wneuper/isa: test/Tools/isac/Knowledge/polyeq.sml@b4f9b188373e (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@42318	17	"----------- (-8 - 2*x + x^^^2 = 0), by rewriting ---------------";
neuper@37906	18	"----------- (-16 + 4x + 2x^^^2 = 0), --------------------------";
neuper@37906	19	"----------- (ab - (a+b)x + x^^^2 = 0), (Schalk 2,S.68Nr.44.a)";
neuper@37906	20	"----------- (-64 + x^^^2 = 0), (Schalk 2, S.66 Nr.1.a~--------)";
neuper@37906	21	"----------- (-147 + 3x^^^2 = 0), (Schalk 2, S.66 Nr.1.b------*)";
neuper@37906	22	"----------- (3x - 1 - (5x - (2 - 4x)) = -11),(Schalk Is86Bsp5";
neuper@37906	23	"----------- ((x+1)(x+2) - (3x - 2)^^^2=.. Schalk II s.68 Bsp 37";
neuper@37906	24	"----------- interSteps ([1],Res); on Schalk Is86Bsp5-------------";
neuper@37906	25	"-----------------------------------------------------------------";
neuper@37906	26	"-----------------------------------------------------------------";
neuper@37906	27	"-----------------------------------------------------------------";
neuper@37906	28
neuper@37906	29	"----------- tests on predicates in problems ---------------------";
neuper@37906	30	"----------- tests on predicates in problems ---------------------";
neuper@37906	31	"----------- tests on predicates in problems ---------------------";
neuper@37906	32	(*
neuper@37906	33	trace_rewrite:=true;
neuper@37906	34	trace_rewrite:=false;
neuper@37906	35	*)
neuper@37906	36	val t1 = (term_of o the o (parse thy)) "lhs (-8 - 2*x + x^^^2 = 0)";
neuper@42248	37	val SOME (t,_) = rewrite_set_ @{theory PolyEq} false PolyEq_prls t1;
neuper@37906	38	if ((term2str t) = "-8 - 2 * x + x ^^^ 2") then ()
neuper@38031	39	else error "polyeq.sml: diff.behav. in lhs";
neuper@37906	40
neuper@37906	41	val t2 = (term_of o the o (parse thy)) "(-8 - 2*x + x^^^2) is_expanded_in x";
neuper@42248	42	val SOME (t,_) = rewrite_set_ @{theory PolyEq} false PolyEq_prls t2;
neuper@42248	43	if (term2str t) = "True" then ()
neuper@38031	44	else error "polyeq.sml: diff.behav. 1 in is_expended_in";
neuper@37906	45
neuper@37906	46	val t0 = (term_of o the o (parse thy)) "(sqrt(x)) is_poly_in x";
neuper@42248	47	val SOME (t,_) = rewrite_set_ @{theory PolyEq} false PolyEq_prls t0;
neuper@42248	48	if (term2str t) = "False" then ()
neuper@38031	49	else error "polyeq.sml: diff.behav. 2 in is_poly_in";
neuper@37906	50
neuper@37906	51	val t3 = (term_of o the o (parse thy)) "(-8 + (-1)2x + x^^^2) is_poly_in x";
neuper@42248	52	val SOME (t,_) = rewrite_set_ @{theory PolyEq} false PolyEq_prls t3;
neuper@42248	53	if (term2str t) = "True" then ()
neuper@38031	54	else error "polyeq.sml: diff.behav. 3 in is_poly_in";
neuper@37906	55
neuper@37906	56	val t4 = (term_of o the o (parse thy)) "(lhs (-8 + (-1)2x + x^^^2 = 0)) is_expanded_in x";
neuper@42248	57	val SOME (t,_) = rewrite_set_ @{theory PolyEq} false PolyEq_prls t4;
neuper@42248	58	if (term2str t) = "True" then ()
neuper@38031	59	else error "polyeq.sml: diff.behav. 4 in is_expended_in";
neuper@37906	60
neuper@37906	61
neuper@37906	62	val t6 = (term_of o the o (parse thy)) "(lhs (-8 - 2*x + x^^^2 = 0)) is_expanded_in x";
neuper@42248	63	val SOME (t,_) = rewrite_set_ @{theory PolyEq} false PolyEq_prls t6;
neuper@42248	64	if (term2str t) = "True" then ()
neuper@38031	65	else error "polyeq.sml: diff.behav. 5 in is_expended_in";
neuper@37906	66
neuper@37906	67	val t3 = (term_of o the o (parse thy))"((-8 - 2*x + x^^^2) has_degree_in x) = 2";
neuper@42248	68	val SOME (t,_) = rewrite_set_ @{theory PolyEq} false PolyEq_prls t3;
neuper@42248	69	if (term2str t) = "True" then ()
neuper@38031	70	else error "polyeq.sml: diff.behav. in has_degree_in_in";
neuper@37906	71
neuper@37906	72	val t3 = (term_of o the o (parse thy)) "((sqrt(x)) has_degree_in x) = 2";
neuper@42248	73	val SOME (t,_) = rewrite_set_ @{theory PolyEq} false PolyEq_prls t3;
neuper@42248	74	if (term2str t) = "False" then ()
neuper@38031	75	else error "polyeq.sml: diff.behav. 6 in has_degree_in_in";
neuper@37906	76
neuper@37906	77	val t4 = (term_of o the o (parse thy))
neuper@37906	78	"((-8 - 2*x + x^^^2) has_degree_in x) = 1";
neuper@42248	79	val SOME (t,_) = rewrite_set_ @{theory PolyEq} false PolyEq_prls t4;
neuper@42248	80	if (term2str t) = "False" then ()
neuper@38031	81	else error "polyeq.sml: diff.behav. 7 in has_degree_in_in";
neuper@37906	82
neuper@37906	83	val t5 = (term_of o the o (parse thy))
neuper@37906	84	"((-8 - 2*x + x^^^2) has_degree_in x) = 2";
neuper@42248	85	val SOME (t,_) = rewrite_set_ @{theory PolyEq} false PolyEq_prls t5;
neuper@42248	86	if (term2str t) = "True" then ()
neuper@38031	87	else error "polyeq.sml: diff.behav. 8 in has_degree_in_in";
neuper@37906	88
neuper@42248	89	"----------- test matching problems --------------------------0---";
neuper@42248	90	"----------- test matching problems --------------------------0---";
neuper@42248	91	"----------- test matching problems --------------------------0---";
neuper@42248	92	val fmz = ["equality (-8 - 2*x + x^^^2 = 0)", "solveFor x","solutions L"];
neuper@42248	93	if match_pbl fmz (get_pbt ["expanded","univariate","equation"]) =
neuper@42248	94	Matches' {Find = [Correct "solutions L"],
neuper@42248	95	With = [],
neuper@42248	96	Given = [Correct "equality (-8 - 2 * x + x ^^^ 2 = 0)", Correct "solveFor x"],
neuper@42248	97	Where = [Correct "matches (?a = 0) (-8 - 2 * x + x ^^^ 2 = 0)",
neuper@42248	98	Correct "lhs (-8 - 2 * x + x ^^^ 2 = 0) is_expanded_in x"],
neuper@42248	99	Relate = []}
neuper@42248	100	then () else error "match_pbl [expanded,univariate,equation]";
neuper@37906	101
neuper@42248	102	if match_pbl fmz (get_pbt ["degree_2","expanded","univariate","equation"]) =
neuper@42248	103	Matches' {Find = [Correct "solutions L"],
neuper@42248	104	With = [],
neuper@42248	105	Given = [Correct "equality (-8 - 2 * x + x ^^^ 2 = 0)", Correct "solveFor x"],
neuper@42248	106	Where = [Correct "lhs (-8 - 2 * x + x ^^^ 2 = 0) has_degree_in x = 2"],
neuper@42248	107	Relate = []} (before WN110906 was: has_degree_in x =!= 2"])
neuper@42248	108	then () else error "match_pbl [degree_2,expanded,univariate,equation]";
neuper@37906	109
neuper@42248	110	"----------- lin.eq degree_0 -------------------------------------";
neuper@42248	111	"----------- lin.eq degree_0 -------------------------------------";
neuper@42248	112	"----------- lin.eq degree_0 -------------------------------------";
neuper@37906	113	"----- d0_false ------";
neuper@42248	114	val fmz = ["equality (1 = (0::real))", "solveFor x", "solutions L"];
neuper@37991	115	val (dI',pI',mI') = ("PolyEq",["degree_0","polynomial","univariate","equation"],
neuper@37906	116	["PolyEq","solve_d0_polyeq_equation"]);
neuper@42283	117	(*=== inhibit exn WN110914: declare_constraints doesnt work with num_str ========
neuper@42283	118	TODO: change to "equality (x + -1*x = (0::real))"
neuper@42283	119	and search for an appropriate problem and method.
neuper@42283	120
neuper@37906	121	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@42272	122	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	123	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	124	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	125	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	126	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	127	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	128	case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[]")) => ()
neuper@38031	129	\| _ => error "polyeq.sml: diff.behav. in 1 = 0 -> []";
neuper@37906	130
neuper@37906	131	"----- d0_true ------";
neuper@42248	132	val fmz = ["equality (0 = (0::real))", "solveFor x","solutions L"];
neuper@37991	133	val (dI',pI',mI') = ("PolyEq",["degree_0","polynomial","univariate","equation"],
neuper@37906	134	["PolyEq","solve_d0_polyeq_equation"]);
neuper@37906	135	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@42272	136	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	137	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	138	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	139	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	140	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	141	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	142	case f of Form' (FormKF (~1,EdUndef,0,Nundef,"UniversalList")) => ()
neuper@38031	143	\| _ => error "polyeq.sml: diff.behav. in 0 = 0 -> UniversalList";
neuper@42272	144	============ inhibit exn WN110914 ============================================*)
neuper@37906	145
neuper@42248	146	"----------- test thm's d2_pq_formulsxx[_neg]---------------------";
neuper@42248	147	"----------- test thm's d2_pq_formulsxx[_neg]---------------------";
neuper@42248	148	"----------- test thm's d2_pq_formulsxx[_neg]---------------------";
neuper@37906	149	"----- d2_pqformula1 ------!!!!";
neuper@42255	150	val fmz = ["equality (-1/8 + (-1/4)*z + z^^^2 = (0::real))", "solveFor z","solutions L"];
neuper@42255	151	val (dI',pI',mI') =
neuper@42255	152	("Isac", ["pqFormula","degree_2","polynomial","univariate","equation"], ["no_met"]);
neuper@37906	153	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
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;
neuper@42255	160	val (p,_,f,nxt,_,pt) = me nxt p [] pt; (Apply_Method ["PolyEq", "solve_d2_polyeq_pq_equation"])
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	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42255	165	([z = 1 / 8 + sqrt (9 / 16) / 2, z = 1 / 8 + -1 sqrt (9 / 16) / 2] TODO sqrt*)
neuper@42255	166	val (p,_,f,nxt,_,pt) = me nxt p [] pt; (nxt =..,Check_elementwise "Assumptions"))
neuper@42255	167	"~~~~~ fun me, args:"; val ((_,tac), (p:pos'), _, (pt:ptree)) = (nxt, p, [], pt);
neuper@42255	168	"~~~~~ fun locatetac, args:"; val (tac, (ptp as (pt, p))) = (tac, (pt, p));
neuper@42255	169	val (mI,m) = mk_tac'_ tac;
neuper@42255	170	val Appl m = applicable_in p pt m;
neuper@42255	171	val Check_elementwise' (trm1, str, (trm2, trms)) = m;
neuper@42255	172	term2str trm1 = "[z = 1 / 8 + sqrt (9 / 16) / 2, z = 1 / 8 + -1 * sqrt (9 / 16) / 2]";
neuper@42255	173	str = "Assumptions";
neuper@42255	174	term2str trm2 = "[z = 1 / 8 + sqrt (9 / 16) / 2, z = 1 / 8 + -1 * sqrt (9 / 16) / 2]";
neuper@42255	175	terms2str trms = "[\"lhs (-1 / 8 + -1 * (1 / 8 + sqrt (9 / 16) / 2) / 4 +\n "^
neuper@42255	176	" (1 / 8 + sqrt (9 / 16) / 2) ^^^ 2 =\n 0) is_poly_in 1 / 8 + sqrt (9 / 16) / 2\","^
neuper@42255	177	"\"lhs (-1 / 8 + -1 * (1 / 8 + sqrt (9 / 16) / 2) / 4 +\n (1 / 8 + sqrt (9 / 16) / 2) ^^^ 2 =\n 0) "^
neuper@42255	178	"has_degree_in 1 / 8 + sqrt (9 / 16) / 2 =\n2\","^
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) is_poly_in 1 / 8 + -1 * sqrt (9 / 16) / 2\","^
neuper@42255	180	"\"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	181	(TODO simplify assumptions (sqrt!) and check ERROR in has_degree_in);
neuper@42255	182	member op = specsteps mI (false);
neuper@42255	183	(*loc_solve_ (mI,m) ptp;
neuper@42255	184	WAS: not-found-in-script: NotLocatable from NasNap (Const ("List...*)
neuper@42255	185	"~~~~~ fun loc_solve_, args:"; val (m, (pt,pos)) = ((mI,m), ptp);
neuper@42255	186	(*solve m (pt, pos);
neuper@42255	187	WAS: not-found-in-script: NotLocatable from NasNap (Const ("List...*)
neuper@42255	188	"~~~~~ fun solve, args:"; val ((mI,m), (pt, po as (p,p_))) = (m, (pt, pos));
neuper@42255	189	e_metID = get_obj g_metID pt (par_pblobj pt p) (false);
neuper@42255	190	val thy' = get_obj g_domID pt (par_pblobj pt p);
neuper@42255	191	val (srls, is, sc) = from_pblobj_or_detail' thy' (p,p_) pt;
neuper@42255	192	val d = e_rls;
neuper@42255	193	(*locate_gen (thy',srls) m (pt,(p,p_)) (sc,d) is;
neuper@42255	194	WAS: not-found-in-script: NotLocatable from NasNap (Const ("List...*)
neuper@42255	195	"~~~~~ fun locate_gen, args:"; val ((ts as (thy',srls)), (m:tac_), ((pt,p):ptree * pos'),
neuper@42255	196	(scr as Script (h $ body),d), (ScrState (E,l,a,v,S,b), ctxt)) =
neuper@42255	197	((thy',srls), m ,(pt,(p,p_)) ,(sc,d) ,is); (* locate_gen 2nd pattern *)
neuper@42255	198	val thy = assoc_thy thy';
neuper@42255	199	l = [] orelse ((last_elem o fst) p = 0 andalso snd p = Res) (false);
neuper@42255	200	(*WAS val NasApp _ =(astep_up (thy',srls,scr,d) ((E,l,a,v,S,b), [(m,EmptyMout,pt,p,[])]) )
neuper@42255	201	... Assoc ... is correct*)
neuper@42255	202	"~~~~~ and astep_up, args:"; val ((ys as (_,_,Script sc,_)), ((E,l,a,v,S,b),ss)) =
neuper@42255	203	((thy',srls,scr,d), ((E,l,a,v,S,b), [(m,EmptyMout,pt,p,[])]));
neuper@42255	204	1 < length l (true);
neuper@42255	205	val up = drop_last l;
neuper@42255	206	term2str (go up sc);
neuper@42255	207	(go up sc);
neuper@42255	208	(*WAS val NasNap _ = ass_up ys ((E,up,a,v,S,b),ss) (go up sc)
neuper@42255	209	... ???? ... is correct*)
neuper@42255	210	"~~~~~ fun ass_up, args:"; val ((ys as (y,s,Script sc,d)), (is as (E,l,a,v,S,b),ss),
neuper@42255	211	(Const ("HOL.Let",_) $ _)) = (ys, ((E,up,a,v,S,b),ss), (go up sc));
neuper@42255	212	val l = drop_last l; (comes from e, goes to Abs)
neuper@42255	213	val (Const ("HOL.Let",_) $ e $ (Abs (i,T,body))) = go l sc;
neuper@42255	214	val i = mk_Free (i, T);
neuper@42255	215	val E = upd_env E (i, v);
neuper@42255	216	(Type error ...: Can't unify _a to pos pos_ (Incompatible types)*)
neuper@42255	217	val [(tac_, mout, ptree, pos', xxx)] = ss;
neuper@42255	218	val ss = [(tac_, mout, ptree, pos', []:(pos * pos_) list)];
neuper@42255	219	(*WAS val NasApp iss = assy (((y,s),d),Aundef) ((E, l@[R,D], a,v,S,b),ss) body
neuper@42255	220	... Assoc ... is correct*)
neuper@42255	221	"~~~~~ 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	222	((((y,s),d),Aundef), ((E, l@[R,D], a,v,S,b),ss), body);
neuper@42255	223	val (a', STac stac) = handle_leaf "locate" thy' sr E a v t
neuper@42255	224	val ctxt = get_ctxt pt (p,p_)
neuper@42255	225	val p' = lev_on p : pos;
neuper@42255	226	(* WAS val NotAss = assod pt d m stac
neuper@42255	227	... Ass ... is correct*)
neuper@42255	228	"~~~~~ fun assod, args:"; val (pt, _, (m as Check_elementwise' (consts,_,(consts_chkd,_))),
neuper@42255	229	(Const ("Script.Check'_elementwise",_) $ consts' $ _)) = (pt, d, m, stac);
neuper@42255	230	term2str consts;
neuper@42255	231	term2str consts';
neuper@42255	232	if consts = consts' (WAS false) then () else error "Check_elementwise changed";
neuper@42260	233	([z = 1 / 8 + sqrt (9 / 16) / 2, z = 1 / 8 + -1 sqrt (9 / 16) / 2] TODO sqrt*)
neuper@37906	234
neuper@37906	235	"----- d2_pqformula1_neg ------";
neuper@42272	236	val fmz = ["equality (2 +(-1)*x + x^^^2 = (0::real))", "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,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@42272	239	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	240	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	241	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	242	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	243	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	244	(*### or2list False
neuper@37906	245	([1],Res) False Or_to_List)*)
neuper@42272	246	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	247	(*### or2list False
neuper@37906	248	([2],Res) [] Check_elementwise "Assumptions"*)
neuper@42272	249	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	250	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	251	val asm = get_assumptions_ pt p;
neuper@42318	252	if f = Form' (FormKF (~1,EdUndef,0,Nundef,"[]")) andalso
neuper@42318	253	terms2str asm = "[\"lhs (2 + -1 * x + x ^^^ 2 = 0) is_poly_in x\"," ^
neuper@42318	254	"\"lhs (2 + -1 * x + x ^^^ 2 = 0) has_degree_in x = 2\"]" then ()
neuper@38031	255	else error "polyeq.sml: diff.behav. in 2 +(-1)*x + x^^^2 = 0";
neuper@37906	256
neuper@37906	257	"----- d2_pqformula2 ------";
neuper@37906	258	val fmz = ["equality (-2 +(-1)x + 1x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	259	val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	260	["PolyEq","solve_d2_polyeq_pq_equation"]);
neuper@42272	261	(*val p = e_pos';
neuper@37906	262	val (mI,m) = ("Init_Proof",Init_Proof (fmz, (dI',pI',mI')));
neuper@42272	263	val (p,_,f,nxt,_,pt) = me (mI,m) p [] EmptyPtree;*)
neuper@37906	264	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@42272	265	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	266	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	267	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	268	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	269	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	270	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	271	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	272	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	273	case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 2, x = -1]")) => ()
neuper@38031	274	\| _ => error "polyeq.sml: diff.behav. in -2 + (-1)*x + x^2 = 0 -> [x = 2, x = -1]";
neuper@37906	275
neuper@37906	276
neuper@37906	277	"----- d2_pqformula2_neg ------";
neuper@37906	278	val fmz = ["equality ( 2 +(-1)x + 1x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	279	val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	280	["PolyEq","solve_d2_polyeq_pq_equation"]);
neuper@37906	281	(*val p = e_pos'; val c = [];
neuper@37906	282	val (mI,m) = ("Init_Proof",Init_Proof (fmz, (dI',pI',mI')));
neuper@37906	283	val (p,_,f,nxt,_,pt) = me (mI,m) p c EmptyPtree;*)
neuper@37906	284	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@42272	285	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	286	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	287	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	288	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	289	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	290	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	291	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	292	"TODO 2 +(-1)x + 1x^^^2 = 0";
neuper@37906	293	"TODO 2 +(-1)x + 1x^^^2 = 0";
neuper@37906	294	"TODO 2 +(-1)x + 1x^^^2 = 0";
neuper@37906	295
neuper@37906	296
neuper@37906	297	"----- d2_pqformula3 ------";
neuper@37906	298	(EP-9)
neuper@37906	299	val fmz = ["equality (-2 + x + x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	300	val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	301	["PolyEq","solve_d2_polyeq_pq_equation"]);
neuper@37906	302	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@42272	303	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	304	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	305	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	306	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	307	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	308	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	309	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	310	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	311	case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 1, x = -2]")) => ()
neuper@38031	312	\| _ => error "polyeq.sml: diff.behav. in -2 + x + x^2 = 0-> [x = 1, x = -2]";
neuper@37906	313
neuper@37906	314	"----- d2_pqformula3_neg ------";
neuper@37906	315	val fmz = ["equality ( 2 + x + x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	316	val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	317	["PolyEq","solve_d2_polyeq_pq_equation"]);
neuper@37906	318	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@42272	319	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	320	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	321	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	322	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	323	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	324	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	325	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	326	"TODO 2 + x + x^^^2 = 0";
neuper@37906	327	"TODO 2 + x + x^^^2 = 0";
neuper@37906	328	"TODO 2 + x + x^^^2 = 0";
neuper@37906	329
neuper@37906	330
neuper@37906	331	"----- d2_pqformula4 ------";
neuper@37906	332	val fmz = ["equality (-2 + x + 1*x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	333	val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	334	["PolyEq","solve_d2_polyeq_pq_equation"]);
neuper@37906	335	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@42272	336	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	337	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	338	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	339	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	340	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	341	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	342	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	343	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	344	case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 1, x = -2]")) => ()
neuper@38031	345	\| _ => error "polyeq.sml: diff.behav. in -2 + x + 1*x^^^2 = 0 -> [x = 1, x = -2]";
neuper@37906	346
neuper@37906	347	"----- d2_pqformula4_neg ------";
neuper@37906	348	val fmz = ["equality ( 2 + x + 1*x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	349	val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	350	["PolyEq","solve_d2_polyeq_pq_equation"]);
neuper@37906	351	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@42272	352	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	353	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	354	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	355	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	356	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	357	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	358	"TODO 2 + x + 1*x^^^2 = 0";
neuper@37906	359	"TODO 2 + x + 1*x^^^2 = 0";
neuper@37906	360	"TODO 2 + x + 1*x^^^2 = 0";
neuper@37906	361
neuper@37906	362	"----- d2_pqformula5 ------";
neuper@37906	363	val fmz = ["equality (1*x + x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	364	val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	365	["PolyEq","solve_d2_polyeq_pq_equation"]);
neuper@37906	366	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@42272	367	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	368	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	369	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	370	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	371	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	372	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	373	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	374	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	375	case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 0, x = -1]")) => ()
neuper@38031	376	\| _ => error "polyeq.sml: diff.behav. in 1*x + x^2 = 0 -> [x = 0, x = -1]";
neuper@37906	377
neuper@37906	378	"----- d2_pqformula6 ------";
neuper@37906	379	val fmz = ["equality (1x + 1x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	380	val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	381	["PolyEq","solve_d2_polyeq_pq_equation"]);
neuper@37906	382	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@42272	383	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	384	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	385	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	386	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	387	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	388	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	389	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	390	val (p,_,f,nxt,_,pt) = me nxt p [] 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 1x + 1x^2 = 0 -> [x = 0, x = -1]";
neuper@37906	393
neuper@37906	394	"----- d2_pqformula7 ------";
neuper@37906	395	(EP-10)
neuper@37906	396	val fmz = ["equality ( x + x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	397	val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	398	["PolyEq","solve_d2_polyeq_pq_equation"]);
neuper@37906	399	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@42272	400	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	401	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	402	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	403	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	404	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	405	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	406	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	407	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	408	case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 0, x = -1]")) => ()
neuper@38031	409	\| _ => error "polyeq.sml: diff.behav. in x + x^2 = 0 -> [x = 0, x = -1]";
neuper@37906	410
neuper@37906	411	"----- d2_pqformula8 ------";
neuper@37906	412	val fmz = ["equality ( x + 1*x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	413	val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	414	["PolyEq","solve_d2_polyeq_pq_equation"]);
neuper@37906	415	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@42272	416	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	417	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	418	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	419	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	420	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	421	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	422	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	423	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	424	case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 0, x = -1]")) => ()
neuper@38031	425	\| _ => error "polyeq.sml: diff.behav. in x + 1*x^2 = 0 -> [x = 0, x = -1]";
neuper@37906	426
neuper@37906	427	"----- d2_pqformula9 ------";
neuper@37906	428	val fmz = ["equality (-4 + x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	429	val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	430	["PolyEq","solve_d2_polyeq_pq_equation"]);
neuper@37906	431	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@42272	432	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	433	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	434	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	435	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	436	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	437	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	438	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	439	case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 2, x = -2]")) => ()
neuper@38031	440	\| _ => error "polyeq.sml: diff.behav. in -4 + x^2 = 0 -> [x = 2, x = -2]";
neuper@37906	441
neuper@37906	442
neuper@37906	443	"----- d2_pqformula10_neg ------";
neuper@37906	444	val fmz = ["equality (4 + x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	445	val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	446	["PolyEq","solve_d2_polyeq_pq_equation"]);
neuper@37906	447	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@42272	448	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	449	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	450	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	451	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	452	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	453	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	454	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	455	"TODO 4 + x^^^2 = 0";
neuper@37906	456	"TODO 4 + x^^^2 = 0";
neuper@37906	457	"TODO 4 + x^^^2 = 0";
neuper@37906	458
neuper@37906	459	"----- d2_pqformula10 ------";
neuper@37906	460	val fmz = ["equality (-4 + 1*x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	461	val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	462	["PolyEq","solve_d2_polyeq_pq_equation"]);
neuper@37906	463	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@42272	464	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	465	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	466	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	467	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	468	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	469	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	470	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	471	case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 2, x = -2]")) => ()
neuper@38031	472	\| _ => error "polyeq.sml: diff.behav. in -4 + 1*x^2 = 0 -> [x = 2, x = -2]";
neuper@37906	473
neuper@37906	474	"----- d2_pqformula9_neg ------";
neuper@37906	475	val fmz = ["equality (4 + 1*x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	476	val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	477	["PolyEq","solve_d2_polyeq_pq_equation"]);
neuper@37906	478	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@42272	479	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	480	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	481	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	482	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	483	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	484	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	485	"TODO 4 + 1*x^^^2 = 0";
neuper@37906	486	"TODO 4 + 1*x^^^2 = 0";
neuper@37906	487	"TODO 4 + 1*x^^^2 = 0";
neuper@37906	488
neuper@37906	489	"-------------------- test thm's d2_abc_formulsxx[_neg]-----";
neuper@37906	490	"-------------------- test thm's d2_abc_formulsxx[_neg]-----";
neuper@37906	491	"-------------------- test thm's d2_abc_formulsxx[_neg]-----";
neuper@37906	492
neuper@37906	493	val fmz = ["equality (-1 +(-1)x + 2x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	494	val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	495	["PolyEq","solve_d2_polyeq_abc_equation"]);
neuper@37906	496	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@42272	497	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	498	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	499	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	500	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	501	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	502	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	503	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	504	case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 1, x = -1 / 2]")) => ()
neuper@38031	505	\| _ => error "polyeq.sml: diff.behav. in -1 + (-1)x + 2x^2 = 0 -> [x = 1, x = -1/2]";
neuper@37906	506
neuper@37906	507	val fmz = ["equality ( 1 +(-1)x + 2x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	508	val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	509	["PolyEq","solve_d2_polyeq_abc_equation"]);
neuper@37906	510	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@42272	511	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	512	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	513	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	514	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	515	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	516	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	517	"TODO 1 +(-1)x + 2x^^^2 = 0";
neuper@37906	518	"TODO 1 +(-1)x + 2x^^^2 = 0";
neuper@37906	519	"TODO 1 +(-1)x + 2x^^^2 = 0";
neuper@37906	520
neuper@37906	521	(EP-11)
neuper@37906	522	val fmz = ["equality (-1 + x + 2*x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	523	val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	524	["PolyEq","solve_d2_polyeq_abc_equation"]);
neuper@37906	525	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@42272	526	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	527	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	528	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	529	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	530	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	531	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	532	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	533	case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 1 / 2, x = -1]")) => ()
neuper@38031	534	\| _ => error "polyeq.sml: diff.behav. in -1 + x + 2*x^2 = 0 -> [x = 1/2, x = -1]";
neuper@37906	535
neuper@37906	536	val fmz = ["equality ( 1 + x + 2*x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	537	val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	538	["PolyEq","solve_d2_polyeq_abc_equation"]);
neuper@37906	539	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@42272	540	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	541	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	542	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	543	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	544	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	545	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	546	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	547	"TODO 1 + x + 2*x^^^2 = 0";
neuper@37906	548	"TODO 1 + x + 2*x^^^2 = 0";
neuper@37906	549	"TODO 1 + x + 2*x^^^2 = 0";
neuper@37906	550
neuper@37906	551	val fmz = ["equality (-2 + 1*x + x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	552	val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	553	["PolyEq","solve_d2_polyeq_abc_equation"]);
neuper@37906	554	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@42272	555	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	556	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	557	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	558	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	559	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	560	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	561	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	562	case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 1, x = -2]")) => ()
neuper@38031	563	\| _ => error "polyeq.sml: diff.behav. in -2 + 1*x + x^2 = 0 -> [x = 1, x = -2]";
neuper@37906	564
neuper@37906	565	val fmz = ["equality ( 2 + 1*x + x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	566	val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	567	["PolyEq","solve_d2_polyeq_abc_equation"]);
neuper@37906	568	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@42272	569	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	570	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	571	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	572	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	573	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	574	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	575	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	576	"TODO 2 + 1*x + x^^^2 = 0";
neuper@37906	577	"TODO 2 + 1*x + x^^^2 = 0";
neuper@37906	578	"TODO 2 + 1*x + x^^^2 = 0";
neuper@37906	579
neuper@37906	580	(EP-12)
neuper@37906	581	val fmz = ["equality (-2 + x + x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	582	val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	583	["PolyEq","solve_d2_polyeq_abc_equation"]);
neuper@37906	584	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@42272	585	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	586	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	587	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	588	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	589	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	590	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	591	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	592	case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 1, x = -2]")) => ()
neuper@38031	593	\| _ => error "polyeq.sml: diff.behav. in -2 + x + x^2 = 0 -> [x = 1, x = -2]";
neuper@37906	594
neuper@37906	595	val fmz = ["equality ( 2 + x + x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	596	val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	597	["PolyEq","solve_d2_polyeq_abc_equation"]);
neuper@37906	598	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@42272	599	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	600	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	601	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	602	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	603	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	604	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	605	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	606	"TODO 2 + x + x^^^2 = 0";
neuper@37906	607	"TODO 2 + x + x^^^2 = 0";
neuper@37906	608	"TODO 2 + x + x^^^2 = 0";
neuper@37906	609
neuper@37906	610	(EP-13)
neuper@37906	611	val fmz = ["equality (-8 + 2*x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	612	val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	613	["PolyEq","solve_d2_polyeq_abc_equation"]);
neuper@37906	614	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@42272	615	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	616	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	617	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	618	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	619	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	620	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	621	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	622	case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 2, x = -2]")) => ()
neuper@38031	623	\| _ => error "polyeq.sml: diff.behav. in -8 + 2*x^2 = 0 -> [x = 2, x = -2]";
neuper@37906	624
neuper@37906	625	val fmz = ["equality ( 8+ 2*x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	626	val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	627	["PolyEq","solve_d2_polyeq_abc_equation"]);
neuper@37906	628	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@42272	629	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	630	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	631	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	632	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	633	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	634	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	635	"TODO 8+ 2*x^^^2 = 0";
neuper@37906	636	"TODO 8+ 2*x^^^2 = 0";
neuper@37906	637	"TODO 8+ 2*x^^^2 = 0";
neuper@37906	638
neuper@37906	639	(EP-14)
neuper@37906	640	val fmz = ["equality (-4 + x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	641	val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"], ["PolyEq","solve_d2_polyeq_abc_equation"]);
neuper@37906	642	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@42272	643	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	644	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	645	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	646	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	647	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	648	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	649	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	650	case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 2, x = -2]")) => ()
neuper@38031	651	\| _ => error "polyeq.sml: diff.behav. in -4 + x^2 = 0 -> [x = 2, x = -2]";
neuper@37906	652
neuper@37906	653
neuper@37906	654	val fmz = ["equality ( 4+ x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	655	val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"], ["PolyEq","solve_d2_polyeq_abc_equation"]);
neuper@37906	656	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@42272	657	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	658	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	659	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	660	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	661	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	662	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	663	"TODO 4+ x^^^2 = 0";
neuper@37906	664	"TODO 4+ x^^^2 = 0";
neuper@37906	665	"TODO 4+ x^^^2 = 0";
neuper@37906	666
neuper@37906	667	(EP-15)
neuper@37906	668	val fmz = ["equality (2x + 2x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	669	val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	670	["PolyEq","solve_d2_polyeq_abc_equation"]);
neuper@37906	671	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@42272	672	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	673	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	674	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	675	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	676	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	677	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	678	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	679	case f of Form' (FormKF (~1,EdUndef,_,Nundef,"[x = 0, x = -1]")) => ()
neuper@38031	680	\| _ => error "polyeq.sml: diff.behav. in x + x^2 = 0 -> [x = 0, x = -1]";
neuper@37906	681
neuper@37906	682	val fmz = ["equality (1*x + x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	683	val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	684	["PolyEq","solve_d2_polyeq_abc_equation"]);
neuper@37906	685	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@42272	686	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	687	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	688	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	689	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	690	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	691	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	692	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	693	case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 0, x = -1]")) => ()
neuper@38031	694	\| _ => error "polyeq.sml: diff.behav. in x + x^2 = 0 -> [x = 0, x = -1]";
neuper@37906	695
neuper@37906	696	(EP-16)
neuper@37906	697	val fmz = ["equality (x + 2*x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	698	val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	699	["PolyEq","solve_d2_polyeq_abc_equation"]);
neuper@37906	700	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@42272	701	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	702	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	703	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	704	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	705	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	706	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	707	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	708	case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 0, x = -1 / 2]")) => ()
neuper@38031	709	\| _ => error "polyeq.sml: diff.behav. in x + x^2 = 0 -> [x = 0, x = -1 / 2]";
neuper@37906	710
neuper@37906	711	(EP-//)
neuper@37906	712	val fmz = ["equality (x + x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	713	val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	714	["PolyEq","solve_d2_polyeq_abc_equation"]);
neuper@37906	715	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@42272	716	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	717	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	718	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	719	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	720	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	721	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	722	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	723	case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 0, x = -1]")) => ()
neuper@38031	724	\| _ => error "polyeq.sml: diff.behav. in x + x^2 = 0 -> [x = 0, x = -1]";
neuper@37906	725
neuper@37906	726	"----------- (-8 - 2x + x^^^2 = 0), (Schalk 2, S.67 Nr.31.b----";
neuper@37906	727	"----------- (-8 - 2x + x^^^2 = 0), (Schalk 2, S.67 Nr.31.b----";
neuper@37906	728	"----------- (-8 - 2x + x^^^2 = 0), (Schalk 2, S.67 Nr.31.b----";
neuper@37906	729	val fmz = ["equality (-8 - 2x + x^^^2 = 0)", (Schalk 2, S.67 Nr.31.b*)
neuper@37906	730	"solveFor x","solutions L"];
neuper@37906	731	val (dI',pI',mI') =
neuper@37991	732	("PolyEq",["degree_2","expanded","univariate","equation"],
neuper@37906	733	["PolyEq","complete_square"]);
neuper@37906	734	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@42272	735	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	736	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	737	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	738	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37991	739	(Apply_Method ("PolyEq","complete_square"))
neuper@42272	740	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	741	("-8 - 2 x + x ^^^ 2 = 0", nxt = Rewrite_Set_Inst ... "complete_square*)
neuper@42272	742	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	743	("-8 + (2 / 2 - x) ^^^ 2 = (2 / 2) ^^^ 2", nxt = Rewrite("square_explicit1")
neuper@42272	744	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	745	("(2 / 2 - x) ^^^ 2 = (2 / 2) ^^^ 2 - -8" nxt = Rewrite("root_plus_minus)
neuper@42272	746	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	747	(*"2 / 2 - x = sqrt ((2 / 2) ^^^ 2 - -8) \|
neuper@37906	748	2 / 2 - x = - sqrt ((2 / 2) ^^^ 2 - -8)" nxt = Rewr_Inst("bdv_explicit2"*)
neuper@42272	749	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	750	(*"2 / 2 - x = sqrt ((2 / 2) ^^^ 2 - -8) \|
neuper@37906	751	-1x = - (2 / 2) + - sqrt ((2 / 2) ^^^ 2 - -8)"nxt = R_Inst("bdv_explt2")
neuper@42272	752	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	753	("-1 x = - (2 / 2) + sqrt ((2 / 2) ^^^ 2 - -8) \|
neuper@37906	754	-1 * x = (- (2 / 2) + - sqrt ((2 / 2) ^^^ 2 - -8))"nxt = bdv_explicit3*)
neuper@42272	755	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	756	("-1 x = - (2 / 2) + sqrt ((2 / 2) ^^^ 2 - -8) \|
neuper@37906	757	x = -1 * (- (2 / 2) + - sqrt ((2 / 2) ^^^ 2 - -8))" nxt = bdv_explicit3*)
neuper@42272	758	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	759	("x = -1 (- (2 / 2) + sqrt ((2 / 2) ^^^ 2 - -8)) \|
neuper@37906	760	x = -1 * (- (2 / 2) + - sqrt ((2 / 2) ^^^ 2 - -8))"nxt = calculate_Ration*)
neuper@42272	761	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	762	("x = -2 \| x = 4" nxt = Or_to_List)
neuper@42272	763	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	764	("[x = -2, x = 4]" nxt = Check_Postcond)
neuper@42272	765	val (p,_,f,nxt,_,pt) = me nxt p [] pt; f2str f;
neuper@37906	766	(* FIXXXME
neuper@37906	767	case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = -2, x = 4]")) => () TODO
neuper@38031	768	\| _ => error "polyeq.sml: diff.behav. in [x = -2, x = 4]";
neuper@37906	769	*)
neuper@37906	770	if f2str f = "[x = -1 * -1 + -1 * sqrt (1 ^^^ 2 - -8),\n x = -1 * -1 + -1 * (-1 * sqrt (1 ^^^ 2 - -8))]" then ()
neuper@38031	771	else error "polyeq.sml corrected?behav. in [x = -2, x = 4]";
neuper@37906	772
neuper@42318	773	"----------- (-8 - 2*x + x^^^2 = 0), by rewriting ---------------";
neuper@42318	774	"----------- (-8 - 2*x + x^^^2 = 0), by rewriting ---------------";
neuper@42318	775	"----------- (-8 - 2*x + x^^^2 = 0), by rewriting ---------------";
neuper@42318	776
neuper@42318	777
neuper@37906	778
neuper@37906	779	"-------------------- (3 - 10x + 3x^^^2 = 0), ----------------------";
neuper@37906	780	"-------------------- (3 - 10x + 3x^^^2 = 0), ----------------------";
neuper@37906	781	"-------------------- (3 - 10x + 3x^^^2 = 0), ----------------------";
neuper@37906	782	"---- test the erls ----";
neuper@37906	783	val t1 = (term_of o the o (parse thy)) "0 <= (10/3/2)^^^2 - 1";
neuper@37926	784	val SOME (t,_) = rewrite_set_ PolyEq.thy false PolyEq_erls t1;
neuper@37906	785	val t' = term2str t;
neuper@41928	786	(*if t'= "HOL.True" then ()
neuper@38031	787	else error "polyeq.sml: diff.behav. in 'rewrite_set_.. PolyEq_erls";*)
neuper@37906	788	(* *)
neuper@37906	789	val fmz = ["equality (3 - 10x + 3x^^^2 = 0)",
neuper@37906	790	"solveFor x","solutions L"];
neuper@37906	791	val (dI',pI',mI') =
neuper@37991	792	("PolyEq",["degree_2","expanded","univariate","equation"],
neuper@37906	793	["PolyEq","complete_square"]);
neuper@37906	794	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@42272	795	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	796	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	797	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	798	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	799	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	800	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	801	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37991	802	(Apply_Method ("PolyEq","complete_square"))
neuper@42272	803	val (p,_,f,nxt,_,pt) = me nxt p [] pt; f2str f;
neuper@37906	804
neuper@37906	805	"----------- (-16 + 4x + 2x^^^2 = 0), --------------------------";
neuper@37906	806	"----------- (-16 + 4x + 2x^^^2 = 0), --------------------------";
neuper@37906	807	"----------- (-16 + 4x + 2x^^^2 = 0), --------------------------";
neuper@37906	808	val fmz = ["equality (-16 + 4x + 2x^^^2 = 0)",
neuper@37906	809	"solveFor x","solutions L"];
neuper@37906	810	val (dI',pI',mI') =
neuper@37991	811	("PolyEq",["degree_2","expanded","univariate","equation"],
neuper@37906	812	["PolyEq","complete_square"]);
neuper@37906	813	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@42272	814	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	815	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	816	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	817	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	818	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	819	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	820	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37991	821	(Apply_Method ("PolyEq","complete_square"))
neuper@42272	822	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	823	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	824	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	825	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	826	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	827	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	828	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	829	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	830	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	831	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	832	(* FIXXXXME n1.,
neuper@37906	833	case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 2, x = -4]")) => () TODO
neuper@38031	834	\| _ => error "polyeq.sml: diff.behav. in [x = 2, x = -4]";
neuper@37906	835	*)
neuper@37906	836
neuper@37906	837	"----------- (ab - (a+b)x + x^^^2 = 0), (Schalk 2,S.68Nr.44.a)";
neuper@37906	838	"----------- (ab - (a+b)x + x^^^2 = 0), (Schalk 2,S.68Nr.44.a)";
neuper@37906	839	"----------- (ab - (a+b)x + x^^^2 = 0), (Schalk 2,S.68Nr.44.a)";
neuper@37906	840	val fmz = ["equality (ab - (a+b)x + x^^^2 = 0)",
neuper@37906	841	"solveFor x","solutions L"];
neuper@37906	842	val (dI',pI',mI') =
neuper@37991	843	("PolyEq",["degree_2","expanded","univariate","equation"],
neuper@37906	844	["PolyEq","complete_square"]);
neuper@37906	845	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@42272	846	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	847	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	848	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	849	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	850	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	851	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	852	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	853	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	854	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	855	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	856
neuper@42272	857	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	858	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	859	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	860	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	861	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	862	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	863	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	864	val (p,_,f,nxt,_,pt) = me nxt p [] pt; f2str f;
neuper@37906	865	(*WN.2.5.03 TODO FIXME Matthias ?
neuper@37906	866	case f of
neuper@37906	867	Form'
neuper@37906	868	(FormKF
neuper@37906	869	(~1,EdUndef,0,Nundef,
neuper@37906	870	"[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	871	=> ()
neuper@38031	872	\| _ => error "polyeq.sml: diff.behav. in ab - (a+b)x + x^^^2 = 0";
neuper@37906	873	this will be simplified [x = a, x = b] to by Factor.ML*)
neuper@37906	874
neuper@37906	875
neuper@37906	876	"----------- (-64 + x^^^2 = 0), (Schalk 2, S.66 Nr.1.a~--------)";
neuper@37906	877	"----------- (-64 + x^^^2 = 0), (Schalk 2, S.66 Nr.1.a~--------)";
neuper@37906	878	"----------- (-64 + x^^^2 = 0), (Schalk 2, S.66 Nr.1.a~--------)";
neuper@37906	879	val fmz = ["equality (-64 + x^^^2 = 0)",(Schalk 2, S.66 Nr.1.a~)
neuper@37906	880	"solveFor x","solutions L"];
neuper@37906	881	val (dI',pI',mI') =
neuper@37991	882	("PolyEq",["degree_2","expanded","univariate","equation"],
neuper@37906	883	["PolyEq","complete_square"]);
neuper@37906	884	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@42272	885	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	886	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	887	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	888	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	889	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	890	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	891	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	892	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	893	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	894	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	895	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	896	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	897	val (p,_,f,nxt,_,pt) = me nxt p [] pt; f2str f;
neuper@37906	898	(WN.2.5.03 TODO "[x = sqrt (0 - -64), x = -1 sqrt (0 - -64)]"
neuper@37906	899	case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 8, x = -8]")) => ()
neuper@38031	900	\| _ => error "polyeq.sml: diff.behav. in [x = 8, x = -8]";
neuper@37906	901	*)
neuper@37906	902
neuper@37906	903	"----------- (-147 + 3x^^^2 = 0), (Schalk 2, S.66 Nr.1.b------*)";
neuper@37906	904	"----------- (-147 + 3x^^^2 = 0), (Schalk 2, S.66 Nr.1.b------*)";
neuper@37906	905	"----------- (-147 + 3x^^^2 = 0), (Schalk 2, S.66 Nr.1.b------*)";
neuper@37906	906	val fmz = ["equality (-147 + 3x^^^2 = 0)",(Schalk 2, S.66 Nr.1.b*)
neuper@37906	907	"solveFor x","solutions L"];
neuper@37906	908	val (dI',pI',mI') =
neuper@37991	909	("PolyEq",["degree_2","expanded","univariate","equation"],
neuper@37906	910	["PolyEq","complete_square"]);
neuper@37906	911	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@42272	912	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	913	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	914	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	915	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	916	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	917	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	918	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	919	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	920	(WN.2.5.03 TODO "[x = sqrt (0 - -49), x = -1 sqrt (0 - -49)]"
neuper@37906	921	case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 7, x = -7]")) => ()
neuper@38031	922	\| _ => error "polyeq.sml: diff.behav. in [x = 7, x = -7]";
neuper@37906	923	*)
neuper@37906	924	if f2str f = "[x = sqrt (0 - -49), x = -1 * sqrt (0 - -49)]" then ()
neuper@38031	925	else error "polyeq.sml CORRECTED?behav. in [x = 7, x = -7]";
neuper@37906	926
neuper@37906	927
neuper@37906	928	"----------- (3x - 1 - (5x - (2 - 4x)) = -11),(Schalk Is86Bsp5";
neuper@37906	929	"----------- (3x - 1 - (5x - (2 - 4x)) = -11),(Schalk Is86Bsp5";
neuper@37906	930	"----------- (3x - 1 - (5x - (2 - 4x)) = -11),(Schalk Is86Bsp5";
neuper@37906	931	(EP-17 Schalk_I_p86_n5)
neuper@37906	932	val fmz = ["equality (3x - 1 - (5x - (2 - 4*x)) = -11)","solveFor x","solutions L"];
neuper@37906	933	(* refine fmz ["univariate","equation"];
neuper@37906	934	*)
neuper@37991	935	val (dI',pI',mI') = ("PolyEq",["univariate","equation"],["no_met"]);
neuper@37906	936	(*val p = e_pos';
neuper@37906	937	val c = [];
neuper@37906	938	val (mI,m) = ("Init_Proof",Init_Proof (fmz, (dI',pI',mI')));
neuper@37906	939	val (p,_,f,nxt,_,pt) = me (mI,m) p c EmptyPtree;*)
neuper@37906	940
neuper@37906	941	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@37906	942	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	943	(* val nxt =
neuper@37906	944	("Model_Problem",
neuper@37906	945	Model_Problem ["normalize","polynomial","univariate","equation"])
neuper@37906	946	: string * tac*)
neuper@37906	947	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	948	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	949	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	950	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	951	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	952	(* val nxt =
neuper@37906	953	("Subproblem",
neuper@37991	954	Subproblem ("PolyEq",["polynomial","univariate","equation"]))
neuper@37906	955	: string * tac *)
neuper@37906	956	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	957	(*val nxt =
neuper@37906	958	("Model_Problem",
neuper@37906	959	Model_Problem ["degree_1","polynomial","univariate","equation"])
neuper@37906	960	: string * tac *)
neuper@37906	961	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	962	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	963
neuper@37906	964	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	965	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	966	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	967	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	968	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	969	case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 2]")) => ()
neuper@38031	970	\| _ => error "polyeq.sml: diff.behav. in [x = 2]";
neuper@37906	971
neuper@37906	972
neuper@37906	973	"----------- ((x+1)(x+2) - (3x - 2)^^^2=.. Schalk II s.68 Bsp 37";
neuper@37906	974	"----------- ((x+1)(x+2) - (3x - 2)^^^2=.. Schalk II s.68 Bsp 37";
neuper@37906	975	"----------- ((x+1)(x+2) - (3x - 2)^^^2=.. Schalk II s.68 Bsp 37";
neuper@37906	976	(is in rlang.sml, too)
neuper@37906	977	val fmz = ["equality ((x+1)(x+2) - (3x - 2)^^^2=(2x - 1)^^^2+(3x - 1)*(x+1))",
neuper@37906	978	"solveFor x","solutions L"];
neuper@37991	979	val (dI',pI',mI') = ("PolyEq",["univariate","equation"],["no_met"]);
neuper@37906	980	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@37906	981	(val nxt = ("Refine_Tacitly",Refine_Tacitly ["univariate","equation"]))
neuper@37906	982	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	983	(* val nxt =
neuper@37906	984	("Model_Problem",
neuper@37906	985	Model_Problem ["normalize","polynomial","univariate","equation"])
neuper@37906	986	: string * tac *)
neuper@37906	987	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	988	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	989	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	990	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	991	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	992	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	993	(* val nxt =
neuper@37906	994	("Subproblem",
neuper@37991	995	Subproblem ("PolyEq",["polynomial","univariate","equation"]))
neuper@37906	996	: string * tac*)
neuper@37906	997	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	998	(*val nxt =
neuper@37906	999	("Model_Problem",
neuper@37906	1000	Model_Problem ["abcFormula","degree_2","polynomial","univariate","equation"])
neuper@37906	1001	: string * tac*)
neuper@37906	1002	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	1003	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	1004	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	1005	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	1006	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	1007	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	1008	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	1009	case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 2 / 15, x = 1]")) => ()
neuper@38031	1010	\| _ => error "polyeq.sml: diff.behav. in [x = 2 / 15, x = 1]";
neuper@37906	1011
neuper@37906	1012
neuper@37906	1013	" -4 + x^^^2 =0 ";
neuper@37906	1014	" -4 + x^^^2 =0 ";
neuper@37906	1015	" -4 + x^^^2 =0 ";
neuper@37906	1016	val fmz = ["equality ( -4 + x^^^2 =0)", "solveFor x","solutions L"];
neuper@37906	1017	(* val fmz = ["equality (1 + x^^^2 =0)", "solveFor x","solutions L"];*)
neuper@37906	1018	(val fmz = ["equality (0 =0)", "solveFor x","solutions L"];)
neuper@37991	1019	val (dI',pI',mI') = ("PolyEq",["univariate","equation"],["no_met"]);
neuper@37906	1020	(*val p = e_pos';
neuper@37906	1021	val c = [];
neuper@37906	1022	val (mI,m) = ("Init_Proof",Init_Proof (fmz, (dI',pI',mI')));
neuper@37906	1023	val (p,_,f,nxt,_,pt) = me (mI,m) p c EmptyPtree;*)
neuper@37906	1024	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@37906	1025
neuper@37906	1026	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	1027	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	1028	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	1029	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	1030	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	1031	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	1032	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	1033	case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 2, x = -2]")) => ()
neuper@38031	1034	\| _ => error "polyeq.sml: diff.behav. in [x = 2, x = -2]";
neuper@37906	1035
neuper@37906	1036	"----------------- polyeq.sml end ------------------";
neuper@37906	1037
neuper@37906	1038	(Punkte aus dem TestBericht, die ich in rlang.sml nicht zuordnen konnte:)
neuper@37906	1039	(WN.19.3.03 ---v-)
neuper@37906	1040	(3(b))val (bdv,v) = (str2term "bdv", str2term "R1");
neuper@37906	1041	val t = str2term "-1 * (R * R2) + R2 * R1 + -1 * (R * R1) = 0";
neuper@37926	1042	val SOME (t',_) = rewrite_set_inst_ thy false [(bdv,v)] make_polynomial_in t;
neuper@37906	1043	term2str t';
neuper@37906	1044	"-1 * R * R2 + (R2 + -1 * R) * R1 = 0";
neuper@37906	1045	(WN.19.3.03 ---^-)
neuper@37906	1046
neuper@37906	1047	(3(c))val (bdv,v) = (str2term "bdv", str2term "p");
neuper@37906	1048	val t = str2term "y ^^^ 2 + -2 * (x * p) = 0";
neuper@37926	1049	val SOME (t',_) = rewrite_set_inst_ thy false [(bdv,v)] make_polynomial_in t;
neuper@37906	1050	term2str t';
neuper@37906	1051	"y ^^^ 2 + -2 * x * p = 0";
neuper@37906	1052
neuper@37906	1053	(3(d))val (bdv,v) = (str2term "bdv", str2term "x2");
neuper@37906	1054	val t = str2term
neuper@37906	1055	"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	1056	val SOME (t',_) = rewrite_set_inst_ thy false [(bdv,v)] make_polynomial_in t;
neuper@37906	1057	term2str t';
neuper@37906	1058	"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	1059	val SOME (t',_) = rewrite_set_inst_ thy false [(bdv,v)] make_ratpoly_in t;
neuper@37906	1060	term2str t';
neuper@37906	1061	"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	1062
neuper@37906	1063	(3(e))val (bdv,v) = (str2term "bdv", str2term "a");
neuper@37906	1064	val t = str2term
neuper@37906	1065	"A ^^^ 2 + c ^^^ 2 * (c / d) ^^^ 2 + (-4 * (c / d) ^^^ 2) * a ^^^ 2 = 0";
neuper@37926	1066	val NONE = rewrite_set_inst_ thy false [(bdv,v)] make_polynomial_in t;
neuper@37906	1067	(die _unsichtbare_ Klammern sind genau wie gew"unscht)
neuper@37906	1068
neuper@37906	1069
neuper@37906	1070	val t = str2term "(x + 1) * (x + 2) - (3 * x - 2) ^^^ 2 - ((2 * x - 1) ^^^ 2 + (3 * x - 1) * (x + 1)) = 0";
neuper@37906	1071	trace_rewrite:=true;
neuper@37906	1072	rewrite_set_ thy false expand_binoms t;
neuper@37906	1073	trace_rewrite:=false;
neuper@37906	1074
neuper@37906	1075
neuper@37906	1076	"----------- interSteps ([1],Res); on Schalk Is86Bsp5-------------";
neuper@37906	1077	"----------- interSteps ([1],Res); on Schalk Is86Bsp5-------------";
neuper@37906	1078	"----------- interSteps ([1],Res); on Schalk Is86Bsp5-------------";
neuper@37906	1079	states:=[];
neuper@37906	1080	CalcTree
neuper@37906	1081	[(["equality (3x - 1 - (5x - (2 - 4*x)) = -11)","solveFor x","solutions L"],
neuper@37991	1082	("PolyEq",["univariate","equation"],["no_met"]))];
neuper@37906	1083	Iterator 1;
neuper@37906	1084	moveActiveRoot 1;
neuper@37906	1085	autoCalculate 1 CompleteCalc;
neuper@37906	1086	val ((pt,p),_) = get_calc 1; show_pt pt;
neuper@37906	1087
neuper@37906	1088	interSteps 1 ([1],Res) (no Rewrite_Set...);
neuper@42248	1089

author	Walther Neuper <neuper@ist.tugraz.at>
	Fri, 14 Oct 2011 11:43:00 +0200
branch	decompose-isar
changeset 42318	b4f9b188373e
parent 42283	b95f0dde56c1
child 42319	ffad491ba8f2
permissions	-rw-r--r--