walther@59627: (* Title:  Knowledge/polyeq-1.sml
walther@59627:            testexamples for PolyEq, poynomial equations and equational systems
walther@59627:    Author: Richard Lang 2003  
walther@59627:    (c) due to copyright terms
walther@59627: WN030609: some expls dont work due to unfinished handling of 'expanded terms';
walther@59627:           others marked with TODO have to be checked, too.
walther@59627: *)
walther@59627: 
walther@59627: "-----------------------------------------------------------------";
walther@59627: "table of contents -----------------------------------------------";
walther@59627: "-----------------------------------------------------------------";
walther@59627: "------ polyeq-1.sml ---------------------------------------------";
walther@59627: "----------- tests on predicates in problems ---------------------";
walther@59627: "----------- test matching problems ------------------------------";
walther@59627: "----------- lin.eq degree_0 -------------------------------------";
walther@59627: "----------- test thm's d2_pq_formulsxx[_neg]---------------------";
walther@59627: "----------- equality (2 +(-1)*x + x^^^2 = (0::real)) ----------------------------------------";
walther@59627: "----------- equality (-2 +(-1)*x + 1*x^^^2 = 0) ---------------------------------------------";
walther@59627: "----------- equality (-2 + x + x^^^2 = 0) ---------------------------------------------------";
walther@59627: "----------- equality (2 + x + x^^^2 = 0) ----------------------------------------------------";
walther@59627: "----------- equality (-2 + x + 1*x^^^2 = 0)) ------------------------------------------------";
walther@59627: "----------- equality (1*x +   x^^^2 = 0) ----------------------------------------------------";
walther@59627: "----------- equality (1*x + 1*x^^^2 = 0) ----------------------------------------------------";
walther@59627: "----------- equality (x +   x^^^2 = 0) ------------------------------------------------------";
walther@59627: "----------- equality (x + 1*x^^^2 = 0) ------------------------------------------------------";
walther@59627: "----------- equality (-4 + x^^^2 = 0) -------------------------------------------------------";
walther@59627: "----------- equality (4 + 1*x^^^2 = 0) -------------------------------------------------------";
walther@59627: "----------- equality (1 +(-1)*x + 2*x^^^2 = 0) ----------------------------------------------";
walther@59627: "----------- equality (-1 + x + 2*x^^^2 = 0) -------------------------------------------------";
walther@59627: "----------- equality (1 + x + 2*x^^^2 = 0) --------------------------------------------------";
walther@59627: "----------- (-8 - 2*x + x^^^2 = 0),  (*Schalk 2, S.67 Nr.31.b----";
walther@59627: "----------- (-8 - 2*x + x^^^2 = 0),  by rewriting ---------------";
walther@59627: "----------- (-16 + 4*x + 2*x^^^2 = 0), --------------------------";
walther@59627: "-----------------------------------------------------------------";
walther@59627: "------ polyeq-2.sml ---------------------------------------------";
walther@59627: "----------- (a*b - (a+b)*x + x^^^2 = 0), (*Schalk 2,S.68Nr.44.a*)";
walther@59627: "----------- (-64 + x^^^2 = 0), (*Schalk 2, S.66 Nr.1.a~--------*)";
walther@59627: "----------- (-147 + 3*x^^^2 = 0), (*Schalk 2, S.66 Nr.1.b------*)";
walther@59627: "----------- (3*x - 1 - (5*x - (2 - 4*x)) = -11),(*Schalk Is86Bsp5";
walther@59627: "----------- ((x+1)*(x+2) - (3*x - 2)^^^2=.. Schalk II s.68 Bsp 37";
walther@59627: "----------- rls make_polynomial_in ------------------------------";
walther@59627: "----------- interSteps ([1],Res); on Schalk Is86Bsp5-------------";
walther@59627: "----------- rls d2_polyeq_bdv_only_simplify ---------------------";
walther@59627: "-----------------------------------------------------------------";
walther@59627: "-----------------------------------------------------------------";
walther@59627: 
walther@59627: "----------- tests on predicates in problems ---------------------";
walther@59627: "----------- tests on predicates in problems ---------------------";
walther@59627: "----------- tests on predicates in problems ---------------------";
walther@59627: (* trace_rewrite:=true;
walther@59627:  trace_rewrite:=false;
walther@59627: *)
walther@59627:  val t1 = (Thm.term_of o the o (parse thy)) "lhs (-8 - 2*x + x^^^2 = 0)";
walther@59627:  val SOME (t,_) = rewrite_set_ @{theory PolyEq} false PolyEq_prls t1;
walther@59627:  if ((term2str t) = "-8 - 2 * x + x ^^^ 2") then ()
walther@59627:  else  error "polyeq.sml: diff.behav. in lhs";
walther@59627: 
walther@59627:  val t2 = (Thm.term_of o the o (parse thy)) "(-8 - 2*x + x^^^2) is_expanded_in x";
walther@59627:  val SOME (t,_) = rewrite_set_ @{theory PolyEq} false PolyEq_prls t2;
walther@59627:  if (term2str t) = "True" then ()
walther@59627:  else  error "polyeq.sml: diff.behav. 1 in is_expended_in";
walther@59627: 
walther@59627:  val t0 = (Thm.term_of o the o (parse thy)) "(sqrt(x)) is_poly_in x";
walther@59627:  val SOME (t,_) = rewrite_set_ @{theory PolyEq} false PolyEq_prls t0;
walther@59627:  if (term2str t) = "False" then ()
walther@59627:  else  error "polyeq.sml: diff.behav. 2 in is_poly_in";
walther@59627: 
walther@59627:  val t3 = (Thm.term_of o the o (parse thy)) "(-8 + (-1)*2*x + x^^^2) is_poly_in x";
walther@59627:  val SOME (t,_) = rewrite_set_ @{theory PolyEq} false PolyEq_prls t3;
walther@59627:  if (term2str t) = "True" then ()
walther@59627:  else  error "polyeq.sml: diff.behav. 3 in is_poly_in";
walther@59627: 
walther@59627:  val t4 = (Thm.term_of o the o (parse thy)) "(lhs (-8 + (-1)*2*x + x^^^2 = 0)) is_expanded_in x";
walther@59627:  val SOME (t,_) = rewrite_set_ @{theory PolyEq} false PolyEq_prls t4;
walther@59627:  if (term2str t) = "True" then ()
walther@59627:  else  error "polyeq.sml: diff.behav. 4 in is_expended_in";
walther@59627: 
walther@59627: 
walther@59627:  val t6 = (Thm.term_of o the o (parse thy)) "(lhs (-8 - 2*x + x^^^2 = 0)) is_expanded_in x";
walther@59627:  val SOME (t,_) = rewrite_set_ @{theory PolyEq} false PolyEq_prls t6;
walther@59627:  if (term2str t) = "True" then ()
walther@59627:  else  error "polyeq.sml: diff.behav. 5 in is_expended_in";
walther@59627:  
walther@59627:  val t3 = (Thm.term_of o the o (parse thy))"((-8 - 2*x + x^^^2) has_degree_in x) = 2";
walther@59627:  val SOME (t,_) = rewrite_set_ @{theory PolyEq} false PolyEq_prls t3;
walther@59627:  if (term2str t) = "True" then ()
walther@59627:  else  error "polyeq.sml: diff.behav. in has_degree_in_in";
walther@59627: 
walther@59627:  val t3 = (Thm.term_of o the o (parse thy)) "((sqrt(x)) has_degree_in x) = 2";
walther@59627:  val SOME (t,_) = rewrite_set_ @{theory PolyEq} false PolyEq_prls t3;
walther@59627:  if (term2str t) = "False" then ()
walther@59627:  else  error "polyeq.sml: diff.behav. 6 in has_degree_in_in";
walther@59627: 
walther@59627:  val t4 = (Thm.term_of o the o (parse thy)) 
walther@59627: 	      "((-8 - 2*x + x^^^2) has_degree_in x) = 1";
walther@59627:  val SOME (t,_) = rewrite_set_ @{theory PolyEq} false PolyEq_prls t4;
walther@59627:  if (term2str t) = "False" then ()
walther@59627:  else  error "polyeq.sml: diff.behav. 7 in has_degree_in_in";
walther@59627: 
walther@59627:  val t5 = (Thm.term_of o the o (parse thy)) 
walther@59627: 	      "((-8 - 2*x + x^^^2) has_degree_in x) = 2";
walther@59627:  val SOME (t,_) = rewrite_set_ @{theory PolyEq} false PolyEq_prls t5;
walther@59627:  if (term2str t) = "True" then ()
walther@59627:  else  error "polyeq.sml: diff.behav. 8 in has_degree_in_in";
walther@59627: 
walther@59627: "----------- test matching problems --------------------------0---";
walther@59627: "----------- test matching problems --------------------------0---";
walther@59627: "----------- test matching problems --------------------------0---";
walther@59627: val fmz = ["equality (-8 - 2*x + x^^^2 = 0)", "solveFor x","solutions L"];
walther@59627: if match_pbl fmz (get_pbt ["expanded","univariate","equation"]) =
walther@59627:   Matches' {Find = [Correct "solutions L"], 
walther@59627:             With = [], 
walther@59627:             Given = [Correct "equality (-8 - 2 * x + x ^^^ 2 = 0)", Correct "solveFor x"], 
walther@59627:             Where = [Correct "matches (?a = 0) (-8 - 2 * x + x ^^^ 2 = 0)", 
walther@59627:                      Correct "lhs (-8 - 2 * x + x ^^^ 2 = 0) is_expanded_in x"], 
walther@59627:             Relate = []}
walther@59627: then () else error "match_pbl [expanded,univariate,equation]";
walther@59627: 
walther@59627: if match_pbl fmz (get_pbt ["degree_2","expanded","univariate","equation"]) =
walther@59627:   Matches' {Find = [Correct "solutions L"], 
walther@59627:             With = [], 
walther@59627:             Given = [Correct "equality (-8 - 2 * x + x ^^^ 2 = 0)", Correct "solveFor x"], 
walther@59627:             Where = [Correct "lhs (-8 - 2 * x + x ^^^ 2 = 0) has_degree_in x = 2"], 
walther@59627:             Relate = []}              (*before WN110906 was: has_degree_in x =!= 2"]*)
walther@59627: then () else error "match_pbl [degree_2,expanded,univariate,equation]";
walther@59627: 
walther@59627: "----------- lin.eq degree_0 -------------------------------------";
walther@59627: "----------- lin.eq degree_0 -------------------------------------";
walther@59627: "----------- lin.eq degree_0 -------------------------------------";
walther@59627: "----- d0_false ------";
walther@59627: val fmz = ["equality (1 = (0::real))", "solveFor x", "solutions L"];
walther@59627: val (dI',pI',mI') = ("PolyEq",["degree_0","polynomial","univariate","equation"],
walther@59627:                      ["PolyEq","solve_d0_polyeq_equation"]);
walther@59627: (*=== inhibit exn WN110914: declare_constraints doesnt work with num_str ========
walther@59627: TODO: change to "equality (x + -1*x = (0::real))"
walther@59627:       and search for an appropriate problem and method.
walther@59627: 
walther@59627: val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[]")) => ()
walther@59627: 	 | _ => error "polyeq.sml: diff.behav. in 1 = 0 -> []";
walther@59627: 
walther@59627: "----- d0_true ------";
walther@59627: val fmz = ["equality (0 = (0::real))", "solveFor x","solutions L"];
walther@59627: val (dI',pI',mI') = ("PolyEq",["degree_0","polynomial","univariate","equation"],
walther@59627:                      ["PolyEq","solve_d0_polyeq_equation"]);
walther@59627: val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: case f of Form' (FormKF (~1,EdUndef,0,Nundef,"UniversalList")) => ()
walther@59627: 	 | _ => error "polyeq.sml: diff.behav. in 0 = 0 -> UniversalList";
walther@59627: ============ inhibit exn WN110914 ============================================*)
walther@59627: 
walther@59627: "----------- test thm's d2_pq_formulsxx[_neg]---------------------";
walther@59627: "----------- test thm's d2_pq_formulsxx[_neg]---------------------";
walther@59627: "----------- test thm's d2_pq_formulsxx[_neg]---------------------";
walther@59627: "----- d2_pqformula1 ------!!!!";
walther@59627: val fmz = ["equality (-1/8 + (-1/4)*z + z^^^2 = (0::real))", "solveFor z","solutions L"];
walther@59627: val (dI',pI',mI') =
walther@59627:   ("Isac_Knowledge", ["pqFormula","degree_2","polynomial","univariate","equation"], ["no_met"]);
walther@59627: val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*Apply_Method ["PolyEq", "solve_d2_polyeq_pq_equation"]*)
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt;         
walther@59627: 
walther@59627: (*[z = 1 / 8 + sqrt (9 / 16) / 2, z = 1 / 8 + -1 * sqrt (9 / 16) / 2] TODO sqrt*)
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt =..,Check_elementwise "Assumptions")*)
walther@59627: "~~~~~ fun me, args:"; val ((_,tac), (p:pos'), _, (pt:ctree)) = (nxt, p, [], pt);
walther@59627: "~~~~~ fun locatetac, args:"; val (tac, (ptp as (pt, p))) = (tac, (pt, p));
walther@59627: val (mI,m) = mk_tac'_ tac;
walther@59627: val Appl m = applicable_in p pt m;
walther@59627: val Check_elementwise' (trm1, str, (trm2, trms)) = m;
walther@59627: term2str trm1 = "[z = 1 / 8 + sqrt (9 / 16) / 2, z = 1 / 8 + -1 * sqrt (9 / 16) / 2]";
walther@59627: str = "Assumptions";
walther@59627: term2str trm2 = "[z = 1 / 8 + sqrt (9 / 16) / 2, z = 1 / 8 + -1 * sqrt (9 / 16) / 2]";
walther@59627: terms2str trms = "[\"lhs (-1 / 8 + -1 * (1 / 8 + sqrt (9 / 16) / 2) / 4 +\n "^
walther@59627:   "    (1 / 8 + sqrt (9 / 16) / 2) ^^^ 2 =\n     0) is_poly_in 1 / 8 + sqrt (9 / 16) / 2\","^
walther@59627:   "\"lhs (-1 / 8 + -1 * (1 / 8 + sqrt (9 / 16) / 2) / 4 +\n     (1 / 8 + sqrt (9 / 16) / 2) ^^^ 2 =\n     0) "^
walther@59627:       "has_degree_in 1 / 8 + sqrt (9 / 16) / 2 =\n2\","^
walther@59627:   "\"lhs (-1 / 8 + -1 * (1 / 8 + -1 * sqrt (9 / 16) / 2) / 4 +\n     (1 / 8 + -1 * sqrt (9 / 16) / 2) ^^^ 2 =\n     0) is_poly_in 1 / 8 + -1 * sqrt (9 / 16) / 2\","^
walther@59627:   "\"lhs (-1 / 8 + -1 * (1 / 8 + -1 * sqrt (9 / 16) / 2) / 4 +\n     (1 / 8 + -1 * sqrt (9 / 16) / 2) ^^^ 2 =\n     0) has_degree_in 1 / 8 + -1 * sqrt (9 / 16) / 2 =\n2\"]";
walther@59627: (*TODO simplify assumptions (sqrt!) and check ERROR in has_degree_in*);
walther@59627: member op = specsteps mI (*false*);
walther@59627: (*loc_solve_ (mI,m) ptp;
walther@59627:   WAS: not-found-in-script: NotLocatable from NasNap (Const ("List...*)
walther@59627: "~~~~~ fun loc_solve_, args:"; val (m, (pt,pos)) = ((mI,m), ptp);
walther@59627: (*solve m (pt, pos);
walther@59627:   WAS: not-found-in-script: NotLocatable from NasNap (Const ("List...*)
walther@59627: "~~~~~ fun solve, args:"; val ((mI,m), (pt, po as (p,p_))) = (m, (pt, pos));
walther@59627: e_metID = get_obj g_metID pt (par_pblobj pt p) (*false*);
walther@59627:         val thy' = get_obj g_domID pt (par_pblobj pt p);
walther@59627: 	        val (srls, is, sc) = from_pblobj_or_detail' thy' (p,p_) pt;
walther@59627: 		        val d = e_rls;
walther@59627: (*locate_input_tactic (thy',srls) m  (pt,(p,p_)) (sc,d) is;
walther@59627:   WAS: not-found-in-script: NotLocatable from NasNap (Const ("List...*)
walther@59679: "~~~~~ fun locate_input_tactic, args:"; val () = ();
walther@59679: (*----- outcommented during cleanup of args in lucas-interpreter.sml ------------------------\\* )
walther@59627: l = [] orelse ((last_elem o fst) p = 0 andalso snd p = Res) (*false*);
walther@59691: (*WAS val NasApp _ =(go_scan_up1 (thy',srls,scr,d) ((E,l,a,v,S,b), [(m,EmptyMout,pt,p,[])]) )
walther@59627:   ... Assoc ... is correct*)
walther@59691: "~~~~~ and go_scan_up1, args:"; val ((ys as (_,_,_,Prog sc,_)), ((E,l,a,v,S,b),ss)) =
walther@59627:    ((thy',ctxt,srls,scr,d), ((E,l,a,v,S,b), [(m,EmptyMout,pt,p,[])]));
walther@59627: 1 < length l (*true*);
walther@59627: val up = drop_last l;
walther@59627:   term2str (go up sc);
walther@59627:   (go up sc);
walther@59691: (*WAS val NasNap _ = scan_up1 ys ((E,up,a,v,S,b),ss) (go up sc)
walther@59627:       ... ???? ... is correct*)
walther@59691: "~~~~~ fun scan_up1, args:"; val ((ys as (y,ctxt,s,Prog sc,d)), (is as (E,l,a,v,S,b),ss), 
walther@59627: 	   (Const ("HOL.Let",_) $ _)) = (ys, ((E,up,a,v,S,b),ss:step list), (go up sc));
walther@59627:       val l = drop_last l; (*comes from e, goes to Abs*)
walther@59627:       val (Const ("HOL.Let",_) $ e $ (Abs (i,T,body))) = go l sc;
walther@59627:       val i = mk_Free (i, T);
walther@59660:       val E = Env.upd_env E (i, v);
walther@59627: (*Type error ...: Can't unify _a to pos * pos_ (Incompatible types)*)
walther@59627: val [(tac_, mout, ctree, pos', xxx)] = ss;
walther@59627: val ss = [(tac_, mout, ctree, pos', []:(pos * pos_) list)];
walther@59691: (*WAS val NasApp iss = scan_dn1 (((y,s),d),Aundef) ((E, l@[R,D], a,v,S,b),ss) body
walther@59627:       ... Assoc ... is correct*)
walther@59691: "~~~~~ fun scan_dn1, args:"; val ((((thy',sr),d),ap), (is as (E,l,a,v,S,b), (m,_,pt,(p,p_),c)::ss), t) =
walther@59627:      ((((y,s),d),Aundef), ((E, l@[R,D], a,v,S,b),ss), body);
walther@59666: val (a', STac stac) = handle_leaf "locate" thy' sr (E, (a, v)) t
walther@59627:              val ctxt = get_ctxt pt (p,p_)
walther@59627:              val p' = lev_on p : pos;
walther@59627: (* WAS val NotAss = associate pt d (m, stac)
walther@59627:       ... Ass ... is correct*)
walther@59627: "~~~~~ fun associate, args:"; val (pt, _, (m as Check_elementwise' (consts,_,(consts_chkd,_))),
walther@59627:     (Const ("Prog_Tac.Check'_elementwise",_) $ consts' $ _)) = (pt, d, m, stac);
walther@59627: term2str consts;
walther@59627: term2str consts';
walther@59627: if consts = consts' (*WAS false*) then () else error "Check_elementwise changed";
walther@59627: (*[z = 1 / 8 + sqrt (9 / 16) / 2, z = 1 / 8 + -1 * sqrt (9 / 16) / 2] TODO sqrt*)
walther@59679: ( *----- outcommented during cleanup of args in lucas-interpreter.sml ------------------------//*)
walther@59627: 
walther@59627: "----------- equality (2 +(-1)*x + x^^^2 = (0::real)) ----------------------------------------";
walther@59627: "----------- equality (2 +(-1)*x + x^^^2 = (0::real)) ----------------------------------------";
walther@59627: "----------- equality (2 +(-1)*x + x^^^2 = (0::real)) ----------------------------------------";
walther@59627: "----- d2_pqformula1_neg ------";
walther@59627: val fmz = ["equality (2 +(-1)*x + x^^^2 = (0::real))", "solveFor x","solutions L"];
walther@59627: val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"], ["PolyEq","solve_d2_polyeq_pq_equation"]);
walther@59627: val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: (*### or2list False
walther@59627:   ([1],Res)  False   Or_to_List)*)
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; 
walther@59627: (*### or2list False                           
walther@59627:   ([2],Res)  []      Check_elementwise "Assumptions"*)
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val asm = get_assumptions_ pt p;
walther@59627: if f2str f = "[]" andalso 
walther@59627:   terms2str asm = "[\"lhs (2 + -1 * x + x ^^^ 2 = 0) is_poly_in x\"," ^
walther@59627:     "\"lhs (2 + -1 * x + x ^^^ 2 = 0) has_degree_in x = 2\"]" then ()
walther@59627: else error "polyeq.sml: diff.behav. in 2 +(-1)*x + x^^^2 = 0";
walther@59627: 
walther@59627: "----------- equality (-2 +(-1)*x + 1*x^^^2 = 0) ---------------------------------------------";
walther@59627: "----------- equality (-2 +(-1)*x + 1*x^^^2 = 0) ---------------------------------------------";
walther@59627: "----------- equality (-2 +(-1)*x + 1*x^^^2 = 0) ---------------------------------------------";
walther@59627: "----- d2_pqformula2 ------";
walther@59627: val fmz = ["equality (-2 +(-1)*x + 1*x^^^2 = 0)", "solveFor x","solutions L"];
walther@59627: val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"],
walther@59627:                      ["PolyEq","solve_d2_polyeq_pq_equation"]);
walther@59627: (*val p = e_pos'; 
walther@59627: val (mI,m) = ("Init_Proof",Init_Proof (fmz, (dI',pI',mI')));
walther@59627: val (p,_,f,nxt,_,pt) = me (mI,m) p [] EmptyPtree;*)
walther@59627: val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: 
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: case f of FormKF "[x = 2, x = -1]" => ()
walther@59627: 	 | _ => error "polyeq.sml: diff.behav. in -2 + (-1)*x + x^2 = 0 -> [x = 2, x = -1]";
walther@59627: 
walther@59627: 
walther@59627: "----------- equality (-2 + x + x^^^2 = 0) ---------------------------------------------------";
walther@59627: "----------- equality (-2 + x + x^^^2 = 0) ---------------------------------------------------";
walther@59627: "----------- equality (-2 + x + x^^^2 = 0) ---------------------------------------------------";
walther@59627: "----- d2_pqformula3 ------";
walther@59627: (*EP-9*)
walther@59627: val fmz = ["equality (-2 + x + x^^^2 = 0)", "solveFor x","solutions L"];
walther@59627: val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"],
walther@59627:                      ["PolyEq","solve_d2_polyeq_pq_equation"]);
walther@59627: val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: 
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; 
walther@59627: case f of FormKF "[x = 1, x = -2]" => ()
walther@59627: 	 | _ => error "polyeq.sml: diff.behav. in  -2 + x + x^2 = 0-> [x = 1, x = -2]";
walther@59627: 
walther@59627: 
walther@59627: "----------- equality (2 + x + x^^^2 = 0) ----------------------------------------------------";
walther@59627: "----------- equality (2 + x + x^^^2 = 0) ----------------------------------------------------";
walther@59627: "----------- equality (2 + x + x^^^2 = 0) ----------------------------------------------------";
walther@59627: "----- d2_pqformula3_neg ------";
walther@59627: val fmz = ["equality (2 + x + x^^^2 = 0)", "solveFor x","solutions L"];
walther@59627: val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"],
walther@59627:                      ["PolyEq","solve_d2_polyeq_pq_equation"]);
walther@59627: val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: 
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: "TODO 2 + x + x^^^2 = 0";
walther@59627: "TODO 2 + x + x^^^2 = 0";
walther@59627: "TODO 2 + x + x^^^2 = 0";
walther@59627: 
walther@59627: "----------- equality (-2 + x + 1*x^^^2 = 0)) ------------------------------------------------";
walther@59627: "----------- equality (-2 + x + 1*x^^^2 = 0)) ------------------------------------------------";
walther@59627: "----------- equality (-2 + x + 1*x^^^2 = 0)) ------------------------------------------------";
walther@59627: "----- d2_pqformula4 ------";
walther@59627: val fmz = ["equality (-2 + x + 1*x^^^2 = 0)", "solveFor x","solutions L"];
walther@59627: val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"],
walther@59627:                      ["PolyEq","solve_d2_polyeq_pq_equation"]);
walther@59627: val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: case f of FormKF "[x = 1, x = -2]" => ()
walther@59627: 	 | _ => error "polyeq.sml: diff.behav. in  -2 + x + 1*x^^^2 = 0 -> [x = 1, x = -2]";
walther@59627: 
walther@59627: "----------- equality (1*x +   x^^^2 = 0) ----------------------------------------------------";
walther@59627: "----------- equality (1*x +   x^^^2 = 0) ----------------------------------------------------";
walther@59627: "----------- equality (1*x +   x^^^2 = 0) ----------------------------------------------------";
walther@59627: "----- d2_pqformula5 ------";
walther@59627: val fmz = ["equality (1*x +   x^^^2 = 0)", "solveFor x","solutions L"];
walther@59627: val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"],
walther@59627:                      ["PolyEq","solve_d2_polyeq_pq_equation"]);
walther@59627: val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: case f of FormKF "[x = 0, x = -1]" => ()
walther@59627: 	 | _ => error "polyeq.sml: diff.behav. in  1*x +   x^2 = 0 -> [x = 0, x = -1]";
walther@59627: 
walther@59627: "----------- equality (1*x + 1*x^^^2 = 0) ----------------------------------------------------";
walther@59627: "----------- equality (1*x + 1*x^^^2 = 0) ----------------------------------------------------";
walther@59627: "----------- equality (1*x + 1*x^^^2 = 0) ----------------------------------------------------";
walther@59627: "----- d2_pqformula6 ------";
walther@59627: val fmz = ["equality (1*x + 1*x^^^2 = 0)", "solveFor x","solutions L"];
walther@59627: val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"],
walther@59627:                      ["PolyEq","solve_d2_polyeq_pq_equation"]);
walther@59627: val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; 
walther@59627: case f of FormKF "[x = 0, x = -1]" => ()
walther@59627: 	 | _ => error "polyeq.sml: diff.behav. in  1*x + 1*x^2 = 0 -> [x = 0, x = -1]";
walther@59627: 
walther@59627: "----------- equality (x +   x^^^2 = 0) ------------------------------------------------------";
walther@59627: "----------- equality (x +   x^^^2 = 0) ------------------------------------------------------";
walther@59627: "----------- equality (x +   x^^^2 = 0) ------------------------------------------------------";
walther@59627: "----- d2_pqformula7 ------";
walther@59627: (*EP-10*)
walther@59627: val fmz = ["equality (  x +   x^^^2 = 0)", "solveFor x","solutions L"];
walther@59627: val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"],
walther@59627:                      ["PolyEq","solve_d2_polyeq_pq_equation"]);
walther@59627: val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; 
walther@59627: case f of FormKF "[x = 0, x = -1]" => ()
walther@59627: 	 | _ => error "polyeq.sml: diff.behav. in  x + x^2 = 0 -> [x = 0, x = -1]";
walther@59627: 
walther@59627: "----------- equality (x + 1*x^^^2 = 0) ------------------------------------------------------";
walther@59627: "----------- equality (x + 1*x^^^2 = 0) ------------------------------------------------------";
walther@59627: "----------- equality (x + 1*x^^^2 = 0) ------------------------------------------------------";
walther@59627: "----- d2_pqformula8 ------";
walther@59627: val fmz = ["equality (x + 1*x^^^2 = 0)", "solveFor x","solutions L"];
walther@59627: val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"],
walther@59627:                      ["PolyEq","solve_d2_polyeq_pq_equation"]);
walther@59627: val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; 
walther@59627: case f of FormKF "[x = 0, x = -1]" => ()
walther@59627: 	 | _ => error "polyeq.sml: diff.behav. in  x + 1*x^2 = 0 -> [x = 0, x = -1]";
walther@59627: 
walther@59627: "----------- equality (-4 + x^^^2 = 0) -------------------------------------------------------";
walther@59627: "----------- equality (-4 + x^^^2 = 0) -------------------------------------------------------";
walther@59627: "----------- equality (-4 + x^^^2 = 0) -------------------------------------------------------";
walther@59627: "----- d2_pqformula9 ------";
walther@59627: val fmz = ["equality (-4 + x^^^2 = 0)", "solveFor x","solutions L"];
walther@59627: val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"],
walther@59627:                      ["PolyEq","solve_d2_polyeq_pq_equation"]);
walther@59627: val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: case f of FormKF "[x = 2, x = -2]" => ()
walther@59627: 	 | _ => error "polyeq.sml: diff.behav. in -4 + x^2 = 0 -> [x = 2, x = -2]";
walther@59627: 
walther@59627: 
walther@59627: "----------- equality (4 + 1*x^^^2 = 0) -------------------------------------------------------";
walther@59627: "----------- equality (4 + 1*x^^^2 = 0) -------------------------------------------------------";
walther@59627: "----------- equality (4 + 1*x^^^2 = 0) -------------------------------------------------------";
walther@59627: "----- d2_pqformula9_neg ------";
walther@59627: val fmz = ["equality (4 + 1*x^^^2 = 0)", "solveFor x","solutions L"];
walther@59627: val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"],
walther@59627:                      ["PolyEq","solve_d2_polyeq_pq_equation"]);
walther@59627: val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: "TODO 4 + 1*x^^^2 = 0";
walther@59627: "TODO 4 + 1*x^^^2 = 0";
walther@59627: "TODO 4 + 1*x^^^2 = 0";
walther@59627: 
walther@59627: "-------------------- test thm's d2_abc_formulsxx[_neg]-----";
walther@59627: "-------------------- test thm's d2_abc_formulsxx[_neg]-----";
walther@59627: "-------------------- test thm's d2_abc_formulsxx[_neg]-----";
walther@59627: val fmz = ["equality (-1 +(-1)*x + 2*x^^^2 = 0)", "solveFor x","solutions L"];
walther@59627: val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
walther@59627:                      ["PolyEq","solve_d2_polyeq_abc_equation"]);
walther@59627: val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: case f of FormKF "[x = 1, x = -1 / 2]" => ()
walther@59627: 	 | _ => error "polyeq.sml: diff.behav. in -1 + (-1)*x + 2*x^2 = 0 -> [x = 1, x = -1/2]";
walther@59627: 
walther@59627: "----------- equality (1 +(-1)*x + 2*x^^^2 = 0) ----------------------------------------------";
walther@59627: "----------- equality (1 +(-1)*x + 2*x^^^2 = 0) ----------------------------------------------";
walther@59627: "----------- equality (1 +(-1)*x + 2*x^^^2 = 0) ----------------------------------------------";
walther@59627: val fmz = ["equality (1 +(-1)*x + 2*x^^^2 = 0)", "solveFor x","solutions L"];
walther@59627: val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
walther@59627:                      ["PolyEq","solve_d2_polyeq_abc_equation"]);
walther@59627: val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: 
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: "TODO 1 +(-1)*x + 2*x^^^2 = 0";
walther@59627: "TODO 1 +(-1)*x + 2*x^^^2 = 0";
walther@59627: "TODO 1 +(-1)*x + 2*x^^^2 = 0";
walther@59627: 
walther@59627: 
walther@59627: "----------- equality (-1 + x + 2*x^^^2 = 0) -------------------------------------------------";
walther@59627: "----------- equality (-1 + x + 2*x^^^2 = 0) -------------------------------------------------";
walther@59627: "----------- equality (-1 + x + 2*x^^^2 = 0) -------------------------------------------------";
walther@59627: (*EP-11*)
walther@59627: val fmz = ["equality (-1 + x + 2*x^^^2 = 0)", "solveFor x","solutions L"];
walther@59627: val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
walther@59627:                      ["PolyEq","solve_d2_polyeq_abc_equation"]);
walther@59627: val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: 
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: 
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: case f of FormKF "[x = 1 / 2, x = -1]" => ()
walther@59627: 	 | _ => error "polyeq.sml: diff.behav. in -1 + x + 2*x^2 = 0 -> [x = 1/2, x = -1]";
walther@59627: 
walther@59627: 
walther@59627: "----------- equality (1 + x + 2*x^^^2 = 0) --------------------------------------------------";
walther@59627: "----------- equality (1 + x + 2*x^^^2 = 0) --------------------------------------------------";
walther@59627: "----------- equality (1 + x + 2*x^^^2 = 0) --------------------------------------------------";
walther@59627: val fmz = ["equality (1 + x + 2*x^^^2 = 0)", "solveFor x","solutions L"];
walther@59627: val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
walther@59627:                      ["PolyEq","solve_d2_polyeq_abc_equation"]);
walther@59627: val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: 
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; 
walther@59627: "TODO 1 + x + 2*x^^^2 = 0";
walther@59627: "TODO 1 + x + 2*x^^^2 = 0";
walther@59627: "TODO 1 + x + 2*x^^^2 = 0";
walther@59627: 
walther@59627: 
walther@59627: val fmz = ["equality (-2 + 1*x + x^^^2 = 0)", "solveFor x","solutions L"];
walther@59627: val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
walther@59627:                      ["PolyEq","solve_d2_polyeq_abc_equation"]);
walther@59627: val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: case f of FormKF "[x = 1, x = -2]" => ()
walther@59627: 	 | _ => error "polyeq.sml: diff.behav. in -2 + 1*x + x^2 = 0 -> [x = 1, x = -2]";
walther@59627: 
walther@59627: val fmz = ["equality ( 2 + 1*x + x^^^2 = 0)", "solveFor x","solutions L"];
walther@59627: val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
walther@59627:                      ["PolyEq","solve_d2_polyeq_abc_equation"]);
walther@59627: val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; 
walther@59627: "TODO 2 + 1*x + x^^^2 = 0";
walther@59627: "TODO 2 + 1*x + x^^^2 = 0";
walther@59627: "TODO 2 + 1*x + x^^^2 = 0";
walther@59627: 
walther@59627: (*EP-12*)
walther@59627: val fmz = ["equality (-2 + x + x^^^2 = 0)", "solveFor x","solutions L"];
walther@59627: val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
walther@59627:                      ["PolyEq","solve_d2_polyeq_abc_equation"]);
walther@59627: val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: case f of FormKF "[x = 1, x = -2]" => ()
walther@59627: 	 | _ => error "polyeq.sml: diff.behav. in -2 + x + x^2 = 0 -> [x = 1, x = -2]";
walther@59627: 
walther@59627: val fmz = ["equality ( 2 + x + x^^^2 = 0)", "solveFor x","solutions L"];
walther@59627: val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
walther@59627:                      ["PolyEq","solve_d2_polyeq_abc_equation"]);
walther@59627: val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; 
walther@59627: "TODO 2 + x + x^^^2 = 0";
walther@59627: "TODO 2 + x + x^^^2 = 0";
walther@59627: "TODO 2 + x + x^^^2 = 0";
walther@59627: 
walther@59627: (*EP-13*)
walther@59627: val fmz = ["equality (-8 + 2*x^^^2 = 0)", "solveFor x","solutions L"];
walther@59627: val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
walther@59627:                      ["PolyEq","solve_d2_polyeq_abc_equation"]);
walther@59627: val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: case f of FormKF "[x = 2, x = -2]" => ()
walther@59627: 	 | _ => error "polyeq.sml: diff.behav. in -8 + 2*x^2 = 0 -> [x = 2, x = -2]";
walther@59627: 
walther@59627: val fmz = ["equality ( 8+ 2*x^^^2 = 0)", "solveFor x","solutions L"];
walther@59627: val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
walther@59627:                      ["PolyEq","solve_d2_polyeq_abc_equation"]);
walther@59627: val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: "TODO 8+ 2*x^^^2 = 0";
walther@59627: "TODO 8+ 2*x^^^2 = 0";
walther@59627: "TODO 8+ 2*x^^^2 = 0";
walther@59627: 
walther@59627: (*EP-14*)
walther@59627: val fmz = ["equality (-4 + x^^^2 = 0)", "solveFor x","solutions L"];
walther@59627: val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"], ["PolyEq","solve_d2_polyeq_abc_equation"]);
walther@59627: val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: case f of FormKF "[x = 2, x = -2]" => ()
walther@59627: 	 | _ => error "polyeq.sml: diff.behav. in -4 + x^2 = 0 -> [x = 2, x = -2]";
walther@59627: 
walther@59627: 
walther@59627: val fmz = ["equality ( 4+ x^^^2 = 0)", "solveFor x","solutions L"];
walther@59627: val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"], ["PolyEq","solve_d2_polyeq_abc_equation"]);
walther@59627: val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: "TODO 4+ x^^^2 = 0";
walther@59627: "TODO 4+ x^^^2 = 0";
walther@59627: "TODO 4+ x^^^2 = 0";
walther@59627: 
walther@59627: (*EP-15*)
walther@59627: val fmz = ["equality (2*x + 2*x^^^2 = 0)", "solveFor x","solutions L"];
walther@59627: val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
walther@59627:                      ["PolyEq","solve_d2_polyeq_abc_equation"]);
walther@59627: val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: case f of FormKF "[x = 0, x = -1]" => ()
walther@59627: 	 | _ => error "polyeq.sml: diff.behav. in x + x^2 = 0 -> [x = 0, x = -1]";
walther@59627: 
walther@59627: val fmz = ["equality (1*x + x^^^2 = 0)", "solveFor x","solutions L"];
walther@59627: val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
walther@59627:                      ["PolyEq","solve_d2_polyeq_abc_equation"]);
walther@59627: val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: case f of FormKF "[x = 0, x = -1]" => ()
walther@59627: 	 | _ => error "polyeq.sml: diff.behav. in x + x^2 = 0 -> [x = 0, x = -1]";
walther@59627: 
walther@59627: (*EP-16*)
walther@59627: val fmz = ["equality (x + 2*x^^^2 = 0)", "solveFor x","solutions L"];
walther@59627: val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
walther@59627:                      ["PolyEq","solve_d2_polyeq_abc_equation"]);
walther@59627: val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: case f of FormKF "[x = 0, x = -1 / 2]" => ()
walther@59627: 	 | _ => error "polyeq.sml: diff.behav. in x + x^2 = 0 -> [x = 0, x = -1 / 2]";
walther@59627: 
walther@59627: (*EP-//*)
walther@59627: val fmz = ["equality (x + x^^^2 = 0)", "solveFor x","solutions L"];
walther@59627: val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
walther@59627:                      ["PolyEq","solve_d2_polyeq_abc_equation"]);
walther@59627: val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: case f of FormKF "[x = 0, x = -1]" => ()
walther@59627: 	 | _ => error "polyeq.sml: diff.behav. in x + x^2 = 0 -> [x = 0, x = -1]";
walther@59627: 
walther@59627: 
walther@59627: "----------- (-8 - 2*x + x^^^2 = 0),  (*Schalk 2, S.67 Nr.31.b----";
walther@59627: "----------- (-8 - 2*x + x^^^2 = 0),  (*Schalk 2, S.67 Nr.31.b----";
walther@59627: "----------- (-8 - 2*x + x^^^2 = 0),  (*Schalk 2, S.67 Nr.31.b----";
walther@59627: (*stopped du to TODO.txt WN111014.TODO calculate_Poly < calculate_Rational < calculate_RootRat
walther@59627: see --- val rls = calculate_RootRat > calculate_Rational ---
walther@59627: calculate_RootRat was a TODO with 2002, requires re-design.
walther@59627: see also --- (-8 - 2*x + x^^^2 = 0),  by rewriting --- below
walther@59627: *)
walther@59627:  val fmz = ["equality (-8 - 2*x + x^^^2 = 0)", (*Schalk 2, S.67 Nr.31.b*)
walther@59627:  	    "solveFor x","solutions L"];
walther@59627:  val (dI',pI',mI') =
walther@59627:      ("PolyEq",["degree_2","expanded","univariate","equation"],
walther@59627:       ["PolyEq","complete_square"]);
walther@59627: val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: 
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: (*Apply_Method ("PolyEq","complete_square")*)
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: (*"-8 - 2 * x + x ^^^ 2 = 0", nxt = Rewrite_Set_Inst ... "complete_square*)
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: (*"-8 + (2 / 2 - x) ^^^ 2 = (2 / 2) ^^^ 2", nxt = Rewrite("square_explicit1"*)
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: (*"(2 / 2 - x) ^^^ 2 = (2 / 2) ^^^ 2 - -8" nxt = Rewrite("root_plus_minus*)
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: (*"2 / 2 - x = sqrt ((2 / 2) ^^^ 2 - -8) |
walther@59627:    2 / 2 - x = - sqrt ((2 / 2) ^^^ 2 - -8)" nxt = Rewr_Inst("bdv_explicit2"*)
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: (*"2 / 2 - x = sqrt ((2 / 2) ^^^ 2 - -8) |
walther@59627:    -1*x = - (2 / 2) + - sqrt ((2 / 2) ^^^ 2 - -8)"nxt = R_Inst("bdv_explt2"*)
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: (*"-1 * x = - (2 / 2) + sqrt ((2 / 2) ^^^ 2 - -8) |
walther@59627:    -1 * x = (- (2 / 2) + - sqrt ((2 / 2) ^^^ 2 - -8))"nxt = bdv_explicit3*)
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: (*"-1 * x = - (2 / 2) + sqrt ((2 / 2) ^^^ 2 - -8) |
walther@59627:   x = -1 * (- (2 / 2) + - sqrt ((2 / 2) ^^^ 2 - -8))" nxt = bdv_explicit3*)
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: (*"x = -1 * (- (2 / 2) + sqrt ((2 / 2) ^^^ 2 - -8)) |
walther@59627:    x = -1 * (- (2 / 2) + - sqrt ((2 / 2) ^^^ 2 - -8))"nxt = calculate_Rational
walther@59627:    NOT IMPLEMENTED SINCE 2002 ------------------------------^^^^^^^^^^^^^^^^^^*)
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: (*"x = -2 | x = 4" nxt = Or_to_List*)
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: (*"[x = -2, x = 4]" nxt = Check_Postcond*)
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt; f2str f;
walther@59627: (* FIXXXME 
walther@59627:  case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = -2, x = 4]")) => () TODO
walther@59627: 	 | _ => error "polyeq.sml: diff.behav. in [x = -2, x = 4]";
walther@59627: *)
walther@59627: if f2str f =
walther@59627: "[x = -1 * -1 + -1 * sqrt (2 ^^^ 2 / 2 ^^^ 2 - -8),\n x = -1 * -1 + -1 * (-1 * sqrt (2 ^^^ 2 / 2 ^^^ 2 - -8))]"
walther@59627: (*"[x = -1 * -1 + -1 * sqrt (1 ^^^ 2 - -8),\n x = -1 * -1 + -1 * (-1 * sqrt (1 ^^^ 2 - -8))]"*)
walther@59627: then () else error "polyeq.sml corrected?behav. in [x = -2, x = 4]";
walther@59627: 
walther@59627: 
walther@59627: "----------- (-8 - 2*x + x^^^2 = 0),  by rewriting ---------------";
walther@59627: "----------- (-8 - 2*x + x^^^2 = 0),  by rewriting ---------------";
walther@59627: "----------- (-8 - 2*x + x^^^2 = 0),  by rewriting ---------------";
walther@59627: (*stopped du to TODO.txt WN111014.TODO calculate_Poly < calculate_Rational < calculate_RootRat
walther@59627: see --- val rls = calculate_RootRat > calculate_Rational ---*)
walther@59627: val thy = @{theory PolyEq};
walther@59627: val ctxt = Proof_Context.init_global thy;
walther@59627: val inst = [((the o (parseNEW  ctxt)) "bdv::real", (the o (parseNEW  ctxt)) "x::real")];
walther@59627: val t = (the o (parseNEW  ctxt)) "-8 - 2*x + x^^^2 = (0::real)";
walther@59627: 
walther@59627: val rls = complete_square;
walther@59627: val SOME (t,asm) = rewrite_set_inst_ thy true inst rls t;
walther@59627: term2str t = "-8 + (2 / 2 - x) ^^^ 2 = (2 / 2) ^^^ 2";
walther@59627: 
walther@59627: val thm = num_str @{thm square_explicit1};
walther@59627: val SOME (t,asm) = rewrite_ thy dummy_ord Erls true thm t;
walther@59627: term2str t = "(2 / 2 - x) ^^^ 2 = (2 / 2) ^^^ 2 - -8";
walther@59627: 
walther@59627: val thm = num_str @{thm root_plus_minus};
walther@59627: val SOME (t,asm) = rewrite_ thy dummy_ord PolyEq_erls true thm t;
walther@59627: term2str t = "2 / 2 - x = sqrt ((2 / 2) ^^^ 2 - -8) |"^
walther@59627:            "\n2 / 2 - x = -1 * sqrt ((2 / 2) ^^^ 2 - -8)";
walther@59627: 
walther@59627: (*the thm bdv_explicit2* here required to be constrained to ::real*)
walther@59627: val thm = num_str @{thm bdv_explicit2};
walther@59627: val SOME (t,asm) = rewrite_inst_ thy dummy_ord Erls true inst thm t;
walther@59627: term2str t = "2 / 2 - x = sqrt ((2 / 2) ^^^ 2 - -8) |"^
walther@59627:               "\n-1 * x = - (2 / 2) + -1 * sqrt ((2 / 2) ^^^ 2 - -8)";
walther@59627: 
walther@59627: val thm = num_str @{thm bdv_explicit3};
walther@59627: val SOME (t,asm) = rewrite_inst_ thy dummy_ord Erls true inst thm t;
walther@59627: term2str t = "2 / 2 - x = sqrt ((2 / 2) ^^^ 2 - -8) |"^
walther@59627:                    "\nx = -1 * (- (2 / 2) + -1 * sqrt ((2 / 2) ^^^ 2 - -8))";
walther@59627: 
walther@59627: val thm = num_str @{thm bdv_explicit2};
walther@59627: val SOME (t,asm) = rewrite_inst_ thy dummy_ord Erls true inst thm t;
walther@59627: term2str t = "-1 * x = - (2 / 2) + sqrt ((2 / 2) ^^^ 2 - -8) |"^
walther@59627:                 "\nx = -1 * (- (2 / 2) + -1 * sqrt ((2 / 2) ^^^ 2 - -8))";
walther@59627: 
walther@59627: val rls = calculate_RootRat;
walther@59627: val SOME (t,asm) = rewrite_set_ thy true rls t;
walther@59627: if term2str t =
walther@59627:   "-1 * x = -1 + sqrt (2 ^^^ 2 / 2 ^^^ 2 - -8) \<or>\nx = -1 * -1 + -1 * (-1 * sqrt (2 ^^^ 2 / 2 ^^^ 2 - -8))"
walther@59627: (*"-1 * x = -1 + sqrt (2 ^^^ 2 / 2 ^^^ 2 - -8) |\nx = -1 * -1 + -1 * (-1 * sqrt (2 ^^^ 2 / 2 ^^^ 2 - -8))"..isabisac15*)
walther@59627: then () else error "(-8 - 2*x + x^^^2 = 0),  by rewriting -- ERROR INDICATES IMPROVEMENT";
walther@59627: (*SHOULD BE: term2str = "x = -2 | x = 4;*)
walther@59627: 
walther@59627: 
walther@59627: "-------------------- (3 - 10*x + 3*x^^^2 = 0), ----------------------";
walther@59627: "-------------------- (3 - 10*x + 3*x^^^2 = 0), ----------------------";
walther@59627: "-------------------- (3 - 10*x + 3*x^^^2 = 0), ----------------------";
walther@59627: "---- test the erls ----";
walther@59627:  val t1 = (Thm.term_of o the o (parse thy)) "0 <= (10/3/2)^^^2 - 1";
walther@59627:  val SOME (t,_) = rewrite_set_ @{theory PolyEq} false PolyEq_erls t1;
walther@59627:  val t' = term2str t;
walther@59627:  (*if t'= "HOL.True" then ()
walther@59627:  else error "polyeq.sml: diff.behav. in 'rewrite_set_.. PolyEq_erls";*)
walther@59627: (* *)
walther@59627:  val fmz = ["equality (3 - 10*x + 3*x^^^2 = 0)",
walther@59627:  	    "solveFor x","solutions L"];
walther@59627:  val (dI',pI',mI') =
walther@59627:      ("PolyEq",["degree_2","expanded","univariate","equation"],
walther@59627:       ["PolyEq","complete_square"]);
walther@59627: val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627:  val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627:  val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627:  val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627:  val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627:  val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627:  val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627:  (*Apply_Method ("PolyEq","complete_square")*)
walther@59627:  val (p,_,f,nxt,_,pt) = me nxt p [] pt; f2str f;
walther@59627: 
walther@59627: "----------- (-16 + 4*x + 2*x^^^2 = 0), --------------------------";
walther@59627: "----------- (-16 + 4*x + 2*x^^^2 = 0), --------------------------";
walther@59627: "----------- (-16 + 4*x + 2*x^^^2 = 0), --------------------------";
walther@59627:  val fmz = ["equality (-16 + 4*x + 2*x^^^2 = 0)",
walther@59627:  	    "solveFor x","solutions L"];
walther@59627:  val (dI',pI',mI') =
walther@59627:      ("PolyEq",["degree_2","expanded","univariate","equation"],
walther@59627:       ["PolyEq","complete_square"]);
walther@59627: val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
walther@59627: val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627:  val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627:  val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627:  val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627:  val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627:  val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627:  val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627:  (*Apply_Method ("PolyEq","complete_square")*)
walther@59627:  val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627:  val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627:  val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627:  val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627:  val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627:  val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627:  val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627:  val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627:  val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627:  val (p,_,f,nxt,_,pt) = me nxt p [] pt;
walther@59627: (* FIXXXXME n1.,
walther@59627:  case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 2, x = -4]")) => () TODO
walther@59627: 	 | _ => error "polyeq.sml: diff.behav. in [x = 2, x = -4]";
walther@59627: *)
walther@59627: