wneuper/isa: test/Tools/isac/Knowledge/polyeq.sml@ac50595ffe6b (annotated)

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

author	Walther Neuper <neuper@ist.tugraz.at>
	Wed, 07 Sep 2011 10:07:13 +0200
branch	decompose-isar
changeset 42248	ac50595ffe6b
parent 41943	f33f6959948b
child 42255	6201b34bd323
permissions	-rw-r--r--