1.1 --- /dev/null Thu Jan 01 00:00:00 1970 +0000
1.2 +++ b/src/Tools/isac/Knowledge/RootRatEq.ML Wed Aug 25 16:20:07 2010 +0200
1.3 @@ -0,0 +1,166 @@
1.4 +(*.(c) by Richard Lang, 2003 .*)
1.5 +(* collecting all knowledge for Root and Rational Equations
1.6 + created by: rlang
1.7 + date: 02.10
1.8 + changed by: rlang
1.9 + last change by: rlang
1.10 + date: 02.11.04
1.11 +*)
1.12 +
1.13 +(* use"knowledge/RootRatEq.ML";
1.14 + use"RootRatEq.ML";
1.15 +
1.16 + use"ROOT.ML";
1.17 + cd"knowledge";
1.18 +
1.19 + remove_thy"RootRatEq";
1.20 + use_thy"Isac";
1.21 + *)
1.22 +
1.23 +"******* RootRatEq.ML begin *******";
1.24 +theory' := overwritel (!theory', [("RootRatEq.thy",RootRatEq.thy)]);
1.25 +
1.26 +(*-------------------------functions---------------------*)
1.27 +(* true if denominator contains (sq)root in + or - term
1.28 + 1/(sqrt(x+3)*(x+4)) -> false; 1/(sqrt(x)+2) -> true
1.29 + if false then (term)^2 contains no (sq)root *)
1.30 +fun is_rootRatAddTerm_in t v =
1.31 + let
1.32 + fun coeff_in c v = member op = (vars c) v;
1.33 + fun rootadd (t as (Const ("op +",_) $ t2 $ t3)) v = (is_rootTerm_in t2 v) orelse
1.34 + (is_rootTerm_in t3 v)
1.35 + | rootadd (t as (Const ("op -",_) $ t2 $ t3)) v = (is_rootTerm_in t2 v) orelse
1.36 + (is_rootTerm_in t3 v)
1.37 + | rootadd _ _ = false;
1.38 + fun findrootrat (_ $ _ $ _ $ _) v = raise error("is_rootRatAddTerm_in:")
1.39 + (* at the moment there is no term like this, but ....*)
1.40 + | findrootrat (t as (Const ("HOL.divide",_) $ _ $ t3)) v =
1.41 + if (is_rootTerm_in t3 v) then rootadd t3 v else false
1.42 + | findrootrat (_ $ t1 $ t2) v = (findrootrat t1 v) orelse (findrootrat t2 v)
1.43 + | findrootrat (_ $ t1) v = (findrootrat t1 v)
1.44 + | findrootrat _ _ = false;
1.45 + in
1.46 + findrootrat t v
1.47 + end;
1.48 +
1.49 +fun eval_is_rootRatAddTerm_in _ _ (p as (Const ("RootRatEq.is'_rootRatAddTerm'_in",_) $ t $ v)) _ =
1.50 + if is_rootRatAddTerm_in t v then
1.51 + SOME ((term2str p) ^ " = True",
1.52 + Trueprop $ (mk_equality (p, HOLogic.true_const)))
1.53 + else SOME ((term2str p) ^ " = True",
1.54 + Trueprop $ (mk_equality (p, HOLogic.false_const)))
1.55 + | eval_is_rootRatAddTerm_in _ _ _ _ = ((*writeln"### nichts matcht";*) NONE);
1.56 +
1.57 +(*-------------------------rulse-------------------------*)
1.58 +val RootRatEq_prls =
1.59 + append_rls "RootRatEq_prls" e_rls
1.60 + [Calc ("Atools.ident",eval_ident "#ident_"),
1.61 + Calc ("Tools.matches",eval_matches ""),
1.62 + Calc ("Tools.lhs" ,eval_lhs ""),
1.63 + Calc ("Tools.rhs" ,eval_rhs ""),
1.64 + Calc ("RootEq.is'_rootTerm'_in",eval_is_rootTerm_in ""),
1.65 + Calc ("RootRatEq.is'_rootRatAddTerm'_in", eval_is_rootRatAddTerm_in ""),
1.66 + Calc ("op =",eval_equal "#equal_"),
1.67 + Thm ("not_true",num_str not_true),
1.68 + Thm ("not_false",num_str not_false),
1.69 + Thm ("and_true",num_str and_true),
1.70 + Thm ("and_false",num_str and_false),
1.71 + Thm ("or_true",num_str or_true),
1.72 + Thm ("or_false",num_str or_false)
1.73 + ];
1.74 +
1.75 +
1.76 +val RooRatEq_erls =
1.77 + merge_rls "RooRatEq_erls" rootrat_erls
1.78 + (merge_rls "" RootEq_erls
1.79 + (merge_rls "" rateq_erls
1.80 + (append_rls "" e_rls
1.81 + [])));
1.82 +
1.83 +val RootRatEq_crls =
1.84 + merge_rls "RootRatEq_crls" rootrat_erls
1.85 + (merge_rls "" RootEq_erls
1.86 + (merge_rls "" rateq_erls
1.87 + (append_rls "" e_rls
1.88 + [])));
1.89 +
1.90 +ruleset' := overwritelthy thy (!ruleset',
1.91 + [("RooRatEq_erls",RooRatEq_erls) (*FIXXXME:del with rls.rls'*)
1.92 + ]);
1.93 +
1.94 +(* Solves a rootrat Equation *)
1.95 + val rootrat_solve = prep_rls(
1.96 + Rls {id = "rootrat_solve", preconds = [],
1.97 + rew_ord = ("termlessI",termlessI),
1.98 + erls = e_rls, srls = Erls, calc = [], (*asm_thm = [],*)
1.99 + rules = [ Thm("rootrat_equation_left_1",num_str rootrat_equation_left_1),
1.100 + (* [|c is_rootTerm_in bdv|] ==> ( (a + b/c = d) = ( b = (d - a) * c )) *)
1.101 + Thm("rootrat_equation_left_2",num_str rootrat_equation_left_2),
1.102 + (* [|c is_rootTerm_in bdv|] ==> ( (b/c = d) = ( b = d * c )) *)
1.103 + Thm("rootrat_equation_right_1",num_str rootrat_equation_right_1),
1.104 + (* [|f is_rootTerm_in bdv|] ==> ( (a = d + e/f) = ( (a - d) * f = e )) *)
1.105 + Thm("rootrat_equation_right_2",num_str rootrat_equation_right_2)
1.106 + (* [|f is_rootTerm_in bdv|] ==> ( (a = e/f) = ( a * f = e )) *)
1.107 + ],
1.108 + scr = Script ((term_of o the o (parse thy)) "empty_script")
1.109 + }:rls);
1.110 +ruleset' := overwritelthy thy (!ruleset',
1.111 + [("rootrat_solve",rootrat_solve)
1.112 + ]);
1.113 +
1.114 +(*-----------------------probleme------------------------*)
1.115 +(*
1.116 +(get_pbt ["rat","root","univariate","equation"]);
1.117 +show_ptyps();
1.118 +*)
1.119 +store_pbt
1.120 + (prep_pbt RootRatEq.thy "pbl_equ_univ_root_sq_rat" [] e_pblID
1.121 + (["rat","sq","root","univariate","equation"],
1.122 + [("#Given" ,["equality e_","solveFor v_"]),
1.123 + ("#Where" ,["( (lhs e_) is_rootRatAddTerm_in (v_::real) )| \
1.124 + \( (rhs e_) is_rootRatAddTerm_in (v_::real) )"]),
1.125 + ("#Find" ,["solutions v_i_"])
1.126 + ],
1.127 + RootRatEq_prls, SOME "solve (e_::bool, v_)",
1.128 + [["RootRatEq","elim_rootrat_equation"]]));
1.129 +
1.130 +(*-------------------------Methode-----------------------*)
1.131 +store_met
1.132 + (prep_met LinEq.thy "met_rootrateq" [] e_metID
1.133 + (["RootRatEq"],
1.134 + [],
1.135 + {rew_ord'="tless_true",rls'=Atools_erls,calc = [], srls = e_rls, prls=e_rls,
1.136 + crls=Atools_erls, nrls=norm_Rational(*,
1.137 + asm_rls=[],asm_thm=[]*)}, "empty_script"));
1.138 +(*-- left 20.10.02 --*)
1.139 +store_met
1.140 + (prep_met RootRatEq.thy "met_rootrateq_elim" [] e_metID
1.141 + (["RootRatEq","elim_rootrat_equation"],
1.142 + [("#Given" ,["equality e_","solveFor v_"]),
1.143 + ("#Where" ,["( (lhs e_) is_rootRatAddTerm_in (v_::real) ) | \
1.144 + \( (rhs e_) is_rootRatAddTerm_in (v_::real) )"]),
1.145 + ("#Find" ,["solutions v_i_"])
1.146 + ],
1.147 + {rew_ord'="termlessI",
1.148 + rls'=RooRatEq_erls,
1.149 + srls=e_rls,
1.150 + prls=RootRatEq_prls,
1.151 + calc=[],
1.152 + crls=RootRatEq_crls, nrls=norm_Rational(*,
1.153 + asm_rls=[],
1.154 + asm_thm=[]*)},
1.155 + "Script Elim_rootrat_equation (e_::bool) (v_::real) = \
1.156 + \(let e_ = ((Try (Rewrite_Set expand_rootbinoms False)) @@ \
1.157 + \ (Try (Rewrite_Set rooteq_simplify False)) @@ \
1.158 + \ (Try (Rewrite_Set make_rooteq False)) @@ \
1.159 + \ (Try (Rewrite_Set rooteq_simplify False)) @@ \
1.160 + \ (Try (Rewrite_Set_Inst [(bdv,v_)] \
1.161 + \ rootrat_solve False))) e_ \
1.162 + \ in (SubProblem (RootEq_,[univariate,equation], \
1.163 + \ [no_met]) [bool_ e_, real_ v_]))"
1.164 + ));
1.165 +calclist':= overwritel (!calclist',
1.166 + [("is_rootRatAddTerm_in", ("RootRatEq.is_rootRatAddTerm_in",
1.167 + eval_is_rootRatAddTerm_in""))
1.168 + ]);(*("", ("", "")),*)
1.169 +"******* RootRatEq.ML end *******";