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neuper@37906
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(*. (c) by Richard Lang, 2003 .*)
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neuper@37906
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(* collecting all knowledge for PolynomialEquations
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neuper@37906
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created by: rlang
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neuper@37906
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date: 02.07
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neuper@37906
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changed by: rlang
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neuper@37906
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last change by: rlang
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neuper@37906
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date: 02.11.26
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neuper@37906
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*)
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neuper@37906
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neuper@37947
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(* use"Knowledge/PolyEq.ML";
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neuper@37906
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use"PolyEq.ML";
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neuper@37906
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neuper@37906
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use"ROOT.ML";
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neuper@37906
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cd"IsacKnowledge";
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neuper@37906
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neuper@37906
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remove_thy"PolyEq";
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neuper@37947
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use_thy"Knowledge/Isac";
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neuper@37906
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*)
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neuper@37906
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"******* PolyEq.ML begin *******";
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neuper@37906
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neuper@37906
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theory' := overwritel (!theory', [("PolyEq.thy",PolyEq.thy)]);
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neuper@37906
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(*-------------------------functions---------------------*)
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neuper@37906
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(* just for try
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neuper@37906
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local
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neuper@37906
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fun add0 l d d_ = if (d_+1) < d then add0 (str2term"0"::l) d (d_+1) else l;
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neuper@37906
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fun poly2list_ (t as (Const ("op +",_) $ t1 $ (Const ("Atools.pow",_) $ v_ $ Free (d_,_)))) v l d =
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neuper@37906
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if (v=v_)
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neuper@37906
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then poly2list_ t1 v (((str2term("1")))::(add0 l d (int_of_str' d_))) (int_of_str' d_)
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neuper@37906
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else t::(add0 l d 0)
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neuper@37906
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| poly2list_ (t as (Const ("op +",_) $ t1 $ (Const ("op *",_) $ t11 $
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neuper@37906
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(Const ("Atools.pow",_) $ v_ $ Free (d_,_))))) v l d =
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neuper@37906
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if (v=v_)
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neuper@37906
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then poly2list_ t1 v (((t11))::(add0 l d (int_of_str' d_))) (int_of_str' d_)
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neuper@37906
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else t::(add0 l d 0)
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neuper@37906
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| poly2list_ (t as (Const ("op +",_) $ t1 $ (Free (v_ , _)) )) v l d =
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neuper@37906
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if (v = (str2term v_))
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neuper@37906
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then poly2list_ t1 v (((str2term("1")))::(add0 l d 1 )) 1
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neuper@37906
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else t::(add0 l d 0)
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neuper@37906
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| poly2list_ (t as (Const ("op +",_) $ t1 $ (Const ("op *",_) $ t11 $ (Free (v_,_)) ))) v l d =
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neuper@37906
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if (v= (str2term v_))
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neuper@37906
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then poly2list_ t1 v ( (t11)::(add0 l d 1 )) 1
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neuper@37906
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else t::(add0 l d 0)
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neuper@37906
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| poly2list_ (t as (Const ("op +",_) $ _ $ _))_ l d = t::(add0 l d 0)
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neuper@37906
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| poly2list_ (t as (Free (_,_))) _ l d = t::(add0 l d 0)
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neuper@37906
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| poly2list_ t _ l d = t::(add0 l d 0);
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neuper@37906
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neuper@37906
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fun poly2list t v = poly2list_ t v [] 0;
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neuper@37906
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fun diffpolylist_ [] _ = []
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neuper@37906
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| diffpolylist_ (x::xs) d = (str2term (if term2str(x)="0"
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neuper@37906
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then "0"
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neuper@37906
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else term2str(x)^"*"^str_of_int(d)))::diffpolylist_ xs (d+1);
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neuper@37906
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fun diffpolylist [] = []
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neuper@37906
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| diffpolylist (x::xs) = diffpolylist_ xs 1;
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neuper@37906
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(* diffpolylist(poly2list (str2term "1+ x +3*x^^^3") (str2term "x"));*)
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neuper@37906
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in
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neuper@37906
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neuper@37906
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end;
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neuper@37906
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*)
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neuper@37906
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(*-------------------------rulse-------------------------*)
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neuper@37906
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val PolyEq_prls = (*3.10.02:just the following order due to subterm evaluation*)
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neuper@37906
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append_rls "PolyEq_prls" e_rls
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neuper@37906
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[Calc ("Atools.ident",eval_ident "#ident_"),
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neuper@37906
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Calc ("Tools.matches",eval_matches ""),
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neuper@37906
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Calc ("Tools.lhs" ,eval_lhs ""),
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neuper@37906
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Calc ("Tools.rhs" ,eval_rhs ""),
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neuper@37906
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Calc ("Poly.is'_expanded'_in",eval_is_expanded_in ""),
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neuper@37906
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Calc ("Poly.is'_poly'_in",eval_is_poly_in ""),
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neuper@37906
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Calc ("Poly.has'_degree'_in",eval_has_degree_in ""),
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neuper@37906
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Calc ("Poly.is'_polyrat'_in",eval_is_polyrat_in ""),
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neuper@37906
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(*Calc ("Atools.occurs'_in",eval_occurs_in ""), *)
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neuper@37906
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(*Calc ("Atools.is'_const",eval_const "#is_const_"),*)
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neuper@37906
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Calc ("op =",eval_equal "#equal_"),
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neuper@37906
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Calc ("RootEq.is'_rootTerm'_in",eval_is_rootTerm_in ""),
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neuper@37906
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Calc ("RatEq.is'_ratequation'_in",eval_is_ratequation_in ""),
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neuper@37906
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Thm ("not_true",num_str not_true),
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neuper@37906
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Thm ("not_false",num_str not_false),
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neuper@37906
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Thm ("and_true",num_str and_true),
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neuper@37906
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Thm ("and_false",num_str and_false),
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neuper@37906
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Thm ("or_true",num_str or_true),
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neuper@37906
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Thm ("or_false",num_str or_false)
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neuper@37906
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];
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neuper@37906
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neuper@37906
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val PolyEq_erls =
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neuper@37906
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merge_rls "PolyEq_erls" LinEq_erls
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neuper@37906
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(append_rls "ops_preds" calculate_Rational
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neuper@37906
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[Calc ("op =",eval_equal "#equal_"),
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neuper@37906
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Thm ("plus_leq", num_str plus_leq),
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neuper@37906
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Thm ("minus_leq", num_str minus_leq),
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neuper@37906
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Thm ("rat_leq1", num_str rat_leq1),
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neuper@37906
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Thm ("rat_leq2", num_str rat_leq2),
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neuper@37906
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Thm ("rat_leq3", num_str rat_leq3)
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neuper@37906
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]);
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neuper@37906
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neuper@37906
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val PolyEq_crls =
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neuper@37906
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merge_rls "PolyEq_crls" LinEq_crls
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neuper@37906
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(append_rls "ops_preds" calculate_Rational
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neuper@37906
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[Calc ("op =",eval_equal "#equal_"),
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neuper@37906
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Thm ("plus_leq", num_str plus_leq),
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neuper@37906
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Thm ("minus_leq", num_str minus_leq),
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neuper@37906
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Thm ("rat_leq1", num_str rat_leq1),
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neuper@37906
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Thm ("rat_leq2", num_str rat_leq2),
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neuper@37906
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Thm ("rat_leq3", num_str rat_leq3)
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neuper@37906
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]);
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neuper@37906
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(*------
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neuper@37906
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val PolyEq_erls =
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neuper@37906
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merge_rls "PolyEq_erls"
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neuper@37906
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(append_rls "" (Rls {(*asm_thm=[],*)calc=[],
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neuper@37906
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erls= Rls {(*asm_thm=[],*)calc=[],
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neuper@37906
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erls= Erls,
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neuper@37906
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id="e_rls",preconds=[],
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neuper@37906
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rew_ord=("dummy_ord",dummy_ord),
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neuper@37906
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rules=[Thm ("",
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neuper@37906
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num_str ),
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neuper@37906
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Thm ("",
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neuper@37906
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num_str ),
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neuper@37906
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Thm ("",
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neuper@37906
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num_str )
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neuper@37906
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],
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neuper@37906
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scr=EmptyScr,srls=Erls},
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neuper@37906
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id="e_rls",preconds=[],rew_ord=("dummy_ord",
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neuper@37906
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dummy_ord),
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neuper@37906
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rules=[],scr=EmptyScr,srls=Erls}
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neuper@37906
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)
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neuper@37906
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((#rules o rep_rls) LinEq_erls))
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neuper@37906
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(append_rls "ops_preds" calculate_Rational
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neuper@37906
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[Calc ("op =",eval_equal "#equal_"),
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neuper@37906
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Thm ("plus_leq", num_str plus_leq),
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neuper@37906
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Thm ("minus_leq", num_str minus_leq),
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neuper@37906
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Thm ("rat_leq1", num_str rat_leq1),
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neuper@37906
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Thm ("rat_leq2", num_str rat_leq2),
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neuper@37906
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Thm ("rat_leq3", num_str rat_leq3)
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neuper@37906
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]);
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neuper@37906
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-----*)
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neuper@37906
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neuper@37906
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neuper@37906
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val cancel_leading_coeff = prep_rls(
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neuper@37906
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Rls {id = "cancel_leading_coeff", preconds = [],
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neuper@37906
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rew_ord = ("e_rew_ord",e_rew_ord),
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neuper@37906
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erls = PolyEq_erls, srls = Erls, calc = [], (*asm_thm = [],*)
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neuper@37906
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rules = [Thm ("cancel_leading_coeff1",num_str cancel_leading_coeff1),
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neuper@37906
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Thm ("cancel_leading_coeff2",num_str cancel_leading_coeff2),
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neuper@37906
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Thm ("cancel_leading_coeff3",num_str cancel_leading_coeff3),
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neuper@37906
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Thm ("cancel_leading_coeff4",num_str cancel_leading_coeff4),
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neuper@37906
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Thm ("cancel_leading_coeff5",num_str cancel_leading_coeff5),
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neuper@37906
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Thm ("cancel_leading_coeff6",num_str cancel_leading_coeff6),
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neuper@37906
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Thm ("cancel_leading_coeff7",num_str cancel_leading_coeff7),
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neuper@37906
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Thm ("cancel_leading_coeff8",num_str cancel_leading_coeff8),
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neuper@37906
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Thm ("cancel_leading_coeff9",num_str cancel_leading_coeff9),
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neuper@37906
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Thm ("cancel_leading_coeff10",num_str cancel_leading_coeff10),
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neuper@37906
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Thm ("cancel_leading_coeff11",num_str cancel_leading_coeff11),
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neuper@37906
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Thm ("cancel_leading_coeff12",num_str cancel_leading_coeff12),
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neuper@37906
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Thm ("cancel_leading_coeff13",num_str cancel_leading_coeff13)
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neuper@37906
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],
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neuper@37906
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scr = Script ((term_of o the o (parse thy))
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neuper@37906
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"empty_script")
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neuper@37906
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}:rls);
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neuper@37906
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val complete_square = prep_rls(
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neuper@37906
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Rls {id = "complete_square", preconds = [],
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neuper@37906
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rew_ord = ("e_rew_ord",e_rew_ord),
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neuper@37906
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erls = PolyEq_erls, srls = Erls, calc = [], (*asm_thm = [],*)
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neuper@37906
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rules = [Thm ("complete_square1",num_str complete_square1),
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neuper@37906
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Thm ("complete_square2",num_str complete_square2),
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neuper@37906
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Thm ("complete_square3",num_str complete_square3),
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neuper@37906
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Thm ("complete_square4",num_str complete_square4),
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neuper@37906
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Thm ("complete_square5",num_str complete_square5)
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neuper@37906
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],
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neuper@37906
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scr = Script ((term_of o the o (parse thy))
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neuper@37906
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"empty_script")
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neuper@37906
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}:rls);
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neuper@37906
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ruleset' := overwritelthy thy (!ruleset',
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neuper@37906
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[("cancel_leading_coeff",cancel_leading_coeff),
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neuper@37906
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("complete_square",complete_square),
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neuper@37906
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("PolyEq_erls",PolyEq_erls)(*FIXXXME:del with rls.rls'*)
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neuper@37906
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]);
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neuper@37906
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val polyeq_simplify = prep_rls(
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neuper@37906
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Rls {id = "polyeq_simplify", preconds = [],
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neuper@37906
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rew_ord = ("termlessI",termlessI),
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neuper@37906
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erls = PolyEq_erls,
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neuper@37906
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srls = Erls,
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neuper@37906
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calc = [],
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neuper@37906
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(*asm_thm = [],*)
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neuper@37906
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rules = [Thm ("real_assoc_1",num_str real_assoc_1),
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neuper@37906
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Thm ("real_assoc_2",num_str real_assoc_2),
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neuper@37906
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Thm ("real_diff_minus",num_str real_diff_minus),
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neuper@37906
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Thm ("real_unari_minus",num_str real_unari_minus),
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neuper@37906
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186 |
Thm ("realpow_multI",num_str realpow_multI),
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neuper@37906
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187 |
Calc ("op +",eval_binop "#add_"),
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neuper@37906
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188 |
Calc ("op -",eval_binop "#sub_"),
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neuper@37906
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189 |
Calc ("op *",eval_binop "#mult_"),
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neuper@37906
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190 |
Calc ("HOL.divide", eval_cancel "#divide_"),
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neuper@37906
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191 |
Calc ("Root.sqrt",eval_sqrt "#sqrt_"),
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neuper@37906
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192 |
Calc ("Atools.pow" ,eval_binop "#power_"),
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neuper@37906
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Rls_ reduce_012
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neuper@37906
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],
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neuper@37906
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scr = Script ((term_of o the o (parse thy)) "empty_script")
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neuper@37906
|
196 |
}:rls);
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neuper@37906
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197 |
ruleset' := overwritelthy thy (!ruleset',
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neuper@37906
|
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[("polyeq_simplify",polyeq_simplify)]);
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neuper@37906
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199 |
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neuper@37906
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200 |
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neuper@37906
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201 |
(* ------------- polySolve ------------------ *)
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neuper@37906
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202 |
(* -- d0 -- *)
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neuper@37906
|
203 |
(*isolate the bound variable in an d0 equation; 'bdv' is a meta-constant*)
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neuper@37906
|
204 |
val d0_polyeq_simplify = prep_rls(
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neuper@37906
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205 |
Rls {id = "d0_polyeq_simplify", preconds = [],
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neuper@37906
|
206 |
rew_ord = ("e_rew_ord",e_rew_ord),
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neuper@37906
|
207 |
erls = PolyEq_erls,
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neuper@37906
|
208 |
srls = Erls,
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neuper@37906
|
209 |
calc = [],
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neuper@37906
|
210 |
(*asm_thm = [],*)
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neuper@37906
|
211 |
rules = [Thm("d0_true",num_str d0_true),
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neuper@37906
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212 |
Thm("d0_false",num_str d0_false)
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neuper@37906
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213 |
],
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neuper@37906
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214 |
scr = Script ((term_of o the o (parse thy)) "empty_script")
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neuper@37906
|
215 |
}:rls);
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neuper@37906
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216 |
(* -- d1 -- *)
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neuper@37906
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217 |
(*isolate the bound variable in an d1 equation; 'bdv' is a meta-constant*)
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neuper@37906
|
218 |
val d1_polyeq_simplify = prep_rls(
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neuper@37906
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219 |
Rls {id = "d1_polyeq_simplify", preconds = [],
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neuper@37906
|
220 |
rew_ord = ("e_rew_ord",e_rew_ord),
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neuper@37906
|
221 |
erls = PolyEq_erls,
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neuper@37906
|
222 |
srls = Erls,
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neuper@37906
|
223 |
calc = [],
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neuper@37906
|
224 |
(*asm_thm = [("d1_isolate_div","")],*)
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neuper@37906
|
225 |
rules = [
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neuper@37906
|
226 |
Thm("d1_isolate_add1",num_str d1_isolate_add1),
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neuper@37906
|
227 |
(* a+bx=0 -> bx=-a *)
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neuper@37906
|
228 |
Thm("d1_isolate_add2",num_str d1_isolate_add2),
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neuper@37906
|
229 |
(* a+ x=0 -> x=-a *)
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neuper@37906
|
230 |
Thm("d1_isolate_div",num_str d1_isolate_div)
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neuper@37906
|
231 |
(* bx=c -> x=c/b *)
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neuper@37906
|
232 |
],
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neuper@37906
|
233 |
scr = Script ((term_of o the o (parse thy)) "empty_script")
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neuper@37906
|
234 |
}:rls);
|
|
neuper@37906
|
235 |
(* -- d2 -- *)
|
|
neuper@37906
|
236 |
(*isolate the bound variable in an d2 equation with bdv only; 'bdv' is a meta-constant*)
|
|
neuper@37906
|
237 |
val d2_polyeq_bdv_only_simplify = prep_rls(
|
|
neuper@37906
|
238 |
Rls {id = "d2_polyeq_bdv_only_simplify", preconds = [],
|
|
neuper@37906
|
239 |
rew_ord = ("e_rew_ord",e_rew_ord),
|
|
neuper@37906
|
240 |
erls = PolyEq_erls,
|
|
neuper@37906
|
241 |
srls = Erls,
|
|
neuper@37906
|
242 |
calc = [],
|
|
neuper@37906
|
243 |
(*asm_thm = [("d2_sqrt_equation1",""),("d2_sqrt_equation1_neg",""),
|
|
neuper@37906
|
244 |
("d2_isolate_div","")],*)
|
|
neuper@37906
|
245 |
rules = [
|
|
neuper@37906
|
246 |
Thm("d2_prescind1",num_str d2_prescind1), (* ax+bx^2=0 -> x(a+bx)=0 *)
|
|
neuper@37906
|
247 |
Thm("d2_prescind2",num_str d2_prescind2), (* ax+ x^2=0 -> x(a+ x)=0 *)
|
|
neuper@37906
|
248 |
Thm("d2_prescind3",num_str d2_prescind3), (* x+bx^2=0 -> x(1+bx)=0 *)
|
|
neuper@37906
|
249 |
Thm("d2_prescind4",num_str d2_prescind4), (* x+ x^2=0 -> x(1+ x)=0 *)
|
|
neuper@37906
|
250 |
Thm("d2_sqrt_equation1",num_str d2_sqrt_equation1), (* x^2=c -> x=+-sqrt(c)*)
|
|
neuper@37906
|
251 |
Thm("d2_sqrt_equation1_neg",num_str d2_sqrt_equation1_neg), (* [0<c] x^2=c -> [] *)
|
|
neuper@37906
|
252 |
Thm("d2_sqrt_equation2",num_str d2_sqrt_equation2), (* x^2=0 -> x=0 *)
|
|
neuper@37906
|
253 |
Thm("d2_reduce_equation1",num_str d2_reduce_equation1),(* x(a+bx)=0 -> x=0 | a+bx=0*)
|
|
neuper@37906
|
254 |
Thm("d2_reduce_equation2",num_str d2_reduce_equation2),(* x(a+ x)=0 -> x=0 | a+ x=0*)
|
|
neuper@37906
|
255 |
Thm("d2_isolate_div",num_str d2_isolate_div) (* bx^2=c -> x^2=c/b*)
|
|
neuper@37906
|
256 |
],
|
|
neuper@37906
|
257 |
scr = Script ((term_of o the o (parse thy)) "empty_script")
|
|
neuper@37906
|
258 |
}:rls);
|
|
neuper@37906
|
259 |
(*isolate the bound variable in an d2 equation with sqrt only; 'bdv' is a meta-constant*)
|
|
neuper@37906
|
260 |
val d2_polyeq_sq_only_simplify = prep_rls(
|
|
neuper@37906
|
261 |
Rls {id = "d2_polyeq_sq_only_simplify", preconds = [],
|
|
neuper@37906
|
262 |
rew_ord = ("e_rew_ord",e_rew_ord),
|
|
neuper@37906
|
263 |
erls = PolyEq_erls,
|
|
neuper@37906
|
264 |
srls = Erls,
|
|
neuper@37906
|
265 |
calc = [],
|
|
neuper@37906
|
266 |
(*asm_thm = [("d2_sqrt_equation1",""),("d2_sqrt_equation1_neg",""),
|
|
neuper@37906
|
267 |
("d2_isolate_div","")],*)
|
|
neuper@37906
|
268 |
rules = [
|
|
neuper@37906
|
269 |
Thm("d2_isolate_add1",num_str d2_isolate_add1), (* a+ bx^2=0 -> bx^2=(-1)a*)
|
|
neuper@37906
|
270 |
Thm("d2_isolate_add2",num_str d2_isolate_add2), (* a+ x^2=0 -> x^2=(-1)a*)
|
|
neuper@37906
|
271 |
Thm("d2_sqrt_equation2",num_str d2_sqrt_equation2), (* x^2=0 -> x=0 *)
|
|
neuper@37906
|
272 |
Thm("d2_sqrt_equation1",num_str d2_sqrt_equation1), (* x^2=c -> x=+-sqrt(c)*)
|
|
neuper@37906
|
273 |
Thm("d2_sqrt_equation1_neg",num_str d2_sqrt_equation1_neg),(* [c<0] x^2=c -> x=[] *)
|
|
neuper@37906
|
274 |
Thm("d2_isolate_div",num_str d2_isolate_div) (* bx^2=c -> x^2=c/b*)
|
|
neuper@37906
|
275 |
],
|
|
neuper@37906
|
276 |
scr = Script ((term_of o the o (parse thy)) "empty_script")
|
|
neuper@37906
|
277 |
}:rls);
|
|
neuper@37906
|
278 |
(*isolate the bound variable in an d2 equation with pqFormula; 'bdv' is a meta-constant*)
|
|
neuper@37906
|
279 |
val d2_polyeq_pqFormula_simplify = prep_rls(
|
|
neuper@37906
|
280 |
Rls {id = "d2_polyeq_pqFormula_simplify", preconds = [],
|
|
neuper@37906
|
281 |
rew_ord = ("e_rew_ord",e_rew_ord),
|
|
neuper@37906
|
282 |
erls = PolyEq_erls,
|
|
neuper@37906
|
283 |
srls = Erls,
|
|
neuper@37906
|
284 |
calc = [],
|
|
neuper@37906
|
285 |
(*asm_thm = [("d2_pqformula1",""),("d2_pqformula2",""),("d2_pqformula3",""),("d2_pqformula4",""),
|
|
neuper@37906
|
286 |
("d2_pqformula5",""),("d2_pqformula6",""),("d2_pqformula7",""),("d2_pqformula8",""),
|
|
neuper@37906
|
287 |
("d2_pqformula9",""),("d2_pqformula10",""),
|
|
neuper@37906
|
288 |
("d2_pqformula1_neg",""),("d2_pqformula2_neg",""),("d2_pqformula3_neg",""),
|
|
neuper@37906
|
289 |
("d2_pqformula4_neg",""),("d2_pqformula9_neg",""),("d2_pqformula10_neg","")],*)
|
|
neuper@37906
|
290 |
rules = [
|
|
neuper@37906
|
291 |
Thm("d2_pqformula1",num_str d2_pqformula1), (* q+px+ x^2=0 *)
|
|
neuper@37906
|
292 |
Thm("d2_pqformula1_neg",num_str d2_pqformula1_neg), (* q+px+ x^2=0 *)
|
|
neuper@37906
|
293 |
Thm("d2_pqformula2",num_str d2_pqformula2), (* q+px+1x^2=0 *)
|
|
neuper@37906
|
294 |
Thm("d2_pqformula2_neg",num_str d2_pqformula2_neg), (* q+px+1x^2=0 *)
|
|
neuper@37906
|
295 |
Thm("d2_pqformula3",num_str d2_pqformula3), (* q+ x+ x^2=0 *)
|
|
neuper@37906
|
296 |
Thm("d2_pqformula3_neg",num_str d2_pqformula3_neg), (* q+ x+ x^2=0 *)
|
|
neuper@37906
|
297 |
Thm("d2_pqformula4",num_str d2_pqformula4), (* q+ x+1x^2=0 *)
|
|
neuper@37906
|
298 |
Thm("d2_pqformula4_neg",num_str d2_pqformula4_neg), (* q+ x+1x^2=0 *)
|
|
neuper@37906
|
299 |
Thm("d2_pqformula5",num_str d2_pqformula5), (* qx+ x^2=0 *)
|
|
neuper@37906
|
300 |
Thm("d2_pqformula6",num_str d2_pqformula6), (* qx+1x^2=0 *)
|
|
neuper@37906
|
301 |
Thm("d2_pqformula7",num_str d2_pqformula7), (* x+ x^2=0 *)
|
|
neuper@37906
|
302 |
Thm("d2_pqformula8",num_str d2_pqformula8), (* x+1x^2=0 *)
|
|
neuper@37906
|
303 |
Thm("d2_pqformula9",num_str d2_pqformula9), (* q +1x^2=0 *)
|
|
neuper@37906
|
304 |
Thm("d2_pqformula9_neg",num_str d2_pqformula9_neg), (* q +1x^2=0 *)
|
|
neuper@37906
|
305 |
Thm("d2_pqformula10",num_str d2_pqformula10), (* q + x^2=0 *)
|
|
neuper@37906
|
306 |
Thm("d2_pqformula10_neg",num_str d2_pqformula10_neg), (* q + x^2=0 *)
|
|
neuper@37906
|
307 |
Thm("d2_sqrt_equation2",num_str d2_sqrt_equation2), (* x^2=0 *)
|
|
neuper@37906
|
308 |
Thm("d2_sqrt_equation3",num_str d2_sqrt_equation3) (* 1x^2=0 *)
|
|
neuper@37906
|
309 |
],
|
|
neuper@37906
|
310 |
scr = Script ((term_of o the o (parse thy)) "empty_script")
|
|
neuper@37906
|
311 |
}:rls);
|
|
neuper@37906
|
312 |
(*isolate the bound variable in an d2 equation with abcFormula; 'bdv' is a meta-constant*)
|
|
neuper@37906
|
313 |
val d2_polyeq_abcFormula_simplify = prep_rls(
|
|
neuper@37906
|
314 |
Rls {id = "d2_polyeq_abcFormula_simplify", preconds = [],
|
|
neuper@37906
|
315 |
rew_ord = ("e_rew_ord",e_rew_ord),
|
|
neuper@37906
|
316 |
erls = PolyEq_erls,
|
|
neuper@37906
|
317 |
srls = Erls,
|
|
neuper@37906
|
318 |
calc = [],
|
|
neuper@37906
|
319 |
(*asm_thm = [("d2_abcformula1",""),("d2_abcformula2",""),("d2_abcformula3",""),
|
|
neuper@37906
|
320 |
("d2_abcformula4",""),("d2_abcformula5",""),("d2_abcformula6",""),
|
|
neuper@37906
|
321 |
("d2_abcformula7",""),("d2_abcformula8",""),("d2_abcformula9",""),
|
|
neuper@37906
|
322 |
("d2_abcformula10",""),("d2_abcformula1_neg",""),("d2_abcformula2_neg",""),
|
|
neuper@37906
|
323 |
("d2_abcformula3_neg",""),("d2_abcformula4_neg",""),("d2_abcformula5_neg",""),
|
|
neuper@37906
|
324 |
("d2_abcformula6_neg","")],*)
|
|
neuper@37906
|
325 |
rules = [
|
|
neuper@37906
|
326 |
Thm("d2_abcformula1",num_str d2_abcformula1), (*c+bx+cx^2=0 *)
|
|
neuper@37906
|
327 |
Thm("d2_abcformula1_neg",num_str d2_abcformula1_neg), (*c+bx+cx^2=0 *)
|
|
neuper@37906
|
328 |
Thm("d2_abcformula2",num_str d2_abcformula2), (*c+ x+cx^2=0 *)
|
|
neuper@37906
|
329 |
Thm("d2_abcformula2_neg",num_str d2_abcformula2_neg), (*c+ x+cx^2=0 *)
|
|
neuper@37906
|
330 |
Thm("d2_abcformula3",num_str d2_abcformula3), (*c+bx+ x^2=0 *)
|
|
neuper@37906
|
331 |
Thm("d2_abcformula3_neg",num_str d2_abcformula3_neg), (*c+bx+ x^2=0 *)
|
|
neuper@37906
|
332 |
Thm("d2_abcformula4",num_str d2_abcformula4), (*c+ x+ x^2=0 *)
|
|
neuper@37906
|
333 |
Thm("d2_abcformula4_neg",num_str d2_abcformula4_neg), (*c+ x+ x^2=0 *)
|
|
neuper@37906
|
334 |
Thm("d2_abcformula5",num_str d2_abcformula5), (*c+ cx^2=0 *)
|
|
neuper@37906
|
335 |
Thm("d2_abcformula5_neg",num_str d2_abcformula5_neg), (*c+ cx^2=0 *)
|
|
neuper@37906
|
336 |
Thm("d2_abcformula6",num_str d2_abcformula6), (*c+ x^2=0 *)
|
|
neuper@37906
|
337 |
Thm("d2_abcformula6_neg",num_str d2_abcformula6_neg), (*c+ x^2=0 *)
|
|
neuper@37906
|
338 |
Thm("d2_abcformula7",num_str d2_abcformula7), (* bx+ax^2=0 *)
|
|
neuper@37906
|
339 |
Thm("d2_abcformula8",num_str d2_abcformula8), (* bx+ x^2=0 *)
|
|
neuper@37906
|
340 |
Thm("d2_abcformula9",num_str d2_abcformula9), (* x+ax^2=0 *)
|
|
neuper@37906
|
341 |
Thm("d2_abcformula10",num_str d2_abcformula10), (* x+ x^2=0 *)
|
|
neuper@37906
|
342 |
Thm("d2_sqrt_equation2",num_str d2_sqrt_equation2), (* x^2=0 *)
|
|
neuper@37906
|
343 |
Thm("d2_sqrt_equation3",num_str d2_sqrt_equation3) (* bx^2=0 *)
|
|
neuper@37906
|
344 |
],
|
|
neuper@37906
|
345 |
scr = Script ((term_of o the o (parse thy)) "empty_script")
|
|
neuper@37906
|
346 |
}:rls);
|
|
neuper@37906
|
347 |
(*isolate the bound variable in an d2 equation; 'bdv' is a meta-constant*)
|
|
neuper@37906
|
348 |
val d2_polyeq_simplify = prep_rls(
|
|
neuper@37906
|
349 |
Rls {id = "d2_polyeq_simplify", preconds = [],
|
|
neuper@37906
|
350 |
rew_ord = ("e_rew_ord",e_rew_ord),
|
|
neuper@37906
|
351 |
erls = PolyEq_erls,
|
|
neuper@37906
|
352 |
srls = Erls,
|
|
neuper@37906
|
353 |
calc = [],
|
|
neuper@37906
|
354 |
(*asm_thm = [("d2_pqformula1",""),("d2_pqformula2",""),("d2_pqformula3",""),("d2_pqformula4",""),
|
|
neuper@37906
|
355 |
("d2_pqformula1_neg",""),("d2_pqformula2_neg",""),("d2_pqformula3_neg",""),
|
|
neuper@37906
|
356 |
("d2_pqformula4_neg",""),
|
|
neuper@37906
|
357 |
("d2_abcformula1",""),("d2_abcformula2",""),("d2_abcformula1_neg",""),
|
|
neuper@37906
|
358 |
("d2_abcformula2_neg",""), ("d2_sqrt_equation1",""),
|
|
neuper@37906
|
359 |
("d2_sqrt_equation1_neg",""),("d2_isolate_div","")],*)
|
|
neuper@37906
|
360 |
rules = [
|
|
neuper@37906
|
361 |
Thm("d2_pqformula1",num_str d2_pqformula1), (* p+qx+ x^2=0 *)
|
|
neuper@37906
|
362 |
Thm("d2_pqformula1_neg",num_str d2_pqformula1_neg), (* p+qx+ x^2=0 *)
|
|
neuper@37906
|
363 |
Thm("d2_pqformula2",num_str d2_pqformula2), (* p+qx+1x^2=0 *)
|
|
neuper@37906
|
364 |
Thm("d2_pqformula2_neg",num_str d2_pqformula2_neg), (* p+qx+1x^2=0 *)
|
|
neuper@37906
|
365 |
Thm("d2_pqformula3",num_str d2_pqformula3), (* p+ x+ x^2=0 *)
|
|
neuper@37906
|
366 |
Thm("d2_pqformula3_neg",num_str d2_pqformula3_neg), (* p+ x+ x^2=0 *)
|
|
neuper@37906
|
367 |
Thm("d2_pqformula4",num_str d2_pqformula4), (* p+ x+1x^2=0 *)
|
|
neuper@37906
|
368 |
Thm("d2_pqformula4_neg",num_str d2_pqformula4_neg), (* p+ x+1x^2=0 *)
|
|
neuper@37906
|
369 |
Thm("d2_abcformula1",num_str d2_abcformula1), (* c+bx+cx^2=0 *)
|
|
neuper@37906
|
370 |
Thm("d2_abcformula1_neg",num_str d2_abcformula1_neg), (* c+bx+cx^2=0 *)
|
|
neuper@37906
|
371 |
Thm("d2_abcformula2",num_str d2_abcformula2), (* c+ x+cx^2=0 *)
|
|
neuper@37906
|
372 |
Thm("d2_abcformula2_neg",num_str d2_abcformula2_neg), (* c+ x+cx^2=0 *)
|
|
neuper@37906
|
373 |
Thm("d2_prescind1",num_str d2_prescind1), (* ax+bx^2=0 -> x(a+bx)=0 *)
|
|
neuper@37906
|
374 |
Thm("d2_prescind2",num_str d2_prescind2), (* ax+ x^2=0 -> x(a+ x)=0 *)
|
|
neuper@37906
|
375 |
Thm("d2_prescind3",num_str d2_prescind3), (* x+bx^2=0 -> x(1+bx)=0 *)
|
|
neuper@37906
|
376 |
Thm("d2_prescind4",num_str d2_prescind4), (* x+ x^2=0 -> x(1+ x)=0 *)
|
|
neuper@37906
|
377 |
Thm("d2_isolate_add1",num_str d2_isolate_add1), (* a+ bx^2=0 -> bx^2=(-1)a*)
|
|
neuper@37906
|
378 |
Thm("d2_isolate_add2",num_str d2_isolate_add2), (* a+ x^2=0 -> x^2=(-1)a*)
|
|
neuper@37906
|
379 |
Thm("d2_sqrt_equation1",num_str d2_sqrt_equation1), (* x^2=c -> x=+-sqrt(c)*)
|
|
neuper@37906
|
380 |
Thm("d2_sqrt_equation1_neg",num_str d2_sqrt_equation1_neg),(* [c<0] x^2=c -> x=[]*)
|
|
neuper@37906
|
381 |
Thm("d2_sqrt_equation2",num_str d2_sqrt_equation2), (* x^2=0 -> x=0 *)
|
|
neuper@37906
|
382 |
Thm("d2_reduce_equation1",num_str d2_reduce_equation1),(* x(a+bx)=0 -> x=0 | a+bx=0*)
|
|
neuper@37906
|
383 |
Thm("d2_reduce_equation2",num_str d2_reduce_equation2),(* x(a+ x)=0 -> x=0 | a+ x=0*)
|
|
neuper@37906
|
384 |
Thm("d2_isolate_div",num_str d2_isolate_div) (* bx^2=c -> x^2=c/b*)
|
|
neuper@37906
|
385 |
],
|
|
neuper@37906
|
386 |
scr = Script ((term_of o the o (parse thy)) "empty_script")
|
|
neuper@37906
|
387 |
}:rls);
|
|
neuper@37906
|
388 |
(* -- d3 -- *)
|
|
neuper@37906
|
389 |
(*isolate the bound variable in an d3 equation; 'bdv' is a meta-constant*)
|
|
neuper@37906
|
390 |
val d3_polyeq_simplify = prep_rls(
|
|
neuper@37906
|
391 |
Rls {id = "d3_polyeq_simplify", preconds = [],
|
|
neuper@37906
|
392 |
rew_ord = ("e_rew_ord",e_rew_ord),
|
|
neuper@37906
|
393 |
erls = PolyEq_erls,
|
|
neuper@37906
|
394 |
srls = Erls,
|
|
neuper@37906
|
395 |
calc = [],
|
|
neuper@37906
|
396 |
(*asm_thm = [("d3_isolate_div","")],*)
|
|
neuper@37906
|
397 |
rules = [
|
|
neuper@37906
|
398 |
Thm("d3_reduce_equation1",num_str d3_reduce_equation1),
|
|
neuper@37906
|
399 |
(*a*bdv + b*bdv^^^2 + c*bdv^^^3=0) = (bdv=0 | (a + b*bdv + c*bdv^^^2=0)*)
|
|
neuper@37906
|
400 |
Thm("d3_reduce_equation2",num_str d3_reduce_equation2),
|
|
neuper@37906
|
401 |
(* bdv + b*bdv^^^2 + c*bdv^^^3=0) = (bdv=0 | (1 + b*bdv + c*bdv^^^2=0)*)
|
|
neuper@37906
|
402 |
Thm("d3_reduce_equation3",num_str d3_reduce_equation3),
|
|
neuper@37906
|
403 |
(*a*bdv + bdv^^^2 + c*bdv^^^3=0) = (bdv=0 | (a + bdv + c*bdv^^^2=0)*)
|
|
neuper@37906
|
404 |
Thm("d3_reduce_equation4",num_str d3_reduce_equation4),
|
|
neuper@37906
|
405 |
(* bdv + bdv^^^2 + c*bdv^^^3=0) = (bdv=0 | (1 + bdv + c*bdv^^^2=0)*)
|
|
neuper@37906
|
406 |
Thm("d3_reduce_equation5",num_str d3_reduce_equation5),
|
|
neuper@37906
|
407 |
(*a*bdv + b*bdv^^^2 + bdv^^^3=0) = (bdv=0 | (a + b*bdv + bdv^^^2=0)*)
|
|
neuper@37906
|
408 |
Thm("d3_reduce_equation6",num_str d3_reduce_equation6),
|
|
neuper@37906
|
409 |
(* bdv + b*bdv^^^2 + bdv^^^3=0) = (bdv=0 | (1 + b*bdv + bdv^^^2=0)*)
|
|
neuper@37906
|
410 |
Thm("d3_reduce_equation7",num_str d3_reduce_equation7),
|
|
neuper@37906
|
411 |
(*a*bdv + bdv^^^2 + bdv^^^3=0) = (bdv=0 | (1 + bdv + bdv^^^2=0)*)
|
|
neuper@37906
|
412 |
Thm("d3_reduce_equation8",num_str d3_reduce_equation8),
|
|
neuper@37906
|
413 |
(* bdv + bdv^^^2 + bdv^^^3=0) = (bdv=0 | (1 + bdv + bdv^^^2=0)*)
|
|
neuper@37906
|
414 |
Thm("d3_reduce_equation9",num_str d3_reduce_equation9),
|
|
neuper@37906
|
415 |
(*a*bdv + c*bdv^^^3=0) = (bdv=0 | (a + c*bdv^^^2=0)*)
|
|
neuper@37906
|
416 |
Thm("d3_reduce_equation10",num_str d3_reduce_equation10),
|
|
neuper@37906
|
417 |
(* bdv + c*bdv^^^3=0) = (bdv=0 | (1 + c*bdv^^^2=0)*)
|
|
neuper@37906
|
418 |
Thm("d3_reduce_equation11",num_str d3_reduce_equation11),
|
|
neuper@37906
|
419 |
(*a*bdv + bdv^^^3=0) = (bdv=0 | (a + bdv^^^2=0)*)
|
|
neuper@37906
|
420 |
Thm("d3_reduce_equation12",num_str d3_reduce_equation12),
|
|
neuper@37906
|
421 |
(* bdv + bdv^^^3=0) = (bdv=0 | (1 + bdv^^^2=0)*)
|
|
neuper@37906
|
422 |
Thm("d3_reduce_equation13",num_str d3_reduce_equation13),
|
|
neuper@37906
|
423 |
(* b*bdv^^^2 + c*bdv^^^3=0) = (bdv=0 | ( b*bdv + c*bdv^^^2=0)*)
|
|
neuper@37906
|
424 |
Thm("d3_reduce_equation14",num_str d3_reduce_equation14),
|
|
neuper@37906
|
425 |
(* bdv^^^2 + c*bdv^^^3=0) = (bdv=0 | ( bdv + c*bdv^^^2=0)*)
|
|
neuper@37906
|
426 |
Thm("d3_reduce_equation15",num_str d3_reduce_equation15),
|
|
neuper@37906
|
427 |
(* b*bdv^^^2 + bdv^^^3=0) = (bdv=0 | ( b*bdv + bdv^^^2=0)*)
|
|
neuper@37906
|
428 |
Thm("d3_reduce_equation16",num_str d3_reduce_equation16),
|
|
neuper@37906
|
429 |
(* bdv^^^2 + bdv^^^3=0) = (bdv=0 | ( bdv + bdv^^^2=0)*)
|
|
neuper@37906
|
430 |
Thm("d3_isolate_add1",num_str d3_isolate_add1),
|
|
neuper@37906
|
431 |
(*[|Not(bdv occurs_in a)|] ==> (a + b*bdv^^^3=0) = (bdv=0 | (b*bdv^^^3=a)*)
|
|
neuper@37906
|
432 |
Thm("d3_isolate_add2",num_str d3_isolate_add2),
|
|
neuper@37906
|
433 |
(*[|Not(bdv occurs_in a)|] ==> (a + bdv^^^3=0) = (bdv=0 | ( bdv^^^3=a)*)
|
|
neuper@37906
|
434 |
Thm("d3_isolate_div",num_str d3_isolate_div),
|
|
neuper@37906
|
435 |
(*[|Not(b=0)|] ==> (b*bdv^^^3=c) = (bdv^^^3=c/b*)
|
|
neuper@37906
|
436 |
Thm("d3_root_equation2",num_str d3_root_equation2),
|
|
neuper@37906
|
437 |
(*(bdv^^^3=0) = (bdv=0) *)
|
|
neuper@37906
|
438 |
Thm("d3_root_equation1",num_str d3_root_equation1)
|
|
neuper@37906
|
439 |
(*bdv^^^3=c) = (bdv = nroot 3 c*)
|
|
neuper@37906
|
440 |
],
|
|
neuper@37906
|
441 |
scr = Script ((term_of o the o (parse thy)) "empty_script")
|
|
neuper@37906
|
442 |
}:rls);
|
|
neuper@37906
|
443 |
(* -- d4 -- *)
|
|
neuper@37906
|
444 |
(*isolate the bound variable in an d4 equation; 'bdv' is a meta-constant*)
|
|
neuper@37906
|
445 |
val d4_polyeq_simplify = prep_rls(
|
|
neuper@37906
|
446 |
Rls {id = "d4_polyeq_simplify", preconds = [],
|
|
neuper@37906
|
447 |
rew_ord = ("e_rew_ord",e_rew_ord),
|
|
neuper@37906
|
448 |
erls = PolyEq_erls,
|
|
neuper@37906
|
449 |
srls = Erls,
|
|
neuper@37906
|
450 |
calc = [],
|
|
neuper@37906
|
451 |
(*asm_thm = [],*)
|
|
neuper@37906
|
452 |
rules = [Thm("d4_sub_u1",num_str d4_sub_u1)
|
|
neuper@37906
|
453 |
(* ax^4+bx^2+c=0 -> x=+-sqrt(ax^2+bx^+c) *)
|
|
neuper@37906
|
454 |
],
|
|
neuper@37906
|
455 |
scr = Script ((term_of o the o (parse thy)) "empty_script")
|
|
neuper@37906
|
456 |
}:rls);
|
|
neuper@37906
|
457 |
|
|
neuper@37906
|
458 |
ruleset' := overwritelthy thy (!ruleset',
|
|
neuper@37906
|
459 |
[("d0_polyeq_simplify", d0_polyeq_simplify),
|
|
neuper@37906
|
460 |
("d1_polyeq_simplify", d1_polyeq_simplify),
|
|
neuper@37906
|
461 |
("d2_polyeq_simplify", d2_polyeq_simplify),
|
|
neuper@37906
|
462 |
("d2_polyeq_bdv_only_simplify", d2_polyeq_bdv_only_simplify),
|
|
neuper@37906
|
463 |
("d2_polyeq_sq_only_simplify", d2_polyeq_sq_only_simplify),
|
|
neuper@37906
|
464 |
("d2_polyeq_pqFormula_simplify", d2_polyeq_pqFormula_simplify),
|
|
neuper@37906
|
465 |
("d2_polyeq_abcFormula_simplify", d2_polyeq_abcFormula_simplify),
|
|
neuper@37906
|
466 |
("d3_polyeq_simplify", d3_polyeq_simplify),
|
|
neuper@37906
|
467 |
("d4_polyeq_simplify", d4_polyeq_simplify)
|
|
neuper@37906
|
468 |
]);
|
|
neuper@37906
|
469 |
|
|
neuper@37906
|
470 |
(*------------------------problems------------------------*)
|
|
neuper@37906
|
471 |
(*
|
|
neuper@37906
|
472 |
(get_pbt ["degree_2","polynomial","univariate","equation"]);
|
|
neuper@37906
|
473 |
show_ptyps();
|
|
neuper@37906
|
474 |
*)
|
|
neuper@37906
|
475 |
|
|
neuper@37906
|
476 |
(*-------------------------poly-----------------------*)
|
|
neuper@37906
|
477 |
store_pbt
|
|
neuper@37906
|
478 |
(prep_pbt PolyEq.thy "pbl_equ_univ_poly" [] e_pblID
|
|
neuper@37906
|
479 |
(["polynomial","univariate","equation"],
|
|
neuper@37906
|
480 |
[("#Given" ,["equality e_","solveFor v_"]),
|
|
neuper@37906
|
481 |
("#Where" ,["~((e_::bool) is_ratequation_in (v_::real))",
|
|
neuper@37906
|
482 |
"~((lhs e_) is_rootTerm_in (v_::real))",
|
|
neuper@37906
|
483 |
"~((rhs e_) is_rootTerm_in (v_::real))"]),
|
|
neuper@37906
|
484 |
("#Find" ,["solutions v_i_"])
|
|
neuper@37906
|
485 |
],
|
|
neuper@37926
|
486 |
PolyEq_prls, SOME "solve (e_::bool, v_)",
|
|
neuper@37906
|
487 |
[]));
|
|
neuper@37906
|
488 |
(*--- d0 ---*)
|
|
neuper@37906
|
489 |
store_pbt
|
|
neuper@37906
|
490 |
(prep_pbt PolyEq.thy "pbl_equ_univ_poly_deg0" [] e_pblID
|
|
neuper@37906
|
491 |
(["degree_0","polynomial","univariate","equation"],
|
|
neuper@37906
|
492 |
[("#Given" ,["equality e_","solveFor v_"]),
|
|
neuper@37906
|
493 |
("#Where" ,["matches (?a = 0) e_",
|
|
neuper@37906
|
494 |
"(lhs e_) is_poly_in v_",
|
|
neuper@37906
|
495 |
"((lhs e_) has_degree_in v_ ) = 0"
|
|
neuper@37906
|
496 |
]),
|
|
neuper@37906
|
497 |
("#Find" ,["solutions v_i_"])
|
|
neuper@37906
|
498 |
],
|
|
neuper@37926
|
499 |
PolyEq_prls, SOME "solve (e_::bool, v_)",
|
|
neuper@37906
|
500 |
[["PolyEq","solve_d0_polyeq_equation"]]));
|
|
neuper@37906
|
501 |
|
|
neuper@37906
|
502 |
(*--- d1 ---*)
|
|
neuper@37906
|
503 |
store_pbt
|
|
neuper@37906
|
504 |
(prep_pbt PolyEq.thy "pbl_equ_univ_poly_deg1" [] e_pblID
|
|
neuper@37906
|
505 |
(["degree_1","polynomial","univariate","equation"],
|
|
neuper@37906
|
506 |
[("#Given" ,["equality e_","solveFor v_"]),
|
|
neuper@37906
|
507 |
("#Where" ,["matches (?a = 0) e_",
|
|
neuper@37906
|
508 |
"(lhs e_) is_poly_in v_",
|
|
neuper@37906
|
509 |
"((lhs e_) has_degree_in v_ ) = 1"
|
|
neuper@37906
|
510 |
]),
|
|
neuper@37906
|
511 |
("#Find" ,["solutions v_i_"])
|
|
neuper@37906
|
512 |
],
|
|
neuper@37926
|
513 |
PolyEq_prls, SOME "solve (e_::bool, v_)",
|
|
neuper@37906
|
514 |
[["PolyEq","solve_d1_polyeq_equation"]]));
|
|
neuper@37906
|
515 |
|
|
neuper@37906
|
516 |
(*--- d2 ---*)
|
|
neuper@37906
|
517 |
store_pbt
|
|
neuper@37906
|
518 |
(prep_pbt PolyEq.thy "pbl_equ_univ_poly_deg2" [] e_pblID
|
|
neuper@37906
|
519 |
(["degree_2","polynomial","univariate","equation"],
|
|
neuper@37906
|
520 |
[("#Given" ,["equality e_","solveFor v_"]),
|
|
neuper@37906
|
521 |
("#Where" ,["matches (?a = 0) e_",
|
|
neuper@37906
|
522 |
"(lhs e_) is_poly_in v_ ",
|
|
neuper@37906
|
523 |
"((lhs e_) has_degree_in v_ ) = 2"]),
|
|
neuper@37906
|
524 |
("#Find" ,["solutions v_i_"])
|
|
neuper@37906
|
525 |
],
|
|
neuper@37926
|
526 |
PolyEq_prls, SOME "solve (e_::bool, v_)",
|
|
neuper@37906
|
527 |
[["PolyEq","solve_d2_polyeq_equation"]]));
|
|
neuper@37906
|
528 |
|
|
neuper@37906
|
529 |
store_pbt
|
|
neuper@37906
|
530 |
(prep_pbt PolyEq.thy "pbl_equ_univ_poly_deg2_sqonly" [] e_pblID
|
|
neuper@37906
|
531 |
(["sq_only","degree_2","polynomial","univariate","equation"],
|
|
neuper@37906
|
532 |
[("#Given" ,["equality e_","solveFor v_"]),
|
|
neuper@37906
|
533 |
("#Where" ,["matches ( ?a + ?v_^^^2 = 0) e_ | \
|
|
neuper@37906
|
534 |
\matches ( ?a + ?b*?v_^^^2 = 0) e_ | \
|
|
neuper@37906
|
535 |
\matches ( ?v_^^^2 = 0) e_ | \
|
|
neuper@37906
|
536 |
\matches ( ?b*?v_^^^2 = 0) e_" ,
|
|
neuper@37906
|
537 |
"Not (matches (?a + ?v_ + ?v_^^^2 = 0) e_) &\
|
|
neuper@37906
|
538 |
\Not (matches (?a + ?b*?v_ + ?v_^^^2 = 0) e_) &\
|
|
neuper@37906
|
539 |
\Not (matches (?a + ?v_ + ?c*?v_^^^2 = 0) e_) &\
|
|
neuper@37906
|
540 |
\Not (matches (?a + ?b*?v_ + ?c*?v_^^^2 = 0) e_) &\
|
|
neuper@37906
|
541 |
\Not (matches ( ?v_ + ?v_^^^2 = 0) e_) &\
|
|
neuper@37906
|
542 |
\Not (matches ( ?b*?v_ + ?v_^^^2 = 0) e_) &\
|
|
neuper@37906
|
543 |
\Not (matches ( ?v_ + ?c*?v_^^^2 = 0) e_) &\
|
|
neuper@37906
|
544 |
\Not (matches ( ?b*?v_ + ?c*?v_^^^2 = 0) e_)"]),
|
|
neuper@37906
|
545 |
("#Find" ,["solutions v_i_"])
|
|
neuper@37906
|
546 |
],
|
|
neuper@37926
|
547 |
PolyEq_prls, SOME "solve (e_::bool, v_)",
|
|
neuper@37906
|
548 |
[["PolyEq","solve_d2_polyeq_sqonly_equation"]]));
|
|
neuper@37906
|
549 |
|
|
neuper@37906
|
550 |
store_pbt
|
|
neuper@37906
|
551 |
(prep_pbt PolyEq.thy "pbl_equ_univ_poly_deg2_bdvonly" [] e_pblID
|
|
neuper@37906
|
552 |
(["bdv_only","degree_2","polynomial","univariate","equation"],
|
|
neuper@37906
|
553 |
[("#Given" ,["equality e_","solveFor v_"]),
|
|
neuper@37906
|
554 |
("#Where" ,["matches (?a*?v_ + ?v_^^^2 = 0) e_ | \
|
|
neuper@37906
|
555 |
\matches ( ?v_ + ?v_^^^2 = 0) e_ | \
|
|
neuper@37906
|
556 |
\matches ( ?v_ + ?b*?v_^^^2 = 0) e_ | \
|
|
neuper@37906
|
557 |
\matches (?a*?v_ + ?b*?v_^^^2 = 0) e_ | \
|
|
neuper@37906
|
558 |
\matches ( ?v_^^^2 = 0) e_ | \
|
|
neuper@37906
|
559 |
\matches ( ?b*?v_^^^2 = 0) e_ "]),
|
|
neuper@37906
|
560 |
("#Find" ,["solutions v_i_"])
|
|
neuper@37906
|
561 |
],
|
|
neuper@37926
|
562 |
PolyEq_prls, SOME "solve (e_::bool, v_)",
|
|
neuper@37906
|
563 |
[["PolyEq","solve_d2_polyeq_bdvonly_equation"]]));
|
|
neuper@37906
|
564 |
|
|
neuper@37906
|
565 |
store_pbt
|
|
neuper@37906
|
566 |
(prep_pbt PolyEq.thy "pbl_equ_univ_poly_deg2_pq" [] e_pblID
|
|
neuper@37906
|
567 |
(["pqFormula","degree_2","polynomial","univariate","equation"],
|
|
neuper@37906
|
568 |
[("#Given" ,["equality e_","solveFor v_"]),
|
|
neuper@37906
|
569 |
("#Where" ,["matches (?a + 1*?v_^^^2 = 0) e_ | \
|
|
neuper@37906
|
570 |
\matches (?a + ?v_^^^2 = 0) e_"]),
|
|
neuper@37906
|
571 |
("#Find" ,["solutions v_i_"])
|
|
neuper@37906
|
572 |
],
|
|
neuper@37926
|
573 |
PolyEq_prls, SOME "solve (e_::bool, v_)",
|
|
neuper@37906
|
574 |
[["PolyEq","solve_d2_polyeq_pq_equation"]]));
|
|
neuper@37906
|
575 |
|
|
neuper@37906
|
576 |
store_pbt
|
|
neuper@37906
|
577 |
(prep_pbt PolyEq.thy "pbl_equ_univ_poly_deg2_abc" [] e_pblID
|
|
neuper@37906
|
578 |
(["abcFormula","degree_2","polynomial","univariate","equation"],
|
|
neuper@37906
|
579 |
[("#Given" ,["equality e_","solveFor v_"]),
|
|
neuper@37906
|
580 |
("#Where" ,["matches (?a + ?v_^^^2 = 0) e_ | \
|
|
neuper@37906
|
581 |
\matches (?a + ?b*?v_^^^2 = 0) e_"]),
|
|
neuper@37906
|
582 |
("#Find" ,["solutions v_i_"])
|
|
neuper@37906
|
583 |
],
|
|
neuper@37926
|
584 |
PolyEq_prls, SOME "solve (e_::bool, v_)",
|
|
neuper@37906
|
585 |
[["PolyEq","solve_d2_polyeq_abc_equation"]]));
|
|
neuper@37906
|
586 |
|
|
neuper@37906
|
587 |
(*--- d3 ---*)
|
|
neuper@37906
|
588 |
store_pbt
|
|
neuper@37906
|
589 |
(prep_pbt PolyEq.thy "pbl_equ_univ_poly_deg3" [] e_pblID
|
|
neuper@37906
|
590 |
(["degree_3","polynomial","univariate","equation"],
|
|
neuper@37906
|
591 |
[("#Given" ,["equality e_","solveFor v_"]),
|
|
neuper@37906
|
592 |
("#Where" ,["matches (?a = 0) e_",
|
|
neuper@37906
|
593 |
"(lhs e_) is_poly_in v_ ",
|
|
neuper@37906
|
594 |
"((lhs e_) has_degree_in v_) = 3"]),
|
|
neuper@37906
|
595 |
("#Find" ,["solutions v_i_"])
|
|
neuper@37906
|
596 |
],
|
|
neuper@37926
|
597 |
PolyEq_prls, SOME "solve (e_::bool, v_)",
|
|
neuper@37906
|
598 |
[["PolyEq","solve_d3_polyeq_equation"]]));
|
|
neuper@37906
|
599 |
|
|
neuper@37906
|
600 |
(*--- d4 ---*)
|
|
neuper@37906
|
601 |
store_pbt
|
|
neuper@37906
|
602 |
(prep_pbt PolyEq.thy "pbl_equ_univ_poly_deg4" [] e_pblID
|
|
neuper@37906
|
603 |
(["degree_4","polynomial","univariate","equation"],
|
|
neuper@37906
|
604 |
[("#Given" ,["equality e_","solveFor v_"]),
|
|
neuper@37906
|
605 |
("#Where" ,["matches (?a = 0) e_",
|
|
neuper@37906
|
606 |
"(lhs e_) is_poly_in v_ ",
|
|
neuper@37906
|
607 |
"((lhs e_) has_degree_in v_) = 4"]),
|
|
neuper@37906
|
608 |
("#Find" ,["solutions v_i_"])
|
|
neuper@37906
|
609 |
],
|
|
neuper@37926
|
610 |
PolyEq_prls, SOME "solve (e_::bool, v_)",
|
|
neuper@37906
|
611 |
[(*["PolyEq","solve_d4_polyeq_equation"]*)]));
|
|
neuper@37906
|
612 |
|
|
neuper@37906
|
613 |
(*--- normalize ---*)
|
|
neuper@37906
|
614 |
store_pbt
|
|
neuper@37906
|
615 |
(prep_pbt PolyEq.thy "pbl_equ_univ_poly_norm" [] e_pblID
|
|
neuper@37906
|
616 |
(["normalize","polynomial","univariate","equation"],
|
|
neuper@37906
|
617 |
[("#Given" ,["equality e_","solveFor v_"]),
|
|
neuper@37906
|
618 |
("#Where" ,["(Not((matches (?a = 0 ) e_ ))) |\
|
|
neuper@37906
|
619 |
\(Not(((lhs e_) is_poly_in v_)))"]),
|
|
neuper@37906
|
620 |
("#Find" ,["solutions v_i_"])
|
|
neuper@37906
|
621 |
],
|
|
neuper@37926
|
622 |
PolyEq_prls, SOME "solve (e_::bool, v_)",
|
|
neuper@37906
|
623 |
[["PolyEq","normalize_poly"]]));
|
|
neuper@37906
|
624 |
(*-------------------------expanded-----------------------*)
|
|
neuper@37906
|
625 |
store_pbt
|
|
neuper@37906
|
626 |
(prep_pbt PolyEq.thy "pbl_equ_univ_expand" [] e_pblID
|
|
neuper@37906
|
627 |
(["expanded","univariate","equation"],
|
|
neuper@37906
|
628 |
[("#Given" ,["equality e_","solveFor v_"]),
|
|
neuper@37906
|
629 |
("#Where" ,["matches (?a = 0) e_",
|
|
neuper@37906
|
630 |
"(lhs e_) is_expanded_in v_ "]),
|
|
neuper@37906
|
631 |
("#Find" ,["solutions v_i_"])
|
|
neuper@37906
|
632 |
],
|
|
neuper@37926
|
633 |
PolyEq_prls, SOME "solve (e_::bool, v_)",
|
|
neuper@37906
|
634 |
[]));
|
|
neuper@37906
|
635 |
|
|
neuper@37906
|
636 |
(*--- d2 ---*)
|
|
neuper@37906
|
637 |
store_pbt
|
|
neuper@37906
|
638 |
(prep_pbt PolyEq.thy "pbl_equ_univ_expand_deg2" [] e_pblID
|
|
neuper@37906
|
639 |
(["degree_2","expanded","univariate","equation"],
|
|
neuper@37906
|
640 |
[("#Given" ,["equality e_","solveFor v_"]),
|
|
neuper@37906
|
641 |
("#Where" ,["((lhs e_) has_degree_in v_) = 2"]),
|
|
neuper@37906
|
642 |
("#Find" ,["solutions v_i_"])
|
|
neuper@37906
|
643 |
],
|
|
neuper@37926
|
644 |
PolyEq_prls, SOME "solve (e_::bool, v_)",
|
|
neuper@37906
|
645 |
[["PolyEq","complete_square"]]));
|
|
neuper@37906
|
646 |
|
|
neuper@37906
|
647 |
|
|
neuper@37906
|
648 |
"-------------------------methods-----------------------";
|
|
neuper@37906
|
649 |
store_met
|
|
neuper@37906
|
650 |
(prep_met PolyEq.thy "met_polyeq" [] e_metID
|
|
neuper@37906
|
651 |
(["PolyEq"],
|
|
neuper@37906
|
652 |
[],
|
|
neuper@37906
|
653 |
{rew_ord'="tless_true",rls'=Atools_erls,calc = [], srls = e_rls, prls=e_rls,
|
|
neuper@37906
|
654 |
crls=PolyEq_crls, nrls=norm_Rational
|
|
neuper@37906
|
655 |
(*, asm_rls=[],asm_thm=[]*)}, "empty_script"));
|
|
neuper@37906
|
656 |
|
|
neuper@37906
|
657 |
store_met
|
|
neuper@37906
|
658 |
(prep_met PolyEq.thy "met_polyeq_norm" [] e_metID
|
|
neuper@37906
|
659 |
(["PolyEq","normalize_poly"],
|
|
neuper@37906
|
660 |
[("#Given" ,["equality e_","solveFor v_"]),
|
|
neuper@37906
|
661 |
("#Where" ,["(Not((matches (?a = 0 ) e_ ))) |\
|
|
neuper@37906
|
662 |
\(Not(((lhs e_) is_poly_in v_)))"]),
|
|
neuper@37906
|
663 |
("#Find" ,["solutions v_i_"])
|
|
neuper@37906
|
664 |
],
|
|
neuper@37906
|
665 |
{rew_ord'="termlessI",
|
|
neuper@37906
|
666 |
rls'=PolyEq_erls,
|
|
neuper@37906
|
667 |
srls=e_rls,
|
|
neuper@37906
|
668 |
prls=PolyEq_prls,
|
|
neuper@37906
|
669 |
calc=[],
|
|
neuper@37906
|
670 |
crls=PolyEq_crls, nrls=norm_Rational(*,
|
|
neuper@37906
|
671 |
asm_rls=[],
|
|
neuper@37906
|
672 |
asm_thm=[]*)},
|
|
neuper@37906
|
673 |
(*RL: Ratpoly loest Brueche ohne bdv*)
|
|
neuper@37906
|
674 |
"Script Normalize_poly (e_::bool) (v_::real) = \
|
|
neuper@37906
|
675 |
\(let e_ =((Try (Rewrite all_left False)) @@ \
|
|
neuper@37906
|
676 |
\ (Try (Repeat (Rewrite makex1_x False))) @@ \
|
|
neuper@37906
|
677 |
\ (Try (Repeat (Rewrite_Set expand_binoms False))) @@ \
|
|
neuper@37906
|
678 |
\ (Try (Repeat (Rewrite_Set_Inst [(bdv,v_::real)] \
|
|
neuper@37906
|
679 |
\ make_ratpoly_in False))) @@ \
|
|
neuper@37906
|
680 |
\ (Try (Repeat (Rewrite_Set polyeq_simplify False)))) e_ \
|
|
neuper@37906
|
681 |
\ in (SubProblem (PolyEq_,[polynomial,univariate,equation], \
|
|
neuper@37906
|
682 |
\ [no_met]) [bool_ e_, real_ v_]))"
|
|
neuper@37906
|
683 |
));
|
|
neuper@37906
|
684 |
|
|
neuper@37906
|
685 |
store_met
|
|
neuper@37906
|
686 |
(prep_met PolyEq.thy "met_polyeq_d0" [] e_metID
|
|
neuper@37906
|
687 |
(["PolyEq","solve_d0_polyeq_equation"],
|
|
neuper@37906
|
688 |
[("#Given" ,["equality e_","solveFor v_"]),
|
|
neuper@37906
|
689 |
("#Where" ,["(lhs e_) is_poly_in v_ ",
|
|
neuper@37906
|
690 |
"((lhs e_) has_degree_in v_) = 0"]),
|
|
neuper@37906
|
691 |
("#Find" ,["solutions v_i_"])
|
|
neuper@37906
|
692 |
],
|
|
neuper@37906
|
693 |
{rew_ord'="termlessI",
|
|
neuper@37906
|
694 |
rls'=PolyEq_erls,
|
|
neuper@37906
|
695 |
srls=e_rls,
|
|
neuper@37906
|
696 |
prls=PolyEq_prls,
|
|
neuper@37906
|
697 |
calc=[("sqrt", ("Root.sqrt", eval_sqrt "#sqrt_"))],
|
|
neuper@37906
|
698 |
crls=PolyEq_crls, nrls=norm_Rational(*,
|
|
neuper@37906
|
699 |
asm_rls=[],
|
|
neuper@37906
|
700 |
asm_thm=[]*)},
|
|
neuper@37906
|
701 |
"Script Solve_d0_polyeq_equation (e_::bool) (v_::real) = \
|
|
neuper@37906
|
702 |
\(let e_ = ((Try (Rewrite_Set_Inst [(bdv,v_::real)] \
|
|
neuper@37906
|
703 |
\ d0_polyeq_simplify False))) e_ \
|
|
neuper@37906
|
704 |
\ in ((Or_to_List e_)::bool list))"
|
|
neuper@37906
|
705 |
));
|
|
neuper@37906
|
706 |
|
|
neuper@37906
|
707 |
store_met
|
|
neuper@37906
|
708 |
(prep_met PolyEq.thy "met_polyeq_d1" [] e_metID
|
|
neuper@37906
|
709 |
(["PolyEq","solve_d1_polyeq_equation"],
|
|
neuper@37906
|
710 |
[("#Given" ,["equality e_","solveFor v_"]),
|
|
neuper@37906
|
711 |
("#Where" ,["(lhs e_) is_poly_in v_ ",
|
|
neuper@37906
|
712 |
"((lhs e_) has_degree_in v_) = 1"]),
|
|
neuper@37906
|
713 |
("#Find" ,["solutions v_i_"])
|
|
neuper@37906
|
714 |
],
|
|
neuper@37906
|
715 |
{rew_ord'="termlessI",
|
|
neuper@37906
|
716 |
rls'=PolyEq_erls,
|
|
neuper@37906
|
717 |
srls=e_rls,
|
|
neuper@37906
|
718 |
prls=PolyEq_prls,
|
|
neuper@37906
|
719 |
calc=[("sqrt", ("Root.sqrt", eval_sqrt "#sqrt_"))],
|
|
neuper@37906
|
720 |
crls=PolyEq_crls, nrls=norm_Rational(*,
|
|
neuper@37906
|
721 |
(* asm_rls=["d1_polyeq_simplify"],*)
|
|
neuper@37906
|
722 |
asm_rls=[],
|
|
neuper@37906
|
723 |
asm_thm=[("d1_isolate_div","")]*)},
|
|
neuper@37906
|
724 |
"Script Solve_d1_polyeq_equation (e_::bool) (v_::real) = \
|
|
neuper@37906
|
725 |
\(let e_ = ((Try (Rewrite_Set_Inst [(bdv,v_::real)] \
|
|
neuper@37906
|
726 |
\ d1_polyeq_simplify True)) @@ \
|
|
neuper@37906
|
727 |
\ (Try (Rewrite_Set polyeq_simplify False)) @@ \
|
|
neuper@37906
|
728 |
\ (Try (Rewrite_Set norm_Rational_parenthesized False))) e_;\
|
|
neuper@37906
|
729 |
\ (L_::bool list) = ((Or_to_List e_)::bool list) \
|
|
neuper@37906
|
730 |
\ in Check_elementwise L_ {(v_::real). Assumptions} )"
|
|
neuper@37906
|
731 |
));
|
|
neuper@37906
|
732 |
|
|
neuper@37906
|
733 |
store_met
|
|
neuper@37906
|
734 |
(prep_met PolyEq.thy "met_polyeq_d22" [] e_metID
|
|
neuper@37906
|
735 |
(["PolyEq","solve_d2_polyeq_equation"],
|
|
neuper@37906
|
736 |
[("#Given" ,["equality e_","solveFor v_"]),
|
|
neuper@37906
|
737 |
("#Where" ,["(lhs e_) is_poly_in v_ ",
|
|
neuper@37906
|
738 |
"((lhs e_) has_degree_in v_) = 2"]),
|
|
neuper@37906
|
739 |
("#Find" ,["solutions v_i_"])
|
|
neuper@37906
|
740 |
],
|
|
neuper@37906
|
741 |
{rew_ord'="termlessI",
|
|
neuper@37906
|
742 |
rls'=PolyEq_erls,
|
|
neuper@37906
|
743 |
srls=e_rls,
|
|
neuper@37906
|
744 |
prls=PolyEq_prls,
|
|
neuper@37906
|
745 |
calc=[("sqrt", ("Root.sqrt", eval_sqrt "#sqrt_"))],
|
|
neuper@37906
|
746 |
crls=PolyEq_crls, nrls=norm_Rational(*,
|
|
neuper@37906
|
747 |
(*asm_rls=["d2_polyeq_simplify","d1_polyeq_simplify"],*)
|
|
neuper@37906
|
748 |
asm_rls=[],
|
|
neuper@37906
|
749 |
asm_thm = [("d1_isolate_div",""),("d2_pqformula1",""),("d2_pqformula2",""),
|
|
neuper@37906
|
750 |
("d2_pqformula3",""),("d2_pqformula4",""),("d2_pqformula1_neg",""),
|
|
neuper@37906
|
751 |
("d2_pqformula2_neg",""),("d2_pqformula3_neg",""),("d2_pqformula4_neg",""),
|
|
neuper@37906
|
752 |
("d2_abcformula1",""),("d2_abcformula2",""),("d2_abcformula1_neg",""),
|
|
neuper@37906
|
753 |
("d2_abcformula2_neg",""), ("d2_sqrt_equation1",""),
|
|
neuper@37906
|
754 |
("d2_sqrt_equation1_neg",""), ("d2_isolate_div","")]*)},
|
|
neuper@37906
|
755 |
"Script Solve_d2_polyeq_equation (e_::bool) (v_::real) = \
|
|
neuper@37906
|
756 |
\ (let e_ = ((Try (Rewrite_Set_Inst [(bdv,v_::real)] \
|
|
neuper@37906
|
757 |
\ d2_polyeq_simplify True)) @@ \
|
|
neuper@37906
|
758 |
\ (Try (Rewrite_Set polyeq_simplify False)) @@ \
|
|
neuper@37906
|
759 |
\ (Try (Rewrite_Set_Inst [(bdv,v_::real)] \
|
|
neuper@37906
|
760 |
\ d1_polyeq_simplify True)) @@ \
|
|
neuper@37906
|
761 |
\ (Try (Rewrite_Set polyeq_simplify False)) @@ \
|
|
neuper@37906
|
762 |
\ (Try (Rewrite_Set norm_Rational_parenthesized False))) e_;\
|
|
neuper@37906
|
763 |
\ (L_::bool list) = ((Or_to_List e_)::bool list) \
|
|
neuper@37906
|
764 |
\ in Check_elementwise L_ {(v_::real). Assumptions} )"
|
|
neuper@37906
|
765 |
));
|
|
neuper@37906
|
766 |
|
|
neuper@37906
|
767 |
store_met
|
|
neuper@37906
|
768 |
(prep_met PolyEq.thy "met_polyeq_d2_bdvonly" [] e_metID
|
|
neuper@37906
|
769 |
(["PolyEq","solve_d2_polyeq_bdvonly_equation"],
|
|
neuper@37906
|
770 |
[("#Given" ,["equality e_","solveFor v_"]),
|
|
neuper@37906
|
771 |
("#Where" ,["(lhs e_) is_poly_in v_ ",
|
|
neuper@37906
|
772 |
"((lhs e_) has_degree_in v_) = 2"]),
|
|
neuper@37906
|
773 |
("#Find" ,["solutions v_i_"])
|
|
neuper@37906
|
774 |
],
|
|
neuper@37906
|
775 |
{rew_ord'="termlessI",
|
|
neuper@37906
|
776 |
rls'=PolyEq_erls,
|
|
neuper@37906
|
777 |
srls=e_rls,
|
|
neuper@37906
|
778 |
prls=PolyEq_prls,
|
|
neuper@37906
|
779 |
calc=[("sqrt", ("Root.sqrt", eval_sqrt "#sqrt_"))],
|
|
neuper@37906
|
780 |
crls=PolyEq_crls, nrls=norm_Rational(*,
|
|
neuper@37906
|
781 |
(*asm_rls=["d2_polyeq_bdv_only_simplify","d1_polyeq_simplify "],*)
|
|
neuper@37906
|
782 |
asm_rls=[],
|
|
neuper@37906
|
783 |
asm_thm=[("d1_isolate_div",""),("d2_isolate_div",""),
|
|
neuper@37906
|
784 |
("d2_sqrt_equation1",""),("d2_sqrt_equation1_neg","")]*)},
|
|
neuper@37906
|
785 |
"Script Solve_d2_polyeq_bdvonly_equation (e_::bool) (v_::real) =\
|
|
neuper@37906
|
786 |
\ (let e_ = ((Try (Rewrite_Set_Inst [(bdv,v_::real)] \
|
|
neuper@37906
|
787 |
\ d2_polyeq_bdv_only_simplify True)) @@ \
|
|
neuper@37906
|
788 |
\ (Try (Rewrite_Set polyeq_simplify False)) @@ \
|
|
neuper@37906
|
789 |
\ (Try (Rewrite_Set_Inst [(bdv,v_::real)] \
|
|
neuper@37906
|
790 |
\ d1_polyeq_simplify True)) @@ \
|
|
neuper@37906
|
791 |
\ (Try (Rewrite_Set polyeq_simplify False)) @@ \
|
|
neuper@37906
|
792 |
\ (Try (Rewrite_Set norm_Rational_parenthesized False))) e_;\
|
|
neuper@37906
|
793 |
\ (L_::bool list) = ((Or_to_List e_)::bool list) \
|
|
neuper@37906
|
794 |
\ in Check_elementwise L_ {(v_::real). Assumptions} )"
|
|
neuper@37906
|
795 |
));
|
|
neuper@37906
|
796 |
|
|
neuper@37906
|
797 |
store_met
|
|
neuper@37906
|
798 |
(prep_met PolyEq.thy "met_polyeq_d2_sqonly" [] e_metID
|
|
neuper@37906
|
799 |
(["PolyEq","solve_d2_polyeq_sqonly_equation"],
|
|
neuper@37906
|
800 |
[("#Given" ,["equality e_","solveFor v_"]),
|
|
neuper@37906
|
801 |
("#Where" ,["(lhs e_) is_poly_in v_ ",
|
|
neuper@37906
|
802 |
"((lhs e_) has_degree_in v_) = 2"]),
|
|
neuper@37906
|
803 |
("#Find" ,["solutions v_i_"])
|
|
neuper@37906
|
804 |
],
|
|
neuper@37906
|
805 |
{rew_ord'="termlessI",
|
|
neuper@37906
|
806 |
rls'=PolyEq_erls,
|
|
neuper@37906
|
807 |
srls=e_rls,
|
|
neuper@37906
|
808 |
prls=PolyEq_prls,
|
|
neuper@37906
|
809 |
calc=[("sqrt", ("Root.sqrt", eval_sqrt "#sqrt_"))],
|
|
neuper@37906
|
810 |
crls=PolyEq_crls, nrls=norm_Rational(*,
|
|
neuper@37906
|
811 |
(*asm_rls=["d2_polyeq_sq_only_simplify"],*)
|
|
neuper@37906
|
812 |
asm_rls=[],
|
|
neuper@37906
|
813 |
asm_thm=[("d2_sqrt_equation1",""),("d2_sqrt_equation1_neg",""),
|
|
neuper@37906
|
814 |
("d2_isolate_div","")]*)},
|
|
neuper@37906
|
815 |
"Script Solve_d2_polyeq_sqonly_equation (e_::bool) (v_::real) =\
|
|
neuper@37906
|
816 |
\ (let e_ = ((Try (Rewrite_Set_Inst [(bdv,v_::real)] \
|
|
neuper@37906
|
817 |
\ d2_polyeq_sq_only_simplify True)) @@ \
|
|
neuper@37906
|
818 |
\ (Try (Rewrite_Set polyeq_simplify False)) @@ \
|
|
neuper@37906
|
819 |
\ (Try (Rewrite_Set norm_Rational_parenthesized False))) e_; \
|
|
neuper@37906
|
820 |
\ (L_::bool list) = ((Or_to_List e_)::bool list) \
|
|
neuper@37906
|
821 |
\ in Check_elementwise L_ {(v_::real). Assumptions} )"
|
|
neuper@37906
|
822 |
));
|
|
neuper@37906
|
823 |
|
|
neuper@37906
|
824 |
store_met
|
|
neuper@37906
|
825 |
(prep_met PolyEq.thy "met_polyeq_d2_pq" [] e_metID
|
|
neuper@37906
|
826 |
(["PolyEq","solve_d2_polyeq_pq_equation"],
|
|
neuper@37906
|
827 |
[("#Given" ,["equality e_","solveFor v_"]),
|
|
neuper@37906
|
828 |
("#Where" ,["(lhs e_) is_poly_in v_ ",
|
|
neuper@37906
|
829 |
"((lhs e_) has_degree_in v_) = 2"]),
|
|
neuper@37906
|
830 |
("#Find" ,["solutions v_i_"])
|
|
neuper@37906
|
831 |
],
|
|
neuper@37906
|
832 |
{rew_ord'="termlessI",
|
|
neuper@37906
|
833 |
rls'=PolyEq_erls,
|
|
neuper@37906
|
834 |
srls=e_rls,
|
|
neuper@37906
|
835 |
prls=PolyEq_prls,
|
|
neuper@37906
|
836 |
calc=[("sqrt", ("Root.sqrt", eval_sqrt "#sqrt_"))],
|
|
neuper@37906
|
837 |
crls=PolyEq_crls, nrls=norm_Rational(*,
|
|
neuper@37906
|
838 |
(*asm_rls=["d2_polyeq_pqFormula_simplify"],*)
|
|
neuper@37906
|
839 |
asm_rls=[],
|
|
neuper@37906
|
840 |
asm_thm=[("d2_pqformula1",""),("d2_pqformula2",""),("d2_pqformula3",""),
|
|
neuper@37906
|
841 |
("d2_pqformula4",""),("d2_pqformula5",""),("d2_pqformula6",""),
|
|
neuper@37906
|
842 |
("d2_pqformula7",""),("d2_pqformula8",""),("d2_pqformula9",""),
|
|
neuper@37906
|
843 |
("d2_pqformula10",""),("d2_pqformula1_neg",""),("d2_pqformula2_neg",""),
|
|
neuper@37906
|
844 |
("d2_pqformula3_neg",""), ("d2_pqformula4_neg",""),("d2_pqformula9_neg",""),
|
|
neuper@37906
|
845 |
("d2_pqformula10_neg","")]*)},
|
|
neuper@37906
|
846 |
"Script Solve_d2_polyeq_pq_equation (e_::bool) (v_::real) = \
|
|
neuper@37906
|
847 |
\ (let e_ = ((Try (Rewrite_Set_Inst [(bdv,v_::real)] \
|
|
neuper@37906
|
848 |
\ d2_polyeq_pqFormula_simplify True)) @@ \
|
|
neuper@37906
|
849 |
\ (Try (Rewrite_Set polyeq_simplify False)) @@ \
|
|
neuper@37906
|
850 |
\ (Try (Rewrite_Set norm_Rational_parenthesized False))) e_;\
|
|
neuper@37906
|
851 |
\ (L_::bool list) = ((Or_to_List e_)::bool list) \
|
|
neuper@37906
|
852 |
\ in Check_elementwise L_ {(v_::real). Assumptions} )"
|
|
neuper@37906
|
853 |
));
|
|
neuper@37906
|
854 |
|
|
neuper@37906
|
855 |
store_met
|
|
neuper@37906
|
856 |
(prep_met PolyEq.thy "met_polyeq_d2_abc" [] e_metID
|
|
neuper@37906
|
857 |
(["PolyEq","solve_d2_polyeq_abc_equation"],
|
|
neuper@37906
|
858 |
[("#Given" ,["equality e_","solveFor v_"]),
|
|
neuper@37906
|
859 |
("#Where" ,["(lhs e_) is_poly_in v_ ",
|
|
neuper@37906
|
860 |
"((lhs e_) has_degree_in v_) = 2"]),
|
|
neuper@37906
|
861 |
("#Find" ,["solutions v_i_"])
|
|
neuper@37906
|
862 |
],
|
|
neuper@37906
|
863 |
{rew_ord'="termlessI",
|
|
neuper@37906
|
864 |
rls'=PolyEq_erls,
|
|
neuper@37906
|
865 |
srls=e_rls,
|
|
neuper@37906
|
866 |
prls=PolyEq_prls,
|
|
neuper@37906
|
867 |
calc=[("sqrt", ("Root.sqrt", eval_sqrt "#sqrt_"))],
|
|
neuper@37906
|
868 |
crls=PolyEq_crls, nrls=norm_Rational(*,
|
|
neuper@37906
|
869 |
(*asm_rls=["d2_polyeq_abcFormula_simplify"],*)
|
|
neuper@37906
|
870 |
asm_rls=[],
|
|
neuper@37906
|
871 |
asm_thm=[("d2_abcformula1",""),("d2_abcformula2",""),("d2_abcformula3",""),
|
|
neuper@37906
|
872 |
("d2_abcformula4",""),("d2_abcformula5",""),("d2_abcformula6",""),
|
|
neuper@37906
|
873 |
("d2_abcformula7",""),("d2_abcformula8",""),("d2_abcformula9",""),
|
|
neuper@37906
|
874 |
("d2_abcformula10",""),("d2_abcformula1_neg",""),("d2_abcformula2_neg",""),
|
|
neuper@37906
|
875 |
("d2_abcformula3_neg",""), ("d2_abcformula4_neg",""),("d2_abcformula5_neg",""),
|
|
neuper@37906
|
876 |
("d2_abcformula6_neg","")]*)},
|
|
neuper@37906
|
877 |
"Script Solve_d2_polyeq_abc_equation (e_::bool) (v_::real) = \
|
|
neuper@37906
|
878 |
\ (let e_ = ((Try (Rewrite_Set_Inst [(bdv,v_::real)] \
|
|
neuper@37906
|
879 |
\ d2_polyeq_abcFormula_simplify True)) @@ \
|
|
neuper@37906
|
880 |
\ (Try (Rewrite_Set polyeq_simplify False)) @@ \
|
|
neuper@37906
|
881 |
\ (Try (Rewrite_Set norm_Rational_parenthesized False))) e_;\
|
|
neuper@37906
|
882 |
\ (L_::bool list) = ((Or_to_List e_)::bool list) \
|
|
neuper@37906
|
883 |
\ in Check_elementwise L_ {(v_::real). Assumptions} )"
|
|
neuper@37906
|
884 |
));
|
|
neuper@37906
|
885 |
|
|
neuper@37906
|
886 |
store_met
|
|
neuper@37906
|
887 |
(prep_met PolyEq.thy "met_polyeq_d3" [] e_metID
|
|
neuper@37906
|
888 |
(["PolyEq","solve_d3_polyeq_equation"],
|
|
neuper@37906
|
889 |
[("#Given" ,["equality e_","solveFor v_"]),
|
|
neuper@37906
|
890 |
("#Where" ,["(lhs e_) is_poly_in v_ ",
|
|
neuper@37906
|
891 |
"((lhs e_) has_degree_in v_) = 3"]),
|
|
neuper@37906
|
892 |
("#Find" ,["solutions v_i_"])
|
|
neuper@37906
|
893 |
],
|
|
neuper@37906
|
894 |
{rew_ord'="termlessI",
|
|
neuper@37906
|
895 |
rls'=PolyEq_erls,
|
|
neuper@37906
|
896 |
srls=e_rls,
|
|
neuper@37906
|
897 |
prls=PolyEq_prls,
|
|
neuper@37906
|
898 |
calc=[("sqrt", ("Root.sqrt", eval_sqrt "#sqrt_"))],
|
|
neuper@37906
|
899 |
crls=PolyEq_crls, nrls=norm_Rational(*,
|
|
neuper@37906
|
900 |
(* asm_rls=["d1_polyeq_simplify","d2_polyeq_simplify","d1_polyeq_simplify"],*)
|
|
neuper@37906
|
901 |
asm_rls=[],
|
|
neuper@37906
|
902 |
asm_thm=[("d3_isolate_div",""),("d1_isolate_div",""),("d2_pqformula1",""),
|
|
neuper@37906
|
903 |
("d2_pqformula2",""),("d2_pqformula3",""),("d2_pqformula4",""),
|
|
neuper@37906
|
904 |
("d2_pqformula1_neg",""), ("d2_pqformula2_neg",""),("d2_pqformula3_neg",""),
|
|
neuper@37906
|
905 |
("d2_pqformula4_neg",""), ("d2_abcformula1",""),("d2_abcformula2",""),
|
|
neuper@37906
|
906 |
("d2_abcformula1_neg",""),("d2_abcformula2_neg",""),
|
|
neuper@37906
|
907 |
("d2_sqrt_equation1",""),("d2_sqrt_equation1_neg",""), ("d2_isolate_div","")]*)},
|
|
neuper@37906
|
908 |
"Script Solve_d3_polyeq_equation (e_::bool) (v_::real) = \
|
|
neuper@37906
|
909 |
\ (let e_ = ((Try (Rewrite_Set_Inst [(bdv,v_::real)] \
|
|
neuper@37906
|
910 |
\ d3_polyeq_simplify True)) @@ \
|
|
neuper@37906
|
911 |
\ (Try (Rewrite_Set polyeq_simplify False)) @@ \
|
|
neuper@37906
|
912 |
\ (Try (Rewrite_Set_Inst [(bdv,v_::real)] \
|
|
neuper@37906
|
913 |
\ d2_polyeq_simplify True)) @@ \
|
|
neuper@37906
|
914 |
\ (Try (Rewrite_Set polyeq_simplify False)) @@ \
|
|
neuper@37906
|
915 |
\ (Try (Rewrite_Set_Inst [(bdv,v_::real)] \
|
|
neuper@37906
|
916 |
\ d1_polyeq_simplify True)) @@ \
|
|
neuper@37906
|
917 |
\ (Try (Rewrite_Set polyeq_simplify False)) @@ \
|
|
neuper@37906
|
918 |
\ (Try (Rewrite_Set norm_Rational_parenthesized False))) e_;\
|
|
neuper@37906
|
919 |
\ (L_::bool list) = ((Or_to_List e_)::bool list) \
|
|
neuper@37906
|
920 |
\ in Check_elementwise L_ {(v_::real). Assumptions} )"
|
|
neuper@37906
|
921 |
));
|
|
neuper@37906
|
922 |
|
|
neuper@37906
|
923 |
(*.solves all expanded (ie. normalized) terms of degree 2.*)
|
|
neuper@37906
|
924 |
(*Oct.02 restriction: 'eval_true 0 =< discriminant' ony for integer values
|
|
neuper@37906
|
925 |
by 'PolyEq_erls'; restricted until Float.thy is implemented*)
|
|
neuper@37906
|
926 |
store_met
|
|
neuper@37906
|
927 |
(prep_met PolyEq.thy "met_polyeq_complsq" [] e_metID
|
|
neuper@37906
|
928 |
(["PolyEq","complete_square"],
|
|
neuper@37906
|
929 |
[("#Given" ,["equality e_","solveFor v_"]),
|
|
neuper@37906
|
930 |
("#Where" ,["matches (?a = 0) e_",
|
|
neuper@37906
|
931 |
"((lhs e_) has_degree_in v_) = 2"]),
|
|
neuper@37906
|
932 |
("#Find" ,["solutions v_i_"])
|
|
neuper@37906
|
933 |
],
|
|
neuper@37906
|
934 |
{rew_ord'="termlessI",rls'=PolyEq_erls,srls=e_rls,prls=PolyEq_prls,
|
|
neuper@37906
|
935 |
calc=[("sqrt", ("Root.sqrt", eval_sqrt "#sqrt_"))],
|
|
neuper@37906
|
936 |
crls=PolyEq_crls, nrls=norm_Rational(*,
|
|
neuper@37906
|
937 |
asm_rls=[],
|
|
neuper@37906
|
938 |
asm_thm=[("root_plus_minus","")]*)},
|
|
neuper@37906
|
939 |
"Script Complete_square (e_::bool) (v_::real) = \
|
|
neuper@37906
|
940 |
\(let e_ = ((Try (Rewrite_Set_Inst [(bdv,v_)] cancel_leading_coeff True))\
|
|
neuper@37906
|
941 |
\ @@ (Try (Rewrite_Set_Inst [(bdv,v_)] complete_square True)) \
|
|
neuper@37906
|
942 |
\ @@ (Try (Rewrite square_explicit1 False)) \
|
|
neuper@37906
|
943 |
\ @@ (Try (Rewrite square_explicit2 False)) \
|
|
neuper@37906
|
944 |
\ @@ (Rewrite root_plus_minus True) \
|
|
neuper@37906
|
945 |
\ @@ (Try (Repeat (Rewrite_Inst [(bdv,v_)] bdv_explicit1 False))) \
|
|
neuper@37906
|
946 |
\ @@ (Try (Repeat (Rewrite_Inst [(bdv,v_)] bdv_explicit2 False))) \
|
|
neuper@37906
|
947 |
\ @@ (Try (Repeat \
|
|
neuper@37906
|
948 |
\ (Rewrite_Inst [(bdv,v_)] bdv_explicit3 False))) \
|
|
neuper@37906
|
949 |
\ @@ (Try (Rewrite_Set calculate_RootRat False)) \
|
|
neuper@37906
|
950 |
\ @@ (Try (Repeat (Calculate sqrt_)))) e_ \
|
|
neuper@37906
|
951 |
\ in ((Or_to_List e_)::bool list))"
|
|
neuper@37906
|
952 |
));
|
|
neuper@37906
|
953 |
(*6.10.02: x^2=64: root_plus_minus -/-/->
|
|
neuper@37906
|
954 |
"Script Complete_square (e_::bool) (v_::real) = \
|
|
neuper@37906
|
955 |
\(let e_ = ((Try (Rewrite_Set_Inst [(bdv,v_)] cancel_leading_coeff True))\
|
|
neuper@37906
|
956 |
\ @@ (Try (Rewrite_Set_Inst [(bdv,v_)] complete_square True)) \
|
|
neuper@37906
|
957 |
\ @@ (Try ((Rewrite square_explicit1 False) \
|
|
neuper@37906
|
958 |
\ Or (Rewrite square_explicit2 False))) \
|
|
neuper@37906
|
959 |
\ @@ (Rewrite root_plus_minus True) \
|
|
neuper@37906
|
960 |
\ @@ ((Repeat (Rewrite_Inst [(bdv,v_)] bdv_explicit1 False)) \
|
|
neuper@37906
|
961 |
\ Or (Repeat (Rewrite_Inst [(bdv,v_)] bdv_explicit2 False))) \
|
|
neuper@37906
|
962 |
\ @@ (Try (Repeat \
|
|
neuper@37906
|
963 |
\ (Rewrite_Inst [(bdv,v_)] bdv_explicit3 False))) \
|
|
neuper@37906
|
964 |
\ @@ (Try (Rewrite_Set calculate_RootRat False)) \
|
|
neuper@37906
|
965 |
\ @@ (Try (Repeat (Calculate sqrt_)))) e_ \
|
|
neuper@37906
|
966 |
\ in ((Or_to_List e_)::bool list))"*)
|
|
neuper@37906
|
967 |
|
|
neuper@37906
|
968 |
"******* PolyEq.ML end *******";
|
|
neuper@37906
|
969 |
|
|
neuper@37906
|
970 |
(*eine gehackte termorder*)
|
|
neuper@37906
|
971 |
local (*. for make_polynomial_in .*)
|
|
neuper@37906
|
972 |
|
|
neuper@37906
|
973 |
open Term; (* for type order = EQUAL | LESS | GREATER *)
|
|
neuper@37906
|
974 |
|
|
neuper@37906
|
975 |
fun pr_ord EQUAL = "EQUAL"
|
|
neuper@37906
|
976 |
| pr_ord LESS = "LESS"
|
|
neuper@37906
|
977 |
| pr_ord GREATER = "GREATER";
|
|
neuper@37906
|
978 |
|
|
neuper@37906
|
979 |
fun dest_hd' x (Const (a, T)) = (((a, 0), T), 0)
|
|
neuper@37906
|
980 |
| dest_hd' x (t as Free (a, T)) =
|
|
neuper@37906
|
981 |
if x = t then ((("|||||||||||||", 0), T), 0) (*WN*)
|
|
neuper@37906
|
982 |
else (((a, 0), T), 1)
|
|
neuper@37906
|
983 |
| dest_hd' x (Var v) = (v, 2)
|
|
neuper@37906
|
984 |
| dest_hd' x (Bound i) = ((("", i), dummyT), 3)
|
|
neuper@37906
|
985 |
| dest_hd' x (Abs (_, T, _)) = ((("", 0), T), 4);
|
|
neuper@37906
|
986 |
|
|
neuper@37906
|
987 |
fun size_of_term' x (Const ("Atools.pow",_) $ Free (var,_) $ Free (pot,_)) =
|
|
neuper@37906
|
988 |
(case x of (*WN*)
|
|
neuper@37906
|
989 |
(Free (xstr,_)) =>
|
|
neuper@37906
|
990 |
(if xstr = var then 1000*(the (int_of_str pot)) else 3)
|
|
neuper@37906
|
991 |
| _ => raise error ("size_of_term' called with subst = "^
|
|
neuper@37906
|
992 |
(term2str x)))
|
|
neuper@37906
|
993 |
| size_of_term' x (Free (subst,_)) =
|
|
neuper@37906
|
994 |
(case x of
|
|
neuper@37906
|
995 |
(Free (xstr,_)) => (if xstr = subst then 1000 else 1)
|
|
neuper@37906
|
996 |
| _ => raise error ("size_of_term' called with subst = "^
|
|
neuper@37906
|
997 |
(term2str x)))
|
|
neuper@37906
|
998 |
| size_of_term' x (Abs (_,_,body)) = 1 + size_of_term' x body
|
|
neuper@37906
|
999 |
| size_of_term' x (f$t) = size_of_term' x f + size_of_term' x t
|
|
neuper@37906
|
1000 |
| size_of_term' x _ = 1;
|
|
neuper@37906
|
1001 |
|
|
neuper@37906
|
1002 |
|
|
neuper@37906
|
1003 |
fun term_ord' x pr thy (Abs (_, T, t), Abs(_, U, u)) = (* ~ term.ML *)
|
|
neuper@37906
|
1004 |
(case term_ord' x pr thy (t, u) of EQUAL => typ_ord (T, U) | ord => ord)
|
|
neuper@37906
|
1005 |
| term_ord' x pr thy (t, u) =
|
|
neuper@37906
|
1006 |
(if pr then
|
|
neuper@37906
|
1007 |
let
|
|
neuper@37906
|
1008 |
val (f, ts) = strip_comb t and (g, us) = strip_comb u;
|
|
neuper@37906
|
1009 |
val _=writeln("t= f@ts= \""^
|
|
neuper@37938
|
1010 |
((Syntax.string_of_term (thy2ctxt thy)) f)^"\" @ \"["^
|
|
neuper@37906
|
1011 |
(commas(map(string_of_cterm o cterm_of(sign_of thy)) ts))^"]\"");
|
|
neuper@37906
|
1012 |
val _=writeln("u= g@us= \""^
|
|
neuper@37938
|
1013 |
((Syntax.string_of_term (thy2ctxt thy)) g)^"\" @ \"["^
|
|
neuper@37906
|
1014 |
(commas(map(string_of_cterm o cterm_of(sign_of thy)) us))^"]\"");
|
|
neuper@37906
|
1015 |
val _=writeln("size_of_term(t,u)= ("^
|
|
neuper@37906
|
1016 |
(string_of_int(size_of_term' x t))^", "^
|
|
neuper@37906
|
1017 |
(string_of_int(size_of_term' x u))^")");
|
|
neuper@37906
|
1018 |
val _=writeln("hd_ord(f,g) = "^((pr_ord o (hd_ord x))(f,g)));
|
|
neuper@37906
|
1019 |
val _=writeln("terms_ord(ts,us) = "^
|
|
neuper@37906
|
1020 |
((pr_ord o (terms_ord x) str false)(ts,us)));
|
|
neuper@37906
|
1021 |
val _=writeln("-------");
|
|
neuper@37906
|
1022 |
in () end
|
|
neuper@37906
|
1023 |
else ();
|
|
neuper@37906
|
1024 |
case int_ord (size_of_term' x t, size_of_term' x u) of
|
|
neuper@37906
|
1025 |
EQUAL =>
|
|
neuper@37906
|
1026 |
let val (f, ts) = strip_comb t and (g, us) = strip_comb u in
|
|
neuper@37906
|
1027 |
(case hd_ord x (f, g) of EQUAL => (terms_ord x str pr) (ts, us)
|
|
neuper@37906
|
1028 |
| ord => ord)
|
|
neuper@37906
|
1029 |
end
|
|
neuper@37906
|
1030 |
| ord => ord)
|
|
neuper@37906
|
1031 |
and hd_ord x (f, g) = (* ~ term.ML *)
|
|
neuper@37906
|
1032 |
prod_ord (prod_ord indexname_ord typ_ord) int_ord (dest_hd' x f,
|
|
neuper@37906
|
1033 |
dest_hd' x g)
|
|
neuper@37906
|
1034 |
and terms_ord x str pr (ts, us) =
|
|
neuper@37906
|
1035 |
list_ord (term_ord' x pr (assoc_thy "Isac.thy"))(ts, us);
|
|
neuper@37906
|
1036 |
(*val x = (term_of o the o (parse thy)) "x"; (*FIXXXXXXME*)
|
|
neuper@37906
|
1037 |
*)
|
|
neuper@37906
|
1038 |
|
|
neuper@37906
|
1039 |
in
|
|
neuper@37906
|
1040 |
|
|
neuper@37906
|
1041 |
fun ord_make_polynomial_in (pr:bool) thy subst tu =
|
|
neuper@37906
|
1042 |
let
|
|
neuper@37906
|
1043 |
(* val _=writeln("*** subs variable is: "^(subst2str subst)); *)
|
|
neuper@37906
|
1044 |
in
|
|
neuper@37906
|
1045 |
case subst of
|
|
neuper@37906
|
1046 |
(_,x)::_ => (term_ord' x pr thy tu = LESS)
|
|
neuper@37906
|
1047 |
| _ => raise error ("ord_make_polynomial_in called with subst = "^
|
|
neuper@37906
|
1048 |
(subst2str subst))
|
|
neuper@37906
|
1049 |
end;
|
|
neuper@37906
|
1050 |
end;
|
|
neuper@37906
|
1051 |
|
|
neuper@37906
|
1052 |
val order_add_mult_in = prep_rls(
|
|
neuper@37906
|
1053 |
Rls{id = "order_add_mult_in", preconds = [],
|
|
neuper@37906
|
1054 |
rew_ord = ("ord_make_polynomial_in",
|
|
neuper@37906
|
1055 |
ord_make_polynomial_in false Poly.thy),
|
|
neuper@37906
|
1056 |
erls = e_rls,srls = Erls,
|
|
neuper@37906
|
1057 |
calc = [],
|
|
neuper@37906
|
1058 |
(*asm_thm = [],*)
|
|
neuper@37906
|
1059 |
rules = [Thm ("real_mult_commute",num_str real_mult_commute),
|
|
neuper@37906
|
1060 |
(* z * w = w * z *)
|
|
neuper@37906
|
1061 |
Thm ("real_mult_left_commute",num_str real_mult_left_commute),
|
|
neuper@37906
|
1062 |
(*z1.0 * (z2.0 * z3.0) = z2.0 * (z1.0 * z3.0)*)
|
|
neuper@37906
|
1063 |
Thm ("real_mult_assoc",num_str real_mult_assoc),
|
|
neuper@37906
|
1064 |
(*z1.0 * z2.0 * z3.0 = z1.0 * (z2.0 * z3.0)*)
|
|
neuper@37906
|
1065 |
Thm ("real_add_commute",num_str real_add_commute),
|
|
neuper@37906
|
1066 |
(*z + w = w + z*)
|
|
neuper@37906
|
1067 |
Thm ("real_add_left_commute",num_str real_add_left_commute),
|
|
neuper@37906
|
1068 |
(*x + (y + z) = y + (x + z)*)
|
|
neuper@37906
|
1069 |
Thm ("real_add_assoc",num_str real_add_assoc)
|
|
neuper@37906
|
1070 |
(*z1.0 + z2.0 + z3.0 = z1.0 + (z2.0 + z3.0)*)
|
|
neuper@37906
|
1071 |
], scr = EmptyScr}:rls);
|
|
neuper@37906
|
1072 |
|
|
neuper@37906
|
1073 |
val collect_bdv = prep_rls(
|
|
neuper@37906
|
1074 |
Rls{id = "collect_bdv", preconds = [],
|
|
neuper@37906
|
1075 |
rew_ord = ("dummy_ord", dummy_ord),
|
|
neuper@37906
|
1076 |
erls = e_rls,srls = Erls,
|
|
neuper@37906
|
1077 |
calc = [],
|
|
neuper@37906
|
1078 |
(*asm_thm = [],*)
|
|
neuper@37906
|
1079 |
rules = [Thm ("bdv_collect_1",num_str bdv_collect_1),
|
|
neuper@37906
|
1080 |
Thm ("bdv_collect_2",num_str bdv_collect_2),
|
|
neuper@37906
|
1081 |
Thm ("bdv_collect_3",num_str bdv_collect_3),
|
|
neuper@37906
|
1082 |
|
|
neuper@37906
|
1083 |
Thm ("bdv_collect_assoc1_1",num_str bdv_collect_assoc1_1),
|
|
neuper@37906
|
1084 |
Thm ("bdv_collect_assoc1_2",num_str bdv_collect_assoc1_2),
|
|
neuper@37906
|
1085 |
Thm ("bdv_collect_assoc1_3",num_str bdv_collect_assoc1_3),
|
|
neuper@37906
|
1086 |
|
|
neuper@37906
|
1087 |
Thm ("bdv_collect_assoc2_1",num_str bdv_collect_assoc2_1),
|
|
neuper@37906
|
1088 |
Thm ("bdv_collect_assoc2_2",num_str bdv_collect_assoc2_2),
|
|
neuper@37906
|
1089 |
Thm ("bdv_collect_assoc2_3",num_str bdv_collect_assoc2_3),
|
|
neuper@37906
|
1090 |
|
|
neuper@37906
|
1091 |
|
|
neuper@37906
|
1092 |
Thm ("bdv_n_collect_1",num_str bdv_n_collect_1),
|
|
neuper@37906
|
1093 |
Thm ("bdv_n_collect_2",num_str bdv_n_collect_2),
|
|
neuper@37906
|
1094 |
Thm ("bdv_n_collect_3",num_str bdv_n_collect_3),
|
|
neuper@37906
|
1095 |
|
|
neuper@37906
|
1096 |
Thm ("bdv_n_collect_assoc1_1",num_str bdv_n_collect_assoc1_1),
|
|
neuper@37906
|
1097 |
Thm ("bdv_n_collect_assoc1_2",num_str bdv_n_collect_assoc1_2),
|
|
neuper@37906
|
1098 |
Thm ("bdv_n_collect_assoc1_3",num_str bdv_n_collect_assoc1_3),
|
|
neuper@37906
|
1099 |
|
|
neuper@37906
|
1100 |
Thm ("bdv_n_collect_assoc2_1",num_str bdv_n_collect_assoc2_1),
|
|
neuper@37906
|
1101 |
Thm ("bdv_n_collect_assoc2_2",num_str bdv_n_collect_assoc2_2),
|
|
neuper@37906
|
1102 |
Thm ("bdv_n_collect_assoc2_3",num_str bdv_n_collect_assoc2_3)
|
|
neuper@37906
|
1103 |
], scr = EmptyScr}:rls);
|
|
neuper@37906
|
1104 |
|
|
neuper@37906
|
1105 |
(*.transforms an arbitrary term without roots to a polynomial [4]
|
|
neuper@37906
|
1106 |
according to knowledge/Poly.sml.*)
|
|
neuper@37906
|
1107 |
val make_polynomial_in = prep_rls(
|
|
neuper@37906
|
1108 |
Seq {id = "make_polynomial_in", preconds = []:term list,
|
|
neuper@37906
|
1109 |
rew_ord = ("dummy_ord", dummy_ord),
|
|
neuper@37906
|
1110 |
erls = Atools_erls, srls = Erls,
|
|
neuper@37906
|
1111 |
calc = [], (*asm_thm = [],*)
|
|
neuper@37906
|
1112 |
rules = [Rls_ expand_poly,
|
|
neuper@37906
|
1113 |
Rls_ order_add_mult_in,
|
|
neuper@37906
|
1114 |
Rls_ simplify_power,
|
|
neuper@37906
|
1115 |
Rls_ collect_numerals,
|
|
neuper@37906
|
1116 |
Rls_ reduce_012,
|
|
neuper@37906
|
1117 |
Thm ("realpow_oneI",num_str realpow_oneI),
|
|
neuper@37906
|
1118 |
Rls_ discard_parentheses,
|
|
neuper@37906
|
1119 |
Rls_ collect_bdv
|
|
neuper@37906
|
1120 |
],
|
|
neuper@37906
|
1121 |
scr = EmptyScr
|
|
neuper@37906
|
1122 |
}:rls);
|
|
neuper@37906
|
1123 |
|
|
neuper@37906
|
1124 |
val separate_bdvs =
|
|
neuper@37906
|
1125 |
append_rls "separate_bdvs"
|
|
neuper@37906
|
1126 |
collect_bdv
|
|
neuper@37906
|
1127 |
[Thm ("separate_bdv", num_str separate_bdv),
|
|
neuper@37906
|
1128 |
(*"?a * ?bdv / ?b = ?a / ?b * ?bdv"*)
|
|
neuper@37906
|
1129 |
Thm ("separate_bdv_n", num_str separate_bdv_n),
|
|
neuper@37906
|
1130 |
Thm ("separate_1_bdv", num_str separate_1_bdv),
|
|
neuper@37906
|
1131 |
(*"?bdv / ?b = (1 / ?b) * ?bdv"*)
|
|
neuper@37906
|
1132 |
Thm ("separate_1_bdv_n", num_str separate_1_bdv_n),
|
|
neuper@37906
|
1133 |
(*"?bdv ^^^ ?n / ?b = 1 / ?b * ?bdv ^^^ ?n"*)
|
|
neuper@37906
|
1134 |
Thm ("real_add_divide_distrib",
|
|
neuper@37906
|
1135 |
num_str real_add_divide_distrib)
|
|
neuper@37906
|
1136 |
(*"(?x + ?y) / ?z = ?x / ?z + ?y / ?z"
|
|
neuper@37906
|
1137 |
WN051031 DOES NOT BELONG TO HERE*)
|
|
neuper@37906
|
1138 |
];
|
|
neuper@37906
|
1139 |
val make_ratpoly_in = prep_rls(
|
|
neuper@37906
|
1140 |
Seq {id = "make_ratpoly_in", preconds = []:term list,
|
|
neuper@37906
|
1141 |
rew_ord = ("dummy_ord", dummy_ord),
|
|
neuper@37906
|
1142 |
erls = Atools_erls, srls = Erls,
|
|
neuper@37906
|
1143 |
calc = [], (*asm_thm = [],*)
|
|
neuper@37906
|
1144 |
rules = [Rls_ norm_Rational,
|
|
neuper@37906
|
1145 |
Rls_ order_add_mult_in,
|
|
neuper@37906
|
1146 |
Rls_ discard_parentheses,
|
|
neuper@37906
|
1147 |
Rls_ separate_bdvs,
|
|
neuper@37906
|
1148 |
(* Rls_ rearrange_assoc, WN060916 why does cancel_p not work?*)
|
|
neuper@37906
|
1149 |
Rls_ cancel_p
|
|
neuper@37906
|
1150 |
(*Calc ("HOL.divide" ,eval_cancel "#divide_") too weak!*)
|
|
neuper@37906
|
1151 |
],
|
|
neuper@37906
|
1152 |
scr = EmptyScr}:rls);
|
|
neuper@37906
|
1153 |
|
|
neuper@37906
|
1154 |
|
|
neuper@37906
|
1155 |
ruleset' := overwritelthy thy (!ruleset',
|
|
neuper@37906
|
1156 |
[("order_add_mult_in", order_add_mult_in),
|
|
neuper@37906
|
1157 |
("collect_bdv", collect_bdv),
|
|
neuper@37906
|
1158 |
("make_polynomial_in", make_polynomial_in),
|
|
neuper@37906
|
1159 |
("make_ratpoly_in", make_ratpoly_in),
|
|
neuper@37906
|
1160 |
("separate_bdvs", separate_bdvs)
|
|
neuper@37906
|
1161 |
]);
|
|
neuper@37906
|
1162 |
|