1 (* Title: Knowledge/polyeq-1.sml
2 testexamples for PolyEq, poynomial equations and equational systems
3 Author: Richard Lang 2003
4 (c) due to copyright terms
5 WN030609: some expls dont work due to unfinished handling of 'expanded terms';
6 others marked with TODO have to be checked, too.
9 "-----------------------------------------------------------------";
10 "table of contents -----------------------------------------------";
11 "-----------------------------------------------------------------";
12 "------ polyeq- 1.sml ---------------------------------------------";
13 "----------- tests on predicates in problems ---------------------";
14 "----------- test matching problems ------------------------------";
15 "----------- prep. for introduction of Matthias Goldgruber 2003 trials on rewrite orders -----";
16 "----------- open local of fun ord_make_polynomial_in ------------------------------------------";
17 "----------- Matthias Goldgruber 2003 trials on rewrite orders -------------------------------";
18 "----------- lin.eq degree_0 -------------------------------------";
19 "----------- test thm's d2_pq_formulsxx[_neg]---------------------";
20 "----------- equality (2 +(- 1)*x + x \<up> 2 = (0::real)) ----------------------------------------";
21 "----------- equality (- 2 +(- 1)*x + 1*x \<up> 2 = 0) ---------------------------------------------";
22 "----------- equality (- 2 + x + x \<up> 2 = 0) ---------------------------------------------------";
23 "----------- equality (2 + x + x \<up> 2 = 0) ----------------------------------------------------";
24 "----------- equality (- 2 + x + 1*x \<up> 2 = 0)) ------------------------------------------------";
25 "----------- equality (1*x + x \<up> 2 = 0) ----------------------------------------------------";
26 "----------- equality (1*x + 1*x \<up> 2 = 0) ----------------------------------------------------";
27 "----------- equality (x + x \<up> 2 = 0) ------------------------------------------------------";
28 "----------- equality (x + 1*x \<up> 2 = 0) ------------------------------------------------------";
29 "----------- equality (-4 + x \<up> 2 = 0) -------------------------------------------------------";
30 "----------- equality (4 + 1*x \<up> 2 = 0) -------------------------------------------------------";
31 "----------- equality (1 +(- 1)*x + 2*x \<up> 2 = 0) ----------------------------------------------";
32 "----------- equality (- 1 + x + 2*x \<up> 2 = 0) -------------------------------------------------";
33 "----------- equality (1 + x + 2*x \<up> 2 = 0) --------------------------------------------------";
34 "----------- (-8 - 2*x + x \<up> 2 = 0), (*Schalk 2, S.67 Nr.31.b----";
35 "----------- (-8 - 2*x + x \<up> 2 = 0), by rewriting ---------------";
36 "----------- (- 16 + 4*x + 2*x \<up> 2 = 0), --------------------------";
37 "-----------------------------------------------------------------";
38 "------ polyeq- 2.sml ---------------------------------------------";
39 "----------- (a*b - (a+b)*x + x \<up> 2 = 0), (*Schalk 2,S.68Nr.44.a*)";
40 "----------- (-64 + x \<up> 2 = 0), (*Schalk 2, S.66 Nr.1.a~--------*)";
41 "----------- (- 147 + 3*x \<up> 2 = 0), (*Schalk 2, S.66 Nr.1.b------*)";
42 "----------- (3*x - 1 - (5*x - (2 - 4*x)) = - 11),(*Schalk Is86Bsp5";
43 "----------- ((x+1)*(x+2) - (3*x - 2) \<up> 2=.. Schalk II s.68 Bsp 37";
44 "----------- rls make_polynomial_in ------------------------------";
45 "----------- interSteps ([1],Res); on Schalk Is86Bsp5-------------";
46 "----------- rls d2_polyeq_bdv_only_simplify ---------------------";
47 "-----------------------------------------------------------------";
48 "-----------------------------------------------------------------";
50 "----------- tests on predicates in problems ---------------------";
51 "----------- tests on predicates in problems ---------------------";
52 "----------- tests on predicates in problems ---------------------";
53 Rewrite.trace_on:=false; (*true false*)
55 val t1 = (Thm.term_of o the o (TermC.parse thy)) "lhs (-8 - 2*x + x \<up> 2 = 0)";
56 val SOME (t,_) = rewrite_set_ @{theory PolyEq} false PolyEq_prls t1;
57 if ((UnparseC.term t) = "- 8 - 2 * x + x \<up> 2") then ()
58 else error "polyeq.sml: diff.behav. in lhs";
60 val t2 = (Thm.term_of o the o (TermC.parse thy)) "(-8 - 2*x + x \<up> 2) is_expanded_in x";
61 val SOME (t,_) = rewrite_set_ @{theory PolyEq} false PolyEq_prls t2;
62 if (UnparseC.term t) = "True" then ()
63 else error "polyeq.sml: diff.behav. 1 in is_expended_in";
65 val t0 = (Thm.term_of o the o (TermC.parse thy)) "(sqrt(x)) is_poly_in x";
66 val SOME (t,_) = rewrite_set_ @{theory PolyEq} false PolyEq_prls t0;
67 if (UnparseC.term t) = "False" then ()
68 else error "polyeq.sml: diff.behav. 2 in is_poly_in";
70 val t3 = (Thm.term_of o the o (TermC.parse thy)) "(-8 + (- 1)*2*x + x \<up> 2) is_poly_in x";
71 val SOME (t,_) = rewrite_set_ @{theory PolyEq} false PolyEq_prls t3;
72 if (UnparseC.term t) = "True" then ()
73 else error "polyeq.sml: diff.behav. 3 in is_poly_in";
75 val t4 = (Thm.term_of o the o (TermC.parse thy)) "(lhs (-8 + (- 1)*2*x + x \<up> 2 = 0)) is_expanded_in x";
76 val SOME (t,_) = rewrite_set_ @{theory PolyEq} false PolyEq_prls t4;
77 if (UnparseC.term t) = "True" then ()
78 else error "polyeq.sml: diff.behav. 4 in is_expended_in";
80 val t6 = (Thm.term_of o the o (TermC.parse thy)) "(lhs (-8 - 2*x + x \<up> 2 = 0)) is_expanded_in x";
81 val SOME (t,_) = rewrite_set_ @{theory PolyEq} false PolyEq_prls t6;
82 if (UnparseC.term t) = "True" then ()
83 else error "polyeq.sml: diff.behav. 5 in is_expended_in";
85 val t3 = (Thm.term_of o the o (TermC.parse thy))"((-8 - 2*x + x \<up> 2) has_degree_in x) = 2";
86 val SOME (t,_) = rewrite_set_ @{theory PolyEq} false PolyEq_prls t3;
87 if (UnparseC.term t) = "True" then ()
88 else error "polyeq.sml: diff.behav. in has_degree_in_in";
90 val t3 = (Thm.term_of o the o (TermC.parse thy)) "((sqrt(x)) has_degree_in x) = 2";
91 val SOME (t,_) = rewrite_set_ @{theory PolyEq} false PolyEq_prls t3;
92 if (UnparseC.term t) = "False" then ()
93 else error "polyeq.sml: diff.behav. 6 in has_degree_in_in";
95 val t4 = (Thm.term_of o the o (TermC.parse thy))
96 "((-8 - 2*x + x \<up> 2) has_degree_in x) = 1";
97 val SOME (t,_) = rewrite_set_ @{theory PolyEq} false PolyEq_prls t4;
98 if (UnparseC.term t) = "False" then ()
99 else error "polyeq.sml: diff.behav. 7 in has_degree_in_in";
101 val t5 = (Thm.term_of o the o (TermC.parse thy))
102 "((-8 - 2*x + x \<up> 2) has_degree_in x) = 2";
103 val SOME (t,_) = rewrite_set_ @{theory PolyEq} false PolyEq_prls t5;
104 if (UnparseC.term t) = "True" then ()
105 else error "polyeq.sml: diff.behav. 8 in has_degree_in_in";
107 "----------- test matching problems --------------------------0---";
108 "----------- test matching problems --------------------------0---";
109 "----------- test matching problems --------------------------0---";
110 val fmz = ["equality (-8 - 2*x + x \<up> 2 = 0)", "solveFor x", "solutions L"];
111 if M_Match.match_pbl fmz (Problem.from_store ["expanded", "univariate", "equation"]) =
112 M_Match.Matches' {Find = [Correct "solutions L"],
114 Given = [Correct "equality (- 8 - 2 * x + x \<up> 2 = 0)", Correct "solveFor x"],
115 Where = [Correct "matches (?a = 0) (- 8 - 2 * x + x \<up> 2 = 0)",
116 Correct "lhs (- 8 - 2 * x + x \<up> 2 = 0) is_expanded_in x"],
118 then () else error "M_Match.match_pbl [expanded,univariate,equation]";
120 if M_Match.match_pbl fmz (Problem.from_store ["degree_2", "expanded", "univariate", "equation"]) =
121 M_Match.Matches' {Find = [Correct "solutions L"],
123 Given = [Correct "equality (- 8 - 2 * x + x \<up> 2 = 0)", Correct "solveFor x"],
124 Where = [Correct "lhs (- 8 - 2 * x + x \<up> 2 = 0) has_degree_in x = 2"],
125 Relate = []} (*before WN110906 was: has_degree_in x =!= 2"]*)
126 then () else error "M_Match.match_pbl [degree_2,expanded,univariate,equation]";
129 "----------- prep. for introduction of Matthias Goldgruber 2003 trials on rewrite orders -----";
130 "----------- prep. for introduction of Matthias Goldgruber 2003 trials on rewrite orders -----";
131 "----------- prep. for introduction of Matthias Goldgruber 2003 trials on rewrite orders -----";
132 (*##################################################################################
133 ----------- 28.2.03: war nicht upgedatet und ausgeklammert in ROOT.ML-->Test_Isac.thy
135 (*Aufgabe zum Einstieg in die Arbeit...*)
136 val t = (Thm.term_of o the o (TermC.parse thy)) "a*b - (a+b)*x + x \<up> 2 = 0";
137 (*ein 'ruleset' aus Poly.ML wird angewandt...*)
138 val SOME (t,_) = rewrite_set_ thy Poly_erls false make_polynomial t;
140 "a * b + (- 1 * (a * x) + (- 1 * (b * x) + x \<up> 2)) = 0";
142 rewrite_set_inst_ thy Poly_erls false [("bdv", "a")] make_polynomial_in t;
144 "x \<up> 2 + (- 1 * (b * x) + (- 1 * (x * a) + b * a)) = 0";
145 (* bei Verwendung von "size_of-term" nach MG :*)
146 (*"x \<up> 2 + (- 1 * (b * x) + (b * a + - 1 * (x * a))) = 0" !!! *)
148 (*wir holen 'a' wieder aus der Klammerung heraus...*)
149 val SOME (t,_) = rewrite_set_ thy Poly_erls false discard_parentheses t;
151 "x \<up> 2 + - 1 * b * x + - 1 * x * a + b * a = 0";
152 (* "x \<up> 2 + - 1 * b * x + b * a + - 1 * x * a = 0" !!! *)
155 rewrite_set_inst_ thy Poly_erls false [("bdv", "a")] make_polynomial_in t;
157 "x \<up> 2 + (- 1 * (b * x) + a * (b + - 1 * x)) = 0";
158 (*da sind wir fast am Ziel: make_polynomial_in 'a' sollte ergeben
159 "x \<up> 2 + (- 1 * (b * x)) + (b + - 1 * x) * a = 0"*)
161 (*das rewriting l"asst sich beobachten mit
162 Rewrite.trace_on := false; (*true false*)
165 "------ 15.11.02 --------------------------";
166 val t = (Thm.term_of o the o (TermC.parse thy)) "1 + a * x + b * x";
167 val bdv = (Thm.term_of o the o (TermC.parse thy)) "bdv";
168 val a = (Thm.term_of o the o (TermC.parse thy)) "a";
170 Rewrite.trace_on := false; (*true false*)
171 (* Anwenden einer Regelmenge aus Termorder.ML: *)
173 rewrite_set_inst_ thy false [(bdv,a)] make_polynomial_in t;
176 rewrite_set_ thy false discard_parentheses t;
180 val t = (Thm.term_of o the o (TermC.parse thy)) "1 + a * (x + b * x) + a \<up> 2";
182 rewrite_set_inst_ thy false [(bdv,a)] make_polynomial_in t;
185 rewrite_set_ thy false discard_parentheses t;
187 "1 + (x + b * x) * a + a \<up> 2";
189 val t = (Thm.term_of o the o (TermC.parse thy)) "1 + a \<up> 2 * x + b * a + 7*a \<up> 2";
191 rewrite_set_inst_ thy false [(bdv,a)] make_polynomial_in t;
194 rewrite_set_ thy false discard_parentheses t;
196 "1 + b * a + (7 + x) * a \<up> 2";
199 Prog_Expr.thy grundlegende Algebra
203 RootRat.thy Wurzen + Br"uche
204 Termorder.thy BITTE NUR HIERHER SCHREIBEN (...WN03)
206 get_thm Termorder.thy "bdv_n_collect";
207 get_thm (theory "Isac_Knowledge") "bdv_n_collect";
209 val t = (Thm.term_of o the o (TermC.parse thy)) "a \<up> 2 * x + 7 * a \<up> 2";
211 rewrite_set_inst_ thy false [(bdv,a)] make_polynomial_in t;
214 rewrite_set_ thy false discard_parentheses t;
216 "(7 + x) * a \<up> 2";
218 val t = (Thm.term_of o the o (TermC.parse Termorder.thy)) "Pi";
220 val t = (Thm.term_of o the o (parseold thy)) "7";
221 ##################################################################################*)
224 "----------- open local of fun ord_make_polynomial_in ------------------------------------------";
225 "----------- open local of fun ord_make_polynomial_in ------------------------------------------";
226 "----------- open local of fun ord_make_polynomial_in ------------------------------------------";
227 (* termorder hacked by MG, adapted later by WN *)
228 (** )local ( *. for make_polynomial_in .*)
230 open Term; (* for type order = EQUAL | LESS | GREATER *)
232 fun pr_ord EQUAL = "EQUAL"
233 | pr_ord LESS = "LESS"
234 | pr_ord GREATER = "GREATER";
236 fun dest_hd' _ (Const (a, T)) = (((a, 0), T), 0)
237 | dest_hd' x (t as Free (a, T)) =
238 if x = t then ((("|||||||||||||", 0), T), 0) (*WN*)
239 else (((a, 0), T), 1)
240 | dest_hd' _ (Var v) = (v, 2)
241 | dest_hd' _ (Bound i) = ((("", i), dummyT), 3)
242 | dest_hd' _ (Abs (_, T, _)) = ((("", 0), T), 4)
243 | dest_hd' _ _ = raise ERROR "dest_hd': uncovered case in fun.def.";
245 fun size_of_term' i pr x (t as Const (\<^const_name>\<open>powr\<close>, _) $
246 Free (var, _) $ Free (pot, _)) =
247 (if pr then tracing (idt "#" i ^ "size_of_term' powr: " ^ UnparseC.term t) else ();
251 then (if pr then tracing (idt "#" i ^ "xstr = var --> " ^ string_of_int (1000 * (the (TermC.int_opt_of_string pot)))) else ();
252 1000 * (the (TermC.int_opt_of_string pot)))
253 else (if pr then tracing (idt "#" i ^ "x <> Free --> " ^ "3") else (); 3)
254 | _ => raise ERROR ("size_of_term' called with subst = " ^ UnparseC.term x))
255 | size_of_term' i pr x (t as Abs (_, _, body)) =
256 (if pr then tracing (idt "#" i ^ "size_of_term' Abs: " ^ UnparseC.term t) else ();
257 1 + size_of_term' (i + 1) pr x body)
258 | size_of_term' i pr x (f $ t) =
260 val _ = if pr then tracing (idt "#" i ^ "size_of_term' $$$: " ^ UnparseC.term f ^ " $$$ " ^ UnparseC.term t) else ();
261 val s1 = size_of_term' (i + 1) pr x f
262 val s2 = size_of_term' (i + 1) pr x t
263 val _ = if pr then tracing (idt "#" i ^ "size_of_term' $$$-->: " ^ string_of_int s1 ^ " + " ^ string_of_int s2 ^ " = " ^ string_of_int(s1 + s2)) else ();
265 | size_of_term' i pr x t =
266 (if pr then tracing (idt "#" i ^ "size_of_term' bot: " ^ UnparseC.term t) else ();
272 then (if pr then tracing (idt "#" i ^ "xstr = var --> " ^ "1000") else (); 1000)
273 else (if pr then tracing (idt "#" i ^ "x <> Free --> " ^ "1") else (); 1)
274 | _ => raise ERROR ("size_of_term' called with subst = " ^ UnparseC.term x))
275 | _ => (if pr then tracing (idt "#" i ^ "bot --> " ^ "1") else (); 1));
277 fun term_ord' i pr x thy (Abs (_, T, t), Abs(_, U, u)) = (* ~ term.ML *)
279 val _ = if pr then tracing (idt "#" i ^ "term_ord' Abs") else ();
281 case term_ord' (i + 1) pr x thy (t, u) of EQUAL => Term_Ord.typ_ord (T, U) | ord => ord
282 val _ = if pr then tracing (idt "#" i ^ "term_ord' Abs --> " ^ pr_ord ord) else ()
284 | term_ord' i pr x _ (t, u) =
286 val _ = if pr then tracing (idt "#" i ^ "term_ord' bot (" ^ UnparseC.term t ^ ", " ^ UnparseC.term u ^ ")") else ();
288 case int_ord (size_of_term' (i + 1) pr x t, size_of_term' (i + 1) pr x u) of
290 let val (f, ts) = strip_comb t and (g, us) = strip_comb u
292 (case hd_ord (i + 1) pr x (f, g) of
293 EQUAL => (terms_ord x (i + 1) pr) (ts, us)
297 val _ = if pr then tracing (idt "#" i ^ "term_ord' bot --> " ^ pr_ord ord) else ()
299 and hd_ord i pr x (f, g) = (* ~ term.ML *)
301 val _ = if pr then tracing (idt "#" i ^ "hd_ord (" ^ UnparseC.term f ^ ", " ^ UnparseC.term g ^ ")") else ();
303 (prod_ord Term_Ord.indexname_ord Term_Ord.typ_ord) int_ord
304 (dest_hd' x f, dest_hd' x g)
305 val _ = if pr then tracing (idt "#" i ^ "hd_ord --> " ^ pr_ord ord) else ();
307 and terms_ord x i pr (ts, us) =
309 val _ = if pr then tracing (idt "#" i ^ "terms_ord (" ^ UnparseC.terms ts ^ ", " ^ UnparseC.terms us ^ ")") else ();
310 val ord = list_ord (term_ord' (i + 1) pr x (ThyC.get_theory "Isac_Knowledge"))(ts, us);
311 val _ = if pr then tracing (idt "#" i ^ "terms_ord --> " ^ pr_ord ord) else ();
316 fun ord_make_polynomial_in (pr:bool) thy subst (ts, us) =
317 ((** )tracing ("*** subs variable is: " ^ Env.subst2str subst); ( **)
320 term_ord' 1 pr x thy (TermC.numerals_to_Free ts, TermC.numerals_to_Free us) = LESS
321 | _ => raise ERROR ("ord_make_polynomial_in called with subst = " ^ Env.subst2str subst))
325 val subs = [(TermC.str2term "bdv::real", TermC.str2term "x::real")];
326 if ord_make_polynomial_in true @{theory} subs (t1, t2) then () else error "still GREATER?";
328 val x = TermC.str2term "x ::real";
330 val t1 = TermC.numerals_to_Free (TermC.str2term "L * q_0 * x \<up> 2 / 4 ::real");
331 if 2006 = size_of_term' 1 true x t1
332 then () else error "size_of_term' (L * q_0 * x \<up> 2) CHANGED)";
334 val t2 = TermC.numerals_to_Free (TermC.str2term "- 1 * (q_0 * x \<up> 3) :: real");
335 if 3004 = size_of_term' 1 true x t2
336 then () else error "size_of_term' (- 1 * (q_0 * x \<up> 3)) CHANGED";
339 "----------- Matthias Goldgruber 2003 trials on rewrite orders -------------------------------";
340 "----------- Matthias Goldgruber 2003 trials on rewrite orders -------------------------------";
341 "----------- Matthias Goldgruber 2003 trials on rewrite orders -------------------------------";
342 val substa = [(TermC.empty, (Thm.term_of o the o (TermC.parse thy)) "a")];
343 val substb = [(TermC.empty, (Thm.term_of o the o (TermC.parse thy)) "b")];
344 val substx = [(TermC.empty, (Thm.term_of o the o (TermC.parse thy)) "x")];
346 val x1 = (Thm.term_of o the o (TermC.parse thy)) "a + b + x";
347 val x2 = (Thm.term_of o the o (TermC.parse thy)) "a + x + b";
348 val x3 = (Thm.term_of o the o (TermC.parse thy)) "a + x + b";
349 val x4 = (Thm.term_of o the o (TermC.parse thy)) "x + a + b";
351 if ord_make_polynomial_in true thy substx (x1,x2) = true(*LESS *) then ()
352 else error "termorder.sml diff.behav ord_make_polynomial_in #1";
354 if ord_make_polynomial_in true thy substa (x1,x2) = true(*LESS *) then ()
355 else error "termorder.sml diff.behav ord_make_polynomial_in #2";
357 if ord_make_polynomial_in true thy substb (x1,x2) = false(*GREATER*) then ()
358 else error "termorder.sml diff.behav ord_make_polynomial_in #3";
360 val aa = (Thm.term_of o the o (TermC.parse thy)) "- 1 * a * x";
361 val bb = (Thm.term_of o the o (TermC.parse thy)) "x \<up> 3";
362 ord_make_polynomial_in true thy substx (aa, bb);
365 val aa = (Thm.term_of o the o (TermC.parse thy)) "- 1 * a * x";
366 val bb = (Thm.term_of o the o (TermC.parse thy)) "x \<up> 3";
367 ord_make_polynomial_in true thy substa (aa, bb);
368 false; (* => GREATER *)
370 (* und nach dem Re-engineering der Termorders in den 'rulesets'
371 kannst Du die 'gr"osste' Variable frei w"ahlen: *)
372 val bdv= TermC.str2term "bdv ::real";
373 val x = TermC.str2term "x ::real";
374 val a = TermC.str2term "a ::real";
375 val b = TermC.str2term "b ::real";
376 val SOME (t',_) = rewrite_set_inst_ thy false [(bdv,a)] make_polynomial_in x2;
377 if UnparseC.term t' = "b + x + a" then ()
378 else error "termorder.sml diff.behav ord_make_polynomial_in #11";
380 val NONE = rewrite_set_inst_ thy false [(bdv,b)] make_polynomial_in x2;
382 val SOME (t',_) = rewrite_set_inst_ thy false [(bdv,x)] make_polynomial_in x2;
383 if UnparseC.term t' = "a + b + x" then ()
384 else error "termorder.sml diff.behav ord_make_polynomial_in #13";
386 val ppp' = "-6 + -5*x + x \<up> 3 + - 1*x \<up> 2 + - 1*x \<up> 3 + - 14*x \<up> 2";
387 val ppp = (Thm.term_of o the o (TermC.parse thy)) ppp';
388 val SOME (t', _) = rewrite_set_inst_ thy false [(bdv,x)] make_polynomial_in ppp;
389 if UnparseC.term t' = "- 6 + - 5 * x + - 15 * x \<up> 2" then ()
390 else error "termorder.sml diff.behav ord_make_polynomial_in #15";
392 val ttt' = "(3*x + 5)/18 ::real";
393 val ttt = (Thm.term_of o the o (TermC.parse thy)) ttt';
394 val SOME (uuu,_) = rewrite_set_inst_ thy false [(bdv,x)] make_polynomial_in ttt;
395 if UnparseC.term uuu = "(5 + 3 * x) / 18" then ()
396 else error "termorder.sml diff.behav ord_make_polynomial_in #16a";
398 val SOME (uuu,_) = rewrite_set_ thy false make_polynomial ttt;
399 if UnparseC.term uuu = "(5 + 3 * x) / 18" then ()
400 else error "termorder.sml diff.behav ord_make_polynomial_in #16b";
402 "----------- lin.eq degree_0 -------------------------------------";
403 "----------- lin.eq degree_0 -------------------------------------";
404 "----------- lin.eq degree_0 -------------------------------------";
405 "----- d0_false ------";
406 val fmz = ["equality (1 = (0::real))", "solveFor x", "solutions L"];
407 val (dI',pI',mI') = ("PolyEq",["degree_0", "polynomial", "univariate", "equation"],
408 ["PolyEq", "solve_d0_polyeq_equation"]);
409 (*=== inhibit exn WN110914: declare_constraints doesnt work with ThmC.numerals_to_Free ========
410 TODO: change to "equality (x + - 1*x = (0::real))"
411 and search for an appropriate problem and method.
413 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
414 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
415 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
416 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
417 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
418 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
419 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
420 case f of Form' (Test_Out.FormKF (~1,EdUndef,0,Nundef,"[]")) => ()
421 | _ => error "polyeq.sml: diff.behav. in 1 = 0 -> []";
423 "----- d0_true ------";
424 val fmz = ["equality (0 = (0::real))", "solveFor x", "solutions L"];
425 val (dI',pI',mI') = ("PolyEq",["degree_0", "polynomial", "univariate", "equation"],
426 ["PolyEq", "solve_d0_polyeq_equation"]);
427 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
428 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
429 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
430 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
431 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
432 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
433 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
434 case f of Form' (Test_Out.FormKF (~1,EdUndef,0,Nundef,"UniversalList")) => ()
435 | _ => error "polyeq.sml: diff.behav. in 0 = 0 -> UniversalList";
436 ============ inhibit exn WN110914 ============================================*)
438 "----------- test thm's d2_pq_formulsxx[_neg]---------------------";
439 "----------- test thm's d2_pq_formulsxx[_neg]---------------------";
440 "----------- test thm's d2_pq_formulsxx[_neg]---------------------";
441 "----- d2_pqformula1 ------!!!!";
442 val fmz = ["equality (- 1/8 + (- 1/4)*z + z \<up> 2 = (0::real))", "solveFor z", "solutions L"];
444 ("Isac_Knowledge", ["pqFormula", "degree_2", "polynomial", "univariate", "equation"], ["no_met"]);
445 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
446 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
447 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
448 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
449 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
450 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
451 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
452 val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*Apply_Method ["PolyEq", "solve_d2_polyeq_pq_equation"]*)
453 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
454 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
455 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
456 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
458 (*[z = 1 / 8 + sqrt (9 / 16) / 2, z = 1 / 8 + - 1 * sqrt (9 / 16) / 2] TODO sqrt*)
459 val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt =..,Check_elementwise "Assumptions")*)
460 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
461 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
463 if p = ([], Res) andalso
464 f2str f = "[z = 1 / 8 + sqrt (9 / 16) / 2, z = 1 / 8 + - 1 * sqrt (9 / 16) / 2]" then
465 case nxt of End_Proof' => () | _ => error "(- 1/8 + (- 1/4)*z + z \<up> 2 = (0::real)) CHANGED 1"
466 else error "(- 1/8 + (- 1/4)*z + z \<up> 2 = (0::real)) CHANGED 2";
468 "----------- equality (2 +(- 1)*x + x \<up> 2 = (0::real)) ----------------------------------------";
469 "----------- equality (2 +(- 1)*x + x \<up> 2 = (0::real)) ----------------------------------------";
470 "----------- equality (2 +(- 1)*x + x \<up> 2 = (0::real)) ----------------------------------------";
471 "----- d2_pqformula1_neg ------";
472 val fmz = ["equality (2 +(- 1)*x + x \<up> 2 = (0::real))", "solveFor x", "solutions L"];
473 val (dI',pI',mI') = ("PolyEq",["pqFormula", "degree_2", "polynomial", "univariate", "equation"], ["PolyEq", "solve_d2_polyeq_pq_equation"]);
474 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
475 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
476 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
477 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
478 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
479 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
481 ([1],Res) False Or_to_List)*)
482 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
484 ([2],Res) [] Check_elementwise "Assumptions"*)
485 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
486 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
487 val asm = Ctree.get_assumptions pt p;
488 if f2str f = "[]" andalso
489 UnparseC.terms asm = "[\"lhs (2 + - 1 * x + x \<up> 2 = 0) is_poly_in x\", " ^
490 "\"lhs (2 + - 1 * x + x \<up> 2 = 0) has_degree_in x = 2\"]" then ()
491 else error "polyeq.sml: diff.behav. in 2 +(- 1)*x + x \<up> 2 = 0";
493 "----------- equality (- 2 +(- 1)*x + 1*x \<up> 2 = 0) ---------------------------------------------";
494 "----------- equality (- 2 +(- 1)*x + 1*x \<up> 2 = 0) ---------------------------------------------";
495 "----------- equality (- 2 +(- 1)*x + 1*x \<up> 2 = 0) ---------------------------------------------";
496 "----- d2_pqformula2 ------";
497 val fmz = ["equality (- 2 +(- 1)*x + 1*x \<up> 2 = 0)", "solveFor x", "solutions L"];
498 val (dI',pI',mI') = ("PolyEq",["pqFormula", "degree_2", "polynomial", "univariate", "equation"],
499 ["PolyEq", "solve_d2_polyeq_pq_equation"]);
500 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
501 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
502 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
503 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
504 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
505 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
507 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
508 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
509 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
510 case f of Test_Out.FormKF "[x = 2, x = - 1]" => ()
511 | _ => error "polyeq.sml: diff.behav. in - 2 + (- 1)*x + x^2 = 0 -> [x = 2, x = - 1]";
514 "----------- equality (- 2 + x + x \<up> 2 = 0) ---------------------------------------------------";
515 "----------- equality (- 2 + x + x \<up> 2 = 0) ---------------------------------------------------";
516 "----------- equality (- 2 + x + x \<up> 2 = 0) ---------------------------------------------------";
517 "----- d2_pqformula3 ------";
519 val fmz = ["equality (- 2 + x + x \<up> 2 = 0)", "solveFor x", "solutions L"];
520 val (dI',pI',mI') = ("PolyEq",["pqFormula", "degree_2", "polynomial", "univariate", "equation"],
521 ["PolyEq", "solve_d2_polyeq_pq_equation"]);
522 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
523 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
524 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
525 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
526 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
527 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
529 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
530 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
531 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
532 case f of Test_Out.FormKF "[x = 1, x = - 2]" => ()
533 | _ => error "polyeq.sml: diff.behav. in - 2 + x + x^2 = 0-> [x = 1, x = - 2]";
536 "----------- equality (2 + x + x \<up> 2 = 0) ----------------------------------------------------";
537 "----------- equality (2 + x + x \<up> 2 = 0) ----------------------------------------------------";
538 "----------- equality (2 + x + x \<up> 2 = 0) ----------------------------------------------------";
539 "----- d2_pqformula3_neg ------";
540 val fmz = ["equality (2 + x + x \<up> 2 = 0)", "solveFor x", "solutions L"];
541 val (dI',pI',mI') = ("PolyEq",["pqFormula", "degree_2", "polynomial", "univariate", "equation"],
542 ["PolyEq", "solve_d2_polyeq_pq_equation"]);
543 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
544 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
545 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
546 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
547 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
548 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
550 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
551 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
552 "TODO 2 + x + x \<up> 2 = 0";
553 "TODO 2 + x + x \<up> 2 = 0";
554 "TODO 2 + x + x \<up> 2 = 0";
556 "----------- equality (- 2 + x + 1*x \<up> 2 = 0)) ------------------------------------------------";
557 "----------- equality (- 2 + x + 1*x \<up> 2 = 0)) ------------------------------------------------";
558 "----------- equality (- 2 + x + 1*x \<up> 2 = 0)) ------------------------------------------------";
559 "----- d2_pqformula4 ------";
560 val fmz = ["equality (- 2 + x + 1*x \<up> 2 = 0)", "solveFor x", "solutions L"];
561 val (dI',pI',mI') = ("PolyEq",["pqFormula", "degree_2", "polynomial", "univariate", "equation"],
562 ["PolyEq", "solve_d2_polyeq_pq_equation"]);
563 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
564 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
565 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
566 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
567 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
568 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
569 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
570 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
571 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
572 case f of Test_Out.FormKF "[x = 1, x = - 2]" => ()
573 | _ => error "polyeq.sml: diff.behav. in - 2 + x + 1*x \<up> 2 = 0 -> [x = 1, x = - 2]";
575 "----------- equality (1*x + x \<up> 2 = 0) ----------------------------------------------------";
576 "----------- equality (1*x + x \<up> 2 = 0) ----------------------------------------------------";
577 "----------- equality (1*x + x \<up> 2 = 0) ----------------------------------------------------";
578 "----- d2_pqformula5 ------";
579 val fmz = ["equality (1*x + x \<up> 2 = 0)", "solveFor x", "solutions L"];
580 val (dI',pI',mI') = ("PolyEq",["pqFormula", "degree_2", "polynomial", "univariate", "equation"],
581 ["PolyEq", "solve_d2_polyeq_pq_equation"]);
582 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
583 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
584 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
585 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
586 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
587 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
588 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
589 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
590 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
591 case f of Test_Out.FormKF "[x = 0, x = - 1]" => ()
592 | _ => error "polyeq.sml: diff.behav. in 1*x + x^2 = 0 -> [x = 0, x = - 1]";
594 "----------- equality (1*x + 1*x \<up> 2 = 0) ----------------------------------------------------";
595 "----------- equality (1*x + 1*x \<up> 2 = 0) ----------------------------------------------------";
596 "----------- equality (1*x + 1*x \<up> 2 = 0) ----------------------------------------------------";
597 "----- d2_pqformula6 ------";
598 val fmz = ["equality (1*x + 1*x \<up> 2 = 0)", "solveFor x", "solutions L"];
599 val (dI',pI',mI') = ("PolyEq",["pqFormula", "degree_2", "polynomial", "univariate", "equation"],
600 ["PolyEq", "solve_d2_polyeq_pq_equation"]);
601 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
602 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
603 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
604 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
605 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
606 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
607 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
608 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
609 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
610 case f of Test_Out.FormKF "[x = 0, x = - 1]" => ()
611 | _ => error "polyeq.sml: diff.behav. in 1*x + 1*x^2 = 0 -> [x = 0, x = - 1]";
613 "----------- equality (x + x \<up> 2 = 0) ------------------------------------------------------";
614 "----------- equality (x + x \<up> 2 = 0) ------------------------------------------------------";
615 "----------- equality (x + x \<up> 2 = 0) ------------------------------------------------------";
616 "----- d2_pqformula7 ------";
618 val fmz = ["equality ( x + x \<up> 2 = 0)", "solveFor x", "solutions L"];
619 val (dI',pI',mI') = ("PolyEq",["pqFormula", "degree_2", "polynomial", "univariate", "equation"],
620 ["PolyEq", "solve_d2_polyeq_pq_equation"]);
621 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
622 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
623 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
624 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
625 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
626 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
627 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
628 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
629 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
630 case f of Test_Out.FormKF "[x = 0, x = - 1]" => ()
631 | _ => error "polyeq.sml: diff.behav. in x + x^2 = 0 -> [x = 0, x = - 1]";
633 "----------- equality (x + 1*x \<up> 2 = 0) ------------------------------------------------------";
634 "----------- equality (x + 1*x \<up> 2 = 0) ------------------------------------------------------";
635 "----------- equality (x + 1*x \<up> 2 = 0) ------------------------------------------------------";
636 "----- d2_pqformula8 ------";
637 val fmz = ["equality (x + 1*x \<up> 2 = 0)", "solveFor x", "solutions L"];
638 val (dI',pI',mI') = ("PolyEq",["pqFormula", "degree_2", "polynomial", "univariate", "equation"],
639 ["PolyEq", "solve_d2_polyeq_pq_equation"]);
640 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
641 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
642 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
643 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
644 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
645 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
646 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
647 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
648 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
649 case f of Test_Out.FormKF "[x = 0, x = - 1]" => ()
650 | _ => error "polyeq.sml: diff.behav. in x + 1*x^2 = 0 -> [x = 0, x = - 1]";
652 "----------- equality (-4 + x \<up> 2 = 0) -------------------------------------------------------";
653 "----------- equality (-4 + x \<up> 2 = 0) -------------------------------------------------------";
654 "----------- equality (-4 + x \<up> 2 = 0) -------------------------------------------------------";
655 "----- d2_pqformula9 ------";
656 val fmz = ["equality (-4 + x \<up> 2 = 0)", "solveFor x", "solutions L"];
657 val (dI',pI',mI') = ("PolyEq",["pqFormula", "degree_2", "polynomial", "univariate", "equation"],
658 ["PolyEq", "solve_d2_polyeq_pq_equation"]);
659 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
660 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
661 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
662 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
663 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
664 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
665 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
666 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
667 case f of Test_Out.FormKF "[x = 2, x = - 2]" => ()
668 | _ => error "polyeq.sml: diff.behav. in -4 + x^2 = 0 -> [x = 2, x = - 2]";
671 "----------- equality (4 + 1*x \<up> 2 = 0) -------------------------------------------------------";
672 "----------- equality (4 + 1*x \<up> 2 = 0) -------------------------------------------------------";
673 "----------- equality (4 + 1*x \<up> 2 = 0) -------------------------------------------------------";
674 "----- d2_pqformula9_neg ------";
675 val fmz = ["equality (4 + 1*x \<up> 2 = 0)", "solveFor x", "solutions L"];
676 val (dI',pI',mI') = ("PolyEq",["pqFormula", "degree_2", "polynomial", "univariate", "equation"],
677 ["PolyEq", "solve_d2_polyeq_pq_equation"]);
678 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
679 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
680 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
681 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
682 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
683 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
684 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
685 "TODO 4 + 1*x \<up> 2 = 0";
686 "TODO 4 + 1*x \<up> 2 = 0";
687 "TODO 4 + 1*x \<up> 2 = 0";
689 "-------------------- test thm's d2_abc_formulsxx[_neg]-----";
690 "-------------------- test thm's d2_abc_formulsxx[_neg]-----";
691 "-------------------- test thm's d2_abc_formulsxx[_neg]-----";
692 val fmz = ["equality (- 1 +(- 1)*x + 2*x \<up> 2 = 0)", "solveFor x", "solutions L"];
693 val (dI',pI',mI') = ("PolyEq",["abcFormula", "degree_2", "polynomial", "univariate", "equation"],
694 ["PolyEq", "solve_d2_polyeq_abc_equation"]);
695 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
696 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
697 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
698 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
699 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
700 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
701 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
702 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
703 case f of Test_Out.FormKF "[x = 1, x = - 1 / 2]" => ()
704 | _ => error "polyeq.sml: diff.behav. in - 1 + (- 1)*x + 2*x^2 = 0 -> [x = 1, x = - 1/2]";
706 "----------- equality (1 +(- 1)*x + 2*x \<up> 2 = 0) ----------------------------------------------";
707 "----------- equality (1 +(- 1)*x + 2*x \<up> 2 = 0) ----------------------------------------------";
708 "----------- equality (1 +(- 1)*x + 2*x \<up> 2 = 0) ----------------------------------------------";
709 val fmz = ["equality (1 +(- 1)*x + 2*x \<up> 2 = 0)", "solveFor x", "solutions L"];
710 val (dI',pI',mI') = ("PolyEq",["abcFormula", "degree_2", "polynomial", "univariate", "equation"],
711 ["PolyEq", "solve_d2_polyeq_abc_equation"]);
712 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
713 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
714 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
715 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
717 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
718 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
719 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
720 "TODO 1 +(- 1)*x + 2*x \<up> 2 = 0";
721 "TODO 1 +(- 1)*x + 2*x \<up> 2 = 0";
722 "TODO 1 +(- 1)*x + 2*x \<up> 2 = 0";
725 "----------- equality (- 1 + x + 2*x \<up> 2 = 0) -------------------------------------------------";
726 "----------- equality (- 1 + x + 2*x \<up> 2 = 0) -------------------------------------------------";
727 "----------- equality (- 1 + x + 2*x \<up> 2 = 0) -------------------------------------------------";
729 val fmz = ["equality (- 1 + x + 2*x \<up> 2 = 0)", "solveFor x", "solutions L"];
730 val (dI',pI',mI') = ("PolyEq",["abcFormula", "degree_2", "polynomial", "univariate", "equation"],
731 ["PolyEq", "solve_d2_polyeq_abc_equation"]);
732 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
733 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
734 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
736 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
737 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
738 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
739 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
741 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
742 case f of Test_Out.FormKF "[x = 1 / 2, x = - 1]" => ()
743 | _ => error "polyeq.sml: diff.behav. in - 1 + x + 2*x^2 = 0 -> [x = 1/2, x = - 1]";
746 "----------- equality (1 + x + 2*x \<up> 2 = 0) --------------------------------------------------";
747 "----------- equality (1 + x + 2*x \<up> 2 = 0) --------------------------------------------------";
748 "----------- equality (1 + x + 2*x \<up> 2 = 0) --------------------------------------------------";
749 val fmz = ["equality (1 + x + 2*x \<up> 2 = 0)", "solveFor x", "solutions L"];
750 val (dI',pI',mI') = ("PolyEq",["abcFormula", "degree_2", "polynomial", "univariate", "equation"],
751 ["PolyEq", "solve_d2_polyeq_abc_equation"]);
752 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
753 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
754 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
756 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
757 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
758 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
759 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
760 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
761 "TODO 1 + x + 2*x \<up> 2 = 0";
762 "TODO 1 + x + 2*x \<up> 2 = 0";
763 "TODO 1 + x + 2*x \<up> 2 = 0";
766 val fmz = ["equality (- 2 + 1*x + x \<up> 2 = 0)", "solveFor x", "solutions L"];
767 val (dI',pI',mI') = ("PolyEq",["abcFormula", "degree_2", "polynomial", "univariate", "equation"],
768 ["PolyEq", "solve_d2_polyeq_abc_equation"]);
769 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
770 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
771 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
772 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
773 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
774 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
775 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
776 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
777 case f of Test_Out.FormKF "[x = 1, x = - 2]" => ()
778 | _ => error "polyeq.sml: diff.behav. in - 2 + 1*x + x^2 = 0 -> [x = 1, x = - 2]";
780 val fmz = ["equality ( 2 + 1*x + x \<up> 2 = 0)", "solveFor x", "solutions L"];
781 val (dI',pI',mI') = ("PolyEq",["abcFormula", "degree_2", "polynomial", "univariate", "equation"],
782 ["PolyEq", "solve_d2_polyeq_abc_equation"]);
783 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
784 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
785 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
786 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
787 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
788 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
789 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
790 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
791 "TODO 2 + 1*x + x \<up> 2 = 0";
792 "TODO 2 + 1*x + x \<up> 2 = 0";
793 "TODO 2 + 1*x + x \<up> 2 = 0";
796 val fmz = ["equality (- 2 + x + x \<up> 2 = 0)", "solveFor x", "solutions L"];
797 val (dI',pI',mI') = ("PolyEq",["abcFormula", "degree_2", "polynomial", "univariate", "equation"],
798 ["PolyEq", "solve_d2_polyeq_abc_equation"]);
799 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
800 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
801 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
802 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
803 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
804 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
805 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
806 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
807 case f of Test_Out.FormKF "[x = 1, x = - 2]" => ()
808 | _ => error "polyeq.sml: diff.behav. in - 2 + x + x^2 = 0 -> [x = 1, x = - 2]";
810 val fmz = ["equality ( 2 + x + x \<up> 2 = 0)", "solveFor x", "solutions L"];
811 val (dI',pI',mI') = ("PolyEq",["abcFormula", "degree_2", "polynomial", "univariate", "equation"],
812 ["PolyEq", "solve_d2_polyeq_abc_equation"]);
813 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
814 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
815 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
816 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
817 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
818 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
819 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
820 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
821 "TODO 2 + x + x \<up> 2 = 0";
822 "TODO 2 + x + x \<up> 2 = 0";
823 "TODO 2 + x + x \<up> 2 = 0";
826 val fmz = ["equality (-8 + 2*x \<up> 2 = 0)", "solveFor x", "solutions L"];
827 val (dI',pI',mI') = ("PolyEq",["abcFormula", "degree_2", "polynomial", "univariate", "equation"],
828 ["PolyEq", "solve_d2_polyeq_abc_equation"]);
829 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
830 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
831 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
832 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
833 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
834 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
835 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
836 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
837 case f of Test_Out.FormKF "[x = 2, x = - 2]" => ()
838 | _ => error "polyeq.sml: diff.behav. in -8 + 2*x^2 = 0 -> [x = 2, x = - 2]";
840 val fmz = ["equality ( 8+ 2*x \<up> 2 = 0)", "solveFor x", "solutions L"];
841 val (dI',pI',mI') = ("PolyEq",["abcFormula", "degree_2", "polynomial", "univariate", "equation"],
842 ["PolyEq", "solve_d2_polyeq_abc_equation"]);
843 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
844 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
845 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
846 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
847 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
848 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
849 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
850 "TODO 8+ 2*x \<up> 2 = 0";
851 "TODO 8+ 2*x \<up> 2 = 0";
852 "TODO 8+ 2*x \<up> 2 = 0";
855 val fmz = ["equality (-4 + x \<up> 2 = 0)", "solveFor x", "solutions L"];
856 val (dI',pI',mI') = ("PolyEq",["abcFormula", "degree_2", "polynomial", "univariate", "equation"], ["PolyEq", "solve_d2_polyeq_abc_equation"]);
857 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
858 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
859 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
860 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
861 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
862 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
863 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
864 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
865 case f of Test_Out.FormKF "[x = 2, x = - 2]" => ()
866 | _ => error "polyeq.sml: diff.behav. in -4 + x^2 = 0 -> [x = 2, x = - 2]";
869 val fmz = ["equality ( 4+ x \<up> 2 = 0)", "solveFor x", "solutions L"];
870 val (dI',pI',mI') = ("PolyEq",["abcFormula", "degree_2", "polynomial", "univariate", "equation"], ["PolyEq", "solve_d2_polyeq_abc_equation"]);
871 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
872 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
873 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
874 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
875 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
876 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
877 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
878 "TODO 4+ x \<up> 2 = 0";
879 "TODO 4+ x \<up> 2 = 0";
880 "TODO 4+ x \<up> 2 = 0";
883 val fmz = ["equality (2*x + 2*x \<up> 2 = 0)", "solveFor x", "solutions L"];
884 val (dI',pI',mI') = ("PolyEq",["abcFormula", "degree_2", "polynomial", "univariate", "equation"],
885 ["PolyEq", "solve_d2_polyeq_abc_equation"]);
886 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
887 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
888 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
889 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
890 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
891 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
892 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
893 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
894 case f of Test_Out.FormKF "[x = 0, x = - 1]" => ()
895 | _ => error "polyeq.sml: diff.behav. in x + x^2 = 0 -> [x = 0, x = - 1]";
897 val fmz = ["equality (1*x + x \<up> 2 = 0)", "solveFor x", "solutions L"];
898 val (dI',pI',mI') = ("PolyEq",["abcFormula", "degree_2", "polynomial", "univariate", "equation"],
899 ["PolyEq", "solve_d2_polyeq_abc_equation"]);
900 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
901 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
902 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
903 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
904 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
905 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
906 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
907 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
908 case f of Test_Out.FormKF "[x = 0, x = - 1]" => ()
909 | _ => error "polyeq.sml: diff.behav. in x + x^2 = 0 -> [x = 0, x = - 1]";
912 val fmz = ["equality (x + 2*x \<up> 2 = 0)", "solveFor x", "solutions L"];
913 val (dI',pI',mI') = ("PolyEq",["abcFormula", "degree_2", "polynomial", "univariate", "equation"],
914 ["PolyEq", "solve_d2_polyeq_abc_equation"]);
915 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
916 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
917 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
918 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
919 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
920 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
921 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
922 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
923 case f of Test_Out.FormKF "[x = 0, x = - 1 / 2]" => ()
924 | _ => error "polyeq.sml: diff.behav. in x + x^2 = 0 -> [x = 0, x = - 1 / 2]";
927 val fmz = ["equality (x + x \<up> 2 = 0)", "solveFor x", "solutions L"];
928 val (dI',pI',mI') = ("PolyEq",["abcFormula", "degree_2", "polynomial", "univariate", "equation"],
929 ["PolyEq", "solve_d2_polyeq_abc_equation"]);
930 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
931 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
932 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
933 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
934 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
935 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
936 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
937 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
938 case f of Test_Out.FormKF "[x = 0, x = - 1]" => ()
939 | _ => error "polyeq.sml: diff.behav. in x + x^2 = 0 -> [x = 0, x = - 1]";
942 "----------- (-8 - 2*x + x \<up> 2 = 0), (*Schalk 2, S.67 Nr.31.b----";
943 "----------- (-8 - 2*x + x \<up> 2 = 0), (*Schalk 2, S.67 Nr.31.b----";
944 "----------- (-8 - 2*x + x \<up> 2 = 0), (*Schalk 2, S.67 Nr.31.b----";
945 (*stopped du to TODO.txt WN111014.TODO calculate_Poly < calculate_Rational < calculate_RootRat
946 see --- val rls = calculate_RootRat > calculate_Rational ---
947 calculate_RootRat was a TODO with 2002, requires re-design.
948 see also --- (-8 - 2*x + x \<up> 2 = 0), by rewriting --- below
950 val fmz = ["equality (-8 - 2*x + x \<up> 2 = 0)", (*Schalk 2, S.67 Nr.31.b*)
951 "solveFor x", "solutions L"];
953 ("PolyEq",["degree_2", "expanded", "univariate", "equation"],
954 ["PolyEq", "complete_square"]);
955 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
956 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
957 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
958 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
960 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
961 (*Apply_Method ("PolyEq", "complete_square")*)
962 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
963 (*"-8 - 2 * x + x \<up> 2 = 0", nxt = Rewrite_Set_Inst ... "complete_square*)
964 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
965 (*"-8 + (2 / 2 - x) \<up> 2 = (2 / 2) \<up> 2", nxt = Rewrite("square_explicit1"*)
966 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
967 (*"(2 / 2 - x) \<up> 2 = (2 / 2) \<up> 2 - -8" nxt = Rewrite("root_plus_minus*)
968 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
969 (*"2 / 2 - x = sqrt ((2 / 2) \<up> 2 - -8) |
970 2 / 2 - x = - sqrt ((2 / 2) \<up> 2 - -8)" nxt = Rewr_Inst("bdv_explicit2"*)
971 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
972 (*"2 / 2 - x = sqrt ((2 / 2) \<up> 2 - -8) |
973 - 1*x = - (2 / 2) + - sqrt ((2 / 2) \<up> 2 - -8)"nxt = R_Inst("bdv_explt2"*)
974 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
975 (*"- 1 * x = - (2 / 2) + sqrt ((2 / 2) \<up> 2 - -8) |
976 - 1 * x = (- (2 / 2) + - sqrt ((2 / 2) \<up> 2 - -8))"nxt = bdv_explicit3*)
977 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
978 (*"- 1 * x = - (2 / 2) + sqrt ((2 / 2) \<up> 2 - -8) |
979 x = - 1 * (- (2 / 2) + - sqrt ((2 / 2) \<up> 2 - -8))" nxt = bdv_explicit3*)
980 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
981 (*"x = - 1 * (- (2 / 2) + sqrt ((2 / 2) \<up> 2 - -8)) |
982 x = - 1 * (- (2 / 2) + - sqrt ((2 / 2) \<up> 2 - -8))"nxt = calculate_Rational
983 NOT IMPLEMENTED SINCE 2002 ------------------------------ \<up> \<up> \<up> \<up> \<up> \<up> *)
984 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
985 (*"x = - 2 | x = 4" nxt = Or_to_List*)
986 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
987 (*"[x = - 2, x = 4]" nxt = Check_Postcond*)
988 val (p,_,f,nxt,_,pt) = me nxt p [] pt; f2str f;
990 case f of Form' (Test_Out.FormKF (~1,EdUndef,0,Nundef,"[x = - 2, x = 4]")) => () TODO
991 | _ => error "polyeq.sml: diff.behav. in [x = - 2, x = 4]";
994 "[x = - 1 * - 1 + - 1 * sqrt (2 \<up> 2 / 2 \<up> 2 - -8),\n x = - 1 * - 1 + - 1 * (- 1 * sqrt (2 \<up> 2 / 2 \<up> 2 - -8))]"
995 (*"[x = - 1 * - 1 + - 1 * sqrt (1 \<up> 2 - -8),\n x = - 1 * - 1 + - 1 * (- 1 * sqrt (1 \<up> 2 - -8))]"*)
996 then () else error "polyeq.sml corrected?behav. in [x = - 2, x = 4]";
999 "----------- (-8 - 2*x + x \<up> 2 = 0), by rewriting ---------------";
1000 "----------- (-8 - 2*x + x \<up> 2 = 0), by rewriting ---------------";
1001 "----------- (-8 - 2*x + x \<up> 2 = 0), by rewriting ---------------";
1002 (*stopped du to TODO.txt WN111014.TODO calculate_Poly < calculate_Rational < calculate_RootRat
1003 see --- val rls = calculate_RootRat > calculate_Rational ---*)
1004 val thy = @{theory PolyEq};
1005 val ctxt = Proof_Context.init_global thy;
1006 val inst = [((the o (parseNEW ctxt)) "bdv::real", (the o (parseNEW ctxt)) "x::real")];
1007 val t = (the o (parseNEW ctxt)) "-8 - 2*x + x \<up> 2 = (0::real)";
1009 val rls = complete_square;
1010 val SOME (t,asm) = rewrite_set_inst_ thy true inst rls t;
1011 UnparseC.term t = "-8 + (2 / 2 - x) \<up> 2 = (2 / 2) \<up> 2";
1013 val thm = ThmC.numerals_to_Free @{thm square_explicit1};
1014 val SOME (t,asm) = rewrite_ thy dummy_ord Rule_Set.Empty true thm t;
1015 UnparseC.term t = "(2 / 2 - x) \<up> 2 = (2 / 2) \<up> 2 - -8";
1017 val thm = ThmC.numerals_to_Free @{thm root_plus_minus};
1018 val SOME (t,asm) = rewrite_ thy dummy_ord PolyEq_erls true thm t;
1019 UnparseC.term t = "2 / 2 - x = sqrt ((2 / 2) \<up> 2 - -8) |"^
1020 "\n2 / 2 - x = - 1 * sqrt ((2 / 2) \<up> 2 - -8)";
1022 (*the thm bdv_explicit2* here required to be constrained to ::real*)
1023 val thm = ThmC.numerals_to_Free @{thm bdv_explicit2};
1024 val SOME (t,asm) = rewrite_inst_ thy dummy_ord Rule_Set.Empty true inst thm t;
1025 UnparseC.term t = "2 / 2 - x = sqrt ((2 / 2) \<up> 2 - -8) |"^
1026 "\n- 1 * x = - (2 / 2) + - 1 * sqrt ((2 / 2) \<up> 2 - -8)";
1028 val thm = ThmC.numerals_to_Free @{thm bdv_explicit3};
1029 val SOME (t,asm) = rewrite_inst_ thy dummy_ord Rule_Set.Empty true inst thm t;
1030 UnparseC.term t = "2 / 2 - x = sqrt ((2 / 2) \<up> 2 - -8) |"^
1031 "\nx = - 1 * (- (2 / 2) + - 1 * sqrt ((2 / 2) \<up> 2 - -8))";
1033 val thm = ThmC.numerals_to_Free @{thm bdv_explicit2};
1034 val SOME (t,asm) = rewrite_inst_ thy dummy_ord Rule_Set.Empty true inst thm t;
1035 UnparseC.term t = "- 1 * x = - (2 / 2) + sqrt ((2 / 2) \<up> 2 - -8) |"^
1036 "\nx = - 1 * (- (2 / 2) + - 1 * sqrt ((2 / 2) \<up> 2 - -8))";
1038 val rls = calculate_RootRat;
1039 val SOME (t,asm) = rewrite_set_ thy true rls t;
1040 if UnparseC.term t =
1041 "- 1 * x = - 1 + sqrt (2 \<up> 2 / 2 \<up> 2 - -8) \<or>\nx = - 1 * - 1 + - 1 * (- 1 * sqrt (2 \<up> 2 / 2 \<up> 2 - -8))"
1042 (*"- 1 * x = - 1 + sqrt (2 \<up> 2 / 2 \<up> 2 - -8) |\nx = - 1 * - 1 + - 1 * (- 1 * sqrt (2 \<up> 2 / 2 \<up> 2 - -8))"..isabisac15*)
1043 then () else error "(-8 - 2*x + x \<up> 2 = 0), by rewriting -- ERROR INDICATES IMPROVEMENT";
1044 (*SHOULD BE: UnparseC.term = "x = - 2 | x = 4;*)
1047 "-------------------- (3 - 10*x + 3*x \<up> 2 = 0), ----------------------";
1048 "-------------------- (3 - 10*x + 3*x \<up> 2 = 0), ----------------------";
1049 "-------------------- (3 - 10*x + 3*x \<up> 2 = 0), ----------------------";
1050 "---- test the erls ----";
1051 val t1 = (Thm.term_of o the o (TermC.parse thy)) "0 <= (10/3/2) \<up> 2 - 1";
1052 val SOME (t,_) = rewrite_set_ @{theory PolyEq} false PolyEq_erls t1;
1053 val t' = UnparseC.term t;
1054 (*if t'= \<^const_name>\<open>True\<close> then ()
1055 else error "polyeq.sml: diff.behav. in 'rewrite_set_.. PolyEq_erls";*)
1057 val fmz = ["equality (3 - 10*x + 3*x \<up> 2 = 0)",
1058 "solveFor x", "solutions L"];
1060 ("PolyEq",["degree_2", "expanded", "univariate", "equation"],
1061 ["PolyEq", "complete_square"]);
1062 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
1063 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
1064 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
1065 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
1066 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
1067 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
1068 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
1069 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
1070 (*Apply_Method ("PolyEq", "complete_square")*)
1071 val (p,_,f,nxt,_,pt) = me nxt p [] pt; f2str f;
1073 "----------- (- 16 + 4*x + 2*x \<up> 2 = 0), --------------------------";
1074 "----------- (- 16 + 4*x + 2*x \<up> 2 = 0), --------------------------";
1075 "----------- (- 16 + 4*x + 2*x \<up> 2 = 0), --------------------------";
1076 val fmz = ["equality (- 16 + 4*x + 2*x \<up> 2 = 0)",
1077 "solveFor x", "solutions L"];
1079 ("PolyEq",["degree_2", "expanded", "univariate", "equation"],
1080 ["PolyEq", "complete_square"]);
1081 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
1082 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
1083 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
1084 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
1085 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
1086 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
1087 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
1088 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
1089 (*Apply_Method ("PolyEq", "complete_square")*)
1090 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
1091 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
1092 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
1093 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
1094 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
1095 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
1096 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
1097 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
1098 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
1099 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
1101 case f of Form' (Test_Out.FormKF (~1,EdUndef,0,Nundef,"[x = 2, x = -4]")) => () TODO
1102 | _ => error "polyeq.sml: diff.behav. in [x = 2, x = -4]";