wneuper/isa: comparison src/Tools/isac/Knowledge/PolyEq.ML

equal deleted inserted replaced

-:2c10fce11472
+:9ddd1000b900
 *)
 "******* PolyEq.ML begin *******";
 theory' := overwritel (!theory', [("PolyEq.thy",PolyEq.thy)]);
 (*-------------------------functions---------------------*)
-(* just for try
-local
-fun add0 l d d_  = if (d_+1) < d then  add0 (str2term"0"::l) d (d_+1) else l;
-fun poly2list_ (t as (Const ("op +",_) $ t1 $ (Const ("Atools.pow",_) $ v_ $ Free (d_,_)))) v l d =
-	    if (v=v_)
-	    then poly2list_ t1 v (((str2term("1")))::(add0 l d (int_of_str' d_))) (int_of_str' d_)
-	    else  t::(add0 l d 0)
-| poly2list_ (t as (Const ("op +",_) $ t1 $ (Const ("op *",_) $ t11 $
-(Const ("Atools.pow",_) $ v_ $ Free (d_,_))))) v l d =
-	    if (v=v_)
-	    then poly2list_ t1 v (((t11))::(add0 l d (int_of_str' d_))) (int_of_str' d_)
-	    else  t::(add0 l d 0)
-| poly2list_ (t as (Const ("op +",_) $ t1 $ (Free (v_ , _)) )) v l d =
-	    if (v = (str2term v_))
-	    then poly2list_ t1 v (((str2term("1")))::(add0 l d 1 )) 1
-	    else  t::(add0 l d 0)
-| poly2list_ (t as (Const ("op +",_) $ t1 $ (Const ("op *",_) $ t11 $ (Free (v_,_)) ))) v l d =
-	    if (v= (str2term v_))
-	    then poly2list_ t1 v ( (t11)::(add0 l d 1 )) 1
-	    else  t::(add0 l d 0)
-| poly2list_ (t as (Const ("op +",_) $ _ $ _))_ l d = t::(add0 l d 0)
-| poly2list_ (t as (Free (_,_))) _ l d  =  t::(add0 l d 0)
-| poly2list_ t _ l d  = t::(add0 l d 0);
-fun poly2list t v = poly2list_ t v [] 0;
-fun diffpolylist_ [] _ = []
-| diffpolylist_ (x::xs) d =  (str2term (if term2str(x)="0"
-					      then "0"
-					      else term2str(x)^"*"^str_of_int(d)))::diffpolylist_ xs (d+1);
-fun diffpolylist [] = []
-| diffpolylist (x::xs) = diffpolylist_ xs 1;
-	(* diffpolylist(poly2list (str2term "1+ x +3*x^^^3") (str2term "x"));*)
-in
-end;
-*)
 (*-------------------------rulse-------------------------*)
 val PolyEq_prls = (*3.10.02:just the following order due to subterm evaluation*)
 append_rls "PolyEq_prls" e_rls
 	     [Calc ("Atools.ident",eval_ident "#ident_"),
 	      Calc ("Tools.matches",eval_matches ""),
 		 Thm ("minus_leq", num_str minus_leq),
 		 Thm ("rat_leq1", num_str rat_leq1),
 		 Thm ("rat_leq2", num_str rat_leq2),
 		 Thm ("rat_leq3", num_str rat_leq3)
 		 ]);
-(*------
-val PolyEq_erls =
-merge_rls "PolyEq_erls"
-	      (append_rls "" (Rls {(*asm_thm=[],*)calc=[],
-				   erls= Rls {(*asm_thm=[],*)calc=[],
-					      erls= Erls,
-					      id="e_rls",preconds=[],
-					      rew_ord=("dummy_ord",dummy_ord),
-					      rules=[Thm ("",
-							  num_str ),
-						     Thm ("",
-							  num_str ),
-						     Thm ("",
-							  num_str )
-						     ],
-					      scr=EmptyScr,srls=Erls},
-				   id="e_rls",preconds=[],rew_ord=("dummy_ord",
-								   dummy_ord),
-				   rules=[],scr=EmptyScr,srls=Erls}
-			      )
-			  ((#rules o rep_rls) LinEq_erls))
-	      (append_rls "ops_preds" calculate_Rational
-			  [Calc ("op =",eval_equal "#equal_"),
-			   Thm ("plus_leq", num_str plus_leq),
-			   Thm ("minus_leq", num_str minus_leq),
-			   Thm ("rat_leq1", num_str rat_leq1),
-			   Thm ("rat_leq2", num_str rat_leq2),
-			   Thm ("rat_leq3", num_str rat_leq3)
-			   ]);
------*)
 val cancel_leading_coeff = prep_rls(
 Rls {id = "cancel_leading_coeff", preconds = [],
 rew_ord = ("e_rew_ord",e_rew_ord),
 erls = PolyEq_erls, srls = Erls, calc = [], (*asm_thm = [],*)
 	       Thm ("cancel_leading_coeff13",num_str cancel_leading_coeff13)
 	       ],
 scr = Script ((term_of o the o (parse thy))
 "empty_script")
 }:rls);
 val complete_square = prep_rls(
 Rls {id = "complete_square", preconds = [],
 rew_ord = ("e_rew_ord",e_rew_ord),
 erls = PolyEq_erls, srls = Erls, calc = [], (*asm_thm = [],*)
 rules = [Thm ("complete_square1",num_str complete_square1),
 	       Thm ("complete_square5",num_str complete_square5)
 	       ],
 scr = Script ((term_of o the o (parse thy))
 "empty_script")
 }:rls);
-ruleset' := overwritelthy thy (!ruleset',
-			[("cancel_leading_coeff",cancel_leading_coeff),
-			 ("complete_square",complete_square),
-			 ("PolyEq_erls",PolyEq_erls)(*FIXXXME:del with rls.rls'*)
-			 ]);
 val polyeq_simplify = prep_rls(
 Rls {id = "polyeq_simplify", preconds = [],
 rew_ord = ("termlessI",termlessI),
 erls = PolyEq_erls,
 srls = Erls,
 		Calc ("Atools.pow" ,eval_binop "#power_"),
 Rls_ reduce_012
 ],
 scr = Script ((term_of o the o (parse thy)) "empty_script")
 }:rls);
 ruleset' := overwritelthy thy (!ruleset',
-			  [("polyeq_simplify",polyeq_simplify)]);
+		[("cancel_leading_coeff",cancel_leading_coeff),
+		 ("complete_square",complete_square),
+		 ("PolyEq_erls",PolyEq_erls),(*FIXXXME:del with rls.rls'*)
+		 ("polyeq_simplify",polyeq_simplify)]);
 (* ------------- polySolve ------------------ *)
 (* -- d0 -- *)
 (*isolate the bound variable in an d0 equation; 'bdv' is a meta-constant*)
 rules = [Thm("d0_true",num_str d0_true),
 		Thm("d0_false",num_str d0_false)
 		],
 scr = Script ((term_of o the o (parse thy)) "empty_script")
 }:rls);
 (* -- d1 -- *)
 (*isolate the bound variable in an d1 equation; 'bdv' is a meta-constant*)
 val d1_polyeq_simplify = prep_rls(
 Rls {id = "d1_polyeq_simplify", preconds = [],
 rew_ord = ("e_rew_ord",e_rew_ord),
 		Thm("d1_isolate_div",num_str d1_isolate_div)
 		(*   bx=c -> x=c/b *)
 		],
 scr = Script ((term_of o the o (parse thy)) "empty_script")
 }:rls);
 (* -- d2 -- *)
-(*isolate the bound variable in an d2 equation with bdv only; 'bdv' is a meta-constant*)
+(* isolate the bound variable in an d2 equation with bdv only;
+'bdv' is a meta-constant*)
 val d2_polyeq_bdv_only_simplify = prep_rls(
 Rls {id = "d2_polyeq_bdv_only_simplify", preconds = [],
 rew_ord = ("e_rew_ord",e_rew_ord),
 erls = PolyEq_erls,
 srls = Erls,
 calc = [],
 (*asm_thm = [("d2_sqrt_equation1",""),("d2_sqrt_equation1_neg",""),
 ("d2_isolate_div","")],*)
-rules = [
+rules = [Thm("d2_prescind1",num_str d2_prescind1),
-		Thm("d2_prescind1",num_str d2_prescind1),              (*   ax+bx^2=0 -> x(a+bx)=0 *)
+(*   ax+bx^2=0 -> x(a+bx)=0 *)
-		Thm("d2_prescind2",num_str d2_prescind2),              (*   ax+ x^2=0 -> x(a+ x)=0 *)
+		Thm("d2_prescind2",num_str d2_prescind2),
-		Thm("d2_prescind3",num_str d2_prescind3),              (*    x+bx^2=0 -> x(1+bx)=0 *)
+(*   ax+ x^2=0 -> x(a+ x)=0 *)
-		Thm("d2_prescind4",num_str d2_prescind4),              (*    x+ x^2=0 -> x(1+ x)=0 *)
+		Thm("d2_prescind3",num_str d2_prescind3),
-		Thm("d2_sqrt_equation1",num_str d2_sqrt_equation1),       (* x^2=c   -> x=+-sqrt(c)*)
+(*    x+bx^2=0 -> x(1+bx)=0 *)
-		Thm("d2_sqrt_equation1_neg",num_str d2_sqrt_equation1_neg),  (* [0<c] x^2=c  -> [] *)
+		Thm("d2_prescind4",num_str d2_prescind4),
-		Thm("d2_sqrt_equation2",num_str d2_sqrt_equation2),         (*  x^2=0 ->    x=0    *)
+(*    x+ x^2=0 -> x(1+ x)=0 *)
-		Thm("d2_reduce_equation1",num_str d2_reduce_equation1),(* x(a+bx)=0 -> x=0 | a+bx=0*)
+		Thm("d2_sqrt_equation1",num_str d2_sqrt_equation1),
-		Thm("d2_reduce_equation2",num_str d2_reduce_equation2),(* x(a+ x)=0 -> x=0 | a+ x=0*)
+(* x^2=c   -> x=+-sqrt(c)*)
-		Thm("d2_isolate_div",num_str d2_isolate_div)                   (* bx^2=c -> x^2=c/b*)
+		Thm("d2_sqrt_equation1_neg",num_str d2_sqrt_equation1_neg),
+(* [0<c] x^2=c  -> [] *)
+		Thm("d2_sqrt_equation2",num_str d2_sqrt_equation2),
+(*  x^2=0 ->    x=0    *)
+		Thm("d2_reduce_equation1",num_str d2_reduce_equation1),
+(* x(a+bx)=0 -> x=0 | a+bx=0*)
+		Thm("d2_reduce_equation2",num_str d2_reduce_equation2),
+(* x(a+ x)=0 -> x=0 | a+ x=0*)
+		Thm("d2_isolate_div",num_str d2_isolate_div)
+(* bx^2=c -> x^2=c/b*)
 		],
 scr = Script ((term_of o the o (parse thy)) "empty_script")
 }:rls);
-(*isolate the bound variable in an d2 equation with sqrt only; 'bdv' is a meta-constant*)
+(* isolate the bound variable in an d2 equation with sqrt only;
+'bdv' is a meta-constant*)
 val d2_polyeq_sq_only_simplify = prep_rls(
 Rls {id = "d2_polyeq_sq_only_simplify", preconds = [],
 rew_ord = ("e_rew_ord",e_rew_ord),
 erls = PolyEq_erls,
 srls = Erls,
 calc = [],
 (*asm_thm = [("d2_sqrt_equation1",""),("d2_sqrt_equation1_neg",""),
 ("d2_isolate_div","")],*)
-rules = [
+rules = [Thm("d2_isolate_add1",num_str d2_isolate_add1),
-		Thm("d2_isolate_add1",num_str d2_isolate_add1),        (* a+   bx^2=0 -> bx^2=(-1)a*)
+(* a+   bx^2=0 -> bx^2=(-1)a*)
-		Thm("d2_isolate_add2",num_str d2_isolate_add2),        (* a+    x^2=0 ->  x^2=(-1)a*)
+		Thm("d2_isolate_add2",num_str d2_isolate_add2),
-		Thm("d2_sqrt_equation2",num_str d2_sqrt_equation2),         (*  x^2=0 ->    x=0    *)
+(* a+    x^2=0 ->  x^2=(-1)a*)
-		Thm("d2_sqrt_equation1",num_str d2_sqrt_equation1),       (* x^2=c   -> x=+-sqrt(c)*)
+		Thm("d2_sqrt_equation2",num_str d2_sqrt_equation2),
-		Thm("d2_sqrt_equation1_neg",num_str d2_sqrt_equation1_neg),(* [c<0] x^2=c  -> x=[] *)
+(*  x^2=0 ->    x=0    *)
-		Thm("d2_isolate_div",num_str d2_isolate_div)                   (* bx^2=c -> x^2=c/b*)
+		Thm("d2_sqrt_equation1",num_str d2_sqrt_equation1),
+(* x^2=c   -> x=+-sqrt(c)*)
+		Thm("d2_sqrt_equation1_neg",num_str d2_sqrt_equation1_neg),
+(* [c<0] x^2=c  -> x=[] *)
+		Thm("d2_isolate_div",num_str d2_isolate_div)
+(* bx^2=c -> x^2=c/b*)
 		],
 scr = Script ((term_of o the o (parse thy)) "empty_script")
 }:rls);
-(*isolate the bound variable in an d2 equation with pqFormula; 'bdv' is a meta-constant*)
+(* isolate the bound variable in an d2 equation with pqFormula;
+'bdv' is a meta-constant*)
 val d2_polyeq_pqFormula_simplify = prep_rls(
 Rls {id = "d2_polyeq_pqFormula_simplify", preconds = [],
-rew_ord = ("e_rew_ord",e_rew_ord),
+rew_ord = ("e_rew_ord",e_rew_ord), erls = PolyEq_erls,
-erls = PolyEq_erls,
+srls = Erls, calc = [],
-srls = Erls,
+rules = [Thm("d2_pqformula1",num_str d2_pqformula1),
-calc = [],
+(* q+px+ x^2=0 *)
-(*asm_thm = [("d2_pqformula1",""),("d2_pqformula2",""),("d2_pqformula3",""),("d2_pqformula4",""),
+		Thm("d2_pqformula1_neg",num_str d2_pqformula1_neg),
-("d2_pqformula5",""),("d2_pqformula6",""),("d2_pqformula7",""),("d2_pqformula8",""),
+(* q+px+ x^2=0 *)
-("d2_pqformula9",""),("d2_pqformula10",""),
+		Thm("d2_pqformula2",num_str d2_pqformula2),
-("d2_pqformula1_neg",""),("d2_pqformula2_neg",""),("d2_pqformula3_neg",""),
+(* q+px+1x^2=0 *)
-("d2_pqformula4_neg",""),("d2_pqformula9_neg",""),("d2_pqformula10_neg","")],*)
+		Thm("d2_pqformula2_neg",num_str d2_pqformula2_neg),
-rules = [
+(* q+px+1x^2=0 *)
-		Thm("d2_pqformula1",num_str d2_pqformula1),                         (* q+px+ x^2=0 *)
+		Thm("d2_pqformula3",num_str d2_pqformula3),
-		Thm("d2_pqformula1_neg",num_str d2_pqformula1_neg),                 (* q+px+ x^2=0 *)
+(* q+ x+ x^2=0 *)
-		Thm("d2_pqformula2",num_str d2_pqformula2),                         (* q+px+1x^2=0 *)
+		Thm("d2_pqformula3_neg",num_str d2_pqformula3_neg),
-		Thm("d2_pqformula2_neg",num_str d2_pqformula2_neg),                 (* q+px+1x^2=0 *)
+(* q+ x+ x^2=0 *)
-		Thm("d2_pqformula3",num_str d2_pqformula3),                         (* q+ x+ x^2=0 *)
+		Thm("d2_pqformula4",num_str d2_pqformula4),
-		Thm("d2_pqformula3_neg",num_str d2_pqformula3_neg),                 (* q+ x+ x^2=0 *)
+(* q+ x+1x^2=0 *)
-		Thm("d2_pqformula4",num_str d2_pqformula4),                         (* q+ x+1x^2=0 *)
+		Thm("d2_pqformula4_neg",num_str d2_pqformula4_neg),
-		Thm("d2_pqformula4_neg",num_str d2_pqformula4_neg),                 (* q+ x+1x^2=0 *)
+(* q+ x+1x^2=0 *)
-		Thm("d2_pqformula5",num_str d2_pqformula5),                         (*   qx+ x^2=0 *)
+		Thm("d2_pqformula5",num_str d2_pqformula5),
-		Thm("d2_pqformula6",num_str d2_pqformula6),                         (*   qx+1x^2=0 *)
+(*   qx+ x^2=0 *)
-		Thm("d2_pqformula7",num_str d2_pqformula7),                         (*    x+ x^2=0 *)
+		Thm("d2_pqformula6",num_str d2_pqformula6),
-		Thm("d2_pqformula8",num_str d2_pqformula8),                         (*    x+1x^2=0 *)
+(*   qx+1x^2=0 *)
-		Thm("d2_pqformula9",num_str d2_pqformula9),                         (* q   +1x^2=0 *)
+		Thm("d2_pqformula7",num_str d2_pqformula7),
-		Thm("d2_pqformula9_neg",num_str d2_pqformula9_neg),                 (* q   +1x^2=0 *)
+(*    x+ x^2=0 *)
-		Thm("d2_pqformula10",num_str d2_pqformula10),                       (* q   + x^2=0 *)
+		Thm("d2_pqformula8",num_str d2_pqformula8),
-		Thm("d2_pqformula10_neg",num_str d2_pqformula10_neg),               (* q   + x^2=0 *)
+(*    x+1x^2=0 *)
-		Thm("d2_sqrt_equation2",num_str d2_sqrt_equation2),                 (*       x^2=0 *)
+		Thm("d2_pqformula9",num_str d2_pqformula9),
-		Thm("d2_sqrt_equation3",num_str d2_sqrt_equation3)                  (*      1x^2=0 *)
+(* q   +1x^2=0 *)
-		],
+		Thm("d2_pqformula9_neg",num_str d2_pqformula9_neg),
+(* q   +1x^2=0 *)
+		Thm("d2_pqformula10",num_str d2_pqformula10),
+(* q   + x^2=0 *)
+		Thm("d2_pqformula10_neg",num_str d2_pqformula10_neg),
+(* q   + x^2=0 *)
+		Thm("d2_sqrt_equation2",num_str d2_sqrt_equation2),
+(*       x^2=0 *)
+		Thm("d2_sqrt_equation3",num_str d2_sqrt_equation3)
+(*      1x^2=0 *)
+	       ],
 scr = Script ((term_of o the o (parse thy)) "empty_script")
 }:rls);
-(*isolate the bound variable in an d2 equation with abcFormula; 'bdv' is a meta-constant*)
+(* isolate the bound variable in an d2 equation with abcFormula;
+'bdv' is a meta-constant*)
 val d2_polyeq_abcFormula_simplify = prep_rls(
 Rls {id = "d2_polyeq_abcFormula_simplify", preconds = [],
-rew_ord = ("e_rew_ord",e_rew_ord),
+rew_ord = ("e_rew_ord",e_rew_ord), erls = PolyEq_erls,
-erls = PolyEq_erls,
+srls = Erls, calc = [],
-srls = Erls,
+rules = [Thm("d2_abcformula1",num_str d2_abcformula1),
-calc = [],
+(*c+bx+cx^2=0 *)
-(*asm_thm = [("d2_abcformula1",""),("d2_abcformula2",""),("d2_abcformula3",""),
+		Thm("d2_abcformula1_neg",num_str d2_abcformula1_neg),
-("d2_abcformula4",""),("d2_abcformula5",""),("d2_abcformula6",""),
+(*c+bx+cx^2=0 *)
-("d2_abcformula7",""),("d2_abcformula8",""),("d2_abcformula9",""),
+		Thm("d2_abcformula2",num_str d2_abcformula2),
-("d2_abcformula10",""),("d2_abcformula1_neg",""),("d2_abcformula2_neg",""),
+(*c+ x+cx^2=0 *)
-("d2_abcformula3_neg",""),("d2_abcformula4_neg",""),("d2_abcformula5_neg",""),
+		Thm("d2_abcformula2_neg",num_str d2_abcformula2_neg),
-("d2_abcformula6_neg","")],*)
+(*c+ x+cx^2=0 *)
-rules = [
+		Thm("d2_abcformula3",num_str d2_abcformula3),
-		Thm("d2_abcformula1",num_str d2_abcformula1),                        (*c+bx+cx^2=0 *)
+(*c+bx+ x^2=0 *)
-		Thm("d2_abcformula1_neg",num_str d2_abcformula1_neg),                (*c+bx+cx^2=0 *)
+		Thm("d2_abcformula3_neg",num_str d2_abcformula3_neg),
-		Thm("d2_abcformula2",num_str d2_abcformula2),                        (*c+ x+cx^2=0 *)
+(*c+bx+ x^2=0 *)
-		Thm("d2_abcformula2_neg",num_str d2_abcformula2_neg),                (*c+ x+cx^2=0 *)
+		Thm("d2_abcformula4",num_str d2_abcformula4),
-		Thm("d2_abcformula3",num_str d2_abcformula3),                        (*c+bx+ x^2=0 *)
+(*c+ x+ x^2=0 *)
-		Thm("d2_abcformula3_neg",num_str d2_abcformula3_neg),                (*c+bx+ x^2=0 *)
+		Thm("d2_abcformula4_neg",num_str d2_abcformula4_neg),
-		Thm("d2_abcformula4",num_str d2_abcformula4),                        (*c+ x+ x^2=0 *)
+(*c+ x+ x^2=0 *)
-		Thm("d2_abcformula4_neg",num_str d2_abcformula4_neg),                (*c+ x+ x^2=0 *)
+		Thm("d2_abcformula5",num_str d2_abcformula5),
-		Thm("d2_abcformula5",num_str d2_abcformula5),                        (*c+   cx^2=0 *)
+(*c+   cx^2=0 *)
-		Thm("d2_abcformula5_neg",num_str d2_abcformula5_neg),                (*c+   cx^2=0 *)
+		Thm("d2_abcformula5_neg",num_str d2_abcformula5_neg),
-		Thm("d2_abcformula6",num_str d2_abcformula6),                        (*c+    x^2=0 *)
+(*c+   cx^2=0 *)
-		Thm("d2_abcformula6_neg",num_str d2_abcformula6_neg),                (*c+    x^2=0 *)
+		Thm("d2_abcformula6",num_str d2_abcformula6),
-		Thm("d2_abcformula7",num_str d2_abcformula7),                        (*  bx+ax^2=0 *)
+(*c+    x^2=0 *)
-		Thm("d2_abcformula8",num_str d2_abcformula8),                        (*  bx+ x^2=0 *)
+		Thm("d2_abcformula6_neg",num_str d2_abcformula6_neg),
-		Thm("d2_abcformula9",num_str d2_abcformula9),                        (*   x+ax^2=0 *)
+(*c+    x^2=0 *)
-		Thm("d2_abcformula10",num_str d2_abcformula10),                      (*   x+ x^2=0 *)
+		Thm("d2_abcformula7",num_str d2_abcformula7),
-		Thm("d2_sqrt_equation2",num_str d2_sqrt_equation2),                  (*      x^2=0 *)
+(*  bx+ax^2=0 *)
-		Thm("d2_sqrt_equation3",num_str d2_sqrt_equation3)                   (*     bx^2=0 *)
+		Thm("d2_abcformula8",num_str d2_abcformula8),
-		],
+(*  bx+ x^2=0 *)
+		Thm("d2_abcformula9",num_str d2_abcformula9),
+(*   x+ax^2=0 *)
+		Thm("d2_abcformula10",num_str d2_abcformula10),
+(*   x+ x^2=0 *)
+		Thm("d2_sqrt_equation2",num_str d2_sqrt_equation2),
+(*      x^2=0 *)
+		Thm("d2_sqrt_equation3",num_str d2_sqrt_equation3)
+(*     bx^2=0 *)
+	       ],
 scr = Script ((term_of o the o (parse thy)) "empty_script")
 }:rls);
-(*isolate the bound variable in an d2 equation; 'bdv' is a meta-constant*)
+(* isolate the bound variable in an d2 equation;
+'bdv' is a meta-constant*)
 val d2_polyeq_simplify = prep_rls(
 Rls {id = "d2_polyeq_simplify", preconds = [],
-rew_ord = ("e_rew_ord",e_rew_ord),
+rew_ord = ("e_rew_ord",e_rew_ord), erls = PolyEq_erls,
-erls = PolyEq_erls,
+srls = Erls, calc = [],
-srls = Erls,
+rules = [Thm("d2_pqformula1",num_str d2_pqformula1),
-calc = [],
+(* p+qx+ x^2=0 *)
-(*asm_thm = [("d2_pqformula1",""),("d2_pqformula2",""),("d2_pqformula3",""),("d2_pqformula4",""),
+		Thm("d2_pqformula1_neg",num_str d2_pqformula1_neg),
-("d2_pqformula1_neg",""),("d2_pqformula2_neg",""),("d2_pqformula3_neg",""),
+(* p+qx+ x^2=0 *)
-("d2_pqformula4_neg",""),
+		Thm("d2_pqformula2",num_str d2_pqformula2),
-("d2_abcformula1",""),("d2_abcformula2",""),("d2_abcformula1_neg",""),
+(* p+qx+1x^2=0 *)
-("d2_abcformula2_neg",""), ("d2_sqrt_equation1",""),
+		Thm("d2_pqformula2_neg",num_str d2_pqformula2_neg),
-("d2_sqrt_equation1_neg",""),("d2_isolate_div","")],*)
+(* p+qx+1x^2=0 *)
-rules = [
+		Thm("d2_pqformula3",num_str d2_pqformula3),
-		Thm("d2_pqformula1",num_str d2_pqformula1),                         (* p+qx+ x^2=0 *)
+(* p+ x+ x^2=0 *)
-		Thm("d2_pqformula1_neg",num_str d2_pqformula1_neg),                 (* p+qx+ x^2=0 *)
+		Thm("d2_pqformula3_neg",num_str d2_pqformula3_neg),
-		Thm("d2_pqformula2",num_str d2_pqformula2),                         (* p+qx+1x^2=0 *)
+(* p+ x+ x^2=0 *)
-		Thm("d2_pqformula2_neg",num_str d2_pqformula2_neg),                 (* p+qx+1x^2=0 *)
+		Thm("d2_pqformula4",num_str d2_pqformula4),
-		Thm("d2_pqformula3",num_str d2_pqformula3),                         (* p+ x+ x^2=0 *)
+(* p+ x+1x^2=0 *)
-		Thm("d2_pqformula3_neg",num_str d2_pqformula3_neg),                 (* p+ x+ x^2=0 *)
+		Thm("d2_pqformula4_neg",num_str d2_pqformula4_neg),
-		Thm("d2_pqformula4",num_str d2_pqformula4),                         (* p+ x+1x^2=0 *)
+(* p+ x+1x^2=0 *)
-		Thm("d2_pqformula4_neg",num_str d2_pqformula4_neg),                 (* p+ x+1x^2=0 *)
+		Thm("d2_abcformula1",num_str d2_abcformula1),
-		Thm("d2_abcformula1",num_str d2_abcformula1),                       (* c+bx+cx^2=0 *)
+(* c+bx+cx^2=0 *)
-		Thm("d2_abcformula1_neg",num_str d2_abcformula1_neg),               (* c+bx+cx^2=0 *)
+		Thm("d2_abcformula1_neg",num_str d2_abcformula1_neg),
-		Thm("d2_abcformula2",num_str d2_abcformula2),                       (* c+ x+cx^2=0 *)
+(* c+bx+cx^2=0 *)
-		Thm("d2_abcformula2_neg",num_str d2_abcformula2_neg),               (* c+ x+cx^2=0 *)
+		Thm("d2_abcformula2",num_str d2_abcformula2),
-		Thm("d2_prescind1",num_str d2_prescind1),              (*   ax+bx^2=0 -> x(a+bx)=0 *)
+(* c+ x+cx^2=0 *)
-		Thm("d2_prescind2",num_str d2_prescind2),              (*   ax+ x^2=0 -> x(a+ x)=0 *)
+		Thm("d2_abcformula2_neg",num_str d2_abcformula2_neg),
-		Thm("d2_prescind3",num_str d2_prescind3),              (*    x+bx^2=0 -> x(1+bx)=0 *)
+(* c+ x+cx^2=0 *)
-		Thm("d2_prescind4",num_str d2_prescind4),              (*    x+ x^2=0 -> x(1+ x)=0 *)
+		Thm("d2_prescind1",num_str d2_prescind1),
-		Thm("d2_isolate_add1",num_str d2_isolate_add1),        (* a+   bx^2=0 -> bx^2=(-1)a*)
+(*   ax+bx^2=0 -> x(a+bx)=0 *)
-		Thm("d2_isolate_add2",num_str d2_isolate_add2),        (* a+    x^2=0 ->  x^2=(-1)a*)
+		Thm("d2_prescind2",num_str d2_prescind2),
-		Thm("d2_sqrt_equation1",num_str d2_sqrt_equation1),       (* x^2=c   -> x=+-sqrt(c)*)
+(*   ax+ x^2=0 -> x(a+ x)=0 *)
-		Thm("d2_sqrt_equation1_neg",num_str d2_sqrt_equation1_neg),(* [c<0] x^2=c   -> x=[]*)
+		Thm("d2_prescind3",num_str d2_prescind3),
-		Thm("d2_sqrt_equation2",num_str d2_sqrt_equation2),         (*  x^2=0 ->    x=0    *)
+(*    x+bx^2=0 -> x(1+bx)=0 *)
-		Thm("d2_reduce_equation1",num_str d2_reduce_equation1),(* x(a+bx)=0 -> x=0 | a+bx=0*)
+		Thm("d2_prescind4",num_str d2_prescind4),
-		Thm("d2_reduce_equation2",num_str d2_reduce_equation2),(* x(a+ x)=0 -> x=0 | a+ x=0*)
+(*    x+ x^2=0 -> x(1+ x)=0 *)
-		Thm("d2_isolate_div",num_str d2_isolate_div)                   (* bx^2=c -> x^2=c/b*)
+		Thm("d2_isolate_add1",num_str d2_isolate_add1),
-		],
+(* a+   bx^2=0 -> bx^2=(-1)a*)
+		Thm("d2_isolate_add2",num_str d2_isolate_add2),
+(* a+    x^2=0 ->  x^2=(-1)a*)
+		Thm("d2_sqrt_equation1",num_str d2_sqrt_equation1),
+(* x^2=c   -> x=+-sqrt(c)*)
+		Thm("d2_sqrt_equation1_neg",num_str d2_sqrt_equation1_neg),
+(* [c<0] x^2=c   -> x=[]*)
+		Thm("d2_sqrt_equation2",num_str d2_sqrt_equation2),
+(*  x^2=0 ->    x=0    *)
+		Thm("d2_reduce_equation1",num_str d2_reduce_equation1),
+(* x(a+bx)=0 -> x=0 | a+bx=0*)
+		Thm("d2_reduce_equation2",num_str d2_reduce_equation2),
+(* x(a+ x)=0 -> x=0 | a+ x=0*)
+		Thm("d2_isolate_div",num_str d2_isolate_div)
+(* bx^2=c -> x^2=c/b*)
+	       ],
 scr = Script ((term_of o the o (parse thy)) "empty_script")
 }:rls);
 (* -- d3 -- *)
-(*isolate the bound variable in an d3 equation; 'bdv' is a meta-constant*)
+(* isolate the bound variable in an d3 equation; 'bdv' is a meta-constant *)
 val d3_polyeq_simplify = prep_rls(
 Rls {id = "d3_polyeq_simplify", preconds = [],
-rew_ord = ("e_rew_ord",e_rew_ord),
+rew_ord = ("e_rew_ord",e_rew_ord), erls = PolyEq_erls,
-erls = PolyEq_erls,
+srls = Erls, calc = [],
-srls = Erls,
+rules =
-calc = [],
+[Thm("d3_reduce_equation1",num_str d3_reduce_equation1),
-(*asm_thm = [("d3_isolate_div","")],*)
+	(*a*bdv + b*bdv^^^2 + c*bdv^^^3=0) =
-rules = [
+(bdv=0 | (a + b*bdv + c*bdv^^^2=0)*)
-		Thm("d3_reduce_equation1",num_str d3_reduce_equation1),
+	Thm("d3_reduce_equation2",num_str d3_reduce_equation2),
-		(*a*bdv + b*bdv^^^2 + c*bdv^^^3=0) = (bdv=0 | (a + b*bdv + c*bdv^^^2=0)*)
+	(*  bdv + b*bdv^^^2 + c*bdv^^^3=0) =
-		Thm("d3_reduce_equation2",num_str d3_reduce_equation2),
+(bdv=0 | (1 + b*bdv + c*bdv^^^2=0)*)
-		(*  bdv + b*bdv^^^2 + c*bdv^^^3=0) = (bdv=0 | (1 + b*bdv + c*bdv^^^2=0)*)
+	Thm("d3_reduce_equation3",num_str d3_reduce_equation3),
-		Thm("d3_reduce_equation3",num_str d3_reduce_equation3),
+	(*a*bdv +   bdv^^^2 + c*bdv^^^3=0) =
-		(*a*bdv +   bdv^^^2 + c*bdv^^^3=0) = (bdv=0 | (a +   bdv + c*bdv^^^2=0)*)
+(bdv=0 | (a +   bdv + c*bdv^^^2=0)*)
-		Thm("d3_reduce_equation4",num_str d3_reduce_equation4),
+	Thm("d3_reduce_equation4",num_str d3_reduce_equation4),
-		(*  bdv +   bdv^^^2 + c*bdv^^^3=0) = (bdv=0 | (1 +   bdv + c*bdv^^^2=0)*)
+	(*  bdv +   bdv^^^2 + c*bdv^^^3=0) =
-		Thm("d3_reduce_equation5",num_str d3_reduce_equation5),
+(bdv=0 | (1 +   bdv + c*bdv^^^2=0)*)
-		(*a*bdv + b*bdv^^^2 +   bdv^^^3=0) = (bdv=0 | (a + b*bdv +   bdv^^^2=0)*)
+	Thm("d3_reduce_equation5",num_str d3_reduce_equation5),
-		Thm("d3_reduce_equation6",num_str d3_reduce_equation6),
+	(*a*bdv + b*bdv^^^2 +   bdv^^^3=0) =
-		(*  bdv + b*bdv^^^2 +   bdv^^^3=0) = (bdv=0 | (1 + b*bdv +   bdv^^^2=0)*)
+(bdv=0 | (a + b*bdv +   bdv^^^2=0)*)
-		Thm("d3_reduce_equation7",num_str d3_reduce_equation7),
+	Thm("d3_reduce_equation6",num_str d3_reduce_equation6),
-		(*a*bdv +   bdv^^^2 +   bdv^^^3=0) = (bdv=0 | (1 +   bdv +   bdv^^^2=0)*)
+	(*  bdv + b*bdv^^^2 +   bdv^^^3=0) =
-		Thm("d3_reduce_equation8",num_str d3_reduce_equation8),
+(bdv=0 | (1 + b*bdv +   bdv^^^2=0)*)
-		(*  bdv +   bdv^^^2 +   bdv^^^3=0) = (bdv=0 | (1 +   bdv +   bdv^^^2=0)*)
+	Thm("d3_reduce_equation7",num_str d3_reduce_equation7),
-		Thm("d3_reduce_equation9",num_str d3_reduce_equation9),
+	     (*a*bdv +   bdv^^^2 +   bdv^^^3=0) =
-		(*a*bdv             + c*bdv^^^3=0) = (bdv=0 | (a         + c*bdv^^^2=0)*)
+(bdv=0 | (1 +   bdv +   bdv^^^2=0)*)
-		Thm("d3_reduce_equation10",num_str d3_reduce_equation10),
+	Thm("d3_reduce_equation8",num_str d3_reduce_equation8),
-		(*  bdv             + c*bdv^^^3=0) = (bdv=0 | (1         + c*bdv^^^2=0)*)
+	     (*  bdv +   bdv^^^2 +   bdv^^^3=0) =
-		Thm("d3_reduce_equation11",num_str d3_reduce_equation11),
+(bdv=0 | (1 +   bdv +   bdv^^^2=0)*)
-		(*a*bdv             +   bdv^^^3=0) = (bdv=0 | (a         +   bdv^^^2=0)*)
+	Thm("d3_reduce_equation9",num_str d3_reduce_equation9),
-		Thm("d3_reduce_equation12",num_str d3_reduce_equation12),
+	     (*a*bdv             + c*bdv^^^3=0) =
-		(*  bdv             +   bdv^^^3=0) = (bdv=0 | (1         +   bdv^^^2=0)*)
+(bdv=0 | (a         + c*bdv^^^2=0)*)
-		Thm("d3_reduce_equation13",num_str d3_reduce_equation13),
+	Thm("d3_reduce_equation10",num_str d3_reduce_equation10),
-		(*        b*bdv^^^2 + c*bdv^^^3=0) = (bdv=0 | (    b*bdv + c*bdv^^^2=0)*)
+	     (*  bdv             + c*bdv^^^3=0) =
-		Thm("d3_reduce_equation14",num_str d3_reduce_equation14),
+(bdv=0 | (1         + c*bdv^^^2=0)*)
-		(*          bdv^^^2 + c*bdv^^^3=0) = (bdv=0 | (      bdv + c*bdv^^^2=0)*)
+	Thm("d3_reduce_equation11",num_str d3_reduce_equation11),
-		Thm("d3_reduce_equation15",num_str d3_reduce_equation15),
+	     (*a*bdv             +   bdv^^^3=0) =
-		(*        b*bdv^^^2 +   bdv^^^3=0) = (bdv=0 | (    b*bdv +   bdv^^^2=0)*)
+(bdv=0 | (a         +   bdv^^^2=0)*)
-		Thm("d3_reduce_equation16",num_str d3_reduce_equation16),
+	Thm("d3_reduce_equation12",num_str d3_reduce_equation12),
-		(*          bdv^^^2 +   bdv^^^3=0) = (bdv=0 | (      bdv +   bdv^^^2=0)*)
+	     (*  bdv             +   bdv^^^3=0) =
-		Thm("d3_isolate_add1",num_str d3_isolate_add1),
+(bdv=0 | (1         +   bdv^^^2=0)*)
-		(*[|Not(bdv occurs_in a)|] ==> (a + b*bdv^^^3=0) = (bdv=0 | (b*bdv^^^3=a)*)
+	Thm("d3_reduce_equation13",num_str d3_reduce_equation13),
-		Thm("d3_isolate_add2",num_str d3_isolate_add2),
+	     (*        b*bdv^^^2 + c*bdv^^^3=0) =
-(*[|Not(bdv occurs_in a)|] ==> (a +   bdv^^^3=0) = (bdv=0 | (  bdv^^^3=a)*)
+(bdv=0 | (    b*bdv + c*bdv^^^2=0)*)
-	        Thm("d3_isolate_div",num_str d3_isolate_div),
+	Thm("d3_reduce_equation14",num_str d3_reduce_equation14),
-(*[|Not(b=0)|] ==> (b*bdv^^^3=c) = (bdv^^^3=c/b*)
+	     (*          bdv^^^2 + c*bdv^^^3=0) =
-Thm("d3_root_equation2",num_str d3_root_equation2),
+(bdv=0 | (      bdv + c*bdv^^^2=0)*)
-(*(bdv^^^3=0) = (bdv=0) *)
+	Thm("d3_reduce_equation15",num_str d3_reduce_equation15),
-	        Thm("d3_root_equation1",num_str d3_root_equation1)
+	     (*        b*bdv^^^2 +   bdv^^^3=0) =
-(*bdv^^^3=c) = (bdv = nroot 3 c*)
+(bdv=0 | (    b*bdv +   bdv^^^2=0)*)
-		],
+	Thm("d3_reduce_equation16",num_str d3_reduce_equation16),
+	     (*          bdv^^^2 +   bdv^^^3=0) =
+(bdv=0 | (      bdv +   bdv^^^2=0)*)
+	Thm("d3_isolate_add1",num_str d3_isolate_add1),
+	     (*[|Not(bdv occurs_in a)|] ==> (a + b*bdv^^^3=0) =
+(bdv=0 | (b*bdv^^^3=a)*)
+	Thm("d3_isolate_add2",num_str d3_isolate_add2),
+(*[|Not(bdv occurs_in a)|] ==> (a +   bdv^^^3=0) =
+(bdv=0 | (  bdv^^^3=a)*)
+	Thm("d3_isolate_div",num_str d3_isolate_div),
+(*[|Not(b=0)|] ==> (b*bdv^^^3=c) = (bdv^^^3=c/b*)
+Thm("d3_root_equation2",num_str d3_root_equation2),
+(*(bdv^^^3=0) = (bdv=0) *)
+	Thm("d3_root_equation1",num_str d3_root_equation1)
+(*bdv^^^3=c) = (bdv = nroot 3 c*)
+],
 scr = Script ((term_of o the o (parse thy)) "empty_script")
 }:rls);
 (* -- d4 -- *)
 (*isolate the bound variable in an d4 equation; 'bdv' is a meta-constant*)
 val d4_polyeq_simplify = prep_rls(
 Rls {id = "d4_polyeq_simplify", preconds = [],
-rew_ord = ("e_rew_ord",e_rew_ord),
+rew_ord = ("e_rew_ord",e_rew_ord), erls = PolyEq_erls,
-erls = PolyEq_erls,
+srls = Erls, calc = [],
-srls = Erls,
+rules =
-calc = [],
+[Thm("d4_sub_u1",num_str d4_sub_u1)
-(*asm_thm = [],*)
+(* ax^4+bx^2+c=0 -> x=+-sqrt(ax^2+bx^+c) *)
-rules = [Thm("d4_sub_u1",num_str d4_sub_u1)
+],
-		(* ax^4+bx^2+c=0 -> x=+-sqrt(ax^2+bx^+c) *)
-		],
 scr = Script ((term_of o the o (parse thy)) "empty_script")
 }:rls);
-ruleset' := overwritelthy thy (!ruleset',
+ruleset' :=
-[("d0_polyeq_simplify", d0_polyeq_simplify),
+overwritelthy thy
-("d1_polyeq_simplify", d1_polyeq_simplify),
+(!ruleset',
-("d2_polyeq_simplify", d2_polyeq_simplify),
+[("d0_polyeq_simplify", d0_polyeq_simplify),
-("d2_polyeq_bdv_only_simplify", d2_polyeq_bdv_only_simplify),
+("d1_polyeq_simplify", d1_polyeq_simplify),
-("d2_polyeq_sq_only_simplify", d2_polyeq_sq_only_simplify),
+("d2_polyeq_simplify", d2_polyeq_simplify),
-("d2_polyeq_pqFormula_simplify", d2_polyeq_pqFormula_simplify),
+("d2_polyeq_bdv_only_simplify", d2_polyeq_bdv_only_simplify),
-("d2_polyeq_abcFormula_simplify", d2_polyeq_abcFormula_simplify),
+("d2_polyeq_sq_only_simplify", d2_polyeq_sq_only_simplify),
-("d3_polyeq_simplify", d3_polyeq_simplify),
+("d2_polyeq_pqFormula_simplify", d2_polyeq_pqFormula_simplify),
-			 ("d4_polyeq_simplify", d4_polyeq_simplify)
+("d2_polyeq_abcFormula_simplify",
-			 ]);
+d2_polyeq_abcFormula_simplify),
+("d3_polyeq_simplify", d3_polyeq_simplify),
+		("d4_polyeq_simplify", d4_polyeq_simplify)
+	      ]);
 (*------------------------problems------------------------*)
 (*
 (get_pbt ["degree_2","polynomial","univariate","equation"]);
 show_ptyps();
 *)
 (*-------------------------poly-----------------------*)
 store_pbt
-(prep_pbt PolyEq.thy "pbl_equ_univ_poly" [] e_pblID
+(prep_pbt (theory "PolyEq") "pbl_equ_univ_poly" [] e_pblID
 (["polynomial","univariate","equation"],
 [("#Given" ,["equality e_","solveFor v_"]),
 ("#Where" ,["~((e_::bool) is_ratequation_in (v_::real))",
 	       "~((lhs e_) is_rootTerm_in (v_::real))",
 	       "~((rhs e_) is_rootTerm_in (v_::real))"]),
 ],
 PolyEq_prls, SOME "solve (e_::bool, v_)",
 []));
 (*--- d0 ---*)
 store_pbt
-(prep_pbt PolyEq.thy "pbl_equ_univ_poly_deg0" [] e_pblID
+(prep_pbt (theory "PolyEq") "pbl_equ_univ_poly_deg0" [] e_pblID
 (["degree_0","polynomial","univariate","equation"],
 [("#Given" ,["equality e_","solveFor v_"]),
 ("#Where" ,["matches (?a = 0) e_",
 	       "(lhs e_) is_poly_in v_",
 	       "((lhs e_) has_degree_in v_ ) = 0"
 PolyEq_prls, SOME "solve (e_::bool, v_)",
 [["PolyEq","solve_d0_polyeq_equation"]]));
 (*--- d1 ---*)
 store_pbt
-(prep_pbt PolyEq.thy "pbl_equ_univ_poly_deg1" [] e_pblID
+(prep_pbt (theory "PolyEq") "pbl_equ_univ_poly_deg1" [] e_pblID
 (["degree_1","polynomial","univariate","equation"],
 [("#Given" ,["equality e_","solveFor v_"]),
 ("#Where" ,["matches (?a = 0) e_",
 	       "(lhs e_) is_poly_in v_",
 	       "((lhs e_) has_degree_in v_ ) = 1"
 PolyEq_prls, SOME "solve (e_::bool, v_)",
 [["PolyEq","solve_d1_polyeq_equation"]]));
 (*--- d2 ---*)
 store_pbt
-(prep_pbt PolyEq.thy "pbl_equ_univ_poly_deg2" [] e_pblID
+(prep_pbt (theory "PolyEq") "pbl_equ_univ_poly_deg2" [] e_pblID
 (["degree_2","polynomial","univariate","equation"],
 [("#Given" ,["equality e_","solveFor v_"]),
 ("#Where" ,["matches (?a = 0) e_",
 	       "(lhs e_) is_poly_in v_ ",
 	       "((lhs e_) has_degree_in v_ ) = 2"]),
 ],
 PolyEq_prls, SOME "solve (e_::bool, v_)",
 [["PolyEq","solve_d2_polyeq_equation"]]));
 store_pbt
-(prep_pbt PolyEq.thy "pbl_equ_univ_poly_deg2_sqonly" [] e_pblID
+(prep_pbt (theory "PolyEq") "pbl_equ_univ_poly_deg2_sqonly" [] e_pblID
 (["sq_only","degree_2","polynomial","univariate","equation"],
 [("#Given" ,["equality e_","solveFor v_"]),
-("#Where" ,["matches ( ?a +    ?v_^^^2 = 0) e_ | \
+("#Where" ,["matches ( ?a +    ?v_^^^2 = 0) e_ | " ^
-	       \matches ( ?a + ?b*?v_^^^2 = 0) e_ | \
+	       "matches ( ?a + ?b*?v_^^^2 = 0) e_ | " ^
-	       \matches (         ?v_^^^2 = 0) e_ | \
+	       "matches (         ?v_^^^2 = 0) e_ | " ^
-	       \matches (      ?b*?v_^^^2 = 0) e_" ,
+	       "matches (      ?b*?v_^^^2 = 0) e_" ,
-	       "Not (matches (?a +    ?v_ +    ?v_^^^2 = 0) e_) &\
+	       "Not (matches (?a +    ?v_ +    ?v_^^^2 = 0) e_) &" ^
-	       \Not (matches (?a + ?b*?v_ +    ?v_^^^2 = 0) e_) &\
+	       "Not (matches (?a + ?b*?v_ +    ?v_^^^2 = 0) e_) &" ^
-	       \Not (matches (?a +    ?v_ + ?c*?v_^^^2 = 0) e_) &\
+	       "Not (matches (?a +    ?v_ + ?c*?v_^^^2 = 0) e_) &" ^
-	       \Not (matches (?a + ?b*?v_ + ?c*?v_^^^2 = 0) e_) &\
+	       "Not (matches (?a + ?b*?v_ + ?c*?v_^^^2 = 0) e_) &" ^
-	       \Not (matches (        ?v_ +    ?v_^^^2 = 0) e_) &\
+	       "Not (matches (        ?v_ +    ?v_^^^2 = 0) e_) &" ^
-	       \Not (matches (     ?b*?v_ +    ?v_^^^2 = 0) e_) &\
+	       "Not (matches (     ?b*?v_ +    ?v_^^^2 = 0) e_) &" ^
-	       \Not (matches (        ?v_ + ?c*?v_^^^2 = 0) e_) &\
+	       "Not (matches (        ?v_ + ?c*?v_^^^2 = 0) e_) &" ^
-	       \Not (matches (     ?b*?v_ + ?c*?v_^^^2 = 0) e_)"]),
+	       "Not (matches (     ?b*?v_ + ?c*?v_^^^2 = 0) e_)"]),
 ("#Find"  ,["solutions v_i_"])
 ],
 PolyEq_prls, SOME "solve (e_::bool, v_)",
 [["PolyEq","solve_d2_polyeq_sqonly_equation"]]));
 store_pbt
-(prep_pbt PolyEq.thy "pbl_equ_univ_poly_deg2_bdvonly" [] e_pblID
+(prep_pbt (theory "PolyEq") "pbl_equ_univ_poly_deg2_bdvonly" [] e_pblID
 (["bdv_only","degree_2","polynomial","univariate","equation"],
 [("#Given" ,["equality e_","solveFor v_"]),
-("#Where" ,["matches (?a*?v_ +    ?v_^^^2 = 0) e_ | \
+("#Where" ,["matches (?a*?v_ +    ?v_^^^2 = 0) e_ | " ^
-	       \matches (   ?v_ +    ?v_^^^2 = 0) e_ | \
+	       "matches (   ?v_ +    ?v_^^^2 = 0) e_ | " ^
-	       \matches (   ?v_ + ?b*?v_^^^2 = 0) e_ | \
+	       "matches (   ?v_ + ?b*?v_^^^2 = 0) e_ | " ^
-	       \matches (?a*?v_ + ?b*?v_^^^2 = 0) e_ | \
+	       "matches (?a*?v_ + ?b*?v_^^^2 = 0) e_ | " ^
-	       \matches (            ?v_^^^2 = 0) e_ | \
+	       "matches (            ?v_^^^2 = 0) e_ | " ^
-	       \matches (         ?b*?v_^^^2 = 0) e_ "]),
+	       "matches (         ?b*?v_^^^2 = 0) e_ "]),
 ("#Find"  ,["solutions v_i_"])
 ],
 PolyEq_prls, SOME "solve (e_::bool, v_)",
 [["PolyEq","solve_d2_polyeq_bdvonly_equation"]]));
 store_pbt
-(prep_pbt PolyEq.thy "pbl_equ_univ_poly_deg2_pq" [] e_pblID
+(prep_pbt (theory "PolyEq") "pbl_equ_univ_poly_deg2_pq" [] e_pblID
 (["pqFormula","degree_2","polynomial","univariate","equation"],
 [("#Given" ,["equality e_","solveFor v_"]),
-("#Where" ,["matches (?a + 1*?v_^^^2 = 0) e_ | \
+("#Where" ,["matches (?a + 1*?v_^^^2 = 0) e_ | " ^
-	       \matches (?a +   ?v_^^^2 = 0) e_"]),
+	       "matches (?a +   ?v_^^^2 = 0) e_"]),
 ("#Find"  ,["solutions v_i_"])
 ],
 PolyEq_prls, SOME "solve (e_::bool, v_)",
 [["PolyEq","solve_d2_polyeq_pq_equation"]]));
 store_pbt
-(prep_pbt PolyEq.thy "pbl_equ_univ_poly_deg2_abc" [] e_pblID
+(prep_pbt (theory "PolyEq") "pbl_equ_univ_poly_deg2_abc" [] e_pblID
 (["abcFormula","degree_2","polynomial","univariate","equation"],
 [("#Given" ,["equality e_","solveFor v_"]),
-("#Where" ,["matches (?a +    ?v_^^^2 = 0) e_ | \
+("#Where" ,["matches (?a +    ?v_^^^2 = 0) e_ | " ^
-	       \matches (?a + ?b*?v_^^^2 = 0) e_"]),
+	       "matches (?a + ?b*?v_^^^2 = 0) e_"]),
 ("#Find"  ,["solutions v_i_"])
 ],
 PolyEq_prls, SOME "solve (e_::bool, v_)",
 [["PolyEq","solve_d2_polyeq_abc_equation"]]));
 (*--- d3 ---*)
 store_pbt
-(prep_pbt PolyEq.thy "pbl_equ_univ_poly_deg3" [] e_pblID
+(prep_pbt (theory "PolyEq") "pbl_equ_univ_poly_deg3" [] e_pblID
 (["degree_3","polynomial","univariate","equation"],
 [("#Given" ,["equality e_","solveFor v_"]),
 ("#Where" ,["matches (?a = 0) e_",
 	       "(lhs e_) is_poly_in v_ ",
 	       "((lhs e_) has_degree_in v_) = 3"]),
 PolyEq_prls, SOME "solve (e_::bool, v_)",
 [["PolyEq","solve_d3_polyeq_equation"]]));
 (*--- d4 ---*)
 store_pbt
-(prep_pbt PolyEq.thy "pbl_equ_univ_poly_deg4" [] e_pblID
+(prep_pbt (theory "PolyEq") "pbl_equ_univ_poly_deg4" [] e_pblID
 (["degree_4","polynomial","univariate","equation"],
 [("#Given" ,["equality e_","solveFor v_"]),
 ("#Where" ,["matches (?a = 0) e_",
 	       "(lhs e_) is_poly_in v_ ",
 	       "((lhs e_) has_degree_in v_) = 4"]),
 PolyEq_prls, SOME "solve (e_::bool, v_)",
 [(*["PolyEq","solve_d4_polyeq_equation"]*)]));
 (*--- normalize ---*)
 store_pbt
-(prep_pbt PolyEq.thy "pbl_equ_univ_poly_norm" [] e_pblID
+(prep_pbt (theory "PolyEq") "pbl_equ_univ_poly_norm" [] e_pblID
 (["normalize","polynomial","univariate","equation"],
 [("#Given" ,["equality e_","solveFor v_"]),
-("#Where" ,["(Not((matches (?a = 0 ) e_ ))) |\
+("#Where" ,["(Not((matches (?a = 0 ) e_ ))) |" ^
-	       \(Not(((lhs e_) is_poly_in v_)))"]),
+	       "(Not(((lhs e_) is_poly_in v_)))"]),
 ("#Find"  ,["solutions v_i_"])
 ],
 PolyEq_prls, SOME "solve (e_::bool, v_)",
 [["PolyEq","normalize_poly"]]));
 (*-------------------------expanded-----------------------*)
 store_pbt
-(prep_pbt PolyEq.thy "pbl_equ_univ_expand" [] e_pblID
+(prep_pbt (theory "PolyEq") "pbl_equ_univ_expand" [] e_pblID
 (["expanded","univariate","equation"],
 [("#Given" ,["equality e_","solveFor v_"]),
 ("#Where" ,["matches (?a = 0) e_",
 	       "(lhs e_) is_expanded_in v_ "]),
 ("#Find"  ,["solutions v_i_"])
 PolyEq_prls, SOME "solve (e_::bool, v_)",
 []));
 (*--- d2 ---*)
 store_pbt
-(prep_pbt PolyEq.thy "pbl_equ_univ_expand_deg2" [] e_pblID
+(prep_pbt (theory "PolyEq") "pbl_equ_univ_expand_deg2" [] e_pblID
 (["degree_2","expanded","univariate","equation"],
 [("#Given" ,["equality e_","solveFor v_"]),
 ("#Where" ,["((lhs e_) has_degree_in v_) = 2"]),
 ("#Find"  ,["solutions v_i_"])
 ],
 [["PolyEq","complete_square"]]));
 "-------------------------methods-----------------------";
 store_met
-(prep_met PolyEq.thy "met_polyeq" [] e_metID
+(prep_met (theory "PolyEq") "met_polyeq" [] e_metID
 (["PolyEq"],
 [],
 {rew_ord'="tless_true",rls'=Atools_erls,calc = [], srls = e_rls, prls=e_rls,
-crls=PolyEq_crls, nrls=norm_Rational
+crls=PolyEq_crls, nrls=norm_Rational}, "empty_script"));
-(*, asm_rls=[],asm_thm=[]*)}, "empty_script"));
 store_met
-(prep_met PolyEq.thy "met_polyeq_norm" [] e_metID
+(prep_met (theory "PolyEq") "met_polyeq_norm" [] e_metID
 (["PolyEq","normalize_poly"],
 [("#Given" ,["equality e_","solveFor v_"]),
-("#Where" ,["(Not((matches (?a = 0 ) e_ ))) |\
+("#Where" ,["(Not((matches (?a = 0 ) e_ ))) |" ^
-	       \(Not(((lhs e_) is_poly_in v_)))"]),
+	       "(Not(((lhs e_) is_poly_in v_)))"]),
 ("#Find"  ,["solutions v_i_"])
 ],
 {rew_ord'="termlessI",
 rls'=PolyEq_erls,
 srls=e_rls,
 prls=PolyEq_prls,
 calc=[],
-crls=PolyEq_crls, nrls=norm_Rational(*,
+crls=PolyEq_crls, nrls=norm_Rational
-asm_rls=[],
+"Script Normalize_poly (e_::bool) (v_::real) =                     " ^
-asm_thm=[]*)},
+"(let e_ =((Try         (Rewrite     all_left          False)) @@  " ^
-(*RL: Ratpoly loest Brueche ohne bdv*)
+"          (Try (Repeat (Rewrite     makex1_x         False))) @@  " ^
-"Script Normalize_poly (e_::bool) (v_::real) =                     \
+"          (Try (Repeat (Rewrite_Set expand_binoms    False))) @@  " ^
-\(let e_ =((Try         (Rewrite     all_left          False)) @@  \
+"          (Try (Repeat (Rewrite_Set_Inst [(bdv,v_::real)]         " ^
-\          (Try (Repeat (Rewrite     makex1_x         False))) @@  \
+"                                 make_ratpoly_in     False))) @@  " ^
-\          (Try (Repeat (Rewrite_Set expand_binoms    False))) @@  \
+"          (Try (Repeat (Rewrite_Set polyeq_simplify  False)))) e_ " ^
-\          (Try (Repeat (Rewrite_Set_Inst [(bdv,v_::real)]         \
+" in (SubProblem (PolyEq_,[polynomial,univariate,equation],        " ^
-\                                 make_ratpoly_in     False))) @@  \
+"                [no_met]) [bool_ e_, real_ v_]))"
-\          (Try (Repeat (Rewrite_Set polyeq_simplify  False)))) e_ \
-\ in (SubProblem (PolyEq_,[polynomial,univariate,equation],        \
-\                [no_met]) [bool_ e_, real_ v_]))"
 ));
 store_met
-(prep_met PolyEq.thy "met_polyeq_d0" [] e_metID
+(prep_met (theory "PolyEq") "met_polyeq_d0" [] e_metID
 (["PolyEq","solve_d0_polyeq_equation"],
 [("#Given" ,["equality e_","solveFor v_"]),
 ("#Where" ,["(lhs e_) is_poly_in v_ ",
 	       "((lhs e_) has_degree_in v_) = 0"]),
 ("#Find"  ,["solutions v_i_"])
 {rew_ord'="termlessI",
 rls'=PolyEq_erls,
 srls=e_rls,
 prls=PolyEq_prls,
 calc=[("sqrt", ("Root.sqrt", eval_sqrt "#sqrt_"))],
-crls=PolyEq_crls, nrls=norm_Rational(*,
+crls=PolyEq_crls, nrls=norm_Rational},
-asm_rls=[],
+"Script Solve_d0_polyeq_equation  (e_::bool) (v_::real)  = " ^
-asm_thm=[]*)},
+"(let e_ =  ((Try (Rewrite_Set_Inst [(bdv,v_::real)]      " ^
-"Script Solve_d0_polyeq_equation  (e_::bool) (v_::real)  = \
+"                  d0_polyeq_simplify  False))) e_        " ^
-\(let e_ =  ((Try (Rewrite_Set_Inst [(bdv,v_::real)]      \
+" in ((Or_to_List e_)::bool list))"
-\                  d0_polyeq_simplify  False))) e_        \
-\ in ((Or_to_List e_)::bool list))"
 ));
 store_met
-(prep_met PolyEq.thy "met_polyeq_d1" [] e_metID
+(prep_met (theory "PolyEq") "met_polyeq_d1" [] e_metID
 (["PolyEq","solve_d1_polyeq_equation"],
 [("#Given" ,["equality e_","solveFor v_"]),
 ("#Where" ,["(lhs e_) is_poly_in v_ ",
 	       "((lhs e_) has_degree_in v_) = 1"]),
 ("#Find"  ,["solutions v_i_"])
 calc=[("sqrt", ("Root.sqrt", eval_sqrt "#sqrt_"))],
 crls=PolyEq_crls, nrls=norm_Rational(*,
 (*    asm_rls=["d1_polyeq_simplify"],*)
 asm_rls=[],
 asm_thm=[("d1_isolate_div","")]*)},
-"Script Solve_d1_polyeq_equation  (e_::bool) (v_::real)  =   \
+"Script Solve_d1_polyeq_equation  (e_::bool) (v_::real)  =   " ^
-\(let e_ =  ((Try (Rewrite_Set_Inst [(bdv,v_::real)]        \
+"(let e_ =  ((Try (Rewrite_Set_Inst [(bdv,v_::real)]        " ^
-\                  d1_polyeq_simplify   True))          @@  \
+"                  d1_polyeq_simplify   True))          @@  " ^
-\            (Try (Rewrite_Set polyeq_simplify  False)) @@  \
+"            (Try (Rewrite_Set polyeq_simplify  False)) @@  " ^
-\            (Try (Rewrite_Set norm_Rational_parenthesized    False))) e_;\
+"            (Try (Rewrite_Set norm_Rational_parenthesized False))) e_;" ^
-\ (L_::bool list) = ((Or_to_List e_)::bool list)            \
+" (L_::bool list) = ((Or_to_List e_)::bool list)            " ^
-\ in Check_elementwise L_ {(v_::real). Assumptions} )"
+" in Check_elementwise L_ {(v_::real). Assumptions} )"
 ));
 store_met
-(prep_met PolyEq.thy "met_polyeq_d22" [] e_metID
+(prep_met (theory "PolyEq") "met_polyeq_d22" [] e_metID
 (["PolyEq","solve_d2_polyeq_equation"],
 [("#Given" ,["equality e_","solveFor v_"]),
 ("#Where" ,["(lhs e_) is_poly_in v_ ",
 	       "((lhs e_) has_degree_in v_) = 2"]),
 ("#Find"  ,["solutions v_i_"])
 {rew_ord'="termlessI",
 rls'=PolyEq_erls,
 srls=e_rls,
 prls=PolyEq_prls,
 calc=[("sqrt", ("Root.sqrt", eval_sqrt "#sqrt_"))],
-crls=PolyEq_crls, nrls=norm_Rational(*,
+crls=PolyEq_crls, nrls=norm_Rational},
-(*asm_rls=["d2_polyeq_simplify","d1_polyeq_simplify"],*)
+"Script Solve_d2_polyeq_equation  (e_::bool) (v_::real) =      " ^
-asm_rls=[],
+"  (let e_ = ((Try (Rewrite_Set_Inst [(bdv,v_::real)]         " ^
-asm_thm = [("d1_isolate_div",""),("d2_pqformula1",""),("d2_pqformula2",""),
+"                    d2_polyeq_simplify           True)) @@   " ^
-("d2_pqformula3",""),("d2_pqformula4",""),("d2_pqformula1_neg",""),
+"             (Try (Rewrite_Set polyeq_simplify   False)) @@  " ^
-("d2_pqformula2_neg",""),("d2_pqformula3_neg",""),("d2_pqformula4_neg",""),
+"             (Try (Rewrite_Set_Inst [(bdv,v_::real)]         " ^
-("d2_abcformula1",""),("d2_abcformula2",""),("d2_abcformula1_neg",""),
+"                    d1_polyeq_simplify            True)) @@  " ^
-("d2_abcformula2_neg",""), ("d2_sqrt_equation1",""),
+"            (Try (Rewrite_Set polyeq_simplify    False)) @@  " ^
-("d2_sqrt_equation1_neg",""), ("d2_isolate_div","")]*)},
+"            (Try (Rewrite_Set norm_Rational_parenthesized False))) e_;" ^
-"Script Solve_d2_polyeq_equation  (e_::bool) (v_::real) =      \
+" (L_::bool list) = ((Or_to_List e_)::bool list)              " ^
-\  (let e_ = ((Try (Rewrite_Set_Inst [(bdv,v_::real)]         \
+" in Check_elementwise L_ {(v_::real). Assumptions} )"
-\                    d2_polyeq_simplify           True)) @@   \
-\             (Try (Rewrite_Set polyeq_simplify   False)) @@  \
-\             (Try (Rewrite_Set_Inst [(bdv,v_::real)]         \
-\                    d1_polyeq_simplify            True)) @@  \
-\            (Try (Rewrite_Set polyeq_simplify    False)) @@  \
-\            (Try (Rewrite_Set norm_Rational_parenthesized      False))) e_;\
-\ (L_::bool list) = ((Or_to_List e_)::bool list)              \
-\ in Check_elementwise L_ {(v_::real). Assumptions} )"
 ));
 store_met
-(prep_met PolyEq.thy "met_polyeq_d2_bdvonly" [] e_metID
+(prep_met (theory "PolyEq") "met_polyeq_d2_bdvonly" [] e_metID
 (["PolyEq","solve_d2_polyeq_bdvonly_equation"],
 [("#Given" ,["equality e_","solveFor v_"]),
 ("#Where" ,["(lhs e_) is_poly_in v_ ",
 	       "((lhs e_) has_degree_in v_) = 2"]),
 ("#Find"  ,["solutions v_i_"])
 {rew_ord'="termlessI",
 rls'=PolyEq_erls,
 srls=e_rls,
 prls=PolyEq_prls,
 calc=[("sqrt", ("Root.sqrt", eval_sqrt "#sqrt_"))],
-crls=PolyEq_crls, nrls=norm_Rational(*,
+crls=PolyEq_crls, nrls=norm_Rational},
-(*asm_rls=["d2_polyeq_bdv_only_simplify","d1_polyeq_simplify "],*)
+"Script Solve_d2_polyeq_bdvonly_equation  (e_::bool) (v_::real) =" ^
-asm_rls=[],
+"  (let e_ = ((Try (Rewrite_Set_Inst [(bdv,v_::real)]         " ^
-asm_thm=[("d1_isolate_div",""),("d2_isolate_div",""),
+"                   d2_polyeq_bdv_only_simplify    True)) @@  " ^
-("d2_sqrt_equation1",""),("d2_sqrt_equation1_neg","")]*)},
+"             (Try (Rewrite_Set polyeq_simplify   False)) @@  " ^
-"Script Solve_d2_polyeq_bdvonly_equation  (e_::bool) (v_::real) =\
+"             (Try (Rewrite_Set_Inst [(bdv,v_::real)]         " ^
-\  (let e_ = ((Try (Rewrite_Set_Inst [(bdv,v_::real)]         \
+"                   d1_polyeq_simplify             True)) @@  " ^
-\                   d2_polyeq_bdv_only_simplify    True)) @@  \
+"            (Try (Rewrite_Set polyeq_simplify    False)) @@  " ^
-\             (Try (Rewrite_Set polyeq_simplify   False)) @@  \
+"            (Try (Rewrite_Set norm_Rational_parenthesized False))) e_;" ^
-\             (Try (Rewrite_Set_Inst [(bdv,v_::real)]         \
+" (L_::bool list) = ((Or_to_List e_)::bool list)              " ^
-\                   d1_polyeq_simplify             True)) @@  \
+" in Check_elementwise L_ {(v_::real). Assumptions} )"
-\            (Try (Rewrite_Set polyeq_simplify    False)) @@  \
-\            (Try (Rewrite_Set norm_Rational_parenthesized      False))) e_;\
-\ (L_::bool list) = ((Or_to_List e_)::bool list)              \
-\ in Check_elementwise L_ {(v_::real). Assumptions} )"
 ));
 store_met
-(prep_met PolyEq.thy "met_polyeq_d2_sqonly" [] e_metID
+(prep_met (theory "PolyEq") "met_polyeq_d2_sqonly" [] e_metID
 (["PolyEq","solve_d2_polyeq_sqonly_equation"],
 [("#Given" ,["equality e_","solveFor v_"]),
 ("#Where" ,["(lhs e_) is_poly_in v_ ",
 	       "((lhs e_) has_degree_in v_) = 2"]),
 ("#Find"  ,["solutions v_i_"])
 {rew_ord'="termlessI",
 rls'=PolyEq_erls,
 srls=e_rls,
 prls=PolyEq_prls,
 calc=[("sqrt", ("Root.sqrt", eval_sqrt "#sqrt_"))],
-crls=PolyEq_crls, nrls=norm_Rational(*,
+crls=PolyEq_crls, nrls=norm_Rational},
-(*asm_rls=["d2_polyeq_sq_only_simplify"],*)
+"Script Solve_d2_polyeq_sqonly_equation  (e_::bool) (v_::real) =" ^
-asm_rls=[],
+"  (let e_ = ((Try (Rewrite_Set_Inst [(bdv,v_::real)]          " ^
-asm_thm=[("d2_sqrt_equation1",""),("d2_sqrt_equation1_neg",""),
+"                   d2_polyeq_sq_only_simplify     True)) @@   " ^
-("d2_isolate_div","")]*)},
+"            (Try (Rewrite_Set polyeq_simplify    False)) @@   " ^
-"Script Solve_d2_polyeq_sqonly_equation  (e_::bool) (v_::real) =\
+"            (Try (Rewrite_Set norm_Rational_parenthesized False))) e_; " ^
-\  (let e_ = ((Try (Rewrite_Set_Inst [(bdv,v_::real)]          \
+" (L_::bool list) = ((Or_to_List e_)::bool list)               " ^
-\                   d2_polyeq_sq_only_simplify     True)) @@   \
+" in Check_elementwise L_ {(v_::real). Assumptions} )"
-\            (Try (Rewrite_Set polyeq_simplify    False)) @@   \
-\            (Try (Rewrite_Set norm_Rational_parenthesized      False))) e_; \
-\ (L_::bool list) = ((Or_to_List e_)::bool list)               \
-\ in Check_elementwise L_ {(v_::real). Assumptions} )"
 ));
 store_met
-(prep_met PolyEq.thy "met_polyeq_d2_pq" [] e_metID
+(prep_met (theory "PolyEq") "met_polyeq_d2_pq" [] e_metID
 (["PolyEq","solve_d2_polyeq_pq_equation"],
 [("#Given" ,["equality e_","solveFor v_"]),
 ("#Where" ,["(lhs e_) is_poly_in v_ ",
 	       "((lhs e_) has_degree_in v_) = 2"]),
 ("#Find"  ,["solutions v_i_"])
 {rew_ord'="termlessI",
 rls'=PolyEq_erls,
 srls=e_rls,
 prls=PolyEq_prls,
 calc=[("sqrt", ("Root.sqrt", eval_sqrt "#sqrt_"))],
-crls=PolyEq_crls, nrls=norm_Rational(*,
+crls=PolyEq_crls, nrls=norm_Rational},
-(*asm_rls=["d2_polyeq_pqFormula_simplify"],*)
+"Script Solve_d2_polyeq_pq_equation  (e_::bool) (v_::real) =   " ^
-asm_rls=[],
+"  (let e_ = ((Try (Rewrite_Set_Inst [(bdv,v_::real)]         " ^
-asm_thm=[("d2_pqformula1",""),("d2_pqformula2",""),("d2_pqformula3",""),
+"                   d2_polyeq_pqFormula_simplify   True)) @@  " ^
-("d2_pqformula4",""),("d2_pqformula5",""),("d2_pqformula6",""),
+"            (Try (Rewrite_Set polyeq_simplify    False)) @@  " ^
-("d2_pqformula7",""),("d2_pqformula8",""),("d2_pqformula9",""),
+"            (Try (Rewrite_Set norm_Rational_parenthesized False))) e_;" ^
-("d2_pqformula10",""),("d2_pqformula1_neg",""),("d2_pqformula2_neg",""),
+" (L_::bool list) = ((Or_to_List e_)::bool list)              " ^
-("d2_pqformula3_neg",""), ("d2_pqformula4_neg",""),("d2_pqformula9_neg",""),
+" in Check_elementwise L_ {(v_::real). Assumptions} )"
-("d2_pqformula10_neg","")]*)},
-"Script Solve_d2_polyeq_pq_equation  (e_::bool) (v_::real) =   \
-\  (let e_ = ((Try (Rewrite_Set_Inst [(bdv,v_::real)]         \
-\                   d2_polyeq_pqFormula_simplify   True)) @@  \
-\            (Try (Rewrite_Set polyeq_simplify    False)) @@  \
-\            (Try (Rewrite_Set norm_Rational_parenthesized      False))) e_;\
-\ (L_::bool list) = ((Or_to_List e_)::bool list)              \
-\ in Check_elementwise L_ {(v_::real). Assumptions} )"
 ));
 store_met
-(prep_met PolyEq.thy "met_polyeq_d2_abc" [] e_metID
+(prep_met (theory "PolyEq") "met_polyeq_d2_abc" [] e_metID
 (["PolyEq","solve_d2_polyeq_abc_equation"],
 [("#Given" ,["equality e_","solveFor v_"]),
 ("#Where" ,["(lhs e_) is_poly_in v_ ",
 	       "((lhs e_) has_degree_in v_) = 2"]),
 ("#Find"  ,["solutions v_i_"])
 {rew_ord'="termlessI",
 rls'=PolyEq_erls,
 srls=e_rls,
 prls=PolyEq_prls,
 calc=[("sqrt", ("Root.sqrt", eval_sqrt "#sqrt_"))],
-crls=PolyEq_crls, nrls=norm_Rational(*,
+crls=PolyEq_crls, nrls=norm_Rational},
-(*asm_rls=["d2_polyeq_abcFormula_simplify"],*)
+"Script Solve_d2_polyeq_abc_equation  (e_::bool) (v_::real) =   " ^
-asm_rls=[],
+"  (let e_ = ((Try (Rewrite_Set_Inst [(bdv,v_::real)]          " ^
-asm_thm=[("d2_abcformula1",""),("d2_abcformula2",""),("d2_abcformula3",""),
+"                   d2_polyeq_abcFormula_simplify   True)) @@  " ^
-("d2_abcformula4",""),("d2_abcformula5",""),("d2_abcformula6",""),
+"            (Try (Rewrite_Set polyeq_simplify     False)) @@  " ^
-("d2_abcformula7",""),("d2_abcformula8",""),("d2_abcformula9",""),
+"            (Try (Rewrite_Set norm_Rational_parenthesized False))) e_;" ^
-("d2_abcformula10",""),("d2_abcformula1_neg",""),("d2_abcformula2_neg",""),
+" (L_::bool list) = ((Or_to_List e_)::bool list)               " ^
-("d2_abcformula3_neg",""), ("d2_abcformula4_neg",""),("d2_abcformula5_neg",""),
+" in Check_elementwise L_ {(v_::real). Assumptions} )"
-("d2_abcformula6_neg","")]*)},
-"Script Solve_d2_polyeq_abc_equation  (e_::bool) (v_::real) =   \
-\  (let e_ = ((Try (Rewrite_Set_Inst [(bdv,v_::real)]          \
-\                   d2_polyeq_abcFormula_simplify   True)) @@  \
-\            (Try (Rewrite_Set polyeq_simplify     False)) @@  \
-\            (Try (Rewrite_Set norm_Rational_parenthesized       False))) e_;\
-\ (L_::bool list) = ((Or_to_List e_)::bool list)               \
-\ in Check_elementwise L_ {(v_::real). Assumptions} )"
 ));
 store_met
-(prep_met PolyEq.thy "met_polyeq_d3" [] e_metID
+(prep_met (theory "PolyEq") "met_polyeq_d3" [] e_metID
 (["PolyEq","solve_d3_polyeq_equation"],
 [("#Given" ,["equality e_","solveFor v_"]),
 ("#Where" ,["(lhs e_) is_poly_in v_ ",
 	       "((lhs e_) has_degree_in v_) = 3"]),
 ("#Find"  ,["solutions v_i_"])
 {rew_ord'="termlessI",
 rls'=PolyEq_erls,
 srls=e_rls,
 prls=PolyEq_prls,
 calc=[("sqrt", ("Root.sqrt", eval_sqrt "#sqrt_"))],
-crls=PolyEq_crls, nrls=norm_Rational(*,
+crls=PolyEq_crls, nrls=norm_Rational},
-(* asm_rls=["d1_polyeq_simplify","d2_polyeq_simplify","d1_polyeq_simplify"],*)
+"Script Solve_d3_polyeq_equation  (e_::bool) (v_::real) =     " ^
-asm_rls=[],
+"  (let e_ = ((Try (Rewrite_Set_Inst [(bdv,v_::real)]        " ^
-asm_thm=[("d3_isolate_div",""),("d1_isolate_div",""),("d2_pqformula1",""),
+"                    d3_polyeq_simplify           True)) @@  " ^
-("d2_pqformula2",""),("d2_pqformula3",""),("d2_pqformula4",""),
+"             (Try (Rewrite_Set polyeq_simplify  False)) @@  " ^
-("d2_pqformula1_neg",""), ("d2_pqformula2_neg",""),("d2_pqformula3_neg",""),
+"             (Try (Rewrite_Set_Inst [(bdv,v_::real)]        " ^
-("d2_pqformula4_neg",""), ("d2_abcformula1",""),("d2_abcformula2",""),
+"                    d2_polyeq_simplify           True)) @@  " ^
-("d2_abcformula1_neg",""),("d2_abcformula2_neg",""),
+"             (Try (Rewrite_Set polyeq_simplify  False)) @@  " ^
-("d2_sqrt_equation1",""),("d2_sqrt_equation1_neg",""), ("d2_isolate_div","")]*)},
+"             (Try (Rewrite_Set_Inst [(bdv,v_::real)]        " ^
-"Script Solve_d3_polyeq_equation  (e_::bool) (v_::real) =     \
+"                    d1_polyeq_simplify           True)) @@  " ^
-\  (let e_ = ((Try (Rewrite_Set_Inst [(bdv,v_::real)]        \
+"             (Try (Rewrite_Set polyeq_simplify  False)) @@  " ^
-\                    d3_polyeq_simplify           True)) @@  \
+"             (Try (Rewrite_Set norm_Rational_parenthesized False))) e_;" ^
-\             (Try (Rewrite_Set polyeq_simplify  False)) @@  \
+" (L_::bool list) = ((Or_to_List e_)::bool list)             " ^
-\             (Try (Rewrite_Set_Inst [(bdv,v_::real)]        \
+" in Check_elementwise L_ {(v_::real). Assumptions} )"
-\                    d2_polyeq_simplify           True)) @@  \
-\             (Try (Rewrite_Set polyeq_simplify  False)) @@  \
-\             (Try (Rewrite_Set_Inst [(bdv,v_::real)]        \
-\                    d1_polyeq_simplify           True)) @@  \
-\             (Try (Rewrite_Set polyeq_simplify  False)) @@  \
-\             (Try (Rewrite_Set norm_Rational_parenthesized False))) e_;\
-\ (L_::bool list) = ((Or_to_List e_)::bool list)             \
-\ in Check_elementwise L_ {(v_::real). Assumptions} )"
 ));
 (*.solves all expanded (ie. normalized) terms of degree 2.*)
 (*Oct.02 restriction: 'eval_true 0 =< discriminant' ony for integer values
 by 'PolyEq_erls'; restricted until Float.thy is implemented*)
 store_met
-(prep_met PolyEq.thy "met_polyeq_complsq" [] e_metID
+(prep_met (theory "PolyEq") "met_polyeq_complsq" [] e_metID
 (["PolyEq","complete_square"],
 [("#Given" ,["equality e_","solveFor v_"]),
 ("#Where" ,["matches (?a = 0) e_",
 	       "((lhs e_) has_degree_in v_) = 2"]),
 ("#Find"  ,["solutions v_i_"])
 ],
 {rew_ord'="termlessI",rls'=PolyEq_erls,srls=e_rls,prls=PolyEq_prls,
 calc=[("sqrt", ("Root.sqrt", eval_sqrt "#sqrt_"))],
-crls=PolyEq_crls, nrls=norm_Rational(*,
+crls=PolyEq_crls, nrls=norm_Rational},
-asm_rls=[],
+"Script Complete_square (e_::bool) (v_::real) =                          " ^
-asm_thm=[("root_plus_minus","")]*)},
+"(let e_ = ((Try (Rewrite_Set_Inst [(bdv,v_)] cancel_leading_coeff True))" ^
-"Script Complete_square (e_::bool) (v_::real) =                          \
+"        @@ (Try (Rewrite_Set_Inst [(bdv,v_)] complete_square True))     " ^
-\(let e_ = ((Try (Rewrite_Set_Inst [(bdv,v_)] cancel_leading_coeff True))\
+"        @@ (Try (Rewrite square_explicit1 False))                       " ^
-\        @@ (Try (Rewrite_Set_Inst [(bdv,v_)] complete_square True))     \
+"        @@ (Try (Rewrite square_explicit2 False))                       " ^
-\        @@ (Try (Rewrite square_explicit1 False))                       \
+"        @@ (Rewrite root_plus_minus True)                               " ^
-\        @@ (Try (Rewrite square_explicit2 False))                       \
+"        @@ (Try (Repeat (Rewrite_Inst [(bdv,v_)] bdv_explicit1 False))) " ^
-\        @@ (Rewrite root_plus_minus True)                               \
+"        @@ (Try (Repeat (Rewrite_Inst [(bdv,v_)] bdv_explicit2 False))) " ^
-\        @@ (Try (Repeat (Rewrite_Inst [(bdv,v_)] bdv_explicit1 False))) \
+"        @@ (Try (Repeat                                                 " ^
-\        @@ (Try (Repeat (Rewrite_Inst [(bdv,v_)] bdv_explicit2 False))) \
+"                  (Rewrite_Inst [(bdv,v_)] bdv_explicit3 False)))       " ^
-\        @@ (Try (Repeat                                                 \
+"        @@ (Try (Rewrite_Set calculate_RootRat False))                  " ^
-\                  (Rewrite_Inst [(bdv,v_)] bdv_explicit3 False)))       \
+"        @@ (Try (Repeat (Calculate sqrt_)))) e_                         " ^
-\        @@ (Try (Rewrite_Set calculate_RootRat False))                  \
+" in ((Or_to_List e_)::bool list))"
-\        @@ (Try (Repeat (Calculate sqrt_)))) e_                         \
-\ in ((Or_to_List e_)::bool list))"
 ));
-(*6.10.02: x^2=64: root_plus_minus -/-/->
-"Script Complete_square (e_::bool) (v_::real) =                          \
-\(let e_ = ((Try (Rewrite_Set_Inst [(bdv,v_)] cancel_leading_coeff True))\
+(* termorder hacked by MG *)
-\        @@ (Try (Rewrite_Set_Inst [(bdv,v_)] complete_square True))     \
-\        @@ (Try ((Rewrite square_explicit1 False)                       \
-\              Or (Rewrite square_explicit2 False)))                     \
-\        @@ (Rewrite root_plus_minus True)                               \
-\        @@ ((Repeat (Rewrite_Inst [(bdv,v_)] bdv_explicit1 False))      \
-\         Or (Repeat (Rewrite_Inst [(bdv,v_)] bdv_explicit2 False)))     \
-\        @@ (Try (Repeat                                                 \
-\                  (Rewrite_Inst [(bdv,v_)] bdv_explicit3 False)))       \
-\        @@ (Try (Rewrite_Set calculate_RootRat False))                  \
-\        @@ (Try (Repeat (Calculate sqrt_)))) e_                         \
-\ in ((Or_to_List e_)::bool list))"*)
-"******* PolyEq.ML end *******";
-(*eine gehackte termorder*)
 local (*. for make_polynomial_in .*)
 open Term;  (* for type order = EQUAL | LESS | GREATER *)
 fun pr_ord EQUAL = "EQUAL"
 and hd_ord x (f, g) =                                        (* ~ term.ML *)
 prod_ord (prod_ord indexname_ord typ_ord) int_ord (dest_hd' x f,
 						     dest_hd' x g)
 and terms_ord x str pr (ts, us) =
 list_ord (term_ord' x pr (assoc_thy "Isac.thy"))(ts, us);
-(*val x = (term_of o the o (parse thy)) "x"; (*FIXXXXXXME*)
-*)
 in
 fun ord_make_polynomial_in (pr:bool) thy subst tu =
 let
 	(* val _=writeln("*** subs variable is: "^(subst2str subst)); *)

branch	isac-update-Isa09-2
changeset 37952	9ddd1000b900
parent 37947	22235e4dbe5f