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 "----------- Matthias Goldgruber 2003 trials on rewrite orders -------------------------------";
17 "----------- lin.eq degree_0 -------------------------------------";
18 "----------- test thm's d2_pq_formulsxx[_neg]---------------------";
19 "----------- equality (2 +(-1)*x + x^^^2 = (0::real)) ----------------------------------------";
20 "----------- equality (-2 +(-1)*x + 1*x^^^2 = 0) ---------------------------------------------";
21 "----------- equality (-2 + x + x^^^2 = 0) ---------------------------------------------------";
22 "----------- equality (2 + x + x^^^2 = 0) ----------------------------------------------------";
23 "----------- equality (-2 + x + 1*x^^^2 = 0)) ------------------------------------------------";
24 "----------- equality (1*x + x^^^2 = 0) ----------------------------------------------------";
25 "----------- equality (1*x + 1*x^^^2 = 0) ----------------------------------------------------";
26 "----------- equality (x + x^^^2 = 0) ------------------------------------------------------";
27 "----------- equality (x + 1*x^^^2 = 0) ------------------------------------------------------";
28 "----------- equality (-4 + x^^^2 = 0) -------------------------------------------------------";
29 "----------- equality (4 + 1*x^^^2 = 0) -------------------------------------------------------";
30 "----------- equality (1 +(-1)*x + 2*x^^^2 = 0) ----------------------------------------------";
31 "----------- equality (-1 + x + 2*x^^^2 = 0) -------------------------------------------------";
32 "----------- equality (1 + x + 2*x^^^2 = 0) --------------------------------------------------";
33 "----------- (-8 - 2*x + x^^^2 = 0), (*Schalk 2, S.67 Nr.31.b----";
34 "----------- (-8 - 2*x + x^^^2 = 0), by rewriting ---------------";
35 "----------- (-16 + 4*x + 2*x^^^2 = 0), --------------------------";
36 "-----------------------------------------------------------------";
37 "------ polyeq-2.sml ---------------------------------------------";
38 "----------- (a*b - (a+b)*x + x^^^2 = 0), (*Schalk 2,S.68Nr.44.a*)";
39 "----------- (-64 + x^^^2 = 0), (*Schalk 2, S.66 Nr.1.a~--------*)";
40 "----------- (-147 + 3*x^^^2 = 0), (*Schalk 2, S.66 Nr.1.b------*)";
41 "----------- (3*x - 1 - (5*x - (2 - 4*x)) = -11),(*Schalk Is86Bsp5";
42 "----------- ((x+1)*(x+2) - (3*x - 2)^^^2=.. Schalk II s.68 Bsp 37";
43 "----------- rls make_polynomial_in ------------------------------";
44 "----------- interSteps ([1],Res); on Schalk Is86Bsp5-------------";
45 "----------- rls d2_polyeq_bdv_only_simplify ---------------------";
46 "-----------------------------------------------------------------";
47 "-----------------------------------------------------------------";
49 "----------- tests on predicates in problems ---------------------";
50 "----------- tests on predicates in problems ---------------------";
51 "----------- tests on predicates in problems ---------------------";
52 (* Rewrite.trace_on:=true;
53 Rewrite.trace_on:=false;
55 val t1 = (Thm.term_of o the o (parse thy)) "lhs (-8 - 2*x + x^^^2 = 0)";
56 val SOME (t,_) = rewrite_set_ @{theory PolyEq} false PolyEq_prls t1;
57 if ((UnparseC.term t) = "-8 - 2 * x + x ^^^ 2") then ()
58 else error "polyeq.sml: diff.behav. in lhs";
60 val t2 = (Thm.term_of o the o (parse thy)) "(-8 - 2*x + x^^^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 (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 (parse thy)) "(-8 + (-1)*2*x + x^^^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 (parse thy)) "(lhs (-8 + (-1)*2*x + x^^^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";
81 val t6 = (Thm.term_of o the o (parse thy)) "(lhs (-8 - 2*x + x^^^2 = 0)) is_expanded_in x";
82 val SOME (t,_) = rewrite_set_ @{theory PolyEq} false PolyEq_prls t6;
83 if (UnparseC.term t) = "True" then ()
84 else error "polyeq.sml: diff.behav. 5 in is_expended_in";
86 val t3 = (Thm.term_of o the o (parse thy))"((-8 - 2*x + x^^^2) has_degree_in x) = 2";
87 val SOME (t,_) = rewrite_set_ @{theory PolyEq} false PolyEq_prls t3;
88 if (UnparseC.term t) = "True" then ()
89 else error "polyeq.sml: diff.behav. in has_degree_in_in";
91 val t3 = (Thm.term_of o the o (parse thy)) "((sqrt(x)) has_degree_in x) = 2";
92 val SOME (t,_) = rewrite_set_ @{theory PolyEq} false PolyEq_prls t3;
93 if (UnparseC.term t) = "False" then ()
94 else error "polyeq.sml: diff.behav. 6 in has_degree_in_in";
96 val t4 = (Thm.term_of o the o (parse thy))
97 "((-8 - 2*x + x^^^2) has_degree_in x) = 1";
98 val SOME (t,_) = rewrite_set_ @{theory PolyEq} false PolyEq_prls t4;
99 if (UnparseC.term t) = "False" then ()
100 else error "polyeq.sml: diff.behav. 7 in has_degree_in_in";
102 val t5 = (Thm.term_of o the o (parse thy))
103 "((-8 - 2*x + x^^^2) has_degree_in x) = 2";
104 val SOME (t,_) = rewrite_set_ @{theory PolyEq} false PolyEq_prls t5;
105 if (UnparseC.term t) = "True" then ()
106 else error "polyeq.sml: diff.behav. 8 in has_degree_in_in";
108 "----------- test matching problems --------------------------0---";
109 "----------- test matching problems --------------------------0---";
110 "----------- test matching problems --------------------------0---";
111 val fmz = ["equality (-8 - 2*x + x^^^2 = 0)", "solveFor x","solutions L"];
112 if match_pbl fmz (get_pbt ["expanded","univariate","equation"]) =
113 Matches' {Find = [Correct "solutions L"],
115 Given = [Correct "equality (-8 - 2 * x + x ^^^ 2 = 0)", Correct "solveFor x"],
116 Where = [Correct "matches (?a = 0) (-8 - 2 * x + x ^^^ 2 = 0)",
117 Correct "lhs (-8 - 2 * x + x ^^^ 2 = 0) is_expanded_in x"],
119 then () else error "match_pbl [expanded,univariate,equation]";
121 if match_pbl fmz (get_pbt ["degree_2","expanded","univariate","equation"]) =
122 Matches' {Find = [Correct "solutions L"],
124 Given = [Correct "equality (-8 - 2 * x + x ^^^ 2 = 0)", Correct "solveFor x"],
125 Where = [Correct "lhs (-8 - 2 * x + x ^^^ 2 = 0) has_degree_in x = 2"],
126 Relate = []} (*before WN110906 was: has_degree_in x =!= 2"]*)
127 then () else error "match_pbl [degree_2,expanded,univariate,equation]";
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 "----------- prep. for introduction of Matthias Goldgruber 2003 trials on rewrite orders -----";
133 (*##################################################################################
134 -----------28.2.03: war nicht upgedatet und ausgeklammert in ROOT.ML-->Test_Isac.thy
136 (*Aufgabe zum Einstieg in die Arbeit...*)
137 val t = (Thm.term_of o the o (parse thy)) "a*b - (a+b)*x + x^^^2 = 0";
138 (*ein 'ruleset' aus Poly.ML wird angewandt...*)
139 val SOME (t,_) = rewrite_set_ thy Poly_erls false make_polynomial t;
141 "a * b + (-1 * (a * x) + (-1 * (b * x) + x ^^^ 2)) = 0";
143 rewrite_set_inst_ thy Poly_erls false [("bdv","a")] make_polynomial_in t;
145 "x ^^^ 2 + (-1 * (b * x) + (-1 * (x * a) + b * a)) = 0";
146 (* bei Verwendung von "size_of-term" nach MG :*)
147 (*"x ^^^ 2 + (-1 * (b * x) + (b * a + -1 * (x * a))) = 0" !!! *)
149 (*wir holen 'a' wieder aus der Klammerung heraus...*)
150 val SOME (t,_) = rewrite_set_ thy Poly_erls false discard_parentheses t;
152 "x ^^^ 2 + -1 * b * x + -1 * x * a + b * a = 0";
153 (* "x ^^^ 2 + -1 * b * x + b * a + -1 * x * a = 0" !!! *)
156 rewrite_set_inst_ thy Poly_erls false [("bdv","a")] make_polynomial_in t;
158 "x ^^^ 2 + (-1 * (b * x) + a * (b + -1 * x)) = 0";
159 (*da sind wir fast am Ziel: make_polynomial_in 'a' sollte ergeben
160 "x ^^^ 2 + (-1 * (b * x)) + (b + -1 * x) * a = 0"*)
162 (*das rewriting l"asst sich beobachten mit
163 Rewrite.trace_on := false;
166 "------15.11.02 --------------------------";
167 val t = (Thm.term_of o the o (parse thy)) "1 + a * x + b * x";
168 val bdv = (Thm.term_of o the o (parse thy)) "bdv";
169 val a = (Thm.term_of o the o (parse thy)) "a";
171 Rewrite.trace_on := false;
172 (* Anwenden einer Regelmenge aus Termorder.ML: *)
174 rewrite_set_inst_ thy false [(bdv,a)] make_polynomial_in t;
177 rewrite_set_ thy false discard_parentheses t;
181 val t = (Thm.term_of o the o (parse thy)) "1 + a * (x + b * x) + a^^^2";
183 rewrite_set_inst_ thy false [(bdv,a)] make_polynomial_in t;
186 rewrite_set_ thy false discard_parentheses t;
188 "1 + (x + b * x) * a + a ^^^ 2";
190 val t = (Thm.term_of o the o (parse thy)) "1 + a ^^^2 * x + b * a + 7*a^^^2";
192 rewrite_set_inst_ thy false [(bdv,a)] make_polynomial_in t;
195 rewrite_set_ thy false discard_parentheses t;
197 "1 + b * a + (7 + x) * a ^^^ 2";
200 Prog_Expr.thy grundlegende Algebra
204 RootRat.thy Wurzen + Br"uche
205 Termorder.thy BITTE NUR HIERHER SCHREIBEN (...WN03)
207 get_thm Termorder.thy "bdv_n_collect";
208 get_thm (theory "Isac_Knowledge") "bdv_n_collect";
210 val t = (Thm.term_of o the o (parse thy)) "a ^^^2 * x + 7 * a^^^2";
212 rewrite_set_inst_ thy false [(bdv,a)] make_polynomial_in t;
215 rewrite_set_ thy false discard_parentheses t;
219 val t = (Thm.term_of o the o (parse Termorder.thy)) "Pi";
221 val t = (Thm.term_of o the o (parseold thy)) "7";
222 ##################################################################################*)
225 "----------- Matthias Goldgruber 2003 trials on rewrite orders -------------------------------";
226 "----------- Matthias Goldgruber 2003 trials on rewrite orders -------------------------------";
227 "----------- Matthias Goldgruber 2003 trials on rewrite orders -------------------------------";
228 val substa = [(TermC.empty, (Thm.term_of o the o (parse thy)) "a")];
229 val substb = [(TermC.empty, (Thm.term_of o the o (parse thy)) "b")];
230 val substx = [(TermC.empty, (Thm.term_of o the o (parse thy)) "x")];
232 val x1 = (Thm.term_of o the o (parse thy)) "a + b + x";
233 val x2 = (Thm.term_of o the o (parse thy)) "a + x + b";
234 val x3 = (Thm.term_of o the o (parse thy)) "a + x + b";
235 val x4 = (Thm.term_of o the o (parse thy)) "x + a + b";
237 if ord_make_polynomial_in true thy substx (x1,x2) = true(*LESS *) then ()
238 else error "termorder.sml diff.behav ord_make_polynomial_in #1";
240 if ord_make_polynomial_in true thy substa (x1,x2) = true(*LESS *) then ()
241 else error "termorder.sml diff.behav ord_make_polynomial_in #2";
243 if ord_make_polynomial_in true thy substb (x1,x2) = false(*GREATER*) then ()
244 else error "termorder.sml diff.behav ord_make_polynomial_in #3";
246 val aa = (Thm.term_of o the o (parse thy)) "-1 * a * x";
247 val bb = (Thm.term_of o the o (parse thy)) "x^^^3";
248 ord_make_polynomial_in true thy substx (aa, bb);
251 val aa = (Thm.term_of o the o (parse thy)) "-1 * a * x";
252 val bb = (Thm.term_of o the o (parse thy)) "x^^^3";
253 ord_make_polynomial_in true thy substa (aa, bb);
254 false; (* => GREATER *)
256 (* und nach dem Re-engineering der Termorders in den 'rulesets'
257 kannst Du die 'gr"osste' Variable frei w"ahlen: *)
258 val bdv= (Thm.term_of o the o (parse thy)) "''bdv''";
259 val x = (Thm.term_of o the o (parse thy)) "x";
260 val a = (Thm.term_of o the o (parse thy)) "a";
261 val b = (Thm.term_of o the o (parse thy)) "b";
262 val SOME (t',_) = rewrite_set_inst_ thy false [(bdv,a)] make_polynomial_in x2;
263 if UnparseC.term t' = "b + x + a" then ()
264 else error "termorder.sml diff.behav ord_make_polynomial_in #11";
266 val NONE = rewrite_set_inst_ thy false [(bdv,b)] make_polynomial_in x2;
268 val SOME (t',_) = rewrite_set_inst_ thy false [(bdv,x)] make_polynomial_in x2;
269 if UnparseC.term t' = "a + b + x" then ()
270 else error "termorder.sml diff.behav ord_make_polynomial_in #13";
272 val ppp' = "-6 + -5*x + x^^^3 + -1*x^^^2 + -1*x^^^3 + -14*x^^^2";
273 val ppp = (Thm.term_of o the o (parse thy)) ppp';
274 val SOME (t',_) = rewrite_set_inst_ thy false [(bdv,x)] make_polynomial_in ppp;
275 if UnparseC.term t' = "-6 + -5 * x + -15 * x ^^^ 2 + 0" then ()
276 else error "termorder.sml diff.behav ord_make_polynomial_in #14";
278 val SOME (t', _) = rewrite_set_inst_ thy false [(bdv,x)] make_polynomial_in ppp;
279 if UnparseC.term t' = "-6 + -5 * x + -15 * x ^^^ 2 + 0" then ()
280 else error "termorder.sml diff.behav ord_make_polynomial_in #15";
282 val ttt' = "(3*x + 5)/18";
283 val ttt = (Thm.term_of o the o (parse thy)) ttt';
284 val SOME (uuu,_) = rewrite_set_inst_ thy false [(bdv,x)] make_polynomial_in ttt;
285 if UnparseC.term uuu = "(5 + 3 * x) / 18" then ()
286 else error "termorder.sml diff.behav ord_make_polynomial_in #16a";
288 (*============ inhibit exn WN120316 ==============================================
289 val SOME (uuu,_) = rewrite_set_ thy false make_polynomial ttt;
290 if UnparseC.term uuu = "(5 + 3 * x) / 18" then ()
291 else error "termorder.sml diff.behav ord_make_polynomial_in #16b";
292 ============ inhibit exn WN120316 ==============================================*)
295 "----------- lin.eq degree_0 -------------------------------------";
296 "----------- lin.eq degree_0 -------------------------------------";
297 "----------- lin.eq degree_0 -------------------------------------";
298 "----- d0_false ------";
299 val fmz = ["equality (1 = (0::real))", "solveFor x", "solutions L"];
300 val (dI',pI',mI') = ("PolyEq",["degree_0","polynomial","univariate","equation"],
301 ["PolyEq","solve_d0_polyeq_equation"]);
302 (*=== inhibit exn WN110914: declare_constraints doesnt work with ThmC.numerals_to_Free ========
303 TODO: change to "equality (x + -1*x = (0::real))"
304 and search for an appropriate problem and method.
306 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
307 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
308 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
309 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
310 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
311 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
312 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
313 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[]")) => ()
314 | _ => error "polyeq.sml: diff.behav. in 1 = 0 -> []";
316 "----- d0_true ------";
317 val fmz = ["equality (0 = (0::real))", "solveFor x","solutions L"];
318 val (dI',pI',mI') = ("PolyEq",["degree_0","polynomial","univariate","equation"],
319 ["PolyEq","solve_d0_polyeq_equation"]);
320 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
321 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
322 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
323 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
324 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
325 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
326 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
327 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"UniversalList")) => ()
328 | _ => error "polyeq.sml: diff.behav. in 0 = 0 -> UniversalList";
329 ============ inhibit exn WN110914 ============================================*)
331 "----------- test thm's d2_pq_formulsxx[_neg]---------------------";
332 "----------- test thm's d2_pq_formulsxx[_neg]---------------------";
333 "----------- test thm's d2_pq_formulsxx[_neg]---------------------";
334 "----- d2_pqformula1 ------!!!!";
335 val fmz = ["equality (-1/8 + (-1/4)*z + z^^^2 = (0::real))", "solveFor z","solutions L"];
337 ("Isac_Knowledge", ["pqFormula","degree_2","polynomial","univariate","equation"], ["no_met"]);
338 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
339 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
340 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
341 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
342 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
343 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
344 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
345 val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*Apply_Method ["PolyEq", "solve_d2_polyeq_pq_equation"]*)
346 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
347 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
348 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
349 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
351 (*[z = 1 / 8 + sqrt (9 / 16) / 2, z = 1 / 8 + -1 * sqrt (9 / 16) / 2] TODO sqrt*)
352 val (p,_,f,nxt,_,pt) = me nxt p [] pt; (*nxt =..,Check_elementwise "Assumptions")*)
353 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
354 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
356 if p = ([], Res) andalso
357 f2str f = "[z = 1 / 8 + sqrt (9 / 16) / 2, z = 1 / 8 + -1 * sqrt (9 / 16) / 2]" then
358 case nxt of End_Proof' => () | _ => error "(-1/8 + (-1/4)*z + z^^^2 = (0::real)) CHANGED 1"
359 else error "(-1/8 + (-1/4)*z + z^^^2 = (0::real)) CHANGED 2";
361 "----------- equality (2 +(-1)*x + x^^^2 = (0::real)) ----------------------------------------";
362 "----------- equality (2 +(-1)*x + x^^^2 = (0::real)) ----------------------------------------";
363 "----------- equality (2 +(-1)*x + x^^^2 = (0::real)) ----------------------------------------";
364 "----- d2_pqformula1_neg ------";
365 val fmz = ["equality (2 +(-1)*x + x^^^2 = (0::real))", "solveFor x","solutions L"];
366 val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"], ["PolyEq","solve_d2_polyeq_pq_equation"]);
367 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
368 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
369 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
370 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
371 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
372 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
374 ([1],Res) False Or_to_List)*)
375 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
377 ([2],Res) [] Check_elementwise "Assumptions"*)
378 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
379 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
380 val asm = Ctree.get_assumptions pt p;
381 if f2str f = "[]" andalso
382 UnparseC.terms asm = "[\"lhs (2 + -1 * x + x ^^^ 2 = 0) is_poly_in x\"," ^
383 "\"lhs (2 + -1 * x + x ^^^ 2 = 0) has_degree_in x = 2\"]" then ()
384 else error "polyeq.sml: diff.behav. in 2 +(-1)*x + x^^^2 = 0";
386 "----------- equality (-2 +(-1)*x + 1*x^^^2 = 0) ---------------------------------------------";
387 "----------- equality (-2 +(-1)*x + 1*x^^^2 = 0) ---------------------------------------------";
388 "----------- equality (-2 +(-1)*x + 1*x^^^2 = 0) ---------------------------------------------";
389 "----- d2_pqformula2 ------";
390 val fmz = ["equality (-2 +(-1)*x + 1*x^^^2 = 0)", "solveFor x","solutions L"];
391 val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"],
392 ["PolyEq","solve_d2_polyeq_pq_equation"]);
394 val (mI,m) = ("Init_Proof",Init_Proof (fmz, (dI',pI',mI')));
395 val (p,_,f,nxt,_,pt) = me (mI,m) p [] EmptyPtree;*)
396 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
397 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
398 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
399 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
400 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
401 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
403 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
404 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
405 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
406 case f of FormKF "[x = 2, x = -1]" => ()
407 | _ => error "polyeq.sml: diff.behav. in -2 + (-1)*x + x^2 = 0 -> [x = 2, x = -1]";
410 "----------- equality (-2 + x + x^^^2 = 0) ---------------------------------------------------";
411 "----------- equality (-2 + x + x^^^2 = 0) ---------------------------------------------------";
412 "----------- equality (-2 + x + x^^^2 = 0) ---------------------------------------------------";
413 "----- d2_pqformula3 ------";
415 val fmz = ["equality (-2 + x + x^^^2 = 0)", "solveFor x","solutions L"];
416 val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"],
417 ["PolyEq","solve_d2_polyeq_pq_equation"]);
418 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
419 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
420 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
421 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
422 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
423 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
425 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
426 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
427 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
428 case f of FormKF "[x = 1, x = -2]" => ()
429 | _ => error "polyeq.sml: diff.behav. in -2 + x + x^2 = 0-> [x = 1, x = -2]";
432 "----------- equality (2 + x + x^^^2 = 0) ----------------------------------------------------";
433 "----------- equality (2 + x + x^^^2 = 0) ----------------------------------------------------";
434 "----------- equality (2 + x + x^^^2 = 0) ----------------------------------------------------";
435 "----- d2_pqformula3_neg ------";
436 val fmz = ["equality (2 + x + x^^^2 = 0)", "solveFor x","solutions L"];
437 val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"],
438 ["PolyEq","solve_d2_polyeq_pq_equation"]);
439 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
440 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
441 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
442 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
443 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
444 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
446 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
447 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
448 "TODO 2 + x + x^^^2 = 0";
449 "TODO 2 + x + x^^^2 = 0";
450 "TODO 2 + x + x^^^2 = 0";
452 "----------- equality (-2 + x + 1*x^^^2 = 0)) ------------------------------------------------";
453 "----------- equality (-2 + x + 1*x^^^2 = 0)) ------------------------------------------------";
454 "----------- equality (-2 + x + 1*x^^^2 = 0)) ------------------------------------------------";
455 "----- d2_pqformula4 ------";
456 val fmz = ["equality (-2 + x + 1*x^^^2 = 0)", "solveFor x","solutions L"];
457 val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"],
458 ["PolyEq","solve_d2_polyeq_pq_equation"]);
459 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
460 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
461 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
462 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
463 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
464 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
465 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
466 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
467 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
468 case f of FormKF "[x = 1, x = -2]" => ()
469 | _ => error "polyeq.sml: diff.behav. in -2 + x + 1*x^^^2 = 0 -> [x = 1, x = -2]";
471 "----------- equality (1*x + x^^^2 = 0) ----------------------------------------------------";
472 "----------- equality (1*x + x^^^2 = 0) ----------------------------------------------------";
473 "----------- equality (1*x + x^^^2 = 0) ----------------------------------------------------";
474 "----- d2_pqformula5 ------";
475 val fmz = ["equality (1*x + x^^^2 = 0)", "solveFor x","solutions L"];
476 val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"],
477 ["PolyEq","solve_d2_polyeq_pq_equation"]);
478 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
479 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
480 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
481 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
482 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
483 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
484 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
485 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
486 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
487 case f of FormKF "[x = 0, x = -1]" => ()
488 | _ => error "polyeq.sml: diff.behav. in 1*x + x^2 = 0 -> [x = 0, x = -1]";
490 "----------- equality (1*x + 1*x^^^2 = 0) ----------------------------------------------------";
491 "----------- equality (1*x + 1*x^^^2 = 0) ----------------------------------------------------";
492 "----------- equality (1*x + 1*x^^^2 = 0) ----------------------------------------------------";
493 "----- d2_pqformula6 ------";
494 val fmz = ["equality (1*x + 1*x^^^2 = 0)", "solveFor x","solutions L"];
495 val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"],
496 ["PolyEq","solve_d2_polyeq_pq_equation"]);
497 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
498 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
499 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
500 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
501 val (p,_,f,nxt,_,pt) = me nxt p [] pt; 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;
506 case f of FormKF "[x = 0, x = -1]" => ()
507 | _ => error "polyeq.sml: diff.behav. in 1*x + 1*x^2 = 0 -> [x = 0, x = -1]";
509 "----------- equality (x + x^^^2 = 0) ------------------------------------------------------";
510 "----------- equality (x + x^^^2 = 0) ------------------------------------------------------";
511 "----------- equality (x + x^^^2 = 0) ------------------------------------------------------";
512 "----- d2_pqformula7 ------";
514 val fmz = ["equality ( x + x^^^2 = 0)", "solveFor x","solutions L"];
515 val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"],
516 ["PolyEq","solve_d2_polyeq_pq_equation"]);
517 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
518 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
519 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
520 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
521 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
522 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
523 val (p,_,f,nxt,_,pt) = me nxt p [] pt; 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;
526 case f of FormKF "[x = 0, x = -1]" => ()
527 | _ => error "polyeq.sml: diff.behav. in x + x^2 = 0 -> [x = 0, x = -1]";
529 "----------- equality (x + 1*x^^^2 = 0) ------------------------------------------------------";
530 "----------- equality (x + 1*x^^^2 = 0) ------------------------------------------------------";
531 "----------- equality (x + 1*x^^^2 = 0) ------------------------------------------------------";
532 "----- d2_pqformula8 ------";
533 val fmz = ["equality (x + 1*x^^^2 = 0)", "solveFor x","solutions L"];
534 val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"],
535 ["PolyEq","solve_d2_polyeq_pq_equation"]);
536 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
537 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
538 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
539 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
540 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
541 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
542 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
543 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
544 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
545 case f of FormKF "[x = 0, x = -1]" => ()
546 | _ => error "polyeq.sml: diff.behav. in x + 1*x^2 = 0 -> [x = 0, x = -1]";
548 "----------- equality (-4 + x^^^2 = 0) -------------------------------------------------------";
549 "----------- equality (-4 + x^^^2 = 0) -------------------------------------------------------";
550 "----------- equality (-4 + x^^^2 = 0) -------------------------------------------------------";
551 "----- d2_pqformula9 ------";
552 val fmz = ["equality (-4 + x^^^2 = 0)", "solveFor x","solutions L"];
553 val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"],
554 ["PolyEq","solve_d2_polyeq_pq_equation"]);
555 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
556 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
557 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
558 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
559 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
560 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
561 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
562 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
563 case f of FormKF "[x = 2, x = -2]" => ()
564 | _ => error "polyeq.sml: diff.behav. in -4 + x^2 = 0 -> [x = 2, x = -2]";
567 "----------- equality (4 + 1*x^^^2 = 0) -------------------------------------------------------";
568 "----------- equality (4 + 1*x^^^2 = 0) -------------------------------------------------------";
569 "----------- equality (4 + 1*x^^^2 = 0) -------------------------------------------------------";
570 "----- d2_pqformula9_neg ------";
571 val fmz = ["equality (4 + 1*x^^^2 = 0)", "solveFor x","solutions L"];
572 val (dI',pI',mI') = ("PolyEq",["pqFormula","degree_2","polynomial","univariate","equation"],
573 ["PolyEq","solve_d2_polyeq_pq_equation"]);
574 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
575 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
576 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
577 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
578 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
579 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
580 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
581 "TODO 4 + 1*x^^^2 = 0";
582 "TODO 4 + 1*x^^^2 = 0";
583 "TODO 4 + 1*x^^^2 = 0";
585 "-------------------- test thm's d2_abc_formulsxx[_neg]-----";
586 "-------------------- test thm's d2_abc_formulsxx[_neg]-----";
587 "-------------------- test thm's d2_abc_formulsxx[_neg]-----";
588 val fmz = ["equality (-1 +(-1)*x + 2*x^^^2 = 0)", "solveFor x","solutions L"];
589 val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
590 ["PolyEq","solve_d2_polyeq_abc_equation"]);
591 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
592 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
593 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
594 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
595 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
596 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
597 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
598 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
599 case f of FormKF "[x = 1, x = -1 / 2]" => ()
600 | _ => error "polyeq.sml: diff.behav. in -1 + (-1)*x + 2*x^2 = 0 -> [x = 1, x = -1/2]";
602 "----------- equality (1 +(-1)*x + 2*x^^^2 = 0) ----------------------------------------------";
603 "----------- equality (1 +(-1)*x + 2*x^^^2 = 0) ----------------------------------------------";
604 "----------- equality (1 +(-1)*x + 2*x^^^2 = 0) ----------------------------------------------";
605 val fmz = ["equality (1 +(-1)*x + 2*x^^^2 = 0)", "solveFor x","solutions L"];
606 val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
607 ["PolyEq","solve_d2_polyeq_abc_equation"]);
608 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
609 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
610 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
611 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
613 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
614 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
615 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
616 "TODO 1 +(-1)*x + 2*x^^^2 = 0";
617 "TODO 1 +(-1)*x + 2*x^^^2 = 0";
618 "TODO 1 +(-1)*x + 2*x^^^2 = 0";
621 "----------- equality (-1 + x + 2*x^^^2 = 0) -------------------------------------------------";
622 "----------- equality (-1 + x + 2*x^^^2 = 0) -------------------------------------------------";
623 "----------- equality (-1 + x + 2*x^^^2 = 0) -------------------------------------------------";
625 val fmz = ["equality (-1 + x + 2*x^^^2 = 0)", "solveFor x","solutions L"];
626 val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
627 ["PolyEq","solve_d2_polyeq_abc_equation"]);
628 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
629 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
630 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
632 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
633 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
634 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
635 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
637 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
638 case f of FormKF "[x = 1 / 2, x = -1]" => ()
639 | _ => error "polyeq.sml: diff.behav. in -1 + x + 2*x^2 = 0 -> [x = 1/2, x = -1]";
642 "----------- equality (1 + x + 2*x^^^2 = 0) --------------------------------------------------";
643 "----------- equality (1 + x + 2*x^^^2 = 0) --------------------------------------------------";
644 "----------- equality (1 + x + 2*x^^^2 = 0) --------------------------------------------------";
645 val fmz = ["equality (1 + x + 2*x^^^2 = 0)", "solveFor x","solutions L"];
646 val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
647 ["PolyEq","solve_d2_polyeq_abc_equation"]);
648 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
649 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
650 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
652 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
653 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
654 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
655 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
656 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
657 "TODO 1 + x + 2*x^^^2 = 0";
658 "TODO 1 + x + 2*x^^^2 = 0";
659 "TODO 1 + x + 2*x^^^2 = 0";
662 val fmz = ["equality (-2 + 1*x + x^^^2 = 0)", "solveFor x","solutions L"];
663 val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
664 ["PolyEq","solve_d2_polyeq_abc_equation"]);
665 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
666 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
667 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
668 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
669 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
670 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
671 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
672 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
673 case f of FormKF "[x = 1, x = -2]" => ()
674 | _ => error "polyeq.sml: diff.behav. in -2 + 1*x + x^2 = 0 -> [x = 1, x = -2]";
676 val fmz = ["equality ( 2 + 1*x + x^^^2 = 0)", "solveFor x","solutions L"];
677 val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
678 ["PolyEq","solve_d2_polyeq_abc_equation"]);
679 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
680 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; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
685 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
686 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
687 "TODO 2 + 1*x + x^^^2 = 0";
688 "TODO 2 + 1*x + x^^^2 = 0";
689 "TODO 2 + 1*x + x^^^2 = 0";
692 val fmz = ["equality (-2 + x + x^^^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 FormKF "[x = 1, x = -2]" => ()
704 | _ => error "polyeq.sml: diff.behav. in -2 + x + x^2 = 0 -> [x = 1, x = -2]";
706 val fmz = ["equality ( 2 + x + x^^^2 = 0)", "solveFor x","solutions L"];
707 val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
708 ["PolyEq","solve_d2_polyeq_abc_equation"]);
709 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
710 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
711 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
712 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
713 val (p,_,f,nxt,_,pt) = me nxt p [] pt; 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;
716 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
717 "TODO 2 + x + x^^^2 = 0";
718 "TODO 2 + x + x^^^2 = 0";
719 "TODO 2 + x + x^^^2 = 0";
722 val fmz = ["equality (-8 + 2*x^^^2 = 0)", "solveFor x","solutions L"];
723 val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
724 ["PolyEq","solve_d2_polyeq_abc_equation"]);
725 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
726 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
727 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
728 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
729 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
730 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
731 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
732 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
733 case f of FormKF "[x = 2, x = -2]" => ()
734 | _ => error "polyeq.sml: diff.behav. in -8 + 2*x^2 = 0 -> [x = 2, x = -2]";
736 val fmz = ["equality ( 8+ 2*x^^^2 = 0)", "solveFor x","solutions L"];
737 val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
738 ["PolyEq","solve_d2_polyeq_abc_equation"]);
739 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
740 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 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
743 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
744 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
745 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
746 "TODO 8+ 2*x^^^2 = 0";
747 "TODO 8+ 2*x^^^2 = 0";
748 "TODO 8+ 2*x^^^2 = 0";
751 val fmz = ["equality (-4 + x^^^2 = 0)", "solveFor x","solutions L"];
752 val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"], ["PolyEq","solve_d2_polyeq_abc_equation"]);
753 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
754 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
755 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; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
761 case f of FormKF "[x = 2, x = -2]" => ()
762 | _ => error "polyeq.sml: diff.behav. in -4 + x^2 = 0 -> [x = 2, x = -2]";
765 val fmz = ["equality ( 4+ x^^^2 = 0)", "solveFor x","solutions L"];
766 val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"], ["PolyEq","solve_d2_polyeq_abc_equation"]);
767 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
768 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
769 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
770 val (p,_,f,nxt,_,pt) = me nxt p [] pt; 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;
779 val fmz = ["equality (2*x + 2*x^^^2 = 0)", "solveFor x","solutions L"];
780 val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
781 ["PolyEq","solve_d2_polyeq_abc_equation"]);
782 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
783 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
784 val (p,_,f,nxt,_,pt) = me nxt p [] pt; 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 case f of FormKF "[x = 0, x = -1]" => ()
791 | _ => error "polyeq.sml: diff.behav. in x + x^2 = 0 -> [x = 0, x = -1]";
793 val fmz = ["equality (1*x + x^^^2 = 0)", "solveFor x","solutions L"];
794 val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
795 ["PolyEq","solve_d2_polyeq_abc_equation"]);
796 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
797 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
798 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
799 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
800 val (p,_,f,nxt,_,pt) = me nxt p [] pt; 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 case f of FormKF "[x = 0, x = -1]" => ()
805 | _ => error "polyeq.sml: diff.behav. in x + x^2 = 0 -> [x = 0, x = -1]";
808 val fmz = ["equality (x + 2*x^^^2 = 0)", "solveFor x","solutions L"];
809 val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
810 ["PolyEq","solve_d2_polyeq_abc_equation"]);
811 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
812 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
813 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
814 val (p,_,f,nxt,_,pt) = me nxt p [] pt; 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 case f of FormKF "[x = 0, x = -1 / 2]" => ()
820 | _ => error "polyeq.sml: diff.behav. in x + x^2 = 0 -> [x = 0, x = -1 / 2]";
823 val fmz = ["equality (x + x^^^2 = 0)", "solveFor x","solutions L"];
824 val (dI',pI',mI') = ("PolyEq",["abcFormula","degree_2","polynomial","univariate","equation"],
825 ["PolyEq","solve_d2_polyeq_abc_equation"]);
826 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
827 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
828 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
829 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
830 val (p,_,f,nxt,_,pt) = me nxt p [] pt; 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 case f of FormKF "[x = 0, x = -1]" => ()
835 | _ => error "polyeq.sml: diff.behav. in x + x^2 = 0 -> [x = 0, x = -1]";
838 "----------- (-8 - 2*x + x^^^2 = 0), (*Schalk 2, S.67 Nr.31.b----";
839 "----------- (-8 - 2*x + x^^^2 = 0), (*Schalk 2, S.67 Nr.31.b----";
840 "----------- (-8 - 2*x + x^^^2 = 0), (*Schalk 2, S.67 Nr.31.b----";
841 (*stopped du to TODO.txt WN111014.TODO calculate_Poly < calculate_Rational < calculate_RootRat
842 see --- val rls = calculate_RootRat > calculate_Rational ---
843 calculate_RootRat was a TODO with 2002, requires re-design.
844 see also --- (-8 - 2*x + x^^^2 = 0), by rewriting --- below
846 val fmz = ["equality (-8 - 2*x + x^^^2 = 0)", (*Schalk 2, S.67 Nr.31.b*)
847 "solveFor x","solutions L"];
849 ("PolyEq",["degree_2","expanded","univariate","equation"],
850 ["PolyEq","complete_square"]);
851 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
852 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
853 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
854 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
856 val (p,_,f,nxt,_,pt) = me nxt p [] pt; val (p,_,f,nxt,_,pt) = me nxt p [] pt;
857 (*Apply_Method ("PolyEq","complete_square")*)
858 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
859 (*"-8 - 2 * x + x ^^^ 2 = 0", nxt = Rewrite_Set_Inst ... "complete_square*)
860 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
861 (*"-8 + (2 / 2 - x) ^^^ 2 = (2 / 2) ^^^ 2", nxt = Rewrite("square_explicit1"*)
862 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
863 (*"(2 / 2 - x) ^^^ 2 = (2 / 2) ^^^ 2 - -8" nxt = Rewrite("root_plus_minus*)
864 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
865 (*"2 / 2 - x = sqrt ((2 / 2) ^^^ 2 - -8) |
866 2 / 2 - x = - sqrt ((2 / 2) ^^^ 2 - -8)" nxt = Rewr_Inst("bdv_explicit2"*)
867 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
868 (*"2 / 2 - x = sqrt ((2 / 2) ^^^ 2 - -8) |
869 -1*x = - (2 / 2) + - sqrt ((2 / 2) ^^^ 2 - -8)"nxt = R_Inst("bdv_explt2"*)
870 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
871 (*"-1 * x = - (2 / 2) + sqrt ((2 / 2) ^^^ 2 - -8) |
872 -1 * x = (- (2 / 2) + - sqrt ((2 / 2) ^^^ 2 - -8))"nxt = bdv_explicit3*)
873 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
874 (*"-1 * x = - (2 / 2) + sqrt ((2 / 2) ^^^ 2 - -8) |
875 x = -1 * (- (2 / 2) + - sqrt ((2 / 2) ^^^ 2 - -8))" nxt = bdv_explicit3*)
876 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
877 (*"x = -1 * (- (2 / 2) + sqrt ((2 / 2) ^^^ 2 - -8)) |
878 x = -1 * (- (2 / 2) + - sqrt ((2 / 2) ^^^ 2 - -8))"nxt = calculate_Rational
879 NOT IMPLEMENTED SINCE 2002 ------------------------------^^^^^^^^^^^^^^^^^^*)
880 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
881 (*"x = -2 | x = 4" nxt = Or_to_List*)
882 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
883 (*"[x = -2, x = 4]" nxt = Check_Postcond*)
884 val (p,_,f,nxt,_,pt) = me nxt p [] pt; f2str f;
886 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = -2, x = 4]")) => () TODO
887 | _ => error "polyeq.sml: diff.behav. in [x = -2, x = 4]";
890 "[x = -1 * -1 + -1 * sqrt (2 ^^^ 2 / 2 ^^^ 2 - -8),\n x = -1 * -1 + -1 * (-1 * sqrt (2 ^^^ 2 / 2 ^^^ 2 - -8))]"
891 (*"[x = -1 * -1 + -1 * sqrt (1 ^^^ 2 - -8),\n x = -1 * -1 + -1 * (-1 * sqrt (1 ^^^ 2 - -8))]"*)
892 then () else error "polyeq.sml corrected?behav. in [x = -2, x = 4]";
895 "----------- (-8 - 2*x + x^^^2 = 0), by rewriting ---------------";
896 "----------- (-8 - 2*x + x^^^2 = 0), by rewriting ---------------";
897 "----------- (-8 - 2*x + x^^^2 = 0), by rewriting ---------------";
898 (*stopped du to TODO.txt WN111014.TODO calculate_Poly < calculate_Rational < calculate_RootRat
899 see --- val rls = calculate_RootRat > calculate_Rational ---*)
900 val thy = @{theory PolyEq};
901 val ctxt = Proof_Context.init_global thy;
902 val inst = [((the o (parseNEW ctxt)) "bdv::real", (the o (parseNEW ctxt)) "x::real")];
903 val t = (the o (parseNEW ctxt)) "-8 - 2*x + x^^^2 = (0::real)";
905 val rls = complete_square;
906 val SOME (t,asm) = rewrite_set_inst_ thy true inst rls t;
907 UnparseC.term t = "-8 + (2 / 2 - x) ^^^ 2 = (2 / 2) ^^^ 2";
909 val thm = ThmC.numerals_to_Free @{thm square_explicit1};
910 val SOME (t,asm) = rewrite_ thy dummy_ord Rule_Set.Empty true thm t;
911 UnparseC.term t = "(2 / 2 - x) ^^^ 2 = (2 / 2) ^^^ 2 - -8";
913 val thm = ThmC.numerals_to_Free @{thm root_plus_minus};
914 val SOME (t,asm) = rewrite_ thy dummy_ord PolyEq_erls true thm t;
915 UnparseC.term t = "2 / 2 - x = sqrt ((2 / 2) ^^^ 2 - -8) |"^
916 "\n2 / 2 - x = -1 * sqrt ((2 / 2) ^^^ 2 - -8)";
918 (*the thm bdv_explicit2* here required to be constrained to ::real*)
919 val thm = ThmC.numerals_to_Free @{thm bdv_explicit2};
920 val SOME (t,asm) = rewrite_inst_ thy dummy_ord Rule_Set.Empty true inst thm t;
921 UnparseC.term t = "2 / 2 - x = sqrt ((2 / 2) ^^^ 2 - -8) |"^
922 "\n-1 * x = - (2 / 2) + -1 * sqrt ((2 / 2) ^^^ 2 - -8)";
924 val thm = ThmC.numerals_to_Free @{thm bdv_explicit3};
925 val SOME (t,asm) = rewrite_inst_ thy dummy_ord Rule_Set.Empty true inst thm t;
926 UnparseC.term t = "2 / 2 - x = sqrt ((2 / 2) ^^^ 2 - -8) |"^
927 "\nx = -1 * (- (2 / 2) + -1 * sqrt ((2 / 2) ^^^ 2 - -8))";
929 val thm = ThmC.numerals_to_Free @{thm bdv_explicit2};
930 val SOME (t,asm) = rewrite_inst_ thy dummy_ord Rule_Set.Empty true inst thm t;
931 UnparseC.term t = "-1 * x = - (2 / 2) + sqrt ((2 / 2) ^^^ 2 - -8) |"^
932 "\nx = -1 * (- (2 / 2) + -1 * sqrt ((2 / 2) ^^^ 2 - -8))";
934 val rls = calculate_RootRat;
935 val SOME (t,asm) = rewrite_set_ thy true rls t;
937 "-1 * x = -1 + sqrt (2 ^^^ 2 / 2 ^^^ 2 - -8) \<or>\nx = -1 * -1 + -1 * (-1 * sqrt (2 ^^^ 2 / 2 ^^^ 2 - -8))"
938 (*"-1 * x = -1 + sqrt (2 ^^^ 2 / 2 ^^^ 2 - -8) |\nx = -1 * -1 + -1 * (-1 * sqrt (2 ^^^ 2 / 2 ^^^ 2 - -8))"..isabisac15*)
939 then () else error "(-8 - 2*x + x^^^2 = 0), by rewriting -- ERROR INDICATES IMPROVEMENT";
940 (*SHOULD BE: UnparseC.term = "x = -2 | x = 4;*)
943 "-------------------- (3 - 10*x + 3*x^^^2 = 0), ----------------------";
944 "-------------------- (3 - 10*x + 3*x^^^2 = 0), ----------------------";
945 "-------------------- (3 - 10*x + 3*x^^^2 = 0), ----------------------";
946 "---- test the erls ----";
947 val t1 = (Thm.term_of o the o (parse thy)) "0 <= (10/3/2)^^^2 - 1";
948 val SOME (t,_) = rewrite_set_ @{theory PolyEq} false PolyEq_erls t1;
949 val t' = UnparseC.term t;
950 (*if t'= "HOL.True" then ()
951 else error "polyeq.sml: diff.behav. in 'rewrite_set_.. PolyEq_erls";*)
953 val fmz = ["equality (3 - 10*x + 3*x^^^2 = 0)",
954 "solveFor x","solutions L"];
956 ("PolyEq",["degree_2","expanded","univariate","equation"],
957 ["PolyEq","complete_square"]);
958 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
959 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
960 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
961 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
962 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
963 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
964 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
965 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
966 (*Apply_Method ("PolyEq","complete_square")*)
967 val (p,_,f,nxt,_,pt) = me nxt p [] pt; f2str f;
969 "----------- (-16 + 4*x + 2*x^^^2 = 0), --------------------------";
970 "----------- (-16 + 4*x + 2*x^^^2 = 0), --------------------------";
971 "----------- (-16 + 4*x + 2*x^^^2 = 0), --------------------------";
972 val fmz = ["equality (-16 + 4*x + 2*x^^^2 = 0)",
973 "solveFor x","solutions L"];
975 ("PolyEq",["degree_2","expanded","univariate","equation"],
976 ["PolyEq","complete_square"]);
977 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
978 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
979 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
980 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
981 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
982 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
983 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
984 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
985 (*Apply_Method ("PolyEq","complete_square")*)
986 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
987 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
988 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
989 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
990 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
991 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
992 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
993 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
994 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
995 val (p,_,f,nxt,_,pt) = me nxt p [] pt;
997 case f of Form' (FormKF (~1,EdUndef,0,Nundef,"[x = 2, x = -4]")) => () TODO
998 | _ => error "polyeq.sml: diff.behav. in [x = 2, x = -4]";