wneuper/isa: test/Tools/isac/Knowledge/polyeq.sml@767debe8a50c (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@42319	10	(*WN060608 some ----- are not in this table.
neuper@42319	11	WN111014.TODO missing checks*)
neuper@37906	12	"-----------------------------------------------------------------";
neuper@37906	13	"----------- tests on predicates in problems ---------------------";
neuper@37906	14	"----------- test matching problems --------------------------0---";
neuper@42248	15	"----------- lin.eq degree_0 -------------------------------------";
neuper@42248	16	"----------- test thm's d2_pq_formulsxx[_neg]---------------------";
neuper@37906	17	"----------- (-8 - 2x + x^^^2 = 0), (Schalk 2, S.67 Nr.31.b----";
neuper@42318	18	"----------- (-8 - 2*x + x^^^2 = 0), by rewriting ---------------";
neuper@37906	19	"----------- (-16 + 4x + 2x^^^2 = 0), --------------------------";
neuper@37906	20	"----------- (ab - (a+b)x + x^^^2 = 0), (Schalk 2,S.68Nr.44.a)";
neuper@37906	21	"----------- (-64 + x^^^2 = 0), (Schalk 2, S.66 Nr.1.a~--------)";
neuper@37906	22	"----------- (-147 + 3x^^^2 = 0), (Schalk 2, S.66 Nr.1.b------*)";
neuper@37906	23	"----------- (3x - 1 - (5x - (2 - 4x)) = -11),(Schalk Is86Bsp5";
neuper@37906	24	"----------- ((x+1)(x+2) - (3x - 2)^^^2=.. Schalk II s.68 Bsp 37";
neuper@37906	25	"----------- interSteps ([1],Res); on Schalk Is86Bsp5-------------";
neuper@37906	26	"-----------------------------------------------------------------";
neuper@37906	27	"-----------------------------------------------------------------";
neuper@37906	28	"-----------------------------------------------------------------";
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	val fmz = ["equality (1 = (0::real))", "solveFor x", "solutions L"];
neuper@37991	116	val (dI',pI',mI') = ("PolyEq",["degree_0","polynomial","univariate","equation"],
neuper@37906	117	["PolyEq","solve_d0_polyeq_equation"]);
neuper@42283	118	(*=== inhibit exn WN110914: declare_constraints doesnt work with num_str ========
neuper@42283	119	TODO: change to "equality (x + -1*x = (0::real))"
neuper@42283	120	and search for an appropriate problem and method.
neuper@42283	121
neuper@37906	122	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@42272	123	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@42272	128	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	129	case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[]")) => ()
neuper@38031	130	\| _ => error "polyeq.sml: diff.behav. in 1 = 0 -> []";
neuper@37906	131
neuper@37906	132	"----- d0_true ------";
neuper@42248	133	val fmz = ["equality (0 = (0::real))", "solveFor x","solutions L"];
neuper@37991	134	val (dI',pI',mI') = ("PolyEq",["degree_0","polynomial","univariate","equation"],
neuper@37906	135	["PolyEq","solve_d0_polyeq_equation"]);
neuper@37906	136	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@42272	137	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@42272	142	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	143	case f of Form' (FormKF (~1,EdUndef,0,Nundef,"UniversalList")) => ()
neuper@38031	144	\| _ => error "polyeq.sml: diff.behav. in 0 = 0 -> UniversalList";
neuper@42272	145	============ inhibit exn WN110914 ============================================*)
neuper@37906	146
neuper@42248	147	"----------- test thm's d2_pq_formulsxx[_neg]---------------------";
neuper@42248	148	"----------- test thm's d2_pq_formulsxx[_neg]---------------------";
neuper@42248	149	"----------- test thm's d2_pq_formulsxx[_neg]---------------------";
neuper@37906	150	"----- d2_pqformula1 ------!!!!";
neuper@42255	151	val fmz = ["equality (-1/8 + (-1/4)*z + z^^^2 = (0::real))", "solveFor z","solutions L"];
neuper@42255	152	val (dI',pI',mI') =
neuper@42255	153	("Isac", ["pqFormula","degree_2","polynomial","univariate","equation"], ["no_met"]);
neuper@37906	154	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
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;
neuper@42255	161	val (p,_,f,nxt,_,pt) = me nxt p [] pt; (Apply_Method ["PolyEq", "solve_d2_polyeq_pq_equation"])
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	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42255	166	([z = 1 / 8 + sqrt (9 / 16) / 2, z = 1 / 8 + -1 sqrt (9 / 16) / 2] TODO sqrt*)
neuper@42255	167	val (p,_,f,nxt,_,pt) = me nxt p [] pt; (nxt =..,Check_elementwise "Assumptions"))
neuper@42255	168	"~~~~~ fun me, args:"; val ((_,tac), (p:pos'), _, (pt:ptree)) = (nxt, p, [], pt);
neuper@42255	169	"~~~~~ fun locatetac, args:"; val (tac, (ptp as (pt, p))) = (tac, (pt, p));
neuper@42255	170	val (mI,m) = mk_tac'_ tac;
neuper@42255	171	val Appl m = applicable_in p pt m;
neuper@42255	172	val Check_elementwise' (trm1, str, (trm2, trms)) = m;
neuper@42255	173	term2str trm1 = "[z = 1 / 8 + sqrt (9 / 16) / 2, z = 1 / 8 + -1 * sqrt (9 / 16) / 2]";
neuper@42255	174	str = "Assumptions";
neuper@42255	175	term2str trm2 = "[z = 1 / 8 + sqrt (9 / 16) / 2, z = 1 / 8 + -1 * sqrt (9 / 16) / 2]";
neuper@42255	176	terms2str trms = "[\"lhs (-1 / 8 + -1 * (1 / 8 + sqrt (9 / 16) / 2) / 4 +\n "^
neuper@42255	177	" (1 / 8 + sqrt (9 / 16) / 2) ^^^ 2 =\n 0) is_poly_in 1 / 8 + sqrt (9 / 16) / 2\","^
neuper@42255	178	"\"lhs (-1 / 8 + -1 * (1 / 8 + sqrt (9 / 16) / 2) / 4 +\n (1 / 8 + sqrt (9 / 16) / 2) ^^^ 2 =\n 0) "^
neuper@42255	179	"has_degree_in 1 / 8 + sqrt (9 / 16) / 2 =\n2\","^
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) is_poly_in 1 / 8 + -1 * sqrt (9 / 16) / 2\","^
neuper@42255	181	"\"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	182	(TODO simplify assumptions (sqrt!) and check ERROR in has_degree_in);
neuper@42255	183	member op = specsteps mI (false);
neuper@42255	184	(*loc_solve_ (mI,m) ptp;
neuper@42255	185	WAS: not-found-in-script: NotLocatable from NasNap (Const ("List...*)
neuper@42255	186	"~~~~~ fun loc_solve_, args:"; val (m, (pt,pos)) = ((mI,m), ptp);
neuper@42255	187	(*solve m (pt, pos);
neuper@42255	188	WAS: not-found-in-script: NotLocatable from NasNap (Const ("List...*)
neuper@42255	189	"~~~~~ fun solve, args:"; val ((mI,m), (pt, po as (p,p_))) = (m, (pt, pos));
neuper@42255	190	e_metID = get_obj g_metID pt (par_pblobj pt p) (false);
neuper@42255	191	val thy' = get_obj g_domID pt (par_pblobj pt p);
neuper@42255	192	val (srls, is, sc) = from_pblobj_or_detail' thy' (p,p_) pt;
neuper@42255	193	val d = e_rls;
neuper@42255	194	(*locate_gen (thy',srls) m (pt,(p,p_)) (sc,d) is;
neuper@42255	195	WAS: not-found-in-script: NotLocatable from NasNap (Const ("List...*)
neuper@42255	196	"~~~~~ fun locate_gen, args:"; val ((ts as (thy',srls)), (m:tac_), ((pt,p):ptree * pos'),
neuper@42255	197	(scr as Script (h $ body),d), (ScrState (E,l,a,v,S,b), ctxt)) =
neuper@42255	198	((thy',srls), m ,(pt,(p,p_)) ,(sc,d) ,is); (* locate_gen 2nd pattern *)
neuper@42255	199	val thy = assoc_thy thy';
neuper@42255	200	l = [] orelse ((last_elem o fst) p = 0 andalso snd p = Res) (false);
neuper@42255	201	(*WAS val NasApp _ =(astep_up (thy',srls,scr,d) ((E,l,a,v,S,b), [(m,EmptyMout,pt,p,[])]) )
neuper@42255	202	... Assoc ... is correct*)
neuper@42387	203	"~~~~~ and astep_up, args:"; val ((ys as (_,_,_,Script sc,_)), ((E,l,a,v,S,b),ss)) =
neuper@42387	204	((thy',ctxt,srls,scr,d), ((E,l,a,v,S,b), [(m,EmptyMout,pt,p,[])]));
neuper@42255	205	1 < length l (true);
neuper@42255	206	val up = drop_last l;
neuper@42255	207	term2str (go up sc);
neuper@42255	208	(go up sc);
neuper@42255	209	(*WAS val NasNap _ = ass_up ys ((E,up,a,v,S,b),ss) (go up sc)
neuper@42255	210	... ???? ... is correct*)
neuper@42387	211	"~~~~~ fun ass_up, args:"; val ((ys as (y,ctxt,s,Script sc,d)), (is as (E,l,a,v,S,b),ss),
neuper@42255	212	(Const ("HOL.Let",_) $ _)) = (ys, ((E,up,a,v,S,b),ss), (go up sc));
neuper@42255	213	val l = drop_last l; (comes from e, goes to Abs)
neuper@42255	214	val (Const ("HOL.Let",_) $ e $ (Abs (i,T,body))) = go l sc;
neuper@42255	215	val i = mk_Free (i, T);
neuper@42255	216	val E = upd_env E (i, v);
neuper@42255	217	(Type error ...: Can't unify _a to pos pos_ (Incompatible types)*)
neuper@42255	218	val [(tac_, mout, ptree, pos', xxx)] = ss;
neuper@42255	219	val ss = [(tac_, mout, ptree, pos', []:(pos * pos_) list)];
neuper@42255	220	(*WAS val NasApp iss = assy (((y,s),d),Aundef) ((E, l@[R,D], a,v,S,b),ss) body
neuper@42255	221	... Assoc ... is correct*)
neuper@42255	222	"~~~~~ 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	223	((((y,s),d),Aundef), ((E, l@[R,D], a,v,S,b),ss), body);
neuper@42255	224	val (a', STac stac) = handle_leaf "locate" thy' sr E a v t
neuper@42255	225	val ctxt = get_ctxt pt (p,p_)
neuper@42255	226	val p' = lev_on p : pos;
neuper@42255	227	(* WAS val NotAss = assod pt d m stac
neuper@42255	228	... Ass ... is correct*)
neuper@42255	229	"~~~~~ fun assod, args:"; val (pt, _, (m as Check_elementwise' (consts,_,(consts_chkd,_))),
neuper@42255	230	(Const ("Script.Check'_elementwise",_) $ consts' $ _)) = (pt, d, m, stac);
neuper@42255	231	term2str consts;
neuper@42255	232	term2str consts';
neuper@42255	233	if consts = consts' (WAS false) then () else error "Check_elementwise changed";
neuper@42260	234	([z = 1 / 8 + sqrt (9 / 16) / 2, z = 1 / 8 + -1 sqrt (9 / 16) / 2] TODO sqrt*)
neuper@37906	235
neuper@37906	236	"----- d2_pqformula1_neg ------";
neuper@42272	237	val fmz = ["equality (2 +(-1)*x + x^^^2 = (0::real))", "solveFor x","solutions L"];
neuper@37991	238	val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"], ["PolyEq","solve_d2_polyeq_pq_equation"]);
neuper@37906	239	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@42272	240	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@42272	244	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	245	(*### or2list False
neuper@37906	246	([1],Res) False Or_to_List)*)
neuper@42272	247	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	248	(*### or2list False
neuper@37906	249	([2],Res) [] Check_elementwise "Assumptions"*)
neuper@42272	250	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	251	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	252	val asm = get_assumptions_ pt p;
neuper@42318	253	if f = Form' (FormKF (~1,EdUndef,0,Nundef,"[]")) andalso
neuper@42318	254	terms2str asm = "[\"lhs (2 + -1 * x + x ^^^ 2 = 0) is_poly_in x\"," ^
neuper@42318	255	"\"lhs (2 + -1 * x + x ^^^ 2 = 0) has_degree_in x = 2\"]" 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@42272	262	(*val p = e_pos';
neuper@37906	263	val (mI,m) = ("Init_Proof",Init_Proof (fmz, (dI',pI',mI')));
neuper@42272	264	val (p,_,f,nxt,_,pt) = me (mI,m) p [] EmptyPtree;*)
neuper@37906	265	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@42272	266	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; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	273	val (p,_,f,nxt,_,pt) = me nxt p [] 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@42272	286	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; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	292	val (p,_,f,nxt,_,pt) = me nxt p [] 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,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@42272	304	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; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	311	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	312	case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 1, x = -2]")) => ()
neuper@38031	313	\| _ => error "polyeq.sml: diff.behav. in -2 + x + x^2 = 0-> [x = 1, x = -2]";
neuper@37906	314
neuper@37906	315	"----- d2_pqformula3_neg ------";
neuper@37906	316	val fmz = ["equality ( 2 + x + x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	317	val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	318	["PolyEq","solve_d2_polyeq_pq_equation"]);
neuper@37906	319	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@42272	320	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; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	326	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	327	"TODO 2 + x + x^^^2 = 0";
neuper@37906	328	"TODO 2 + x + x^^^2 = 0";
neuper@37906	329	"TODO 2 + x + x^^^2 = 0";
neuper@37906	330
neuper@37906	331
neuper@37906	332	"----- d2_pqformula4 ------";
neuper@37906	333	val fmz = ["equality (-2 + x + 1*x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	334	val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	335	["PolyEq","solve_d2_polyeq_pq_equation"]);
neuper@37906	336	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@42272	337	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; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	344	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	345	case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 1, x = -2]")) => ()
neuper@38031	346	\| _ => error "polyeq.sml: diff.behav. in -2 + x + 1*x^^^2 = 0 -> [x = 1, x = -2]";
neuper@37906	347
neuper@37906	348	"----- d2_pqformula4_neg ------";
neuper@37906	349	val fmz = ["equality ( 2 + x + 1*x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	350	val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	351	["PolyEq","solve_d2_polyeq_pq_equation"]);
neuper@37906	352	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@42272	353	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@42272	358	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	359	"TODO 2 + x + 1*x^^^2 = 0";
neuper@37906	360	"TODO 2 + x + 1*x^^^2 = 0";
neuper@37906	361	"TODO 2 + x + 1*x^^^2 = 0";
neuper@37906	362
neuper@37906	363	"----- d2_pqformula5 ------";
neuper@37906	364	val fmz = ["equality (1*x + x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	365	val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	366	["PolyEq","solve_d2_polyeq_pq_equation"]);
neuper@37906	367	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@42272	368	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; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	375	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	376	case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 0, x = -1]")) => ()
neuper@38031	377	\| _ => error "polyeq.sml: diff.behav. in 1*x + x^2 = 0 -> [x = 0, x = -1]";
neuper@37906	378
neuper@37906	379	"----- d2_pqformula6 ------";
neuper@37906	380	val fmz = ["equality (1x + 1x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	381	val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	382	["PolyEq","solve_d2_polyeq_pq_equation"]);
neuper@37906	383	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@42272	384	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; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	391	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	392	case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 0, x = -1]")) => ()
neuper@38031	393	\| _ => error "polyeq.sml: diff.behav. in 1x + 1x^2 = 0 -> [x = 0, x = -1]";
neuper@37906	394
neuper@37906	395	"----- d2_pqformula7 ------";
neuper@37906	396	(EP-10)
neuper@37906	397	val fmz = ["equality ( x + x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	398	val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	399	["PolyEq","solve_d2_polyeq_pq_equation"]);
neuper@37906	400	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@42272	401	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; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	408	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	409	case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 0, x = -1]")) => ()
neuper@38031	410	\| _ => error "polyeq.sml: diff.behav. in x + x^2 = 0 -> [x = 0, x = -1]";
neuper@37906	411
neuper@37906	412	"----- d2_pqformula8 ------";
neuper@37906	413	val fmz = ["equality ( x + 1*x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	414	val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	415	["PolyEq","solve_d2_polyeq_pq_equation"]);
neuper@37906	416	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@42272	417	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; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	424	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	425	case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 0, x = -1]")) => ()
neuper@38031	426	\| _ => error "polyeq.sml: diff.behav. in x + 1*x^2 = 0 -> [x = 0, x = -1]";
neuper@37906	427
neuper@37906	428	"----- d2_pqformula9 ------";
neuper@37906	429	val fmz = ["equality (-4 + x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	430	val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	431	["PolyEq","solve_d2_polyeq_pq_equation"]);
neuper@37906	432	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@42272	433	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@42272	439	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	440	case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 2, x = -2]")) => ()
neuper@38031	441	\| _ => error "polyeq.sml: diff.behav. in -4 + x^2 = 0 -> [x = 2, x = -2]";
neuper@37906	442
neuper@37906	443
neuper@37906	444	"----- d2_pqformula10_neg ------";
neuper@37906	445	val fmz = ["equality (4 + x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	446	val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	447	["PolyEq","solve_d2_polyeq_pq_equation"]);
neuper@37906	448	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@42272	449	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; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	455	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	456	"TODO 4 + x^^^2 = 0";
neuper@37906	457	"TODO 4 + x^^^2 = 0";
neuper@37906	458	"TODO 4 + x^^^2 = 0";
neuper@37906	459
neuper@37906	460	"----- d2_pqformula10 ------";
neuper@37906	461	val fmz = ["equality (-4 + 1*x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	462	val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	463	["PolyEq","solve_d2_polyeq_pq_equation"]);
neuper@37906	464	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@42272	465	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@42272	471	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	472	case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 2, x = -2]")) => ()
neuper@38031	473	\| _ => error "polyeq.sml: diff.behav. in -4 + 1*x^2 = 0 -> [x = 2, x = -2]";
neuper@37906	474
neuper@37906	475	"----- d2_pqformula9_neg ------";
neuper@37906	476	val fmz = ["equality (4 + 1*x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	477	val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	478	["PolyEq","solve_d2_polyeq_pq_equation"]);
neuper@37906	479	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@42272	480	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; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	485	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	486	"TODO 4 + 1*x^^^2 = 0";
neuper@37906	487	"TODO 4 + 1*x^^^2 = 0";
neuper@37906	488	"TODO 4 + 1*x^^^2 = 0";
neuper@37906	489
neuper@37906	490	"-------------------- test thm's d2_abc_formulsxx[_neg]-----";
neuper@37906	491	"-------------------- test thm's d2_abc_formulsxx[_neg]-----";
neuper@37906	492	"-------------------- test thm's d2_abc_formulsxx[_neg]-----";
neuper@37906	493
neuper@37906	494	val fmz = ["equality (-1 +(-1)x + 2x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	495	val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	496	["PolyEq","solve_d2_polyeq_abc_equation"]);
neuper@37906	497	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@42272	498	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@42272	504	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	505	case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 1, x = -1 / 2]")) => ()
neuper@38031	506	\| _ => error "polyeq.sml: diff.behav. in -1 + (-1)x + 2x^2 = 0 -> [x = 1, x = -1/2]";
neuper@37906	507
neuper@37906	508	val fmz = ["equality ( 1 +(-1)x + 2x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	509	val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	510	["PolyEq","solve_d2_polyeq_abc_equation"]);
neuper@37906	511	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@42272	512	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@42272	517	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	518	"TODO 1 +(-1)x + 2x^^^2 = 0";
neuper@37906	519	"TODO 1 +(-1)x + 2x^^^2 = 0";
neuper@37906	520	"TODO 1 +(-1)x + 2x^^^2 = 0";
neuper@37906	521
neuper@37906	522	(EP-11)
neuper@37906	523	val fmz = ["equality (-1 + x + 2*x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	524	val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	525	["PolyEq","solve_d2_polyeq_abc_equation"]);
neuper@37906	526	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@42272	527	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@42272	533	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	534	case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 1 / 2, x = -1]")) => ()
neuper@38031	535	\| _ => error "polyeq.sml: diff.behav. in -1 + x + 2*x^2 = 0 -> [x = 1/2, x = -1]";
neuper@37906	536
neuper@37906	537	val fmz = ["equality ( 1 + x + 2*x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	538	val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	539	["PolyEq","solve_d2_polyeq_abc_equation"]);
neuper@37906	540	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@42272	541	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; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	547	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	548	"TODO 1 + x + 2*x^^^2 = 0";
neuper@37906	549	"TODO 1 + x + 2*x^^^2 = 0";
neuper@37906	550	"TODO 1 + x + 2*x^^^2 = 0";
neuper@37906	551
neuper@37906	552	val fmz = ["equality (-2 + 1*x + x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	553	val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	554	["PolyEq","solve_d2_polyeq_abc_equation"]);
neuper@37906	555	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@42272	556	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@42272	562	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	563	case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 1, x = -2]")) => ()
neuper@38031	564	\| _ => error "polyeq.sml: diff.behav. in -2 + 1*x + x^2 = 0 -> [x = 1, x = -2]";
neuper@37906	565
neuper@37906	566	val fmz = ["equality ( 2 + 1*x + x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	567	val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	568	["PolyEq","solve_d2_polyeq_abc_equation"]);
neuper@37906	569	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@42272	570	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; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	576	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	577	"TODO 2 + 1*x + x^^^2 = 0";
neuper@37906	578	"TODO 2 + 1*x + x^^^2 = 0";
neuper@37906	579	"TODO 2 + 1*x + x^^^2 = 0";
neuper@37906	580
neuper@37906	581	(EP-12)
neuper@37906	582	val fmz = ["equality (-2 + x + x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	583	val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	584	["PolyEq","solve_d2_polyeq_abc_equation"]);
neuper@37906	585	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@42272	586	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@42272	592	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	593	case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 1, x = -2]")) => ()
neuper@38031	594	\| _ => error "polyeq.sml: diff.behav. in -2 + x + x^2 = 0 -> [x = 1, x = -2]";
neuper@37906	595
neuper@37906	596	val fmz = ["equality ( 2 + x + x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	597	val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	598	["PolyEq","solve_d2_polyeq_abc_equation"]);
neuper@37906	599	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@42272	600	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; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	606	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	607	"TODO 2 + x + x^^^2 = 0";
neuper@37906	608	"TODO 2 + x + x^^^2 = 0";
neuper@37906	609	"TODO 2 + x + x^^^2 = 0";
neuper@37906	610
neuper@37906	611	(EP-13)
neuper@37906	612	val fmz = ["equality (-8 + 2*x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	613	val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	614	["PolyEq","solve_d2_polyeq_abc_equation"]);
neuper@37906	615	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@42272	616	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@42272	622	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	623	case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 2, x = -2]")) => ()
neuper@38031	624	\| _ => error "polyeq.sml: diff.behav. in -8 + 2*x^2 = 0 -> [x = 2, x = -2]";
neuper@37906	625
neuper@37906	626	val fmz = ["equality ( 8+ 2*x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	627	val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	628	["PolyEq","solve_d2_polyeq_abc_equation"]);
neuper@37906	629	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@42272	630	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@42272	635	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	636	"TODO 8+ 2*x^^^2 = 0";
neuper@37906	637	"TODO 8+ 2*x^^^2 = 0";
neuper@37906	638	"TODO 8+ 2*x^^^2 = 0";
neuper@37906	639
neuper@37906	640	(EP-14)
neuper@37906	641	val fmz = ["equality (-4 + x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	642	val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"], ["PolyEq","solve_d2_polyeq_abc_equation"]);
neuper@37906	643	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@42272	644	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@42272	650	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	651	case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 2, x = -2]")) => ()
neuper@38031	652	\| _ => error "polyeq.sml: diff.behav. in -4 + x^2 = 0 -> [x = 2, x = -2]";
neuper@37906	653
neuper@37906	654
neuper@37906	655	val fmz = ["equality ( 4+ x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	656	val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"], ["PolyEq","solve_d2_polyeq_abc_equation"]);
neuper@37906	657	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@42272	658	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@42272	663	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	664	"TODO 4+ x^^^2 = 0";
neuper@37906	665	"TODO 4+ x^^^2 = 0";
neuper@37906	666	"TODO 4+ x^^^2 = 0";
neuper@37906	667
neuper@37906	668	(EP-15)
neuper@37906	669	val fmz = ["equality (2x + 2x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	670	val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	671	["PolyEq","solve_d2_polyeq_abc_equation"]);
neuper@37906	672	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@42272	673	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@42272	679	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	680	case f of Form' (FormKF (~1,EdUndef,_,Nundef,"[x = 0, x = -1]")) => ()
neuper@38031	681	\| _ => error "polyeq.sml: diff.behav. in x + x^2 = 0 -> [x = 0, x = -1]";
neuper@37906	682
neuper@37906	683	val fmz = ["equality (1*x + x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	684	val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	685	["PolyEq","solve_d2_polyeq_abc_equation"]);
neuper@37906	686	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@42272	687	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@42272	693	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	694	case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 0, x = -1]")) => ()
neuper@38031	695	\| _ => error "polyeq.sml: diff.behav. in x + x^2 = 0 -> [x = 0, x = -1]";
neuper@37906	696
neuper@37906	697	(EP-16)
neuper@37906	698	val fmz = ["equality (x + 2*x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	699	val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	700	["PolyEq","solve_d2_polyeq_abc_equation"]);
neuper@37906	701	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@42272	702	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@42272	708	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	709	case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 0, x = -1 / 2]")) => ()
neuper@38031	710	\| _ => error "polyeq.sml: diff.behav. in x + x^2 = 0 -> [x = 0, x = -1 / 2]";
neuper@37906	711
neuper@37906	712	(EP-//)
neuper@37906	713	val fmz = ["equality (x + x^^^2 = 0)", "solveFor x","solutions L"];
neuper@37991	714	val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
neuper@37906	715	["PolyEq","solve_d2_polyeq_abc_equation"]);
neuper@37906	716	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@42272	717	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@42272	723	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	724	case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 0, x = -1]")) => ()
neuper@38031	725	\| _ => error "polyeq.sml: diff.behav. in x + x^2 = 0 -> [x = 0, x = -1]";
neuper@37906	726
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	"----------- (-8 - 2x + x^^^2 = 0), (Schalk 2, S.67 Nr.31.b----";
neuper@42319	730	(*stopped du to TODO.txt WN111014.TODO calculate_Poly < calculate_Rational < calculate_RootRat
neuper@42319	731	see --- val rls = calculate_RootRat > calculate_Rational ---
neuper@42319	732	calculate_RootRat was a TODO with 2002, requires re-design.
neuper@42319	733	see also --- (-8 - 2*x + x^^^2 = 0), by rewriting --- below
neuper@42319	734	*)
neuper@37906	735	val fmz = ["equality (-8 - 2x + x^^^2 = 0)", (Schalk 2, S.67 Nr.31.b*)
neuper@37906	736	"solveFor x","solutions L"];
neuper@37906	737	val (dI',pI',mI') =
neuper@37991	738	("PolyEq",["degree_2","expanded","univariate","equation"],
neuper@37906	739	["PolyEq","complete_square"]);
neuper@37906	740	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@42272	741	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	742	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	743	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	744	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37991	745	(Apply_Method ("PolyEq","complete_square"))
neuper@42272	746	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	747	("-8 - 2 x + x ^^^ 2 = 0", nxt = Rewrite_Set_Inst ... "complete_square*)
neuper@42272	748	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	749	("-8 + (2 / 2 - x) ^^^ 2 = (2 / 2) ^^^ 2", nxt = Rewrite("square_explicit1")
neuper@42272	750	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	751	("(2 / 2 - x) ^^^ 2 = (2 / 2) ^^^ 2 - -8" nxt = Rewrite("root_plus_minus)
neuper@42272	752	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	753	(*"2 / 2 - x = sqrt ((2 / 2) ^^^ 2 - -8) \|
neuper@37906	754	2 / 2 - x = - sqrt ((2 / 2) ^^^ 2 - -8)" nxt = Rewr_Inst("bdv_explicit2"*)
neuper@42272	755	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	756	(*"2 / 2 - x = sqrt ((2 / 2) ^^^ 2 - -8) \|
neuper@37906	757	-1x = - (2 / 2) + - sqrt ((2 / 2) ^^^ 2 - -8)"nxt = R_Inst("bdv_explt2")
neuper@42272	758	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	759	("-1 x = - (2 / 2) + sqrt ((2 / 2) ^^^ 2 - -8) \|
neuper@37906	760	-1 * x = (- (2 / 2) + - sqrt ((2 / 2) ^^^ 2 - -8))"nxt = bdv_explicit3*)
neuper@42272	761	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	762	("-1 x = - (2 / 2) + sqrt ((2 / 2) ^^^ 2 - -8) \|
neuper@37906	763	x = -1 * (- (2 / 2) + - sqrt ((2 / 2) ^^^ 2 - -8))" nxt = bdv_explicit3*)
neuper@42272	764	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	765	("x = -1 (- (2 / 2) + sqrt ((2 / 2) ^^^ 2 - -8)) \|
neuper@42319	766	x = -1 * (- (2 / 2) + - sqrt ((2 / 2) ^^^ 2 - -8))"nxt = calculate_Rational
neuper@42319	767	NOT IMPLEMENTED SINCE 2002 ------------------------------^^^^^^^^^^^^^^^^^^*)
neuper@42272	768	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	769	("x = -2 \| x = 4" nxt = Or_to_List)
neuper@42272	770	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	771	("[x = -2, x = 4]" nxt = Check_Postcond)
neuper@42272	772	val (p,_,f,nxt,_,pt) = me nxt p [] pt; f2str f;
neuper@37906	773	(* FIXXXME
neuper@37906	774	case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = -2, x = 4]")) => () TODO
neuper@38031	775	\| _ => error "polyeq.sml: diff.behav. in [x = -2, x = 4]";
neuper@37906	776	*)
neuper@37906	777	if f2str f = "[x = -1 * -1 + -1 * sqrt (1 ^^^ 2 - -8),\n x = -1 * -1 + -1 * (-1 * sqrt (1 ^^^ 2 - -8))]" then ()
neuper@38031	778	else error "polyeq.sml corrected?behav. in [x = -2, x = 4]";
neuper@37906	779
neuper@42318	780	"----------- (-8 - 2*x + x^^^2 = 0), by rewriting ---------------";
neuper@42318	781	"----------- (-8 - 2*x + x^^^2 = 0), by rewriting ---------------";
neuper@42318	782	"----------- (-8 - 2*x + x^^^2 = 0), by rewriting ---------------";
neuper@42319	783	(*stopped du to TODO.txt WN111014.TODO calculate_Poly < calculate_Rational < calculate_RootRat
neuper@42319	784	see --- val rls = calculate_RootRat > calculate_Rational ---*)
neuper@42319	785	val thy = @{theory PolyEq};
neuper@42319	786	val ctxt = ProofContext.init_global thy;
neuper@42319	787	val inst = [((the o (parseNEW ctxt)) "bdv::real", (the o (parseNEW ctxt)) "x::real")];
neuper@42319	788	val t = (the o (parseNEW ctxt)) "-8 - 2*x + x^^^2 = (0::real)";
neuper@42319	789
neuper@42319	790	val rls = complete_square;
neuper@42319	791	val SOME (t,asm) = rewrite_set_inst_ thy true inst rls t;
neuper@42319	792	term2str t = "-8 + (2 / 2 - x) ^^^ 2 = (2 / 2) ^^^ 2";
neuper@42319	793
neuper@42319	794	val thm = num_str @{thm square_explicit1};
neuper@42319	795	val SOME (t,asm) = rewrite_ thy dummy_ord Erls true thm t;
neuper@42319	796	term2str t = "(2 / 2 - x) ^^^ 2 = (2 / 2) ^^^ 2 - -8";
neuper@42319	797
neuper@42319	798	val thm = num_str @{thm root_plus_minus};
neuper@42319	799	val SOME (t,asm) = rewrite_ thy dummy_ord PolyEq_erls true thm t;
neuper@42319	800	term2str t = "2 / 2 - x = sqrt ((2 / 2) ^^^ 2 - -8) \|"^
neuper@42319	801	"\n2 / 2 - x = -1 * sqrt ((2 / 2) ^^^ 2 - -8)";
neuper@42319	802
neuper@42319	803	(the thm bdv_explicit2 here required to be constrained to ::real*)
neuper@42319	804	val thm = num_str @{thm bdv_explicit2};
neuper@42319	805	val SOME (t,asm) = rewrite_inst_ thy dummy_ord Erls true inst thm t;
neuper@42319	806	term2str t = "2 / 2 - x = sqrt ((2 / 2) ^^^ 2 - -8) \|"^
neuper@42319	807	"\n-1 * x = - (2 / 2) + -1 * sqrt ((2 / 2) ^^^ 2 - -8)";
neuper@42319	808
neuper@42319	809	val thm = num_str @{thm bdv_explicit3};
neuper@42319	810	val SOME (t,asm) = rewrite_inst_ thy dummy_ord Erls true inst thm t;
neuper@42319	811	term2str t = "2 / 2 - x = sqrt ((2 / 2) ^^^ 2 - -8) \|"^
neuper@42319	812	"\nx = -1 * (- (2 / 2) + -1 * sqrt ((2 / 2) ^^^ 2 - -8))";
neuper@42319	813
neuper@42319	814	val thm = num_str @{thm bdv_explicit2};
neuper@42319	815	val SOME (t,asm) = rewrite_inst_ thy dummy_ord Erls true inst thm t;
neuper@42319	816	term2str t = "-1 * x = - (2 / 2) + sqrt ((2 / 2) ^^^ 2 - -8) \|"^
neuper@42319	817	"\nx = -1 * (- (2 / 2) + -1 * sqrt ((2 / 2) ^^^ 2 - -8))";
neuper@42319	818
neuper@42319	819	val rls = calculate_RootRat;
neuper@42319	820	val SOME (t,asm) = rewrite_set_ thy true rls t;
neuper@42319	821	if term2str t = "-1 * x = -1 + sqrt (1 ^^^ 2 - -8) \|\nx = -1 * -1 + -1 * (-1 * sqrt (1 ^^^ 2 - -8))"
neuper@42319	822	then () else error "(-8 - 2*x + x^^^2 = 0), by rewriting -- ERROR INDICATES IMPROVEMENT";
neuper@42319	823	(SHOULD BE: term2str = "x = -2 \| x = 4;)
neuper@42318	824
neuper@42318	825
neuper@37906	826
neuper@37906	827	"-------------------- (3 - 10x + 3x^^^2 = 0), ----------------------";
neuper@37906	828	"-------------------- (3 - 10x + 3x^^^2 = 0), ----------------------";
neuper@37906	829	"-------------------- (3 - 10x + 3x^^^2 = 0), ----------------------";
neuper@37906	830	"---- test the erls ----";
neuper@37906	831	val t1 = (term_of o the o (parse thy)) "0 <= (10/3/2)^^^2 - 1";
neuper@42319	832	val SOME (t,_) = rewrite_set_ @{theory PolyEq} false PolyEq_erls t1;
neuper@37906	833	val t' = term2str t;
neuper@41928	834	(*if t'= "HOL.True" then ()
neuper@38031	835	else error "polyeq.sml: diff.behav. in 'rewrite_set_.. PolyEq_erls";*)
neuper@37906	836	(* *)
neuper@37906	837	val fmz = ["equality (3 - 10x + 3x^^^2 = 0)",
neuper@37906	838	"solveFor x","solutions L"];
neuper@37906	839	val (dI',pI',mI') =
neuper@37991	840	("PolyEq",["degree_2","expanded","univariate","equation"],
neuper@37906	841	["PolyEq","complete_square"]);
neuper@37906	842	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@42272	843	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	844	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	845	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
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@37991	850	(Apply_Method ("PolyEq","complete_square"))
neuper@42272	851	val (p,_,f,nxt,_,pt) = me nxt p [] pt; f2str f;
neuper@37906	852
neuper@37906	853	"----------- (-16 + 4x + 2x^^^2 = 0), --------------------------";
neuper@37906	854	"----------- (-16 + 4x + 2x^^^2 = 0), --------------------------";
neuper@37906	855	"----------- (-16 + 4x + 2x^^^2 = 0), --------------------------";
neuper@37906	856	val fmz = ["equality (-16 + 4x + 2x^^^2 = 0)",
neuper@37906	857	"solveFor x","solutions L"];
neuper@37906	858	val (dI',pI',mI') =
neuper@37991	859	("PolyEq",["degree_2","expanded","univariate","equation"],
neuper@37906	860	["PolyEq","complete_square"]);
neuper@37906	861	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
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;
neuper@42272	865	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	866	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	867	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	868	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37991	869	(Apply_Method ("PolyEq","complete_square"))
neuper@42272	870	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	871	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	872	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	873	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	874	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	875	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	876	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	877	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	878	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	879	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	880	(* FIXXXXME n1.,
neuper@37906	881	case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 2, x = -4]")) => () TODO
neuper@38031	882	\| _ => error "polyeq.sml: diff.behav. in [x = 2, x = -4]";
neuper@37906	883	*)
neuper@37906	884
neuper@37906	885	"----------- (ab - (a+b)x + x^^^2 = 0), (Schalk 2,S.68Nr.44.a)";
neuper@37906	886	"----------- (ab - (a+b)x + x^^^2 = 0), (Schalk 2,S.68Nr.44.a)";
neuper@37906	887	"----------- (ab - (a+b)x + x^^^2 = 0), (Schalk 2,S.68Nr.44.a)";
neuper@37906	888	val fmz = ["equality (ab - (a+b)x + x^^^2 = 0)",
neuper@37906	889	"solveFor x","solutions L"];
neuper@37906	890	val (dI',pI',mI') =
neuper@37991	891	("PolyEq",["degree_2","expanded","univariate","equation"],
neuper@37906	892	["PolyEq","complete_square"]);
neuper@37906	893	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
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;
neuper@42272	898	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	899	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	900	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	901	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	902	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	903	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	904
neuper@42272	905	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	906	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	907	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	908	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	909	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	910	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	911	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	912	val (p,_,f,nxt,_,pt) = me nxt p [] pt; f2str f;
neuper@37906	913	(*WN.2.5.03 TODO FIXME Matthias ?
neuper@37906	914	case f of
neuper@37906	915	Form'
neuper@37906	916	(FormKF
neuper@37906	917	(~1,EdUndef,0,Nundef,
neuper@37906	918	"[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	919	=> ()
neuper@38031	920	\| _ => error "polyeq.sml: diff.behav. in ab - (a+b)x + x^^^2 = 0";
neuper@37906	921	this will be simplified [x = a, x = b] to by Factor.ML*)
neuper@37906	922
neuper@37906	923
neuper@37906	924	"----------- (-64 + x^^^2 = 0), (Schalk 2, S.66 Nr.1.a~--------)";
neuper@37906	925	"----------- (-64 + x^^^2 = 0), (Schalk 2, S.66 Nr.1.a~--------)";
neuper@37906	926	"----------- (-64 + x^^^2 = 0), (Schalk 2, S.66 Nr.1.a~--------)";
neuper@37906	927	val fmz = ["equality (-64 + x^^^2 = 0)",(Schalk 2, S.66 Nr.1.a~)
neuper@37906	928	"solveFor x","solutions L"];
neuper@37906	929	val (dI',pI',mI') =
neuper@37991	930	("PolyEq",["degree_2","expanded","univariate","equation"],
neuper@37906	931	["PolyEq","complete_square"]);
neuper@37906	932	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@42272	933	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	934	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	935	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	936	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	937	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	938	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	939	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	940	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	941	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	942	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	943	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	944	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	945	val (p,_,f,nxt,_,pt) = me nxt p [] pt; f2str f;
neuper@37906	946	(WN.2.5.03 TODO "[x = sqrt (0 - -64), x = -1 sqrt (0 - -64)]"
neuper@37906	947	case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 8, x = -8]")) => ()
neuper@38031	948	\| _ => error "polyeq.sml: diff.behav. in [x = 8, x = -8]";
neuper@37906	949	*)
neuper@37906	950
neuper@37906	951	"----------- (-147 + 3x^^^2 = 0), (Schalk 2, S.66 Nr.1.b------*)";
neuper@37906	952	"----------- (-147 + 3x^^^2 = 0), (Schalk 2, S.66 Nr.1.b------*)";
neuper@37906	953	"----------- (-147 + 3x^^^2 = 0), (Schalk 2, S.66 Nr.1.b------*)";
neuper@37906	954	val fmz = ["equality (-147 + 3x^^^2 = 0)",(Schalk 2, S.66 Nr.1.b*)
neuper@37906	955	"solveFor x","solutions L"];
neuper@37906	956	val (dI',pI',mI') =
neuper@37991	957	("PolyEq",["degree_2","expanded","univariate","equation"],
neuper@37906	958	["PolyEq","complete_square"]);
neuper@37906	959	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@42272	960	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	961	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	962	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	963	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	964	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	965	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	966	val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@42272	967	val (p,_,f,nxt,_,pt) = me nxt p [] pt;
neuper@37906	968	(WN.2.5.03 TODO "[x = sqrt (0 - -49), x = -1 sqrt (0 - -49)]"
neuper@37906	969	case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 7, x = -7]")) => ()
neuper@38031	970	\| _ => error "polyeq.sml: diff.behav. in [x = 7, x = -7]";
neuper@37906	971	*)
neuper@37906	972	if f2str f = "[x = sqrt (0 - -49), x = -1 * sqrt (0 - -49)]" then ()
neuper@38031	973	else error "polyeq.sml CORRECTED?behav. in [x = 7, x = -7]";
neuper@37906	974
neuper@37906	975
neuper@37906	976	"----------- (3x - 1 - (5x - (2 - 4x)) = -11),(Schalk Is86Bsp5";
neuper@37906	977	"----------- (3x - 1 - (5x - (2 - 4x)) = -11),(Schalk Is86Bsp5";
neuper@37906	978	"----------- (3x - 1 - (5x - (2 - 4x)) = -11),(Schalk Is86Bsp5";
neuper@37906	979	(EP-17 Schalk_I_p86_n5)
neuper@42319	980	val fmz = ["equality ((3::real)x - 1 - (5x - (2 - 4*x)) = -11)","solveFor x","solutions L"];
neuper@37906	981	(* refine fmz ["univariate","equation"];
neuper@37906	982	*)
neuper@37991	983	val (dI',pI',mI') = ("PolyEq",["univariate","equation"],["no_met"]);
neuper@37906	984	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@37906	985	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	986	(* val nxt =
neuper@37906	987	("Model_Problem",
neuper@37906	988	Model_Problem ["normalize","polynomial","univariate","equation"])
neuper@37906	989	: string * tac*)
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;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	993	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	994	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	995	(* val nxt =
neuper@37906	996	("Subproblem",
neuper@37991	997	Subproblem ("PolyEq",["polynomial","univariate","equation"]))
neuper@37906	998	: string * tac *)
neuper@37906	999	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	1000	(*val nxt =
neuper@37906	1001	("Model_Problem",
neuper@37906	1002	Model_Problem ["degree_1","polynomial","univariate","equation"])
neuper@37906	1003	: string * tac *)
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
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	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	1010	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	1011	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	1012	case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 2]")) => ()
neuper@38031	1013	\| _ => error "polyeq.sml: diff.behav. in [x = 2]";
neuper@37906	1014
neuper@37906	1015
neuper@37906	1016	"----------- ((x+1)(x+2) - (3x - 2)^^^2=.. Schalk II s.68 Bsp 37";
neuper@37906	1017	"----------- ((x+1)(x+2) - (3x - 2)^^^2=.. Schalk II s.68 Bsp 37";
neuper@37906	1018	"----------- ((x+1)(x+2) - (3x - 2)^^^2=.. Schalk II s.68 Bsp 37";
neuper@37906	1019	(is in rlang.sml, too)
neuper@37906	1020	val fmz = ["equality ((x+1)(x+2) - (3x - 2)^^^2=(2x - 1)^^^2+(3x - 1)*(x+1))",
neuper@37906	1021	"solveFor x","solutions L"];
neuper@37991	1022	val (dI',pI',mI') = ("PolyEq",["univariate","equation"],["no_met"]);
neuper@37906	1023	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@37906	1024	(val nxt = ("Refine_Tacitly",Refine_Tacitly ["univariate","equation"]))
neuper@37906	1025	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	1026	(* val nxt =
neuper@37906	1027	("Model_Problem",
neuper@37906	1028	Model_Problem ["normalize","polynomial","univariate","equation"])
neuper@37906	1029	: string * tac *)
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	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	1034	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	1035	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	1036	(* val nxt =
neuper@37906	1037	("Subproblem",
neuper@37991	1038	Subproblem ("PolyEq",["polynomial","univariate","equation"]))
neuper@37906	1039	: string * tac*)
neuper@37906	1040	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	1041	(*val nxt =
neuper@37906	1042	("Model_Problem",
neuper@37906	1043	Model_Problem ["abcFormula","degree_2","polynomial","univariate","equation"])
neuper@37906	1044	: string * tac*)
neuper@37906	1045	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	1046	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	1047	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	1048	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	1049	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	1050	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	1051	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	1052	case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 2 / 15, x = 1]")) => ()
neuper@38031	1053	\| _ => error "polyeq.sml: diff.behav. in [x = 2 / 15, x = 1]";
neuper@37906	1054
neuper@37906	1055
neuper@37906	1056	" -4 + x^^^2 =0 ";
neuper@37906	1057	" -4 + x^^^2 =0 ";
neuper@37906	1058	" -4 + x^^^2 =0 ";
neuper@37906	1059	val fmz = ["equality ( -4 + x^^^2 =0)", "solveFor x","solutions L"];
neuper@37906	1060	(* val fmz = ["equality (1 + x^^^2 =0)", "solveFor x","solutions L"];*)
neuper@37906	1061	(val fmz = ["equality (0 =0)", "solveFor x","solutions L"];)
neuper@37991	1062	val (dI',pI',mI') = ("PolyEq",["univariate","equation"],["no_met"]);
neuper@37906	1063	(*val p = e_pos';
neuper@37906	1064	val c = [];
neuper@37906	1065	val (mI,m) = ("Init_Proof",Init_Proof (fmz, (dI',pI',mI')));
neuper@37906	1066	val (p,_,f,nxt,_,pt) = me (mI,m) p c EmptyPtree;*)
neuper@37906	1067	val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
neuper@37906	1068
neuper@37906	1069	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	1070	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
neuper@37906	1071	val (p,_,f,nxt,_,pt) = me nxt p [1] pt;val (p,_,f,nxt,_,pt) = me nxt p [1] pt;
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	case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 2, x = -2]")) => ()
neuper@38031	1077	\| _ => error "polyeq.sml: diff.behav. in [x = 2, x = -2]";
neuper@37906	1078
neuper@37906	1079	"----------------- polyeq.sml end ------------------";
neuper@37906	1080
neuper@37906	1081	(Punkte aus dem TestBericht, die ich in rlang.sml nicht zuordnen konnte:)
neuper@37906	1082	(WN.19.3.03 ---v-)
neuper@37906	1083	(3(b))val (bdv,v) = (str2term "bdv", str2term "R1");
neuper@37906	1084	val t = str2term "-1 * (R * R2) + R2 * R1 + -1 * (R * R1) = 0";
neuper@37926	1085	val SOME (t',_) = rewrite_set_inst_ thy false [(bdv,v)] make_polynomial_in t;
neuper@37906	1086	term2str t';
neuper@37906	1087	"-1 * R * R2 + (R2 + -1 * R) * R1 = 0";
neuper@37906	1088	(WN.19.3.03 ---^-)
neuper@37906	1089
neuper@37906	1090	(3(c))val (bdv,v) = (str2term "bdv", str2term "p");
neuper@37906	1091	val t = str2term "y ^^^ 2 + -2 * (x * p) = 0";
neuper@37926	1092	val SOME (t',_) = rewrite_set_inst_ thy false [(bdv,v)] make_polynomial_in t;
neuper@37906	1093	term2str t';
neuper@37906	1094	"y ^^^ 2 + -2 * x * p = 0";
neuper@37906	1095
neuper@37906	1096	(3(d))val (bdv,v) = (str2term "bdv", str2term "x2");
neuper@37906	1097	val t = str2term
neuper@37906	1098	"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	1099	val SOME (t',_) = rewrite_set_inst_ thy false [(bdv,v)] make_polynomial_in t;
neuper@37906	1100	term2str t';
neuper@37906	1101	"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	1102	val SOME (t',_) = rewrite_set_inst_ thy false [(bdv,v)] make_ratpoly_in t;
neuper@37906	1103	term2str t';
neuper@37906	1104	"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	1105
neuper@37906	1106	(3(e))val (bdv,v) = (str2term "bdv", str2term "a");
neuper@37906	1107	val t = str2term
neuper@37906	1108	"A ^^^ 2 + c ^^^ 2 * (c / d) ^^^ 2 + (-4 * (c / d) ^^^ 2) * a ^^^ 2 = 0";
neuper@37926	1109	val NONE = rewrite_set_inst_ thy false [(bdv,v)] make_polynomial_in t;
neuper@37906	1110	(die _unsichtbare_ Klammern sind genau wie gew"unscht)
neuper@37906	1111
neuper@37906	1112
neuper@37906	1113	val t = str2term "(x + 1) * (x + 2) - (3 * x - 2) ^^^ 2 - ((2 * x - 1) ^^^ 2 + (3 * x - 1) * (x + 1)) = 0";
neuper@37906	1114	trace_rewrite:=true;
neuper@37906	1115	rewrite_set_ thy false expand_binoms t;
neuper@37906	1116	trace_rewrite:=false;
neuper@37906	1117
neuper@37906	1118
neuper@37906	1119	"----------- interSteps ([1],Res); on Schalk Is86Bsp5-------------";
neuper@37906	1120	"----------- interSteps ([1],Res); on Schalk Is86Bsp5-------------";
neuper@37906	1121	"----------- interSteps ([1],Res); on Schalk Is86Bsp5-------------";
neuper@37906	1122	states:=[];
neuper@37906	1123	CalcTree
neuper@42319	1124	[(["equality ((3::real)x - 1 - (5x - (2 - 4*x)) = -11)","solveFor x","solutions L"],
neuper@37991	1125	("PolyEq",["univariate","equation"],["no_met"]))];
neuper@37906	1126	Iterator 1;
neuper@37906	1127	moveActiveRoot 1;
neuper@37906	1128	autoCalculate 1 CompleteCalc;
neuper@37906	1129	val ((pt,p),_) = get_calc 1; show_pt pt;
neuper@37906	1130
neuper@42319	1131	interSteps 1 ([1],Res) (<ERROR> no Rewrite_Set... </ERROR> ?see fun prep_rls?);
neuper@42248	1132

author	Walther Neuper <neuper@ist.tugraz.at>
	Sat, 10 Mar 2012 09:41:09 +0100
changeset 42387	767debe8a50c
parent 42319	ffad491ba8f2
child 42394	977788dfed26
permissions	-rw-r--r--