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[])));
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ruleset' := overwritelthy thy (!ruleset',
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[("RooRatEq_erls",RooRatEq_erls) (*FIXXXME:del with rls.rls'*)
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]);
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(* Solves a rootrat Equation *)
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val rootrat_solve = prep_rls(
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Rls {id = "rootrat_solve", preconds = [],
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rew_ord = ("termlessI",termlessI),
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erls = e_rls, srls = Erls, calc = [], (*asm_thm = [],*)
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rules = [ Thm("rootrat_equation_left_1",num_str rootrat_equation_left_1),
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(* [|c is_rootTerm_in bdv|] ==> ( (a + b/c = d) = ( b = (d - a) * c )) *)
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Thm("rootrat_equation_left_2",num_str rootrat_equation_left_2),
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(* [|c is_rootTerm_in bdv|] ==> ( (b/c = d) = ( b = d * c )) *)
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Thm("rootrat_equation_right_1",num_str rootrat_equation_right_1),
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(* [|f is_rootTerm_in bdv|] ==> ( (a = d + e/f) = ( (a - d) * f = e )) *)
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Thm("rootrat_equation_right_2",num_str rootrat_equation_right_2)
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(* [|f is_rootTerm_in bdv|] ==> ( (a = e/f) = ( a * f = e )) *)
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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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[("rootrat_solve",rootrat_solve)
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]);
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(*-----------------------probleme------------------------*)
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(*
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(get_pbt ["rat","root","univariate","equation"]);
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show_ptyps();
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*)
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store_pbt
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(prep_pbt RootRatEq.thy "pbl_equ_univ_root_sq_rat" [] e_pblID
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(["rat","sq","root","univariate","equation"],
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[("#Given" ,["equality e_","solveFor v_"]),
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("#Where" ,["( (lhs e_) is_rootRatAddTerm_in (v_::real) )| \
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\( (rhs e_) is_rootRatAddTerm_in (v_::real) )"]),
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("#Find" ,["solutions v_i_"])
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],
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RootRatEq_prls, SOME "solve (e_::bool, v_)",
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[["RootRatEq","elim_rootrat_equation"]]));
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(*-------------------------Methode-----------------------*)
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store_met
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(prep_met LinEq.thy "met_rootrateq" [] e_metID
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(["RootRatEq"],
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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=Atools_erls, nrls=norm_Rational(*,
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asm_rls=[],asm_thm=[]*)}, "empty_script"));
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(*-- left 20.10.02 --*)
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store_met
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(prep_met RootRatEq.thy "met_rootrateq_elim" [] e_metID
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(["RootRatEq","elim_rootrat_equation"],
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[("#Given" ,["equality e_","solveFor v_"]),
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("#Where" ,["( (lhs e_) is_rootRatAddTerm_in (v_::real) ) | \
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\( (rhs e_) is_rootRatAddTerm_in (v_::real) )"]),
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("#Find" ,["solutions v_i_"])
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],
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{rew_ord'="termlessI",
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rls'=RooRatEq_erls,
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srls=e_rls,
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prls=RootRatEq_prls,
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calc=[],
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crls=RootRatEq_crls, nrls=norm_Rational(*,
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asm_rls=[],
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asm_thm=[]*)},
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"Script Elim_rootrat_equation (e_::bool) (v_::real) = \
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\(let e_ = ((Try (Rewrite_Set expand_rootbinoms False)) @@ \
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\ (Try (Rewrite_Set rooteq_simplify False)) @@ \
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\ (Try (Rewrite_Set make_rooteq False)) @@ \
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\ (Try (Rewrite_Set rooteq_simplify False)) @@ \
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\ (Try (Rewrite_Set_Inst [(bdv,v_)] \
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\ rootrat_solve False))) e_ \
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\ in (SubProblem (RootEq_,[univariate,equation], \
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\ [no_met]) [bool_ e_, real_ v_]))"
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));
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calclist':= overwritel (!calclist',
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[("is_rootRatAddTerm_in", ("RootRatEq.is_rootRatAddTerm_in",
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eval_is_rootRatAddTerm_in""))
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]);(*("", ("", "")),*)
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"******* RootRatEq.ML end *******";
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