wneuper/isa: test/Tools/isac/Knowledge/polyeq.sml@537d95d1fdb2 (annotated)

neuper@37906	1	(* testexamples for PolyEq, poynomial equations and equational systems
neuper@42248	2	author: Richard Lang 2003
neuper@37906	3	(c) due to copyright terms
neuper@37906	4	WN030609: some expls dont work due to unfinished handling of 'expanded terms';
neuper@37906	5	others marked with TODO have to be checked, too.
neuper@37906	6	*)
neuper@37906	7
neuper@37906	8	"-----------------------------------------------------------------";
neuper@37906	9	"table of contents -----------------------------------------------";
neuper@37906	10	(WN060608 some ----- are not in this table)
neuper@37906	11	"-----------------------------------------------------------------";
neuper@37906	12	"----------- tests on predicates in problems ---------------------";
neuper@37906	13	"----------- test matching problems --------------------------0---";
neuper@42248	14	"----------- lin.eq degree_0 -------------------------------------";
neuper@42248	15	"----------- test thm's d2_pq_formulsxx[_neg]---------------------";
neuper@37906	16	"----------- (-8 - 2x + x^^^2 = 0), (Schalk 2, S.67 Nr.31.b----";
neuper@37906	17	"----------- (-16 + 4x + 2x^^^2 = 0), --------------------------";
neuper@37906	18	"----------- (ab - (a+b)x + x^^^2 = 0), (Schalk 2,S.68Nr.44.a)";
neuper@37906	19	"----------- (-64 + x^^^2 = 0), (Schalk 2, S.66 Nr.1.a~--------)";
neuper@37906	20	"----------- (-147 + 3x^^^2 = 0), (Schalk 2, S.66 Nr.1.b------*)";
neuper@37906	21	"----------- (3x - 1 - (5x - (2 - 4x)) = -11),(Schalk Is86Bsp5";
neuper@37906	22	"----------- ((x+1)(x+2) - (3x - 2)^^^2=.. Schalk II s.68 Bsp 37";
neuper@37906	23	"----------- interSteps ([1],Res); on Schalk Is86Bsp5-------------";
neuper@37906	24	"-----------------------------------------------------------------";
neuper@37906	25	"-----------------------------------------------------------------";
neuper@37906	26	"-----------------------------------------------------------------";
neuper@37906	27
neuper@42248	28	val c = []; print_depth 5;
neuper@37906	29
neuper@37906	30	"----------- tests on predicates in problems ---------------------";
neuper@37906	31	"----------- tests on predicates in problems ---------------------";
neuper@37906	32	"----------- tests on predicates in problems ---------------------";
neuper@37906	33	(*
neuper@37906	34	trace_rewrite:=true;
neuper@37906	35	trace_rewrite:=false;
neuper@37906	36	*)
neuper@37906	37	val t1 = (term_of o the o (parse thy)) "lhs (-8 - 2*x + x^^^2 = 0)";
neuper@42248	38	val SOME (t,_) = rewrite_set_ @{theory PolyEq} false PolyEq_prls t1;
neuper@37906	39	if ((term2str t) = "-8 - 2 * x + x ^^^ 2") then ()
neuper@38031	40	else error "polyeq.sml: diff.behav. in lhs";
neuper@37906	41
neuper@37906	42	val t2 = (term_of o the o (parse thy)) "(-8 - 2*x + x^^^2) is_expanded_in x";
neuper@42248	43	val SOME (t,_) = rewrite_set_ @{theory PolyEq} false PolyEq_prls t2;
neuper@42248	44	if (term2str t) = "True" then ()
neuper@38031	45	else error "polyeq.sml: diff.behav. 1 in is_expended_in";
neuper@37906	46
neuper@37906	47	val t0 = (term_of o the o (parse thy)) "(sqrt(x)) is_poly_in x";
neuper@42248	48	val SOME (t,_) = rewrite_set_ @{theory PolyEq} false PolyEq_prls t0;
neuper@42248	49	if (term2str t) = "False" then ()
neuper@38031	50	else error "polyeq.sml: diff.behav. 2 in is_poly_in";
neuper@37906	51
neuper@37906	52	val t3 = (term_of o the o (parse thy)) "(-8 + (-1)2x + x^^^2) is_poly_in x";
neuper@42248	53	val SOME (t,_) = rewrite_set_ @{theory PolyEq} false PolyEq_prls t3;
neuper@42248	54	if (term2str t) = "True" then ()
neuper@38031	55	else error "polyeq.sml: diff.behav. 3 in is_poly_in";
neuper@37906	56
neuper@37906	57	val t4 = (term_of o the o (parse thy)) "(lhs (-8 + (-1)2x + x^^^2 = 0)) is_expanded_in x";
neuper@42248	58	val SOME (t,_) = rewrite_set_ @{theory PolyEq} false PolyEq_prls t4;
neuper@42248	59	if (term2str t) = "True" then ()
neuper@38031	60	else error "polyeq.sml: diff.behav. 4 in is_expended_in";
neuper@37906	61
neuper@37906	62
neuper@37906	63	val t6 = (term_of o the o (parse thy)) "(lhs (-8 - 2*x + x^^^2 = 0)) is_expanded_in x";
neuper@42248	64	val SOME (t,_) = rewrite_set_ @{theory PolyEq} false PolyEq_prls t6;
neuper@42248	65	if (term2str t) = "True" then ()
neuper@38031	66	else error "polyeq.sml: diff.behav. 5 in is_expended_in";
neuper@37906	67
neuper@37906	68	val t3 = (term_of o the o (parse thy))"((-8 - 2*x + x^^^2) has_degree_in x) = 2";
neuper@42248	69	val SOME (t,_) = rewrite_set_ @{theory PolyEq} false PolyEq_prls t3;
neuper@42248	70	if (term2str t) = "True" then ()
neuper@38031	71	else error "polyeq.sml: diff.behav. in has_degree_in_in";
neuper@37906	72
neuper@37906	73	val t3 = (term_of o the o (parse thy)) "((sqrt(x)) has_degree_in x) = 2";
neuper@42248	74	val SOME (t,_) = rewrite_set_ @{theory PolyEq} false PolyEq_prls t3;
neuper@42248	75	if (term2str t) = "False" then ()
neuper@38031	76	else error "polyeq.sml: diff.behav. 6 in has_degree_in_in";
neuper@37906	77
neuper@37906	78	val t4 = (term_of o the o (parse thy))
neuper@37906	79	"((-8 - 2*x + x^^^2) has_degree_in x) = 1";
neuper@42248	80	val SOME (t,_) = rewrite_set_ @{theory PolyEq} false PolyEq_prls t4;
neuper@42248	81	if (term2str t) = "False" then ()
neuper@38031	82	else error "polyeq.sml: diff.behav. 7 in has_degree_in_in";
neuper@37906	83
neuper@37906	84	val t5 = (term_of o the o (parse thy))
neuper@37906	85	"((-8 - 2*x + x^^^2) has_degree_in x) = 2";
neuper@42248	86	val SOME (t,_) = rewrite_set_ @{theory PolyEq} false PolyEq_prls t5;
neuper@42248	87	if (term2str t) = "True" then ()
neuper@38031	88	else error "polyeq.sml: diff.behav. 8 in has_degree_in_in";
neuper@37906	89
neuper@42248	90	"----------- test matching problems --------------------------0---";
neuper@42248	91	"----------- test matching problems --------------------------0---";
neuper@42248	92	"----------- test matching problems --------------------------0---";
neuper@42248	93	val fmz = ["equality (-8 - 2*x + x^^^2 = 0)", "solveFor x","solutions L"];
neuper@42248	94	if match_pbl fmz (get_pbt ["expanded","univariate","equation"]) =
neuper@42248	95	Matches' {Find = [Correct "solutions L"],
neuper@42248	96	With = [],
neuper@42248	97	Given = [Correct "equality (-8 - 2 * x + x ^^^ 2 = 0)", Correct "solveFor x"],
neuper@42248	98	Where = [Correct "matches (?a = 0) (-8 - 2 * x + x ^^^ 2 = 0)",
neuper@42248	99	Correct "lhs (-8 - 2 * x + x ^^^ 2 = 0) is_expanded_in x"],
neuper@42248	100	Relate = []}
neuper@42248	101	then () else error "match_pbl [expanded,univariate,equation]";
neuper@37906	102
neuper@42248	103	if match_pbl fmz (get_pbt ["degree_2","expanded","univariate","equation"]) =
neuper@42248	104	Matches' {Find = [Correct "solutions L"],
neuper@42248	105	With = [],
neuper@42248	106	Given = [Correct "equality (-8 - 2 * x + x ^^^ 2 = 0)", Correct "solveFor x"],
neuper@42248	107	Where = [Correct "lhs (-8 - 2 * x + x ^^^ 2 = 0) has_degree_in x = 2"],
neuper@42248	108	Relate = []} (before WN110906 was: has_degree_in x =!= 2"])
neuper@42248	109	then () else error "match_pbl [degree_2,expanded,univariate,equation]";
neuper@37906	110
neuper@42248	111	"----------- lin.eq degree_0 -------------------------------------";
neuper@42248	112	"----------- lin.eq degree_0 -------------------------------------";
neuper@42248	113	"----------- lin.eq degree_0 -------------------------------------";
neuper@37906	114	"----- d0_false ------";
neuper@42248	115	(*=== inhibit exn WN110906 ======================================================
neuper@42248	116	val fmz = ["equality (1 = (0::real))", "solveFor x", "solutions L"];
neuper@37991	117	val (dI',pI',mI') = ("PolyEq",["degree_0","polynomial","univariate","equation"],
neuper@37906	118	["PolyEq","solve_d0_polyeq_equation"]);
neuper@37906	119	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@37906	120	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	121	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	122	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	123	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	124	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	125	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	126	case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[]")) => ()
neuper@38031	127	\| _ => error "polyeq.sml: diff.behav. in 1 = 0 -> []";
neuper@37906	128
neuper@37906	129	"----- d0_true ------";
neuper@37906	130	(EP-7)
neuper@42248	131	val fmz = ["equality (0 = (0::real))", "solveFor x","solutions L"];
neuper@37991	132	val (dI',pI',mI') = ("PolyEq",["degree_0","polynomial","univariate","equation"],
neuper@37906	133	["PolyEq","solve_d0_polyeq_equation"]);
neuper@37906	134	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@37906	135	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	136	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	137	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	138	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	139	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	140	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	141	case f of Form' (FormKF (~1,EdUndef,0,Nundef,"UniversalList")) => ()
neuper@38031	142	\| _ => error "polyeq.sml: diff.behav. in 0 = 0 -> UniversalList";
neuper@42248	143	============ inhibit exn WN110906 ============================================*)
neuper@37906	144
neuper@42248	145	"----------- test thm's d2_pq_formulsxx[_neg]---------------------";
neuper@42248	146	"----------- test thm's d2_pq_formulsxx[_neg]---------------------";
neuper@42248	147	"----------- test thm's d2_pq_formulsxx[_neg]---------------------";
neuper@37906	148	"----- d2_pqformula1 ------!!!!";
neuper@42255	149	val fmz = ["equality (-1/8 + (-1/4)*z + z^^^2 = (0::real))", "solveFor z","solutions L"];
neuper@42255	150	val (dI',pI',mI') =
neuper@42255	151	("Isac", ["pqFormula","degree_2","polynomial","univariate","equation"], ["no_met"]);
neuper@37906	152	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@42255	153	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42255	154	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42255	155	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42255	156	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42255	157	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42255	158	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42255	159	val (p,_,f,nxt,_,pt) = me nxt p [] pt; (Apply_Method ["PolyEq", "solve_d2_polyeq_pq_equation"])
neuper@42255	160	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42255	161	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42255	162	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42255	163	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42255	164	([z = 1 / 8 + sqrt (9 / 16) / 2, z = 1 / 8 + -1 sqrt (9 / 16) / 2] TODO sqrt*)
neuper@42255	165	val (p,_,f,nxt,_,pt) = me nxt p [] pt; (nxt =..,Check_elementwise "Assumptions"))
neuper@42255	166	"~~~~~ fun me, args:"; val ((_,tac), (p:pos'), _, (pt:ptree)) = (nxt, p, [], pt);
neuper@42255	167	"~~~~~ fun locatetac, args:"; val (tac, (ptp as (pt, p))) = (tac, (pt, p));
neuper@42255	168	val (mI,m) = mk_tac'_ tac;
neuper@42255	169	val Appl m = applicable_in p pt m;
neuper@42255	170	val Check_elementwise' (trm1, str, (trm2, trms)) = m;
neuper@42255	171	term2str trm1 = "[z = 1 / 8 + sqrt (9 / 16) / 2, z = 1 / 8 + -1 * sqrt (9 / 16) / 2]";
neuper@42255	172	str = "Assumptions";
neuper@42255	173	term2str trm2 = "[z = 1 / 8 + sqrt (9 / 16) / 2, z = 1 / 8 + -1 * sqrt (9 / 16) / 2]";
neuper@42255	174	terms2str trms = "[\"lhs (-1 / 8 + -1 * (1 / 8 + sqrt (9 / 16) / 2) / 4 +\n "^
neuper@42255	175	" (1 / 8 + sqrt (9 / 16) / 2) ^^^ 2 =\n 0) is_poly_in 1 / 8 + sqrt (9 / 16) / 2\","^
neuper@42255	176	"\"lhs (-1 / 8 + -1 * (1 / 8 + sqrt (9 / 16) / 2) / 4 +\n (1 / 8 + sqrt (9 / 16) / 2) ^^^ 2 =\n 0) "^
neuper@42255	177	"has_degree_in 1 / 8 + sqrt (9 / 16) / 2 =\n2\","^
neuper@42255	178	"\"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\","^
neuper@42255	179	"\"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\"]";
neuper@42255	180	(TODO simplify assumptions (sqrt!) and check ERROR in has_degree_in);
neuper@42255	181	member op = specsteps mI (false);
neuper@42255	182	(*loc_solve_ (mI,m) ptp;
neuper@42255	183	WAS: not-found-in-script: NotLocatable from NasNap (Const ("List...*)
neuper@42255	184	"~~~~~ fun loc_solve_, args:"; val (m, (pt,pos)) = ((mI,m), ptp);
neuper@42255	185	(*solve m (pt, pos);
neuper@42255	186	WAS: not-found-in-script: NotLocatable from NasNap (Const ("List...*)
neuper@42255	187	"~~~~~ fun solve, args:"; val ((mI,m), (pt, po as (p,p_))) = (m, (pt, pos));
neuper@42255	188	e_metID = get_obj g_metID pt (par_pblobj pt p) (false);
neuper@42255	189	val thy' = get_obj g_domID pt (par_pblobj pt p);
neuper@42255	190	val (srls, is, sc) = from_pblobj_or_detail' thy' (p,p_) pt;
neuper@42255	191	val d = e_rls;
neuper@42255	192	(*locate_gen (thy',srls) m (pt,(p,p_)) (sc,d) is;
neuper@42255	193	WAS: not-found-in-script: NotLocatable from NasNap (Const ("List...*)
neuper@42255	194	"~~~~~ fun locate_gen, args:"; val ((ts as (thy',srls)), (m:tac_), ((pt,p):ptree * pos'),
neuper@42255	195	(scr as Script (h $ body),d), (ScrState (E,l,a,v,S,b), ctxt)) =
neuper@42255	196	((thy',srls), m ,(pt,(p,p_)) ,(sc,d) ,is); (* locate_gen 2nd pattern *)
neuper@42255	197	val thy = assoc_thy thy';
neuper@42255	198	l = [] orelse ((last_elem o fst) p = 0 andalso snd p = Res) (false);
neuper@42255	199	(*WAS val NasApp _ =(astep_up (thy',srls,scr,d) ((E,l,a,v,S,b), [(m,EmptyMout,pt,p,[])]) )
neuper@42255	200	... Assoc ... is correct*)
neuper@42255	201	"~~~~~ and astep_up, args:"; val ((ys as (_,_,Script sc,_)), ((E,l,a,v,S,b),ss)) =
neuper@42255	202	((thy',srls,scr,d), ((E,l,a,v,S,b), [(m,EmptyMout,pt,p,[])]));
neuper@42255	203	1 < length l (true);
neuper@42255	204	val up = drop_last l;
neuper@42255	205	term2str (go up sc);
neuper@42255	206	(go up sc);
neuper@42255	207	(*WAS val NasNap _ = ass_up ys ((E,up,a,v,S,b),ss) (go up sc)
neuper@42255	208	... ???? ... is correct*)
neuper@42255	209	"~~~~~ fun ass_up, args:"; val ((ys as (y,s,Script sc,d)), (is as (E,l,a,v,S,b),ss),
neuper@42255	210	(Const ("HOL.Let",_) $ _)) = (ys, ((E,up,a,v,S,b),ss), (go up sc));
neuper@42255	211	val l = drop_last l; (comes from e, goes to Abs)
neuper@42255	212	val (Const ("HOL.Let",_) $ e $ (Abs (i,T,body))) = go l sc;
neuper@42255	213	val i = mk_Free (i, T);
neuper@42255	214	val E = upd_env E (i, v);
neuper@42255	215	(Type error ...: Can't unify _a to pos pos_ (Incompatible types)*)
neuper@42255	216	val [(tac_, mout, ptree, pos', xxx)] = ss;
neuper@42255	217	val ss = [(tac_, mout, ptree, pos', []:(pos * pos_) list)];
neuper@42255	218	(*WAS val NasApp iss = assy (((y,s),d),Aundef) ((E, l@[R,D], a,v,S,b),ss) body
neuper@42255	219	... Assoc ... is correct*)
neuper@42255	220	"~~~~~ fun assy, args:"; val ((((thy',sr),d),ap), (is as (E,l,a,v,S,b), (m,_,pt,(p,p_),c)::ss), t) =
neuper@42255	221	((((y,s),d),Aundef), ((E, l@[R,D], a,v,S,b),ss), body);
neuper@42255	222	val (a', STac stac) = handle_leaf "locate" thy' sr E a v t
neuper@42255	223	val ctxt = get_ctxt pt (p,p_)
neuper@42255	224	val p' = lev_on p : pos;
neuper@42255	225	(* WAS val NotAss = assod pt d m stac
neuper@42255	226	... Ass ... is correct*)
neuper@42255	227	"~~~~~ fun assod, args:"; val (pt, _, (m as Check_elementwise' (consts,_,(consts_chkd,_))),
neuper@42255	228	(Const ("Script.Check'_elementwise",_) $ consts' $ _)) = (pt, d, m, stac);
neuper@42255	229	term2str consts;
neuper@42255	230	term2str consts';
neuper@42255	231	if consts = consts' (WAS false) then () else error "Check_elementwise changed";
neuper@42260	232	([z = 1 / 8 + sqrt (9 / 16) / 2, z = 1 / 8 + -1 sqrt (9 / 16) / 2] TODO sqrt*)
neuper@37906	233
neuper@37906	234	"----- d2_pqformula1_neg ------";
neuper@37906	235	(EP-8)
neuper@37906	236	val fmz = ["equality ( 2 +(-1)*x + x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	237	val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"], ["PolyEq","solve_d2_polyeq_pq_equation"]);
neuper@37906	238	(*val p = e_pos'; val c = [];
neuper@37906	239	val (mI,m) = ("Init_Proof",Init_Proof (fmz, (dI',pI',mI')));
neuper@37906	240	val (p,_,f,nxt,_,pt) = me (mI,m) p c EmptyPtree;*)
neuper@37906	241	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@37906	242	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	243	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	244	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	245	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	246	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	247	(*### or2list False
neuper@37906	248	([1],Res) False Or_to_List)*)
neuper@37906	249	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	250	(*### or2list False
neuper@37906	251	([2],Res) [] Check_elementwise "Assumptions"*)
neuper@37906	252	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	253	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	254	val asm = get_assumptions_ pt p;
neuper@37906	255	if f = Form' (FormKF (~1,EdUndef,0,Nundef,"[]")) andalso asm = [] then ()
neuper@38031	256	else error "polyeq.sml: diff.behav. in 2 +(-1)*x + x^^^2 = 0";
neuper@37906	257
neuper@37906	258	"----- d2_pqformula2 ------";
neuper@37906	259	val fmz = ["equality (-2 +(-1)x + 1x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	260	val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	261	["PolyEq","solve_d2_polyeq_pq_equation"]);
neuper@37906	262	(*val p = e_pos'; val c = [];
neuper@37906	263	val (mI,m) = ("Init_Proof",Init_Proof (fmz, (dI',pI',mI')));
neuper@37906	264	val (p,_,f,nxt,_,pt) = me (mI,m) p c EmptyPtree;*)
neuper@37906	265	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@37906	266	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	267	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	268	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	269	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	270	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	271	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	272	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	273	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	274	case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 2, x = -1]")) => ()
neuper@38031	275	\| _ => error "polyeq.sml: diff.behav. in -2 + (-1)*x + x^2 = 0 -> [x = 2, x = -1]";
neuper@37906	276
neuper@37906	277
neuper@37906	278	"----- d2_pqformula2_neg ------";
neuper@37906	279	val fmz = ["equality ( 2 +(-1)x + 1x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	280	val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	281	["PolyEq","solve_d2_polyeq_pq_equation"]);
neuper@37906	282	(*val p = e_pos'; val c = [];
neuper@37906	283	val (mI,m) = ("Init_Proof",Init_Proof (fmz, (dI',pI',mI')));
neuper@37906	284	val (p,_,f,nxt,_,pt) = me (mI,m) p c EmptyPtree;*)
neuper@37906	285	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@37906	286	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	287	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	288	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	289	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	290	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	291	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	292	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	293	"TODO 2 +(-1)x + 1x^^^2 = 0";
neuper@37906	294	"TODO 2 +(-1)x + 1x^^^2 = 0";
neuper@37906	295	"TODO 2 +(-1)x + 1x^^^2 = 0";
neuper@37906	296
neuper@37906	297
neuper@37906	298	"----- d2_pqformula3 ------";
neuper@37906	299	(EP-9)
neuper@37906	300	val fmz = ["equality (-2 + x + x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	301	val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	302	["PolyEq","solve_d2_polyeq_pq_equation"]);
neuper@37906	303	(*val p = e_pos'; val c = [];
neuper@37906	304	val (mI,m) = ("Init_Proof",Init_Proof (fmz, (dI',pI',mI')));
neuper@37906	305	val (p,_,f,nxt,_,pt) = me (mI,m) p c EmptyPtree;*)
neuper@37906	306	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@37906	307	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	308	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	309	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	310	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	311	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	312	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	313	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	314	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	315	case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 1, x = -2]")) => ()
neuper@38031	316	\| _ => error "polyeq.sml: diff.behav. in -2 + x + x^2 = 0-> [x = 1, x = -2]";
neuper@37906	317
neuper@37906	318	"----- d2_pqformula3_neg ------";
neuper@37906	319	val fmz = ["equality ( 2 + x + x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	320	val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	321	["PolyEq","solve_d2_polyeq_pq_equation"]);
neuper@37906	322	(*val p = e_pos'; val c = [];
neuper@37906	323	val (mI,m) = ("Init_Proof",Init_Proof (fmz, (dI',pI',mI')));
neuper@37906	324	val (p,_,f,nxt,_,pt) = me (mI,m) p c EmptyPtree;*)
neuper@37906	325	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@37906	326	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	327	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	328	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	329	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	330	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	331	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	332	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	333	"TODO 2 + x + x^^^2 = 0";
neuper@37906	334	"TODO 2 + x + x^^^2 = 0";
neuper@37906	335	"TODO 2 + x + x^^^2 = 0";
neuper@37906	336
neuper@37906	337
neuper@37906	338	"----- d2_pqformula4 ------";
neuper@37906	339	val fmz = ["equality (-2 + x + 1*x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	340	val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	341	["PolyEq","solve_d2_polyeq_pq_equation"]);
neuper@37906	342	(*val p = e_pos'; val c = [];
neuper@37906	343	val (mI,m) = ("Init_Proof",Init_Proof (fmz, (dI',pI',mI')));
neuper@37906	344	val (p,_,f,nxt,_,pt) = me (mI,m) p c EmptyPtree;*)
neuper@37906	345	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@37906	346	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	347	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	348	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	349	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	350	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	351	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	352	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	353	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	354	case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 1, x = -2]")) => ()
neuper@38031	355	\| _ => error "polyeq.sml: diff.behav. in -2 + x + 1*x^^^2 = 0 -> [x = 1, x = -2]";
neuper@37906	356
neuper@37906	357	"----- d2_pqformula4_neg ------";
neuper@37906	358	val fmz = ["equality ( 2 + x + 1*x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	359	val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	360	["PolyEq","solve_d2_polyeq_pq_equation"]);
neuper@37906	361	(*val p = e_pos'; val c = [];
neuper@37906	362	val (mI,m) = ("Init_Proof",Init_Proof (fmz, (dI',pI',mI')));
neuper@37906	363	val (p,_,f,nxt,_,pt) = me (mI,m) p c EmptyPtree;*)
neuper@37906	364	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@37906	365	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	366	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	367	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	368	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	369	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	370	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	371	"TODO 2 + x + 1*x^^^2 = 0";
neuper@37906	372	"TODO 2 + x + 1*x^^^2 = 0";
neuper@37906	373	"TODO 2 + x + 1*x^^^2 = 0";
neuper@37906	374
neuper@37906	375	"----- d2_pqformula5 ------";
neuper@37906	376	val fmz = ["equality (1*x + x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	377	val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	378	["PolyEq","solve_d2_polyeq_pq_equation"]);
neuper@37906	379	(*val p = e_pos'; val c = [];
neuper@37906	380	val (mI,m) = ("Init_Proof",Init_Proof (fmz, (dI',pI',mI')));
neuper@37906	381	val (p,_,f,nxt,_,pt) = me (mI,m) p c EmptyPtree;*)
neuper@37906	382	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@37906	383	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	384	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	385	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	386	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	387	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	388	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	389	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	390	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	391	case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 0, x = -1]")) => ()
neuper@38031	392	\| _ => error "polyeq.sml: diff.behav. in 1*x + x^2 = 0 -> [x = 0, x = -1]";
neuper@37906	393
neuper@37906	394	"----- d2_pqformula6 ------";
neuper@37906	395	val fmz = ["equality (1x + 1x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	396	val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	397	["PolyEq","solve_d2_polyeq_pq_equation"]);
neuper@37906	398	(*val p = e_pos'; val c = [];
neuper@37906	399	val (mI,m) = ("Init_Proof",Init_Proof (fmz, (dI',pI',mI')));
neuper@37906	400	val (p,_,f,nxt,_,pt) = me (mI,m) p c EmptyPtree;*)
neuper@37906	401	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@37906	402	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	403	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	404	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	405	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	406	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	407	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	408	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	409	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	410	case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 0, x = -1]")) => ()
neuper@38031	411	\| _ => error "polyeq.sml: diff.behav. in 1x + 1x^2 = 0 -> [x = 0, x = -1]";
neuper@37906	412
neuper@37906	413	"----- d2_pqformula7 ------";
neuper@37906	414	(EP-10)
neuper@37906	415	val fmz = ["equality ( x + x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	416	val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	417	["PolyEq","solve_d2_polyeq_pq_equation"]);
neuper@37906	418	(*val p = e_pos'; val c = [];
neuper@37906	419	val (mI,m) = ("Init_Proof",Init_Proof (fmz, (dI',pI',mI')));
neuper@37906	420	val (p,_,f,nxt,_,pt) = me (mI,m) p c EmptyPtree;*)
neuper@37906	421	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@37906	422	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	423	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	424	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	425	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	426	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	427	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	428	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	429	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	430	case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 0, x = -1]")) => ()
neuper@38031	431	\| _ => error "polyeq.sml: diff.behav. in x + x^2 = 0 -> [x = 0, x = -1]";
neuper@37906	432
neuper@37906	433	"----- d2_pqformula8 ------";
neuper@37906	434	val fmz = ["equality ( x + 1*x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	435	val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	436	["PolyEq","solve_d2_polyeq_pq_equation"]);
neuper@37906	437	(*val p = e_pos'; val c = [];
neuper@37906	438	val (mI,m) = ("Init_Proof",Init_Proof (fmz, (dI',pI',mI')));
neuper@37906	439	val (p,_,f,nxt,_,pt) = me (mI,m) p c EmptyPtree;*)
neuper@37906	440
neuper@37906	441	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@37906	442	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	443	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	444	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	445	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	446	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	447	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	448	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	449	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	450	case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 0, x = -1]")) => ()
neuper@38031	451	\| _ => error "polyeq.sml: diff.behav. in x + 1*x^2 = 0 -> [x = 0, x = -1]";
neuper@37906	452
neuper@37906	453	"----- d2_pqformula9 ------";
neuper@37906	454	val fmz = ["equality (-4 + x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	455	val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	456	["PolyEq","solve_d2_polyeq_pq_equation"]);
neuper@37906	457	(*val p = e_pos'; val c = [];
neuper@37906	458	val (mI,m) = ("Init_Proof",Init_Proof (fmz, (dI',pI',mI')));
neuper@37906	459	val (p,_,f,nxt,_,pt) = me (mI,m) p c EmptyPtree;*)
neuper@37906	460
neuper@37906	461	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@37906	462	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	463	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	464	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	465	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	466	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	467	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	468	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	469	case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 2, x = -2]")) => ()
neuper@38031	470	\| _ => error "polyeq.sml: diff.behav. in -4 + x^2 = 0 -> [x = 2, x = -2]";
neuper@37906	471
neuper@37906	472
neuper@37906	473	"----- d2_pqformula10_neg ------";
neuper@37906	474	val fmz = ["equality (4 + x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	475	val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	476	["PolyEq","solve_d2_polyeq_pq_equation"]);
neuper@37906	477	(*val p = e_pos'; val c = [];
neuper@37906	478	val (mI,m) = ("Init_Proof",Init_Proof (fmz, (dI',pI',mI')));
neuper@37906	479	val (p,_,f,nxt,_,pt) = me (mI,m) p c EmptyPtree;*)
neuper@37906	480
neuper@37906	481	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@37906	482	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	483	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	484	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	485	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	486	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	487	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	488	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	489	"TODO 4 + x^^^2 = 0";
neuper@37906	490	"TODO 4 + x^^^2 = 0";
neuper@37906	491	"TODO 4 + x^^^2 = 0";
neuper@37906	492
neuper@37906	493	"----- d2_pqformula10 ------";
neuper@37906	494	val fmz = ["equality (-4 + 1*x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	495	val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	496	["PolyEq","solve_d2_polyeq_pq_equation"]);
neuper@37906	497	(*val p = e_pos'; val c = [];
neuper@37906	498	val (mI,m) = ("Init_Proof",Init_Proof (fmz, (dI',pI',mI')));
neuper@37906	499	val (p,_,f,nxt,_,pt) = me (mI,m) p c EmptyPtree;*)
neuper@37906	500
neuper@37906	501	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@37906	502	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	503	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	504	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	505	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	506	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	507	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	508	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	509	case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 2, x = -2]")) => ()
neuper@38031	510	\| _ => error "polyeq.sml: diff.behav. in -4 + 1*x^2 = 0 -> [x = 2, x = -2]";
neuper@37906	511
neuper@37906	512	"----- d2_pqformula9_neg ------";
neuper@37906	513	val fmz = ["equality (4 + 1*x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	514	val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	515	["PolyEq","solve_d2_polyeq_pq_equation"]);
neuper@37906	516	(*val p = e_pos'; val c = [];
neuper@37906	517	val (mI,m) = ("Init_Proof",Init_Proof (fmz, (dI',pI',mI')));
neuper@37906	518	val (p,_,f,nxt,_,pt) = me (mI,m) p c EmptyPtree;*)
neuper@37906	519
neuper@37906	520	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@37906	521	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	522	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	523	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	524	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	525	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	526	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	527	"TODO 4 + 1*x^^^2 = 0";
neuper@37906	528	"TODO 4 + 1*x^^^2 = 0";
neuper@37906	529	"TODO 4 + 1*x^^^2 = 0";
neuper@37906	530
neuper@37906	531	"-------------------- test thm's d2_abc_formulsxx[_neg]-----";
neuper@37906	532	"-------------------- test thm's d2_abc_formulsxx[_neg]-----";
neuper@37906	533	"-------------------- test thm's d2_abc_formulsxx[_neg]-----";
neuper@37906	534
neuper@37906	535	val fmz = ["equality (-1 +(-1)x + 2x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	536	val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	537	["PolyEq","solve_d2_polyeq_abc_equation"]);
neuper@37906	538	(*val p = e_pos'; val c = [];
neuper@37906	539	val (mI,m) = ("Init_Proof",Init_Proof (fmz, (dI',pI',mI')));
neuper@37906	540	val (p,_,f,nxt,_,pt) = me (mI,m) p c EmptyPtree;*)
neuper@37906	541
neuper@37906	542	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@37906	543	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	544	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	545	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	546	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	547	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	548	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	549	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	550	case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 1, x = -1 / 2]")) => ()
neuper@38031	551	\| _ => error "polyeq.sml: diff.behav. in -1 + (-1)x + 2x^2 = 0 -> [x = 1, x = -1/2]";
neuper@37906	552
neuper@37906	553	val fmz = ["equality ( 1 +(-1)x + 2x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	554	val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	555	["PolyEq","solve_d2_polyeq_abc_equation"]);
neuper@37906	556	(*val p = e_pos'; val c = [];
neuper@37906	557	val (mI,m) = ("Init_Proof",Init_Proof (fmz, (dI',pI',mI')));
neuper@37906	558	val (p,_,f,nxt,_,pt) = me (mI,m) p c EmptyPtree;*)
neuper@37906	559
neuper@37906	560	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@37906	561	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	562	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	563	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	564	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	565	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	566	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	567	"TODO 1 +(-1)x + 2x^^^2 = 0";
neuper@37906	568	"TODO 1 +(-1)x + 2x^^^2 = 0";
neuper@37906	569	"TODO 1 +(-1)x + 2x^^^2 = 0";
neuper@37906	570
neuper@37906	571	(EP-11)
neuper@37906	572	val fmz = ["equality (-1 + x + 2*x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	573	val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	574	["PolyEq","solve_d2_polyeq_abc_equation"]);
neuper@37906	575	(*val p = e_pos'; val c = [];
neuper@37906	576	val (mI,m) = ("Init_Proof",Init_Proof (fmz, (dI',pI',mI')));
neuper@37906	577	val (p,_,f,nxt,_,pt) = me (mI,m) p c EmptyPtree;*)
neuper@37906	578
neuper@37906	579	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@37906	580	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	581	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	582	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	583	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	584	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	585	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	586	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	587	case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 1 / 2, x = -1]")) => ()
neuper@38031	588	\| _ => error "polyeq.sml: diff.behav. in -1 + x + 2*x^2 = 0 -> [x = 1/2, x = -1]";
neuper@37906	589
neuper@37906	590	val fmz = ["equality ( 1 + x + 2*x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	591	val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	592	["PolyEq","solve_d2_polyeq_abc_equation"]);
neuper@37906	593	(*val p = e_pos'; val c = [];
neuper@37906	594	val (mI,m) = ("Init_Proof",Init_Proof (fmz, (dI',pI',mI')));
neuper@37906	595	val (p,_,f,nxt,_,pt) = me (mI,m) p c EmptyPtree;*)
neuper@37906	596
neuper@37906	597	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@37906	598	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	599	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	600	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	601	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	602	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	603	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	604	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	605	"TODO 1 + x + 2*x^^^2 = 0";
neuper@37906	606	"TODO 1 + x + 2*x^^^2 = 0";
neuper@37906	607	"TODO 1 + x + 2*x^^^2 = 0";
neuper@37906	608
neuper@37906	609	val fmz = ["equality (-2 + 1*x + x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	610	val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	611	["PolyEq","solve_d2_polyeq_abc_equation"]);
neuper@37906	612	(*val p = e_pos'; val c = [];
neuper@37906	613	val (mI,m) = ("Init_Proof",Init_Proof (fmz, (dI',pI',mI')));
neuper@37906	614	val (p,_,f,nxt,_,pt) = me (mI,m) p c EmptyPtree;*)
neuper@37906	615
neuper@37906	616	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@37906	617	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	618	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	619	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	620	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	621	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	622	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	623	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	624	case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 1, x = -2]")) => ()
neuper@38031	625	\| _ => error "polyeq.sml: diff.behav. in -2 + 1*x + x^2 = 0 -> [x = 1, x = -2]";
neuper@37906	626
neuper@37906	627	val fmz = ["equality ( 2 + 1*x + x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	628	val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	629	["PolyEq","solve_d2_polyeq_abc_equation"]);
neuper@37906	630	(*val p = e_pos'; val c = [];
neuper@37906	631	val (mI,m) = ("Init_Proof",Init_Proof (fmz, (dI',pI',mI')));
neuper@37906	632	val (p,_,f,nxt,_,pt) = me (mI,m) p c EmptyPtree;*)
neuper@37906	633
neuper@37906	634	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@37906	635	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	636	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	637	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	638	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	639	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	640	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	641	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	642	"TODO 2 + 1*x + x^^^2 = 0";
neuper@37906	643	"TODO 2 + 1*x + x^^^2 = 0";
neuper@37906	644	"TODO 2 + 1*x + x^^^2 = 0";
neuper@37906	645
neuper@37906	646	(EP-12)
neuper@37906	647	val fmz = ["equality (-2 + x + x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	648	val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	649	["PolyEq","solve_d2_polyeq_abc_equation"]);
neuper@37906	650	(*val p = e_pos'; val c = [];
neuper@37906	651	val (mI,m) = ("Init_Proof",Init_Proof (fmz, (dI',pI',mI')));
neuper@37906	652	val (p,_,f,nxt,_,pt) = me (mI,m) p c EmptyPtree;*)
neuper@37906	653
neuper@37906	654	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@37906	655	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	656	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	657	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	658	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	659	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	660	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	661	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	662	case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 1, x = -2]")) => ()
neuper@38031	663	\| _ => error "polyeq.sml: diff.behav. in -2 + x + x^2 = 0 -> [x = 1, x = -2]";
neuper@37906	664
neuper@37906	665	val fmz = ["equality ( 2 + x + x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	666	val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	667	["PolyEq","solve_d2_polyeq_abc_equation"]);
neuper@37906	668	(*val p = e_pos'; val c = [];
neuper@37906	669	val (mI,m) = ("Init_Proof",Init_Proof (fmz, (dI',pI',mI')));
neuper@37906	670	val (p,_,f,nxt,_,pt) = me (mI,m) p c EmptyPtree;*)
neuper@37906	671
neuper@37906	672	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@37906	673	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	674	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	675	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	676	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	677	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	678	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	679	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	680	"TODO 2 + x + x^^^2 = 0";
neuper@37906	681	"TODO 2 + x + x^^^2 = 0";
neuper@37906	682	"TODO 2 + x + x^^^2 = 0";
neuper@37906	683
neuper@37906	684	(EP-13)
neuper@37906	685	val fmz = ["equality (-8 + 2*x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	686	val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	687	["PolyEq","solve_d2_polyeq_abc_equation"]);
neuper@37906	688	(*val p = e_pos'; val c = [];
neuper@37906	689	val (mI,m) = ("Init_Proof",Init_Proof (fmz, (dI',pI',mI')));
neuper@37906	690	val (p,_,f,nxt,_,pt) = me (mI,m) p c EmptyPtree;*)
neuper@37906	691
neuper@37906	692	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@37906	693	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	694	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	695	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	696	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	697	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	698	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	699	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	700	case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 2, x = -2]")) => ()
neuper@38031	701	\| _ => error "polyeq.sml: diff.behav. in -8 + 2*x^2 = 0 -> [x = 2, x = -2]";
neuper@37906	702
neuper@37906	703	val fmz = ["equality ( 8+ 2*x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	704	val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	705	["PolyEq","solve_d2_polyeq_abc_equation"]);
neuper@37906	706	(*val p = e_pos'; val c = [];
neuper@37906	707	val (mI,m) = ("Init_Proof",Init_Proof (fmz, (dI',pI',mI')));
neuper@37906	708	val (p,_,f,nxt,_,pt) = me (mI,m) p c EmptyPtree;*)
neuper@37906	709
neuper@37906	710	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@37906	711	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	712	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	713	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	714	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	715	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	716	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	717	"TODO 8+ 2*x^^^2 = 0";
neuper@37906	718	"TODO 8+ 2*x^^^2 = 0";
neuper@37906	719	"TODO 8+ 2*x^^^2 = 0";
neuper@37906	720
neuper@37906	721	(EP-14)
neuper@37906	722	val fmz = ["equality (-4 + x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	723	val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"], ["PolyEq","solve_d2_polyeq_abc_equation"]);
neuper@37906	724	(*val p = e_pos'; val c = [];
neuper@37906	725	val (mI,m) = ("Init_Proof",Init_Proof (fmz, (dI',pI',mI')));
neuper@37906	726	val (p,_,f,nxt,_,pt) = me (mI,m) p c EmptyPtree;*)
neuper@37906	727
neuper@37906	728	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@37906	729	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	730	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	731	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	732	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	733	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	734	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	735	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	736	case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 2, x = -2]")) => ()
neuper@38031	737	\| _ => error "polyeq.sml: diff.behav. in -4 + x^2 = 0 -> [x = 2, x = -2]";
neuper@37906	738
neuper@37906	739
neuper@37906	740	val fmz = ["equality ( 4+ x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	741	val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"], ["PolyEq","solve_d2_polyeq_abc_equation"]);
neuper@37906	742	(*val p = e_pos'; val c = [];
neuper@37906	743	val (mI,m) = ("Init_Proof",Init_Proof (fmz, (dI',pI',mI')));
neuper@37906	744	val (p,_,f,nxt,_,pt) = me (mI,m) p c EmptyPtree;*)
neuper@37906	745
neuper@37906	746	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@37906	747	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	748	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	749	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	750	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	751	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	752	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	753	"TODO 4+ x^^^2 = 0";
neuper@37906	754	"TODO 4+ x^^^2 = 0";
neuper@37906	755	"TODO 4+ x^^^2 = 0";
neuper@37906	756
neuper@37906	757	(EP-15)
neuper@37906	758	val fmz = ["equality (2x + 2x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	759	val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	760	["PolyEq","solve_d2_polyeq_abc_equation"]);
neuper@37906	761	(*val p = e_pos'; val c = [];
neuper@37906	762	val (mI,m) = ("Init_Proof",Init_Proof (fmz, (dI',pI',mI')));
neuper@37906	763	val (p,_,f,nxt,_,pt) = me (mI,m) p c EmptyPtree;*)
neuper@37906	764
neuper@37906	765	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@37906	766	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	767	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	768	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	769	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	770	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	771	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	772	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	773	case f of Form' (FormKF (~1,EdUndef,_,Nundef,"[x = 0, x = -1]")) => ()
neuper@38031	774	\| _ => error "polyeq.sml: diff.behav. in x + x^2 = 0 -> [x = 0, x = -1]";
neuper@37906	775
neuper@37906	776	val fmz = ["equality (1*x + x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	777	val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	778	["PolyEq","solve_d2_polyeq_abc_equation"]);
neuper@37906	779	(*val p = e_pos'; val c = [];
neuper@37906	780	val (mI,m) = ("Init_Proof",Init_Proof (fmz, (dI',pI',mI')));
neuper@37906	781	val (p,_,f,nxt,_,pt) = me (mI,m) p c EmptyPtree;*)
neuper@37906	782
neuper@37906	783	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@37906	784	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	785	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	786	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	787	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	788	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	789	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	790	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	791	case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 0, x = -1]")) => ()
neuper@38031	792	\| _ => error "polyeq.sml: diff.behav. in x + x^2 = 0 -> [x = 0, x = -1]";
neuper@37906	793
neuper@37906	794	(EP-16)
neuper@37906	795	val fmz = ["equality (x + 2*x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	796	val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	797	["PolyEq","solve_d2_polyeq_abc_equation"]);
neuper@37906	798	(*val p = e_pos'; val c = [];
neuper@37906	799	val (mI,m) = ("Init_Proof",Init_Proof (fmz, (dI',pI',mI')));
neuper@37906	800	val (p,_,f,nxt,_,pt) = me (mI,m) p c EmptyPtree;*)
neuper@37906	801
neuper@37906	802	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@37906	803	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	804	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	805	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	806	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	807	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	808	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	809	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	810	case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 0, x = -1 / 2]")) => ()
neuper@38031	811	\| _ => error "polyeq.sml: diff.behav. in x + x^2 = 0 -> [x = 0, x = -1 / 2]";
neuper@37906	812
neuper@37906	813	(EP-//)
neuper@37906	814	val fmz = ["equality (x + x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	815	val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	816	["PolyEq","solve_d2_polyeq_abc_equation"]);
neuper@37906	817	(*val p = e_pos'; val c = [];
neuper@37906	818	val (mI,m) = ("Init_Proof",Init_Proof (fmz, (dI',pI',mI')));
neuper@37906	819	val (p,_,f,nxt,_,pt) = me (mI,m) p c EmptyPtree;*)
neuper@37906	820
neuper@37906	821	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@37906	822	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	823	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	824	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	825	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	826	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	827	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	828	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	829	case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 0, x = -1]")) => ()
neuper@38031	830	\| _ => error "polyeq.sml: diff.behav. in x + x^2 = 0 -> [x = 0, x = -1]";
neuper@37906	831
neuper@37906	832	"----------- (-8 - 2x + x^^^2 = 0), (Schalk 2, S.67 Nr.31.b----";
neuper@37906	833	"----------- (-8 - 2x + x^^^2 = 0), (Schalk 2, S.67 Nr.31.b----";
neuper@37906	834	"----------- (-8 - 2x + x^^^2 = 0), (Schalk 2, S.67 Nr.31.b----";
neuper@37906	835	val fmz = ["equality (-8 - 2x + x^^^2 = 0)", (Schalk 2, S.67 Nr.31.b*)
neuper@37906	836	"solveFor x","solutions L"];
neuper@37906	837	val (dI',pI',mI') =
neuper@37991	838	("PolyEq",["degree_2","expanded","univariate","equation"],
neuper@37906	839	["PolyEq","complete_square"]);
neuper@37906	840	(* val p = e_pos'; val c = [];
neuper@37906	841	val (mI,m) = ("Init_Proof",Init_Proof (fmz, (dI',pI',mI')));
neuper@37906	842	val (p,_,f,nxt,_,pt) = me (mI,m) p c EmptyPtree;*)
neuper@37906	843
neuper@37906	844	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@37906	845	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	846	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	847	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	848	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37991	849	(Apply_Method ("PolyEq","complete_square"))
neuper@37906	850	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	851	("-8 - 2 x + x ^^^ 2 = 0", nxt = Rewrite_Set_Inst ... "complete_square*)
neuper@37906	852	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	853	("-8 + (2 / 2 - x) ^^^ 2 = (2 / 2) ^^^ 2", nxt = Rewrite("square_explicit1")
neuper@37906	854	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	855	("(2 / 2 - x) ^^^ 2 = (2 / 2) ^^^ 2 - -8" nxt = Rewrite("root_plus_minus)
neuper@37906	856	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	857	(*"2 / 2 - x = sqrt ((2 / 2) ^^^ 2 - -8) \|
neuper@37906	858	2 / 2 - x = - sqrt ((2 / 2) ^^^ 2 - -8)" nxt = Rewr_Inst("bdv_explicit2"*)
neuper@37906	859	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	860	(*"2 / 2 - x = sqrt ((2 / 2) ^^^ 2 - -8) \|
neuper@37906	861	-1x = - (2 / 2) + - sqrt ((2 / 2) ^^^ 2 - -8)"nxt = R_Inst("bdv_explt2")
neuper@37906	862	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	863	("-1 x = - (2 / 2) + sqrt ((2 / 2) ^^^ 2 - -8) \|
neuper@37906	864	-1 * x = (- (2 / 2) + - sqrt ((2 / 2) ^^^ 2 - -8))"nxt = bdv_explicit3*)
neuper@37906	865	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	866	("-1 x = - (2 / 2) + sqrt ((2 / 2) ^^^ 2 - -8) \|
neuper@37906	867	x = -1 * (- (2 / 2) + - sqrt ((2 / 2) ^^^ 2 - -8))" nxt = bdv_explicit3*)
neuper@37906	868	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	869	("x = -1 (- (2 / 2) + sqrt ((2 / 2) ^^^ 2 - -8)) \|
neuper@37906	870	x = -1 * (- (2 / 2) + - sqrt ((2 / 2) ^^^ 2 - -8))"nxt = calculate_Ration*)
neuper@37906	871	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	872	("x = -2 \| x = 4" nxt = Or_to_List)
neuper@37906	873	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	874	("[x = -2, x = 4]" nxt = Check_Postcond)
neuper@37906	875	val (p,_,f,nxt,_,pt) = me nxt p c pt; f2str f;
neuper@37906	876	(* FIXXXME
neuper@37906	877	case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = -2, x = 4]")) => () TODO
neuper@38031	878	\| _ => error "polyeq.sml: diff.behav. in [x = -2, x = 4]";
neuper@37906	879	*)
neuper@37906	880	if f2str f = "[x = -1 * -1 + -1 * sqrt (1 ^^^ 2 - -8),\n x = -1 * -1 + -1 * (-1 * sqrt (1 ^^^ 2 - -8))]" then ()
neuper@38031	881	else error "polyeq.sml corrected?behav. in [x = -2, x = 4]";
neuper@37906	882
neuper@37906	883
neuper@37906	884	"-------------------- (3 - 10x + 3x^^^2 = 0), ----------------------";
neuper@37906	885	"-------------------- (3 - 10x + 3x^^^2 = 0), ----------------------";
neuper@37906	886	"-------------------- (3 - 10x + 3x^^^2 = 0), ----------------------";
neuper@37906	887	"---- test the erls ----";
neuper@37906	888	val t1 = (term_of o the o (parse thy)) "0 <= (10/3/2)^^^2 - 1";
neuper@37926	889	val SOME (t,_) = rewrite_set_ PolyEq.thy false PolyEq_erls t1;
neuper@37906	890	val t' = term2str t;
neuper@41928	891	(*if t'= "HOL.True" then ()
neuper@38031	892	else error "polyeq.sml: diff.behav. in 'rewrite_set_.. PolyEq_erls";*)
neuper@37906	893	(* *)
neuper@37906	894	val fmz = ["equality (3 - 10x + 3x^^^2 = 0)",
neuper@37906	895	"solveFor x","solutions L"];
neuper@37906	896	val (dI',pI',mI') =
neuper@37991	897	("PolyEq",["degree_2","expanded","univariate","equation"],
neuper@37906	898	["PolyEq","complete_square"]);
neuper@37906	899	(* val p = e_pos'; val c = [];
neuper@37906	900	val (mI,m) = ("Init_Proof",Init_Proof (fmz, (dI',pI',mI')));
neuper@37906	901	val (p,_,f,nxt,_,pt) = me (mI,m) p c EmptyPtree;*)
neuper@37906	902
neuper@37906	903	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@37906	904	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	905	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	906	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	907	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	908	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	909	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	910	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37991	911	(Apply_Method ("PolyEq","complete_square"))
neuper@37906	912	val (p,_,f,nxt,_,pt) = me nxt p c pt; f2str f;
neuper@37906	913
neuper@37906	914	"----------- (-16 + 4x + 2x^^^2 = 0), --------------------------";
neuper@37906	915	"----------- (-16 + 4x + 2x^^^2 = 0), --------------------------";
neuper@37906	916	"----------- (-16 + 4x + 2x^^^2 = 0), --------------------------";
neuper@37906	917	val fmz = ["equality (-16 + 4x + 2x^^^2 = 0)",
neuper@37906	918	"solveFor x","solutions L"];
neuper@37906	919	val (dI',pI',mI') =
neuper@37991	920	("PolyEq",["degree_2","expanded","univariate","equation"],
neuper@37906	921	["PolyEq","complete_square"]);
neuper@37906	922	(* val p = e_pos'; val c = [];
neuper@37906	923	val (mI,m) = ("Init_Proof",Init_Proof (fmz, (dI',pI',mI')));
neuper@37906	924	val (p,_,f,nxt,_,pt) = me (mI,m) p c EmptyPtree;*)
neuper@37906	925
neuper@37906	926	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@37906	927	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	928	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	929	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	930	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	931	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	932	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	933	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37991	934	(Apply_Method ("PolyEq","complete_square"))
neuper@37906	935	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	936	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	937	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	938	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	939	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	940	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	941	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	942	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	943	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	944	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	945	(* FIXXXXME n1.,
neuper@37906	946	case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 2, x = -4]")) => () TODO
neuper@38031	947	\| _ => error "polyeq.sml: diff.behav. in [x = 2, x = -4]";
neuper@37906	948	*)
neuper@37906	949
neuper@37906	950	"----------- (ab - (a+b)x + x^^^2 = 0), (Schalk 2,S.68Nr.44.a)";
neuper@37906	951	"----------- (ab - (a+b)x + x^^^2 = 0), (Schalk 2,S.68Nr.44.a)";
neuper@37906	952	"----------- (ab - (a+b)x + x^^^2 = 0), (Schalk 2,S.68Nr.44.a)";
neuper@37906	953	val fmz = ["equality (ab - (a+b)x + x^^^2 = 0)",
neuper@37906	954	"solveFor x","solutions L"];
neuper@37906	955	val (dI',pI',mI') =
neuper@37991	956	("PolyEq",["degree_2","expanded","univariate","equation"],
neuper@37906	957	["PolyEq","complete_square"]);
neuper@37906	958	(* val p = e_pos'; val c = [];
neuper@37906	959	val (mI,m) = ("Init_Proof",Init_Proof (fmz, (dI',pI',mI')));
neuper@37906	960	val (p,_,f,nxt,_,pt) = me (mI,m) p c EmptyPtree;*)
neuper@37906	961
neuper@37906	962	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@37906	963	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	964	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	965	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	966	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	967	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	968	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	969	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	970	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	971	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	972	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	973
neuper@37906	974	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	975	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	976	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	977	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	978	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	979	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	980	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	981	val (p,_,f,nxt,_,pt) = me nxt p c pt; f2str f;
neuper@37906	982	(*WN.2.5.03 TODO FIXME Matthias ?
neuper@37906	983	case f of
neuper@37906	984	Form'
neuper@37906	985	(FormKF
neuper@37906	986	(~1,EdUndef,0,Nundef,
neuper@37906	987	"[x = (a + b) / 2 + -1 * sqrt ((a + b) ^^^ 2 / 2 ^^^ 2 - a * b),\n x = (a + b) / 2 + sqrt ((a + b) ^^^ 2 / 2 ^^^ 2 - a * b)]"))
neuper@37906	988	=> ()
neuper@38031	989	\| _ => error "polyeq.sml: diff.behav. in ab - (a+b)x + x^^^2 = 0";
neuper@37906	990	this will be simplified [x = a, x = b] to by Factor.ML*)
neuper@37906	991
neuper@37906	992
neuper@37906	993	"----------- (-64 + x^^^2 = 0), (Schalk 2, S.66 Nr.1.a~--------)";
neuper@37906	994	"----------- (-64 + x^^^2 = 0), (Schalk 2, S.66 Nr.1.a~--------)";
neuper@37906	995	"----------- (-64 + x^^^2 = 0), (Schalk 2, S.66 Nr.1.a~--------)";
neuper@37906	996	val fmz = ["equality (-64 + x^^^2 = 0)",(Schalk 2, S.66 Nr.1.a~)
neuper@37906	997	"solveFor x","solutions L"];
neuper@37906	998	val (dI',pI',mI') =
neuper@37991	999	("PolyEq",["degree_2","expanded","univariate","equation"],
neuper@37906	1000	["PolyEq","complete_square"]);
neuper@37906	1001	(* val p = e_pos'; val c = [];
neuper@37906	1002	val (mI,m) = ("Init_Proof",Init_Proof (fmz, (dI',pI',mI')));
neuper@37906	1003	val (p,_,f,nxt,_,pt) = me (mI,m) p c EmptyPtree;*)
neuper@37906	1004
neuper@37906	1005	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@37906	1006	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	1007	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	1008	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	1009	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	1010	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	1011	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	1012	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	1013	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	1014	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	1015	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	1016	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	1017	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	1018	val (p,_,f,nxt,_,pt) = me nxt p c pt; f2str f;
neuper@37906	1019	(WN.2.5.03 TODO "[x = sqrt (0 - -64), x = -1 sqrt (0 - -64)]"
neuper@37906	1020	case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 8, x = -8]")) => ()
neuper@38031	1021	\| _ => error "polyeq.sml: diff.behav. in [x = 8, x = -8]";
neuper@37906	1022	*)
neuper@37906	1023
neuper@37906	1024	"----------- (-147 + 3x^^^2 = 0), (Schalk 2, S.66 Nr.1.b------*)";
neuper@37906	1025	"----------- (-147 + 3x^^^2 = 0), (Schalk 2, S.66 Nr.1.b------*)";
neuper@37906	1026	"----------- (-147 + 3x^^^2 = 0), (Schalk 2, S.66 Nr.1.b------*)";
neuper@37906	1027	val fmz = ["equality (-147 + 3x^^^2 = 0)",(Schalk 2, S.66 Nr.1.b*)
neuper@37906	1028	"solveFor x","solutions L"];
neuper@37906	1029	val (dI',pI',mI') =
neuper@37991	1030	("PolyEq",["degree_2","expanded","univariate","equation"],
neuper@37906	1031	["PolyEq","complete_square"]);
neuper@37906	1032	(* val p = e_pos'; val c = [];
neuper@37906	1033	val (mI,m) = ("Init_Proof",Init_Proof (fmz, (dI',pI',mI')));
neuper@37906	1034	val (p,_,f,nxt,_,pt) = me (mI,m) p c EmptyPtree;*)
neuper@37906	1035
neuper@37906	1036	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@37906	1037	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	1038	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	1039	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	1040	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	1041	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	1042	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	1043	val (p,_,f,nxt,_,pt) = me nxt p c pt; val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	1044	val (p,_,f,nxt,_,pt) = me nxt p c pt;
neuper@37906	1045	(WN.2.5.03 TODO "[x = sqrt (0 - -49), x = -1 sqrt (0 - -49)]"
neuper@37906	1046	case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 7, x = -7]")) => ()
neuper@38031	1047	\| _ => error "polyeq.sml: diff.behav. in [x = 7, x = -7]";
neuper@37906	1048	*)
neuper@37906	1049	if f2str f = "[x = sqrt (0 - -49), x = -1 * sqrt (0 - -49)]" then ()
neuper@38031	1050	else error "polyeq.sml CORRECTED?behav. in [x = 7, x = -7]";
neuper@37906	1051
neuper@37906	1052
neuper@37906	1053	"----------- (3x - 1 - (5x - (2 - 4x)) = -11),(Schalk Is86Bsp5";
neuper@37906	1054	"----------- (3x - 1 - (5x - (2 - 4x)) = -11),(Schalk Is86Bsp5";
neuper@37906	1055	"----------- (3x - 1 - (5x - (2 - 4x)) = -11),(Schalk Is86Bsp5";
neuper@37906	1056	(EP-17 Schalk_I_p86_n5)
neuper@37906	1057	val fmz = ["equality (3x - 1 - (5x - (2 - 4*x)) = -11)","solveFor x","solutions L"];
neuper@37906	1058	(* refine fmz ["univariate","equation"];
neuper@37906	1059	*)
neuper@37991	1060	val (dI',pI',mI') = ("PolyEq",["univariate","equation"],["no_met"]);
neuper@37906	1061	(*val p = e_pos';
neuper@37906	1062	val c = [];
neuper@37906	1063	val (mI,m) = ("Init_Proof",Init_Proof (fmz, (dI',pI',mI')));
neuper@37906	1064	val (p,_,f,nxt,_,pt) = me (mI,m) p c EmptyPtree;*)
neuper@37906	1065
neuper@37906	1066	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@37906	1067	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	1068	(* val nxt =
neuper@37906	1069	("Model_Problem",
neuper@37906	1070	Model_Problem ["normalize","polynomial","univariate","equation"])
neuper@37906	1071	: string * tac*)
neuper@37906	1072	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	1073	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	1074	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	1075	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	1076	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	1077	(* val nxt =
neuper@37906	1078	("Subproblem",
neuper@37991	1079	Subproblem ("PolyEq",["polynomial","univariate","equation"]))
neuper@37906	1080	: string * tac *)
neuper@37906	1081	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	1082	(*val nxt =
neuper@37906	1083	("Model_Problem",
neuper@37906	1084	Model_Problem ["degree_1","polynomial","univariate","equation"])
neuper@37906	1085	: string * tac *)
neuper@37906	1086	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	1087	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	1088
neuper@37906	1089	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	1090	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	1091	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	1092	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	1093	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	1094	case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 2]")) => ()
neuper@38031	1095	\| _ => error "polyeq.sml: diff.behav. in [x = 2]";
neuper@37906	1096
neuper@37906	1097
neuper@37906	1098	"----------- ((x+1)(x+2) - (3x - 2)^^^2=.. Schalk II s.68 Bsp 37";
neuper@37906	1099	"----------- ((x+1)(x+2) - (3x - 2)^^^2=.. Schalk II s.68 Bsp 37";
neuper@37906	1100	"----------- ((x+1)(x+2) - (3x - 2)^^^2=.. Schalk II s.68 Bsp 37";
neuper@37906	1101	(is in rlang.sml, too)
neuper@37906	1102	val fmz = ["equality ((x+1)(x+2) - (3x - 2)^^^2=(2x - 1)^^^2+(3x - 1)*(x+1))",
neuper@37906	1103	"solveFor x","solutions L"];
neuper@37991	1104	val (dI',pI',mI') = ("PolyEq",["univariate","equation"],["no_met"]);
neuper@37906	1105
neuper@37906	1106	(*val p = e_pos'; val c = [];
neuper@37906	1107	val (mI,m) = ("Init_Proof",Init_Proof (fmz, (dI',pI',mI')));
neuper@37906	1108	val (p,_,f,nxt,_,pt) = me (mI,m) p c EmptyPtree;*)
neuper@37906	1109
neuper@37906	1110	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@37906	1111	(val nxt = ("Refine_Tacitly",Refine_Tacitly ["univariate","equation"]))
neuper@37906	1112	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	1113	(* val nxt =
neuper@37906	1114	("Model_Problem",
neuper@37906	1115	Model_Problem ["normalize","polynomial","univariate","equation"])
neuper@37906	1116	: string * tac *)
neuper@37906	1117	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	1118	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	1119	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	1120	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	1121	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	1122	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	1123	(* val nxt =
neuper@37906	1124	("Subproblem",
neuper@37991	1125	Subproblem ("PolyEq",["polynomial","univariate","equation"]))
neuper@37906	1126	: string * tac*)
neuper@37906	1127	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	1128	(*val nxt =
neuper@37906	1129	("Model_Problem",
neuper@37906	1130	Model_Problem ["abcFormula","degree_2","polynomial","univariate","equation"])
neuper@37906	1131	: string * tac*)
neuper@37906	1132	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	1133	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	1134	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	1135	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	1136	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	1137	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	1138	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	1139	case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 2 / 15, x = 1]")) => ()
neuper@38031	1140	\| _ => error "polyeq.sml: diff.behav. in [x = 2 / 15, x = 1]";
neuper@37906	1141
neuper@37906	1142
neuper@37906	1143	" -4 + x^^^2 =0 ";
neuper@37906	1144	" -4 + x^^^2 =0 ";
neuper@37906	1145	" -4 + x^^^2 =0 ";
neuper@37906	1146	val fmz = ["equality ( -4 + x^^^2 =0)", "solveFor x","solutions L"];
neuper@37906	1147	(* val fmz = ["equality (1 + x^^^2 =0)", "solveFor x","solutions L"];*)
neuper@37906	1148	(val fmz = ["equality (0 =0)", "solveFor x","solutions L"];)
neuper@37991	1149	val (dI',pI',mI') = ("PolyEq",["univariate","equation"],["no_met"]);
neuper@37906	1150	(*val p = e_pos';
neuper@37906	1151	val c = [];
neuper@37906	1152	val (mI,m) = ("Init_Proof",Init_Proof (fmz, (dI',pI',mI')));
neuper@37906	1153	val (p,_,f,nxt,_,pt) = me (mI,m) p c EmptyPtree;*)
neuper@37906	1154	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@37906	1155
neuper@37906	1156	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	1157	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	1158	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	1159	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	1160	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	1161	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	1162	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	1163	case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 2, x = -2]")) => ()
neuper@38031	1164	\| _ => error "polyeq.sml: diff.behav. in [x = 2, x = -2]";
neuper@37906	1165
neuper@37906	1166	"----------------- polyeq.sml end ------------------";
neuper@37906	1167
neuper@37906	1168	(Punkte aus dem TestBericht, die ich in rlang.sml nicht zuordnen konnte:)
neuper@37906	1169	(WN.19.3.03 ---v-)
neuper@37906	1170	(3(b))val (bdv,v) = (str2term "bdv", str2term "R1");
neuper@37906	1171	val t = str2term "-1 * (R * R2) + R2 * R1 + -1 * (R * R1) = 0";
neuper@37926	1172	val SOME (t',_) = rewrite_set_inst_ thy false [(bdv,v)] make_polynomial_in t;
neuper@37906	1173	term2str t';
neuper@37906	1174	"-1 * R * R2 + (R2 + -1 * R) * R1 = 0";
neuper@37906	1175	(WN.19.3.03 ---^-)
neuper@37906	1176
neuper@37906	1177	(3(c))val (bdv,v) = (str2term "bdv", str2term "p");
neuper@37906	1178	val t = str2term "y ^^^ 2 + -2 * (x * p) = 0";
neuper@37926	1179	val SOME (t',_) = rewrite_set_inst_ thy false [(bdv,v)] make_polynomial_in t;
neuper@37906	1180	term2str t';
neuper@37906	1181	"y ^^^ 2 + -2 * x * p = 0";
neuper@37906	1182
neuper@37906	1183	(3(d))val (bdv,v) = (str2term "bdv", str2term "x2");
neuper@37906	1184	val t = str2term
neuper@37906	1185	"A + x1 * (y3 * (1 / 2)) + x3 * (y2 * (1 / 2)) + -1 * (x1 * (y2 * (1 / 2))) + -1 * (x3 * (y1 * (1 / 2 ))) + y1 * (1 / 2 * x2) + -1 * (y3 * (1 / 2 * x2)) = 0";
neuper@37926	1186	val SOME (t',_) = rewrite_set_inst_ thy false [(bdv,v)] make_polynomial_in t;
neuper@37906	1187	term2str t';
neuper@37906	1188	"A + x1 * y3 * (1 / 2) + x3 * y2 * (1 / 2) + - x1 * y2 * (1 / 2) + - x3 * y1 * (1 / 2) + (y1 * (1 / 2) + - y3 * (1 / 2)) * x2 = 0";
neuper@37926	1189	val SOME (t',_) = rewrite_set_inst_ thy false [(bdv,v)] make_ratpoly_in t;
neuper@37906	1190	term2str t';
neuper@37906	1191	"A + x1 * y3 * (1 / 2) + x3 * y2 * (1 / 2) + -1 * x1 * y2 * (1 / 2) + -1 * x3 * y1 * (1 / 2) + (y1 * (1 / 2) + -1 * y3 * (1 / 2)) * x2 = 0";
neuper@37906	1192
neuper@37906	1193	(3(e))val (bdv,v) = (str2term "bdv", str2term "a");
neuper@37906	1194	val t = str2term
neuper@37906	1195	"A ^^^ 2 + c ^^^ 2 * (c / d) ^^^ 2 + (-4 * (c / d) ^^^ 2) * a ^^^ 2 = 0";
neuper@37926	1196	val NONE = rewrite_set_inst_ thy false [(bdv,v)] make_polynomial_in t;
neuper@37906	1197	(die _unsichtbare_ Klammern sind genau wie gew"unscht)
neuper@37906	1198
neuper@37906	1199
neuper@37906	1200	val t = str2term "(x + 1) * (x + 2) - (3 * x - 2) ^^^ 2 - ((2 * x - 1) ^^^ 2 + (3 * x - 1) * (x + 1)) = 0";
neuper@37906	1201	trace_rewrite:=true;
neuper@37906	1202	rewrite_set_ thy false expand_binoms t;
neuper@37906	1203	trace_rewrite:=false;
neuper@37906	1204
neuper@37906	1205
neuper@37906	1206	"----------- interSteps ([1],Res); on Schalk Is86Bsp5-------------";
neuper@37906	1207	"----------- interSteps ([1],Res); on Schalk Is86Bsp5-------------";
neuper@37906	1208	"----------- interSteps ([1],Res); on Schalk Is86Bsp5-------------";
neuper@37906	1209	states:=[];
neuper@37906	1210	CalcTree
neuper@37906	1211	[(["equality (3x - 1 - (5x - (2 - 4*x)) = -11)","solveFor x","solutions L"],
neuper@37991	1212	("PolyEq",["univariate","equation"],["no_met"]))];
neuper@37906	1213	Iterator 1;
neuper@37906	1214	moveActiveRoot 1;
neuper@37906	1215	autoCalculate 1 CompleteCalc;
neuper@37906	1216	val ((pt,p),_) = get_calc 1; show_pt pt;
neuper@37906	1217
neuper@37906	1218	interSteps 1 ([1],Res) (no Rewrite_Set...);
neuper@42248	1219
neuper@42248	1220	============ inhibit exn WN110906 ==============================================*)
neuper@42248	1221

author	Walther Neuper <neuper@ist.tugraz.at>
	Sat, 10 Sep 2011 10:56:24 +0200
branch	decompose-isar
changeset 42260	537d95d1fdb2
parent 42255	6201b34bd323
child 42272	dcc5d2601cf7
permissions	-rw-r--r--