removed error *** nxt_add: EX itm. not(dat(itm)<=dat(ori))
the reason was: 'TERM' and 'term' are occupied by Isabelle.
TODO: improve error diagnosis already in/near prep_ori.
1 (* Title: tests for rationals
3 Copyright (c) Stefan Karnel 2002
4 Use is subject to license terms.
6 12345678901234567890123456789012345678901234567890123456789012345678901234567890
7 10 20 30 40 50 60 70 80
10 nonterm.SK marks non-terminating examples
11 ord.SK PARTIALLY marks crucial ordering examples
12 *SK* of some (secondary) interest (on 070906)
13 *******************************************************************)
15 (******************************************************************
16 WN060104 transfer marked (*SR..*)examples to the exp-collection
17 # exp_IsacCore_Simp_Rat_Cancel.xml from rational.sml (*SRC*) 10 exp
18 # exp_IsacCore_Simp_Rat_Add.xml from rational.sml (*SRA*) 11 exp
19 # exp_IsacCore_Simp_Rat_Mult.xml from rational.sml (*SRM*) 5 exp
20 # exp_IsacCore_Simp_Rat_AddMult.xml from rational.sml (*SRAM*) 11 exp
21 # exp_IsacCore_Simp_Rat_Double.xml from rational.sml (*SRD*) 12 exp
22 *******************************************************************)
23 "--------------------------------------------------------";
24 "--------------------------------------------------------";
25 "table of contents --------------------------------------";
26 "--------------------------------------------------------";
27 "~~~~~BEGIN: decomment structure RationalI : RATIONALI ~~";
28 "-------- ... missing WN060103 --------------------------";
29 "-------- fun monom2term, fun poly2term' ---------------";
30 "~~~~~END: decomment structure RationalI : RATIONALI ~~~~";
31 "-------- external calculating functions test -----------";
32 "-------- cancel from: Mathematik 1 Schalk Reniets Verlag";
33 "-------- common_nominator_p ----------------------------";
34 "-------- reverse rewrite -------------------------------";
35 "-------- 'reverse-ruleset' cancel_p --------------------";
36 "-------- norm_Rational ---------------------------------";
37 "-------- numeral rationals -----------------------------";
38 "-------- cancellation ----------------------------------";
39 "-------- common denominator ----------------------------";
40 "-------- multiply and cancel ---------------------------";
41 "-------- common denominator and multiplication ---------";
42 "-------- double fractions ------------------------------";
43 "-------- crucial examples ------------------------------";
44 "-------- examples for Stefan Karnels thesis ------------";
45 "-------- me Schalk I No.186 ----------------------------";
46 "-------- interSteps ..Simp_Rat_Double_No-1.xml ---------";
47 "-------- interSteps ..Simp_Rat_Cancel_No-1.xml ---------";
48 "-------- investigate rulesets for cancel_p -------------";
49 "-------- investigate format of factout_ and factout_p_ -";
50 "-------- how to stepwise construct Scripts -------------";
51 "--------------------------------------------------------";
52 "--------------------------------------------------------";
53 "--------------------------------------------------------";
56 "~~~~~BEGIN: decomment structure RationalI : RATIONALI ~~";
57 (*.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
58 tests of internal functions: to make them work,
59 out-comment (*!!!*) in knowledge/Rational.ML:
61 structure RationalI : RATIONALI =
68 !!!##*)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~.*)
70 "-------- ... missing WN060103 --------------------------";
71 "-------- ... missing WN060103 --------------------------";
72 "-------- ... missing WN060103 --------------------------";
73 (*~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
74 writeln ("********************* rational.sml - TESTS *************************");
75 writeln ("***** divide tests *****");
76 val mv_pquot1 = (#1(mv_division([(1,[1,1,1]),(1,[1,1,0]),(1,[1,0,1]),(1,[0,0,0])],[(1,[1,1,0]),(1,[0,0,0])],LEX_)));
77 (* result: [(1,[0,0,1]),(1,[0,0,0])] *)
78 if mv_pquot1=[(1,[0,0,1]),(1,[0,0,0])] then () else error ("rational.sml: example failed");
80 val mv_prest1 = (#2(mv_division([(1,[1,1,1]),(1,[1,1,0]),(1,[1,0,1]),(1,[0,0,0])],[(1,[1,1,0]),(1,[0,0,0])],LEX_)));
81 (* result: [(1,[1,0,1]),(~1,[0,0,1])] *)
82 if mv_prest1=[(1,[1,0,1]),(~1,[0,0,1])] then () else error ("rational.sml: example failed");
84 val mv_pquot2 = (#1(mv_division([(4,[2]),(8,[1]),(16,[0])],[(1,[1]),(1,[0])],LEX_)));
85 (* result: [(4,[1]),(4,[0])] *)
86 if mv_pquot2=[(4,[1]),(4,[0])] then () else error ("rational.sml: example failed");
88 val mv_prest2 = (#2(mv_division([(4,[2]),(8,[1]),(16,[0])],[(1,[1]),(1,[0])],LEX_)));
89 (* result: [(12,[0]] *)
90 if mv_prest2=[(12,[0])] then () else error ("rational.sml: example failed");
92 val mv_pquot3 = (#1(mv_division([(4,[2]),(~4,[0])],[(2,[1]),(2,[0])],LEX_)));
93 (* [(2,[1]),(~2,[0])] *)
94 if mv_pquot3=[(2,[1]),(~2,[0])] then () else error ("rational.sml: example failed");
96 val mv_prest3 = (#2(mv_division([(1,[2]),(~1,[0])],[(2,[1]),(2,[0])],LEX_)));
97 (* [(1,[2]),(~1,[0])] *)
98 if mv_prest3=[(1,[2]),(~1,[0])] then () else error ("rational.sml: example failed");
100 val mv_pquot4 = (#1(mv_division([(3,[1,1,1]),(4,[1,0,1]),(3,[0,0,1])],[(2,[1,0,0]),(4,[0,0,1])],LEX_)));
102 if mv_pquot4=[(1,[0,1,1])] then () else error ("rational.sml: example failed");
104 val mv_prest4 = (#2(mv_division([(3,[1,1,1]),(4,[1,0,1]),(3,[0,0,1])],[(2,[1,0,0]),(4,[0,0,1])],GGO_)));
105 (* [(1,[1,1,1]),(~4,[0,1,2]),(4,[1,0,1]),(3,[0,0,1])] *)
106 if mv_prest4 =[(1,[1,1,1]),(~4,[0,1,2]),(4,[1,0,1]),(3,[0,0,1])] then () else error ("rational.sml: example failed");
108 val mv_pquot5 = (#1(mv_division([(3,[1,1,1]),(4,[1,0,1]),(3,[0,0,1]),(6,[2,1,3]),(4,[0,4,1]),(1,[2,2,1])],[(1,[0,0,1])],LEX_)));
109 (* [(1,[2,2,0]),(6,[2,1,2]),(3,[1,1,0]),(4,[1,0,0]),(4,[0,4,0]),(3,[0,0,0])]*)
110 if mv_pquot5=[(1,[2,2,0]),(6,[2,1,2]),(3,[1,1,0]),(4,[1,0,0]),(4,[0,4,0]),(3,[0,0,0])] then () else error ("rational.sml: example failed");
112 val mv_prest5 = (#2(mv_division([(3,[1,1,1]),(4,[1,0,1]),(3,[0,0,1]),(6,[2,1,3]),(4,[0,4,1]),(1,[2,2,1])],[(1,[0,0,1])],LEX_)));
114 if mv_prest5=[] then () else error ("rational.sml: example failed");
116 (* (x^2 + 2(a+1)x + (a^2+2a+1)) / (x+a+1) = x+a+1 *)
117 val mv_pquot6 = (#1(mv_division([(1,[2,0,0]),(2,[1,1,0]),(2,[1,0,0]),(1,[0,2,0]),(2,[0,1,0]),(1,[0,0,0])],[(1,[1,0,0]),(1,[0,1,0]),(1,[0,0,0])],LEX_)));
118 if mv_pquot6=[(1,[1,0,0]),(1,[0,1,0]),(1,[0,0,0])] then () else error ("rational.sml: example failed");
120 val mv_prest6 = (#2(mv_division([(1,[2,0,0]),(2,[1,1,0]),(2,[1,0,0]),(1,[0,2,0]),(2,[0,1,0]),(1,[0,0,0])],[(1,[1,0,0]),(1,[0,1,0]),(1,[0,0,0])],LEX_)));
121 if mv_prest6=[] then () else error ("rational.sml: example failed");
124 writeln ("***** MV_CONTENT-TESTS *****");
125 val mv_cont1=mv_content([(1,[2,1]),(1,[2,0]),(1,[1,1]),(1,[1,0]),(1,[0,1]),(1,[0,0])]);
126 (* [(1,[0,1]),(1,[0,0])] *)
127 if mv_cont1=[(1,[0,1]),(1,[0,0])] then () else error ("rational.sml: example failed");
129 val mv_pp1=mv_pp([(1,[1,1]),(1,[1,0]),(1,[0,1]),(1,[0,0])]);
130 (*[(1,[1,0]),(1,[0,0])]*)
131 if mv_pp1=[(1,[1,0]),(1,[0,0])] then () else error ("rational.sml: example failed");
133 val mv_cont2=mv_content([(2,[1]),(4,[0])]);
135 if mv_cont2=[(2,[0])] then () else error ("rational.sml: example failed");
137 val mv_pp2=mv_pp([(2,[1]),(4,[0])]);
138 (* [(1,[1]),(2,[0])] *)
139 if mv_pp2=[(1,[1]),(2,[0])] then () else error ("rational.sml: example failed");
141 val mv_cont3=mv_content[(8,[2,1,1]),(12,[1,0,2]),(10,[2,2,0]),(16,[1,1,1])];
143 if mv_cont3=[(2,[0,0,0])] then () else error ("rational.sml: example failed");
145 val mv_pp3=mv_pp[(8,[2,1,1]),(12,[1,0,2]),(10,[2,2,0]),(16,[1,1,1])];
146 (* [(5,[2,2,0]),(4,[2,1,1]),(8,[1,1,1]),(6,[1,0,2])] *)
147 if mv_pp3=[(5,[2,2,0]),(4,[2,1,1]),(8,[1,1,1]),(6,[1,0,2])] then () else error ("rational.sml: example failed");
149 val mv_cont4=mv_content[(2,[2,1,0]),(3,[1,0,1]),(2,[1,1,0]),(3,[0,0,1])];
151 if mv_cont4=[(1,[0,0,0])] then () else error ("rational.sml: example failed");
153 val mv_pp4=mv_pp [(2,[2,1,0]),(3,[1,0,1]),(2,[1,1,0]),(3,[0,0,1])];
154 (* [(2,[2,1,0]),(2,[1,1,0]),(3,[1,0,1]),(3,[0,0,1])] *)
155 if mv_pp4=[(2,[2,1,0]),(2,[1,1,0]),(3,[1,0,1]),(3,[0,0,1])] then () else error ("rational.sml: example failed");
157 val con1=mv_content([(9,[2,0]),(15,[1,1]),(12,[1,0]),(6,[0,2]),(12,[0,1])]);
159 if con1=[(3,[0,0])] then () else error ("rational.sml: example failed");
161 val pp1=mv_pp([(9,[2,0]),(15,[1,1]),(12,[1,0]),(6,[0,2]),(12,[0,1])]);
162 (* [(3,[2,0]),(5,[1,1]),(4,[1,0]),(2,[0,2]),(4,[0,1])] *)
163 if pp1=[(3,[2,0]),(5,[1,1]),(4,[1,0]),(2,[0,2]),(4,[0,1])] then () else error ("rational.sml: example failed");
165 val con2=mv_content([(1,[2,0]),(1,[1,1]),(1,[1,0]),(1,[0,2]),(1,[0,1])]);
167 if con2=[(1,[0,0])] then () else error ("rational.sml: example failed");
169 val pp2 =mv_pp([(1,[2,0]),(1,[1,1]),(1,[1,0]),(1,[0,2]),(1,[0,1])]);
170 (* [(1,[2,0]),(1,[1,1]),(1,[1,0]),(1,[0,2]),(1,[0,1])] *)
171 if pp2=[(1,[2,0]),(1,[1,1]),(1,[1,0]),(1,[0,2]),(1,[0,1])] then () else error ("rational.sml: example failed");
173 val cont1 = mv_content [(1,[2,1,0]),(2,[2,1,0])];
175 if cont1=[(3,[0,1,0])] then () else error ("rational.sml: example failed");
177 val pp1 = mv_pp [(1,[2,1,0]),(2,[2,1,0])];
179 if pp1=[(1,[2,0,0])] then () else error ("rational.sml: example failed");
181 val cont2 = mv_content [(4,[1,2,0]),(2,[2,1,0])];
183 if cont2=[(2,[0,1,0])] then () else error ("rational.sml: example failed");
185 val pp2 = mv_pp [(4,[1,2,0]),(2,[2,1,0])];
186 (* [(1,[2,0,0]),(2,[1,1,0])] *)
187 if pp2=[(1,[2,0,0]),(2,[1,1,0])] then () else error ("rational.sml: example failed");
189 writeln ("********************************************************");
190 val cont3=mv_content [(65,[3,2,2]),(52,[3,2,1]),(26,[3,1,2]),(~95,[2,2,3]),(~76,[2,2,2]),(35,[2,2,1]),(28,[2,2,0]),(~38,[2,1,3]),(14,[2,1,1])];
191 if cont3=[(5,[0,2,1]),(4,[0,2,0]),(2,[0,1,1])] then () else error ("rational.sml: example failed");
192 val pp3=mv_pp [(65,[3,2,2]),(52,[3,2,1]),(26,[3,1,2]),(~95,[2,2,3]),(~76,[2,2,2]),(35,[2,2,1]),(28,[2,2,0]),(~38,[2,1,3]),(14,[2,1,1])];
195 "-------- fun monom2term, fun poly2term' ---------------";
196 "-------- fun monom2term, fun poly2term' ---------------";
197 "-------- fun monom2term, fun poly2term' ---------------";
198 val t = monom2term ((3,[2,1,0]), ["c","b","a"](*reverse ???SK-*));
199 term2str t = "3 * (c ^^^ 2 * b)" (*true*);
201 val t = monom2term ((1,[1,0]), ["b","a"]);
202 term2str t = "b" (*true*);
204 val t = poly2term ([(1,[0,0,0]),(2,[1,0,0]),(3,[2,1,0]),(4,[3,2,1])],
206 term2str t = "1 + 2 * c + 3 * (c ^^^ 2 * b) + 4 * (c ^^^ 3 * (b ^^^ 2 * a))";
208 val t = poly2term ([(1,[1,0]),(1,[0,1])], ["b","a"]);
209 term2str t = "a + b" (*true*);
211 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~*)
212 "~~~~~END: decomment structure RationalI : RATIONALI ~~~~";
213 "~~~~~END: decomment structure RationalI : RATIONALI ~~~~";
214 "~~~~~END: decomment structure RationalI : RATIONALI ~~~~";
217 fun parse_rat str = (term_of o the o (parse thy)) str;
219 writeln ("***** mv_gcd-tests *****");
220 val ggt1 = mv_gcd [(4,[2,2]),(8,[1,1]),(4,[0,0])] [(2,[1,1]),(2,[0,0])];
221 (* [(2,[1,1]),(2,[0,0])] *)
222 if ggt1=[(2,[1,1]),(2,[0,0])] then () else error ("rational.sml: example failed");
224 val ggt2 = mv_gcd [(8,[2,1,1]),(12,[1,0,2]),(10,[2,2,0]),(15,[1,1,1])] [(2,[2,1,0]),(3,[1,0,1]),(2,[1,1,0]),(3,[0,0,1])];
225 (* [(2,[1,1,0]),(3,[0,0,1])] *)
226 if ggt2=[(2,[1,1,0]),(3,[0,0,1])] then () else error ("rational.sml: example failed");
229 val ggt3 = mv_gcd [(1,[2,0]),(~2,[1,1]),(1,[0,2])] [(1,[1,0]),(~1,[0,1])];
230 (* [(1,[1,0]),(~1,[0,1])] *)
231 if ggt3=[(1,[1,0]),(~1,[0,1])] then () else error ("rational.sml: example failed");
234 val ggt4 = mv_gcd [(1,[2,1,0]),(2,[2,1,0])] [(5,[1,0,0])];
236 if ggt4=[(1,[1,0,0])] then () else error ("rational.sml: example failed");
239 val ggt5 = mv_gcd [(4,[2,0]),(~8,[1,1]),(4,[0,2])] [(1,[2,0]),(~1,[0,2])];
240 (* [(1,[1,0]),(~1,[0,1])] *)
241 if ggt5=[(1,[1,0]),(~1,[0,1])] then () else error ("rational.sml: example failed");
244 val ggt6 = mv_gcd [(10,[2,1,1]),(14,[1,1,0]),(3,[1,0,1]),(20,[1,2,1])] [(5,[1,1,1]),(7,[2,1,1])];
246 if ggt6=[(1,[1,0,0])] then () else error ("rational.sml: example failed");
248 writeln ("***** kgv-tests *****");
249 val kgv1=mv_lcm [(10,[])] [(15,[])];
251 if kgv1=[(30,[])] then () else error ("rational.sml: example failed");
253 val kgv2=mv_lcm [(1,[2,0]),(~2,[1,1]),(1,[0,2])] [(1,[1,0]),(~1,[0,1])];
254 (* [(1,[2,0]),(~2,[1,1]),(1,[0,2])] *)
255 if kgv2=[(1,[2,0]),(~2,[1,1]),(1,[0,2])] then () else error ("rational.sml: example failed");
257 val kgv3=mv_lcm [(4,[2,0]),(~8,[1,1]),(4,[0,2])] [(1,[2,0]),(~1,[0,2])];
258 (* [(4,[3,0]),(~4,[2,1]),(~4,[1,2]),(4,[0,3])] *)
259 if kgv3=[(4,[3,0]),(~4,[2,1]),(~4,[1,2]),(4,[0,3])] then () else error ("rational.sml: example failed");
262 writeln ("***** STEP_CANCEL_TESTS: *****");
264 val term2 = (term_of o the o (parse thy)) " (9 * a^^^2 * b) / (6 * a * c)";
265 val div2 = term2str (step_cancel term2);
266 if div2 = "3 * (a * b) * (3 * a) / (2 * c * (3 * a))" then () else error ("rational.sml: example failed");
269 val term1 = (term_of o the o (parse thy)) "(10 * a^^^2 * b * c + 14 * a * b + 3 * a * c + 20 * a * b^^^2 * c) / a";
270 val div1 = term2str(step_cancel term1);
271 if div1 = "(3 * c + 14 * b + 20 * (b ^^^ 2 * c) + 10 * (a * (b * c))) * a / (1 * a)" then () else error ("rational.sml: example failed");
273 val term3 = (term_of o the o (parse thy)) "(10 * a^^^2 * b * c) / (1 * x * y * z) ";
274 val div3 = term2str(step_cancel term3);
275 if div3="10 * a ^^^ 2 * b * c / (1 * x * y * z)" then () else error ("rational.sml: example failed");
277 --------------------------------------------------------------------------!!!*)
279 (*-----versuche 13.3.03-----
280 val t = str2term "1 - x^^^2 - 5 * x^^^5";
281 val vs=(((map free2str) o vars) t);
282 val SOME ml = expanded2poly t vs;
284 poly2term'(rev(sort (mv_geq LEX_) (ml)),vs);
285 poly2term'([(~5,[5]),(~1,[2]),(1,[0])], vs);
286 monom2term((~5,[5]),vs);
287 monom2term((~1,[2]),vs);
288 val t' = monom2term((1,[0]),vs);(*uncaught exception LIST*)
290 val (i,is) = (~1,[2]);
291 val ttt = Const ("Groups.times_class.times", [HOLogic.realT,HOLogic.realT]---> HOLogic.realT) $
292 (Const ("uminus", HOLogic.realT --> HOLogic.realT) $
293 Free ((str_of_int o abs) i, HOLogic.realT)) $
294 powerproduct2term(is, vs);
296 -------versuche 13.3.03-----*)
298 val t = str2term "1 - x^^^2 - 5 * x^^^5";
299 val SOME t' = expanded2polynomial t; term2str t';
300 "1 + - 1 * x ^^^ 2 + - 5 * x ^^^ 5";
301 val t = str2term "1 - x";
302 val SOME t' = expanded2polynomial t; term2str t';
304 val t = str2term "1 + (-1) * x";
305 val SOME t' = expanded2polynomial t; term2str t';
307 val t = (term_of o the o (parse thy)) "1 + (-1) * x ^^^ 2 + (-5) * x ^^^5";
308 val SOME t' = polynomial2expanded t; term2str t';
309 "1 - x ^^^ 2 - 5 * x ^^^ 5";
312 "-------- external calculating functions test -----------";
313 "-------- external calculating functions test -----------";
314 "-------- external calculating functions test -----------";
315 val t1 = (term_of o the o (parse thy)) "((3 * x^^^2 + 6 *x + 3) / (2*x + 2))";
316 val SOME (t1',asm)= factout_p_ thy t1;
317 term2str t1'; terms2str asm;
318 "(3 + 3 * x) * (1 + 1 * x) / (2 * (1 + 1 * x))";
320 val SOME (t1',asm)= cancel_p_ thy t1;
321 term2str t1'; terms2str asm;
323 "[\"1 + 1 * x ~= 0\"]";
325 val t = (term_of o the o (parse thy)) "((-3 * x^^^2 + 6 *x - 3) / (2*x - 2))";
326 val SOME (t',asm)= cancel_ thy t;
327 term2str t'; terms2str asm;
330 val SOME (t',asm)= factout_ thy t;
331 term2str t'; terms2str asm;
332 "(3 - 3 * x) * (-1 + x) / (2 * (-1 + x))";
335 val t = str2term "((x+ (-1)) / (x + 1)) + ((x + 1) / (x + (-1)))";
336 val SOME (t',asm) = add_fraction_p_ thy t;
337 term2str t'; terms2str asm;
338 "(2 + 2 * x ^^^ 2) / (-1 + 1 * x ^^^ 2)";
340 val SOME (t',asm) = common_nominator_p_ thy t;
341 term2str t'; terms2str asm;
342 "(-1 + 1 * x) * (-1 + 1 * x) / ((1 + 1 * x) * (-1 + 1 * x)) +\n(1 + 1 * x) * (1 + 1 * x) / ((1 + 1 * x) * (-1 + 1 * x))";
345 val t = str2term "((x - 1) / (x + 1)) + ((x + 1) / (x - 1))";
346 val SOME (t',asm) = add_fraction_ thy t;
347 term2str t'; terms2str asm;
348 "(2 + 2 * x ^^^ 2) / (-1 + x ^^^ 2)";
350 val SOME (t',asm) = common_nominator_ thy t;
351 term2str t'; terms2str asm;
352 "(-1 + x) * (-1 + x) / ((1 + x) * (-1 + x)) +\n(1 + x) * (1 + x) / ((1 + x) * (-1 + x))";
355 val t = str2term "((1) / (2*x + 2)) + ((1) / (2*x + (-2))) + ((1) / ( x^^^2 + (-1)))+((1) / (x^^^2 + (-2)*x + 1))";
356 val SOME (t',asm) = common_nominator_p_ thy t;
357 term2str t'; terms2str asm;
358 "1 * (1 + -2 * x + 1 * x ^^^ 2) /\n((-1 + 1 * x) * (2 * ((-1 + 1 * x) * (1 + 1 * x)))) +\n(1 * (-1 + 1 * x ^^^ 2) /\n ((-1 + 1 * x) * (2 * ((-1 + 1 * x) * (1 + 1 * x)))) +\n (1 * (-2 + 2 * x) / ((-1 + 1 * x) * (2 * ((-1 + 1 * x) * (1 + 1 * x)))) +\n 1 * (#";
360 val SOME (t',asm) = add_fraction_p_ thy t;
361 term2str t'; terms2str asm;
362 "1 * x / (1 + -2 * x + 1 * x ^^^ 2)";
363 "[\"1 + 1 * x ~= 0\"]";
364 val SOME(t',asm) = norm_rational_ thy t;
365 term2str t'; terms2str asm;
366 "1 * x / (1 + -2 * x + 1 * x ^^^ 2)";
367 "[\"1 + 1 * x ~= 0\"]";
369 val t3 = (term_of o the o (parse thy)) "((1) / (2*x + 2)) + ((1) / (2*x - 2)) + ((1) / ( x^^^2 - 1))+((1) / (x^^^2 - 2 * x + 1))";
370 val SOME (t3',_) = common_nominator_ thy t3;
371 val SOME (t3'',_) = add_fraction_ thy t3;
375 val SOME(t4,t5) = norm_expanded_rat_ thy t3;
381 val t=(term_of o the o (parse thy)) "(9 - x^^^2)/(9 - 6*x + x^^^2)";
382 val SOME (t',_) = factout_ thy t;
383 val SOME (t'',_) = cancel_ thy t;
386 "(3 + x) * (3 - x) / ((3 - x) * (3 - x))";
389 val t=(term_of o the o (parse thy))
390 "(9 - x^^^2) / (9 - 6*x + x^^^2) + 1 / (3 - x)";
391 val SOME (t',_) = common_nominator_ thy t;
392 val SOME (t'',_) = add_fraction_ thy t;
395 "(9 - x ^^^ 2) / ((3 - x) * (3 - x)) + 1 * (3 - x) / ((3 - x) * (3 - x))";
398 (*WN021016 added -----vv---*)
399 val t = str2term "(9 - x^^^2) / (9 - 6*x + x^^^2) + 1";
400 val SOME (t',_) = common_nominator_ thy t;
401 val SOME (t'',_) = add_fraction_ thy t;
402 term2str t' = "(9 - x ^^^ 2) / (9 - 6 * x + x ^^^ 2) +\n1" ^
403 " * (9 - 6 * x + x ^^^ 2) / (9 - 6 * x + x ^^^ 2)" (*true*);
404 term2str t'' = "6 / (3 - x)" (*true*);
406 val t = str2term "1 + (9 - x^^^2) / (9 - 6*x + x^^^2)";
407 val SOME (t',_) = common_nominator_ thy t;
408 val SOME (t'',_) = add_fraction_ thy t;
409 term2str t' = "1 * (9 - 6 * x + x ^^^ 2) / (9 - 6 * x + x ^^^ 2) +\n" ^
410 "(9 - x ^^^ 2) / (9 - 6 * x + x ^^^ 2)" (*true*);
411 term2str t'' = "6 / (3 - x)" (*true*);
412 (*WN021016 added -----^^---*)
413 (*WN030602 added -----vv--- no rewrite -> NONE !*)
414 val t = str2term "1 / a";
415 val NONE = cancel_p_ thy t;
416 val NONE = rewrite_set_ thy false cancel_p t;
417 (*WN.2.6.03 added -------^^---*)
419 val t = str2term "(y^^^2 - x^^^2)/(y^^^2 - 2*y*x + x^^^2)";
420 val SOME (t',_) = factout_ thy t;
421 val SOME (t'',_) = cancel_ thy t;
422 term2str t' = "(y + x) * (y - x) / ((y - x) * (y - x))"(*true*);
423 term2str t'' = "(y + x) / (y - x)";
425 val t = str2term "(y^^^2 - x^^^2)/(y^^^2 - 2*y*x + x^^^2) + 1 / (y - x)";
426 val SOME (t',_) = common_nominator_ thy t;
427 val SOME (t'',_) = add_fraction_ thy t;
429 "(-1 * x ^^^ 2 + y ^^^ 2) / ((-1 * x + y) * (-1 * x + y)) +\n1" ^
430 " * (-1 * x + y) / ((-1 * x + y) * (-1 * x + y))" (*true*);
431 term2str t'' = "(-1 - x - y) / (x - y)" (*true*);
433 val t = str2term "(x^^^2 - y^^^2)/(x^^^2 - 2*x*y + y^^^2) + 1 / (x - y)";
434 val SOME (t',_) = common_nominator_ thy t;
435 val SOME (t'',_) = add_fraction_ thy t;
436 if term2str t' = "(-1 * y ^^^ 2 + x ^^^ 2) / ((-1 * y + x) * (-1 * y + x))" ^
437 " +\n1 * (-1 * y + x) / ((-1 * y + x) * (-1 * y + x))" then ()
438 else error "rational.sml lex-ord 1";
439 if term2str t'' = "(-1 - y - x) / (y - x)" then ()
440 else error "rational.sml lex-ord 2";
441 (*WN.16.10.02 WN070905 lexicographische Ordnung erhalten ! SK.ord*)
444 val t = str2term "(x^^^2 - y^^^2)/(x^^^2 - 2*x*y + y^^^2)";
445 val SOME (t',_) = norm_expanded_rat_ thy t;
446 if term2str t' = "(x + y) / (x - y)" then ()
447 else error "rational.sml term2poly: invalid x ^^^ 2 - y ^^^ 2 No.1";
448 (*val SOME (t'',_) = norm_rational_ thy t;
449 *** RATIONALS_TERM2POLY_EXCEPTION: Invalid Polynomial
450 WN.16.10.02 ?! + WN060831???SK4
451 WN070905 *** term2poly: invalid = x ^^^ 2 - y ^^^ 2*)
454 val t = str2term "(9 - x^^^2)/(9 - 6*x + x^^^2) + (1)/(3 + x)";
455 val SOME (t',_) = norm_expanded_rat_ thy t;
456 if term2str t' = "(12 + 5 * x + x ^^^ 2) / (9 - x ^^^ 2)" then ()
457 else error "rational.sml (9 - x^^^2)/(9 - 6*x + x^^^2) +...";
458 (*val SOME (t'',_) = norm_rational_ thy t;
459 *** RATIONALS_TERM2POLY_EXCEPTION: Invalid Polynomial WN.16.10.02 ?!
460 WN070906 *** term2poly: invalid = 9 - x ^^^ 2 SK.term2poly*)
462 val t=(term_of o the o (parse thy))
463 "(9 + (-1)* x^^^2)/(9 + (-1)* 6*x + x^^^2) + (1)/(3 + x)";
464 val SOME (t',_) = norm_expanded_rat_ thy t;
465 val SOME (t'',_) = norm_rational_ thy t;
468 "(12 + 5 * x + x ^^^ 2) / (9 - x ^^^ 2)";
469 "(12 + 5 * x + x ^^^ 2) / (9 + (-1) * x ^^^ 2)";
472 "-------- cancel from: Mathematik 1 Schalk Reniets Verlag";
473 "-------- cancel from: Mathematik 1 Schalk Reniets Verlag";
474 "-------- cancel from: Mathematik 1 Schalk Reniets Verlag";
475 val thy = theory "Rational"
476 val thy' = "Rational";
478 val mp = "make_polynomial";
480 writeln ("example 186:");
482 val e186a'="(14 * x * y) / ( x * y )";(*SRC*)
483 rewrite_set_ thy false cancel (str2term e186a');
485 val e186a = the (rewrite_set thy' false "cancel" e186a');
486 is_expanded (parse_rat "14 * x * y");
487 is_expanded (parse_rat "x * y");
488 if e186a = ("14 / 1", "[\"y * x ~= 0\"]") then ()
489 else error "rational.sml cancel Schalk e186a";
492 val e186b'="(60 * a * b) / ( 15 * a * b )";
493 val e186b = the (rewrite_set thy' false "cancel" e186b');
495 val e186c'="(144 * a^^^2 * b * c) / (12 * a * b * c )";
496 val e186c = (the (rewrite_set thy' false "cancel" e186c'))
497 handle e => OldGoals.print_exn e;
498 val t = (term_of o the o (parse thy)) e186c';
499 if e186c = ("12 * a / 1", "[\"12 * (c * (b * a)) ~= 0\"]") then ()
500 else error "rational.sml cancel Schalk e186c";
502 writeln ("example 187:");
504 val e187a'="(12 * x * y) / (8 * y^^^2 )";(*SRC*)
505 val e187a = the (rewrite_set thy' false "cancel" e187a');
507 val e187b'="(8 * x^^^2 * y * z ) / (18 * x * y^^^2 * z )";
508 val e187b = the (rewrite_set thy' false "cancel" e187b');
510 val e187d'="(9 * x^^^5 * y^^^2 * z^^^4) / (15 * x^^^6 * y^^^3 * z )";(*SRC*)
511 val e187d = the (rewrite_set thy' false "cancel" e187d');
512 if e187d = ("3 * z ^^^ 3 / (5 * (y * x))",
513 "[\"3 * (z * (y ^^^ 2 * x ^^^ 5)) ~= 0\"]") then ()
514 else error "rational.sml cancel Schalk e186d";
516 writeln "example 188:";
517 val e188a'="(-8 + 8 * x) / (-9 + 9 * x)";(*SRC*)
518 val e188a = the (rewrite_set thy' false "cancel" e188a');
519 is_expanded (parse_rat "8 * x + -8");
520 (* e188a = ("8 / 9",["not ((-1) + x = 0)"]) then () 13.3.03*)
521 if e188a = ("8 / 9", "[\"-1 + x ~= 0\"]") then ()
522 else error "rational.sml: e188a new behaviour";
524 val SOME (t,_) = rewrite_set thy' false mp "(8*((-1) + x))/(9*((-1) + x))";
526 val e188b'="(-15 + 5 * x) / (-18 + 6 * x)";(*SRC*)
527 val SOME (t, asm) = rewrite_set thy' false "cancel" e188b';
528 t = "5 / 6" (*true*);
531 val e188c'="( a + -1 * b ) / ( b + -1 * a )";
532 val e188c = the (rewrite_set thy' false "cancel_p" e188c');
533 (*is_expanded (parse_rat "a + -1 * b");*)
535 rewrite_set thy' false mp "((-1)*(b + (-1) * a))/(1*(b + (-1) * a))";
536 if t= "(a + -1 * b) / (-1 * a + b)" then()
537 else error "rational.sml: e188c new behaviour";
539 writeln ("example 190:");
541 val e190c'="( 27 * a^^^3 + 9 * a^^^2 + 3 * a + 1 ) / ( 27 * a^^^3 + 18 * a^^^2 + 3 * a )";
542 val e190c = the (rewrite_set thy' false "cancel" e190c');
543 val SOME (t,_) = rewrite_set thy' false mp "((1 + 9 * a ^^^ 2)*(1 + 3 * a))/((3 * a + 9 * a ^^^ 2)*(1 + 3 * a))";
544 if t = "(1 + 3 * a + 9 * a ^^^ 2 + 27 * a ^^^ 3) /\n(3 * a + 18 * a ^^^ 2 + 27 * a ^^^ 3)" then ()
545 else error "rational.sml: e190c new behaviour";
547 writeln ("example 191:");
549 val e191a'="( x^^^2 + -1 * y^^^2 ) / ( x + y )";
551 val e191a = the (rewrite_set thy' false "cancel" e191a');
552 is_expanded (parse_rat "x^^^2 + -1 * y^^^2");
554 is_expanded (parse_rat "x + y");
556 val SOME (t,_) = rewrite_set thy' false mp "((x + (-1) * y)*(x + y))/((1)*(x + y))";
557 (* t="(x ^^^ 2 + -1 * y ^^^ 2) / (x + y)" then() WN.13.3.03*)
558 if t="(x ^^^ 2 + -1 * y ^^^ 2) / (x + y)" then()
559 else error "rational.sml: e191a new behaviour";
562 val e191c'="( 9 * x^^^2 + -30 * x + 25 ) / ( 9 * x^^^2 + -25 )";
564 val e191c = the (rewrite_set thy' false "cancel" e191c');
565 is_expanded (parse_rat "9 * x^^^2 + -30 * x + 25");
567 is_expanded (parse_rat "25 + -30*x + 9*x^^^2");
569 is_expanded (parse_rat "-25 + 9*x^^^2");
571 val SOME (t,_) = rewrite_set thy' false mp "(((-5) + 3 * x)*((-5) + 3 * x))/((5 + 3 * x)*((-5) + 3 * x))";
572 (* t="(25 + ((-30) * x + 9 * x ^^^ 2)) / ((-25) + 9 * x ^^^ 2)"then() 13.3.03*)
573 if t= "(25 + -30 * x + 9 * x ^^^ 2) / (-25 + 9 * x ^^^ 2)" then()
574 else error "rational.sml: 'e191c' new behaviour";
577 writeln ("example 192:");
579 val e192b'="( 7 * x^^^3 + -1 * x^^^2 * y ) / ( 7 * x * y^^^2 + -1 * y^^^3 )";
581 val e192b = the (rewrite_set thy' false "cancel" e192b');
582 -------------------*)
583 val SOME (t',_) = rewrite_set thy' false mp "((x ^^^ 2)*(7 * x + (-1) * y))/((y ^^^ 2)*(7 * x + (-1) * y))";
584 if t' = "(7 * x ^^^ 3 + -1 * x ^^^ 2 * y) / (7 * x * y ^^^ 2 + -1 * y ^^^ 3)"
585 (*"(-1 * y * x ^^^ 2 + 7 * x ^^^ 3) / (-1 * y ^^^ 3 + 7 * x * y ^^^ 2)"WN050929*)
586 then () else error "rational.sml: 'e192b' new behaviour";
587 (*^^^ works with MG's simplifier vvv*)
588 val t =str2term"((x ^^^ 2)*(7 * x + (-1) * y))/((y ^^^ 2)*(7 * x + (-1) * y))";
589 val SOME (t',_) = rewrite_set_ thy false make_polynomial t;
590 if term2str t' = "(7 * x ^^^ 3 + -1 * x ^^^ 2 * y) / (7 * x * y ^^^ 2 + -1 * y ^^^ 3)" then () else error "rational.sml: 'e192b'MG new behaviour";
593 writeln ("example 193:");
595 val e193a'="( x^^^2 + -6 * x + 9 ) / ( x^^^2 + -9 )";
597 val e193a = the (rewrite_set thy' false "cancel" e193a');
598 -------------------*)
600 val e193b'="( x^^^2 + -8 * x + 16 ) / ( 2 * x^^^2 + -32 )";
602 val e193b = the (rewrite_set thy' false "cancel" e193b');
604 val e193c'="( 2 * x + -50 * x^^^3 ) / ( 25 * x^^^2 + -10 * x + 1 )";
605 val SOME(t,_) = rewrite_set thy' false "cancel" e193c';
606 -------------------*)
608 val wn01 = "(-25 + 9*x^^^2)/(5 + 3*x)";
609 val SOME (t, asm) = rewrite_set thy' false "cancel" wn01;
610 (* t = "((-5) + 3 * x) / 1" then () WN.13.3.03*)
611 if t = "(-5 + 3 * x) / 1" andalso asm = "[\"5 + 3 * x ~= 0\"]" then ()
612 else error "rational.sml: new behav. in cancel wn01";
615 "-------- common_nominator_p ----------------------------";
616 "-------- common_nominator_p ----------------------------";
617 "-------- common_nominator_p ----------------------------";
618 val rls' = "common_nominator_p";
620 writeln ("example 204:");
622 val e204a'="((5 * x) / 9) + ((3 * x) / 9) + (x / 9)";
623 val e204a = the (rewrite_set thy' false "common_nominator_p" e204a');
625 val e204b'="5 / x + -3 / x + -1 / x";
626 val e204b = the (rewrite_set thy' false "common_nominator_p" e204b');
627 if e204b = ("1 / x", "[]") then ()
628 else error "rational.sml common_nominator_p example e204b";
630 writeln ("example 205:");
632 val e205a'="((4 * x + 7) / 8) + ((4 * x + 3) / 8)";
633 val e205a = the (rewrite_set thy' false "common_nominator_p" e205a');
635 val e205b'="((5 * x + 2) / 3) + ((-2 * x + 1) / 3)";
636 val e205b = the (rewrite_set thy' false "common_nominator_p" e205b');
637 if e205b = ("(1 + x) / 1", "[]") then ()
638 else error "rational.sml common_nominator_p example e204b";
640 writeln ("example 206:");
642 val e206a'="((5 * x + 4) / (2 * x + -1)) + ((9 * x + 5) / (2 * x + -1))";
643 val e206a = the (rewrite_set thy' false "common_nominator_p" e206a');
645 val e206b'="((17 * x + -23) / (5 * x + 4)) + ((-25 + -17 * x) / (5 * x + 4))";
646 val e206b = the (rewrite_set thy' false "common_nominator_p" e206b');
648 writeln ("example 207:");
649 val e207'="((3 * x * y + 3 * y) / (x * y)) + ((5 * x * y + 7 * y) / (x * y)) + ((9 * x * y + -2 * y) / (x * y)) + ((x * y + 4 * y) / (x * y)) ";
650 val e207 = the (rewrite_set thy' false "common_nominator_p" e207');
652 writeln ("example 208:");
653 val e208'="((3 * x + 2) / (x + 2)) + ((5 * x + -1) / (x + 2)) + ((-7 * x + -3) / (x + 2)) + ((-1 * x + -3) / (x + 2)) ";
654 val e208 = the (rewrite_set thy' false "common_nominator_p" e208');
656 writeln ("example 209:");
657 val e209'="((3 * x + -7 * y + 3 * z) / (4)) + ((2 * x + 17 * y + 10 * z) / (4)) + ((-1 * x + 2 * y + z) / (4)) ";
658 val e209 = the (rewrite_set thy' false "common_nominator_p" e209');
660 writeln ("example 210:");
661 val e210'="((2 * x + 3 + -1 * x^^^2) / (5 * x)) + ((5 * x^^^2 + -2 * x + 1) / (5 * x)) + ((-3 * x^^^2 + -2 * x + 1) / (5 * x)) + ((-1 * x^^^2 + -3 * x + -5) / (5 * x)) ";
662 val e210 = the (rewrite_set thy' false "common_nominator_p" e210');
664 writeln ("example 211:");
666 val e211a'="((b) / (a + -1 * b)) + ((-1 * a) / (a + -1 * b))";
667 val e211a = the (rewrite_set thy' false "common_nominator_p" e211a');
669 val e211b'="((b) / (b^^^2 + -1 * a^^^2)) + ((-1 * a) / (b^^^2 + -1 * a^^^2))";
670 val e211b = the (rewrite_set thy' false "common_nominator_p" e211b');
672 writeln ("example 212:");
674 val e212a'="((4) / (x)) + ((-3) / (y)) + -1";
675 val e212a = the (rewrite_set thy' false "common_nominator_p" e212a');
677 val e212b'="((4) / (x)) + ((-5) / (y)) + ((6) / (x*y))";
678 val e212b = the (rewrite_set thy' false "common_nominator_p" e212b');
680 writeln ("example 213:");
682 val e213a'="((5 * x) / (3 * y^^^2)) + ((19 * z) / (6 * x * y)) + ((-2 * x) / (3 * y^^^2)) + ((7 * y^^^2) / (6 * x^^^2)) ";
683 val e213a = the (rewrite_set thy' false "common_nominator_p" e213a');
685 val e213b'="((2 * b) / (3 * a^^^2)) + ((3 * c) / (7 * a * b)) + ((4 * b) / (3 * a^^^2)) + ((3 * a) / (7 * b^^^2))";
686 val e213b = the (rewrite_set thy' false "common_nominator_p" e213b');
688 writeln ("example 214:");
690 val e214a'="((3 * x + 2 * y + 2 * z) / (4)) + ((-5 * x + -3 * y) / (3)) + ((x + y + -2 * z) / (2))";
691 val e214a = the (rewrite_set thy' false "common_nominator_p" e214a');
693 val e214b'="((5 * x + 2 * y + z) / (2)) + ((-7 * x + -3 * y) / (3)) + ((3 * x + 6 * y + -1 * z) / (12))";
694 val e214b = the (rewrite_set thy' false "common_nominator_p" e214b');
696 writeln ("example 216:");
698 val e216a'="((2 * b + 3 * c) / (a * c)) + ((3 * a + b) / (a * b)) + ((-2 * b^^^2 + -3 * a * c) / (a * b * c))";
699 val e216a = the (rewrite_set thy' false "common_nominator_p" e216a');
701 val e216b'="((2 * a + 3 * b) / (b * c)) + ((3 * c + a) / (a * c)) + ((-2 * a^^^2 + -3 * b * c) / (a * b * c))";
702 val e216b = the (rewrite_set thy' false "common_nominator_p" e216b');
704 writeln ("example 217:");
705 val e217'="((z + -1) / (z)) + ((3 * z ^^^2 + -6 * z + 5) / (z^^^2)) + ((-4 * z^^^3 + 7 * z^^^2 + -5 * z + 5) / (z^^^3))";
706 val e217 = the (rewrite_set thy' false "common_nominator_p" e217');
709 val rls' = "common_nominator";
710 writeln ("example 218:");
711 val e218'="((9 * a^^^3 - 5 * a^^^2 + 2 * a + 8) / (108 * a^^^4)) + ((-5 * a + 3 * a^^^2 + 4) / (8 * a^^^3)) + ((-261 * a^^^3 + 19 * a^^^2 + -112 * a + 16) / (216 * a^^^4))";
712 val e218 = the (rewrite_set thy' false "common_nominator" e218');
713 if e218 = ("(16 - 63 * a ^^^ 2 - 81 * a ^^^ 3) / (108 * a ^^^ 4)", "[]") then ()
714 else error "rationa.sml common_nominator example e218";
716 writeln ("example 219:");
718 val e219a'="((1) / (y + 1)) + ((1) / (y + 2)) + ((1) / (y + 3))";
719 val e219a = the (rewrite_set thy' false "common_nominator" e219a');
721 val e219b'="((1) / (x + 1)) + ((1) / (x + 2)) + ((-2) / (x + 3))";
722 val e219b = the (rewrite_set thy' false "common_nominator" e219b');
723 if e219b = ("(5 + 3 * x) / (6 + 11 * x + 6 * x ^^^ 2 + x ^^^ 3)", "[]") then ()
724 else error "rationa.sml common_nominator example e219b";
726 writeln ("example 220:");
728 val e220a'="((17) / (5 * r + -2)) + ((-13) / (2 * r + 3)) + ((4) / (3 * r + -5))";
729 val e220a = the (rewrite_set thy' false "common_nominator" e220a');
731 val e220b'="((20 * a) / (a + -3)) + ((-19 * a) / (a + -4)) + ((a) / (a + -5))";
732 val e220b = the (rewrite_set thy' false "common_nominator" e220b');
734 writeln ("example 221:");
736 val e221a'="((a + b) / (a + -1 * b)) + ((a + -1 * b) / (a + b))";
737 val e221a = the (rewrite_set thy' false "common_nominator" e221a');
739 val e221b'="((x + -1 * y) / (x + y)) + ((x + y) / (x + -1 * y)) ";
740 val e221b = the (rewrite_set thy' false "common_nominator" e221b');
742 writeln ("example 222:");
744 val e222a'="((1 + -1 * x) / (1 + x)) + ((-1 + -1 * x) / (1 + -1 * x)) + ((4 * x) / (1 + -1 * x^^^2))";
745 val e222a = the (rewrite_set thy' false "common_nominator" e222a');
747 val e222b'="((1 + x ) / (1 + -1 * x)) + ((-1 + x) / (1 + x)) + ((2 * x) / (1 + -1 * x^^^2))";
748 val e222b = the (rewrite_set thy' false "common_nominator" e222b');
750 writeln ("example 225:");
752 val e225a'="((6 * a) / (a^^^2 + -64)) + ((a + 2) / (2 * a + 16)) + ((-1) / (2))";
753 val e225a = the (rewrite_set thy' false "common_nominator" e225a');
755 val e225b'="((a + 2 ) / (2 * a + 12)) + ((4 * a) / (a^^^2 + -36)) + ((-1) / (2))";
756 val e225b = the (rewrite_set thy' false "common_nominator" e225b');
758 writeln ("example 226:");
760 val e226a'="((35 * z) / (49 * z^^^2 + -4)) + -1 + ((14 * z + -1) / (14 * z + 4)) ";
761 val e226a = the (rewrite_set thy' false "common_nominator" e226a');
763 val e226b'="((45 * a * b) / (25 * a^^^2 + -9 * b^^^2)) + ((20 * a + 3 * b) / (10 * a + 6 * b)) + -2";
764 val e226b = the (rewrite_set thy' false "common_nominator" e226b');
766 writeln ("example 227:");
768 val e227a'="((6 * z + 11) / (6 * z + 14)) + ((9 * z ) / (9 * z^^^2 + -49)) + -1 ";
769 val e227a = the (rewrite_set thy' false "common_nominator" e227a');
771 val e227b'="((16 * a + 37 * b) / (4 * a + 10 * b)) + ((6 * a * b) / (4 * a^^^2 + -25 * b^^^2)) + -4 ";
772 val e227b = the (rewrite_set thy' false "common_nominator" e227b');
774 writeln ("example 228:");
776 val e228a'="((7 * a + 11) / (3 * a^^^2 + -3)) + ((-2 * a + -1) / (a^^^2 + -1 * a)) + ((-1) / (3 * a + 3))";
777 val e228a = the (rewrite_set thy' false "common_nominator" e228a');
779 val e228b'="((11 * z + 2 * b) / (4 * b * z + -8 * b^^^2)) + ((-8 * z) / (z^^^2 + -4 * b^^^2)) + ((-9 * z + -2 * b) / (4 * b * z + 8 * b^^^2))";
780 val e228b = the (rewrite_set thy' false "common_nominator" e228b');
783 writeln ("example 229:");
785 val e229a'="((5 * x^^^2 + y) / (x + 2 * y)) + ((-8 * x^^^3 + 4 * x^^^2 * y + 3 * x * y) / (x^^^2 + -4 * y^^^2)) + ((3 * x^^^2 + -4 * y) / (x + -2 * y))";
786 val e229a = the (rewrite_set thy' false "common_nominator" e229a');
788 val e229b'="((7 * x^^^2 + y) / (x + 3 * y)) + ((-24 * x^^^2 * y + 5 * x * y + 21 * y^^^2) / (x^^^2 + -9 * y^^^2)) + ((4 * x^^^2 + -6 * y) / (x + -3 * y))";
789 val e229b = the (rewrite_set thy' false "common_nominator" e229b');
791 writeln ("example 230:");
793 val e230a'="((5 * x^^^2 + y) / (2 * x + y)) + ((-16 * x^^^3 + 2 * x^^^2 * y + 6 * x * y) / (4 * x^^^2 + -1 * y^^^2)) + ((3 * x^^^2 + -4 * y) / (2 * x + -1 * y))";
794 val e230a = the (rewrite_set thy' false "common_nominator" e230a');
796 val e230b'="((7 * x^^^2 + y) / (3 * x + y)) + ((-3 * x^^^3 + 15 * x * y + -7 * x^^^2 * y + 7 * y^^^2) / (9 * x^^^2 + -1 * y^^^2)) + ((4 * x^^^2 + -6 * y) / (3 * x + -1 * y))";
797 val e230b = the (rewrite_set thy' false "common_nominator" e230b');
799 writeln ("example 231:");
801 val e231a'="((2 * x + 5 * y) / (x)) + ((2 * x^^^3 + -5 * y^^^3 + 3 * x * y^^^2) / (x^^^3 + -2 * x^^^2 * y + x * y^^^2)) + ((-3 * x + -6 * y) / (x + -1 * y))";
802 val e231a = the (rewrite_set thy' false "common_nominator" e231a');
804 val e231b'="((6 * x + 2 * y) / (x)) + ((6 * x^^^2 * y + -4 * x * y^^^2 + -2 * y^^^3) / (x^^^3 + -2 * x^^^2 * y + x * y^^^2)) + ((-5 * x + -3 * y) / (x + -1 * y))";
805 val e231b = the (rewrite_set thy' false "common_nominator" e231b');
807 writeln ("example 232:");
809 val e232a'="((2 * x + 3 * y) / (x)) + ((4 * x^^^3 + -1 * x * y^^^2 + -3 * y^^^3) / (x^^^3 + -2 * x^^^2 * y + x * y^^^2)) + ((-5 * x + -6 * y) / (x + -1 * y))";
810 val e232a = the (rewrite_set thy' false "common_nominator" e232a');
812 val e232b'="((5 * x + 2 * y) / (x)) + ((2 * x^^^3 + -3 * x * y^^^2 + 3 * x^^^2 * y + -2 * y^^^3) / (x^^^3 + -2 * x^^^2 * y + x * y^^^2)) + ((-6 * x + -3 * y) / (x + -1 * y))";
813 val e232b = the (rewrite_set thy' false "common_nominator" e232b');
815 writeln ("example 233:");
817 val e233a'="((5 * x + 6 * y) / (x)) + ((5 * x * y^^^2 + -6 * y^^^3 + -2 * x^^^3 + 3 * x^^^2 * y) / (x^^^3 + -2 * x^^^2 * y + x * y^^^2)) + ((-2 * x + -3 * y) / (x + -1 * y))";
818 val e233a = the (rewrite_set thy' false "common_nominator" e233a');
820 val e233b'="((6 * x + 5 * y) / (x)) + ((4 * x^^^2 * y + 3 * x * y^^^2 + -5 * y^^^3 + -2 * x^^^3) / (x^^^3 + -2 * x^^^2 * y + x * y^^^2)) + ((-3 * x + -2 * y) / (x + -1 * y))";
821 val e233b = the (rewrite_set thy' false "common_nominator" e233b');
823 writeln ("example 234:");
825 val e234a'="((5 * a + b) / (2 * a * b + -2 * b^^^2)) + ((-3 * a + -1 * b) / (2 * a * b + 2 * b^^^2)) + ((-2 * a) / (a^^^2 + -1 * b^^^2))";
826 val e234a = the (rewrite_set thy' false "common_nominator" e234a');
828 val e234b'="((5 * a + 3 * b) / (6 * a * b + -18 * b^^^2)) + ((-3 * a + -3 * b) / (6 * a * b + 18 * b^^^2)) + ((-2 * a) / (a^^^2 + -9 * b^^^2)) ";
829 val e234b = the (rewrite_set thy' false "common_nominator" e234b');
831 writeln ("example 235:");
833 val e235a'="((10 * x + 3 * y) / (12 * x * y + -18 * y^^^2)) + ((-6 * x + -3 * y) / (12 * x * y + 18 * y^^^2)) + ((-4 * x) / (4 * x^^^2 + -9 * y^^^2))";
834 val e235a = the (rewrite_set thy' false "common_nominator" e235a');
836 val e235b'="((8 * a + b) / (4 * a * b + -2 * b^^^2)) + ((-4 * a + -1 * b) / (4 * a * b + 2 * b^^^2)) + ((-2 * a) / (4 * a^^^2 + -1 * b^^^2)) ";
837 val e235b = the (rewrite_set thy' false "common_nominator" e235b');
839 writeln ("example 236:");
841 val e236a'="((8 * a + 5 * b) / (20 * a * b + -50 * b^^^2)) + ((-4 * a + -5 * b) / (20 * a * b + 50 * b^^^2)) + ((-2 * a) / (4 * a^^^2 + -25 * b^^^2))";
842 val e236a = the (rewrite_set thy' false "common_nominator" e236a');
844 val e236b'="((24 * x + y) / (6 * x * y + -2 * y^^^2)) + ((-18 * x + -1 * y) / (6 * x * y + 2 * y^^^2)) + ((-15 * x) / (9 * x^^^2 + -1 * y^^^2)) ";
845 val e236b = the (rewrite_set thy' false "common_nominator" e236b');
849 writeln ("example heuberger:");
850 val eheu'="(x^^^4 + x * y + x^^^3 * y + y^^^2) / (x + 5 * x^^^2 + y + 5 * x * y + x^^^2 * y^^^3 + x * y^^^4)";
851 val eheu = the (rewrite_set thy' false "cancel" eheu');
853 val rls' = "common_nominator_p";
854 writeln ("example stiefel:");
855 val est1'="(7) / (-14) + (-2) / (4)";
856 val est1 = the (rewrite_set thy' false "common_nominator_p" est1');
857 if est1 = ("-1 / 1", "[]") then ()
858 else error "new behaviour in rational.sml: est1'";
860 val t = (term_of o the o (parse thy))
861 "(9 - x ^^^ 2) / (9 - 6 * x + x ^^^ 2)";
862 val SOME (t',_) = factout_ thy t;
863 if term2str t' = "(3 + x) * (3 - x) / ((3 - x) * (3 - x))" then ()
864 else error "rational.sml factout_ (9 - x ^^^ 2) / (9 - 6 * x + x ^^^ 2)";
867 "-------- reverse rewrite -------------------------------";
868 "-------- reverse rewrite -------------------------------";
869 "-------- reverse rewrite -------------------------------";
870 (*WN.28.8.02: tests for the 'reverse-rewrite' functions:
871 these are defined in Rationals.ML and stored in
872 the 'reverse-ruleset' cancel*)
874 (*the term for which reverse rewriting is demonstrated*)
875 val t = (term_of o the o (parse thy))
876 "(9 - x ^^^ 2) / (9 + 6 * x + x ^^^ 2)";
877 val Rrls {scr=Rfuns {init_state=ini,locate_rule=loc,
878 next_rule=nex,normal_form=nor,...},...} = cancel;
880 (*normal_form produces the result in ONE step*)
881 val SOME (t',_) = nor t;
882 if term2str t' = "(3 - x) / (3 + x)" then ()
883 else error "rational.sml normal_form (9 - x ^^^ 2) / (9 - 6 * x + x ^^^ 2)";
885 (*initialize the interpreter state used by the 'me'*)
886 val (t,_,revsets,_) = ini t;
888 (*find the rule 'r' to apply to term 't'*)
889 val SOME (r as (Thm (str, thm))) = nex revsets t;
890 if str = "sym_#power_Float ((3,0), (0,0)) __ ((2,0), (0,0))"
891 andalso string_of_thm thm =
892 (string_of_thm o make_thm o (cterm_of (theory "Isac")))
893 (Trueprop $ (term_of o the o (parse thy)) "9 = 3 ^^^ 2") then ()
894 else error "rational.sml next_rule (9 - x ^^^ 2) / (9 - 6 * x + x ^^^ 2)";
895 (* before Isa02->09-2 was not checked automatically, ?was different?:
896 val SOME r = nex revsets t;
897 val r = Thm ("sym_#mult_2_3","6 = 2 * 3") : rule*)
899 (* check, if the rule 'r' applied by the user to 't' belongs to the ruleset;
900 if the rule is OK, the term resulting from applying the rule is returned,too;
901 there might be several rule applications inbetween,
902 which are listed after the head in reverse order *)
903 val (r, (t, asm))::_ = loc revsets t r;
904 if term2str t = "(9 - x ^^^ 2) / (3 ^^^ 2 + 6 * x + x ^^^ 2)" andalso asm = []
906 else error "rational.sml locate_rule (9 - x ^^^ 2) / (9 - 6 * x + x ^^^ 2)";
908 (* find the next rule to apply *)
909 val SOME (r as (Thm (str, thm))) = nex revsets t;
910 if str = "sym_#power_Float ((3,0), (0,0)) __ ((2,0), (0,0))" andalso
911 string_of_thm thm = (string_of_thm o make_thm o (cterm_of (theory "Isac")))
912 (Trueprop $ (term_of o the o (parse thy)) "9 = 3 ^^^ 2") then ()
913 else error "rational.sml next_rule (9 - x ^^^ 2) / (9 - 6 * x + x ^^^ 2)";
915 (*check the next rule*)
916 val (r, (t, asm)) :: _ = loc revsets t r;
917 if term2str t = "(3 ^^^ 2 - x ^^^ 2) / (3 ^^^ 2 + 6 * x + x ^^^ 2)" then ()
918 else error "rational.sml locate_rule (9 - x ^^^ 2) / (9 - 6 * x + x ^^^ 2) II";
920 (*find and check the next rules, rewrite*)
921 val SOME r = nex revsets t;
922 val (r,(t,asm))::_ = loc revsets t r;
923 if term2str t = "(3 ^^^ 2 - x ^^^ 2) / (3 ^^^ 2 + 2 * 3 * x + x ^^^ 2)" then ()
924 else error "rational.sml locate_rule II";
926 val SOME r = nex revsets t;
927 val (r,(t,asm))::_ = loc revsets t r;
928 if term2str t = "(3 - x) * (3 + x) / (3 ^^^ 2 + 2 * 3 * x + x ^^^ 2)" then ()
929 else error "rational.sml next_rule II";
931 val SOME r = nex revsets t;
932 val (r,(t,asm))::_ = loc revsets t r;
933 if term2str t = "(3 - x) * (3 + x) / ((3 + x) * (3 + x))" then ()
934 else error "rational.sml next_rule III";
936 val SOME r = nex revsets t;
937 val (r, (t, asm)) :: _ = loc revsets t r;
939 if ss = "(3 - x) / (3 + x)" andalso terms2str asm = "[\"3 + x ~= 0\"]" then ()
940 else error "rational.sml: new behav. in rev-set cancel";
943 "-------- 'reverse-ruleset' cancel_p --------------------";
944 "-------- 'reverse-ruleset' cancel_p --------------------";
945 "-------- 'reverse-ruleset' cancel_p --------------------";
946 (*WN.11.9.02: the 'reverse-ruleset' cancel_p*)
948 (*the term for which reverse rewriting is demonstrated*)
949 val t = str2term "(9 + (-1)*x^^^2) / (9 + ((-6)*x + x^^^2))";
950 val Rrls {scr=Rfuns {init_state=ini,locate_rule=loc,
951 next_rule=nex,normal_form=nor,...},...} = cancel_p;
953 (*normal_form produces the result in ONE step*)
954 val SOME (t',_) = nor t;
955 term2str t' = "(3 + 1 * x) / (3 + -1 * x)";
957 (*initialize the interpreter state used by the 'me'*)
958 val SOME (t', asm) = cancel_p_ thy t;
959 term2str t' = "(3 + x) / (3 + -1 * x)" (*true*);
960 terms2str asm = "[\"3 + -1 * x ~= 0\"]" (*true*);
961 val (t,_,revsets,_) = ini t;
963 (* WN.10.10.02: dieser Fall terminiert nicht
964 (make_polynomial enth"alt zu viele rules)
965 WN060823 'init_state' requires rewriting on specified location in the term
966 print_depth 99; Rfuns; print_depth 3;
967 WN060831 cycling "sym_order_mult_rls_" "sym_real_mult_assoc"
968 as was with make_polynomial before ?!?*)
970 val SOME r = nex revsets t;
971 eq_Thm (r, Thm ("sym_#power_Float ((3,0), (0,0)) __ ((2,0), (0,0))",
972 mk_thm thy "9 = 3 ^^^ 2"));
973 (*WN060831 *** id_of_thm
974 Exception- ERROR raised ...
975 val (r,(t,asm))::_ = loc revsets t r;
978 val SOME r = nex revsets t;
979 val (r,(t,asm))::_ = loc revsets t r;
983 writeln "****************** all tests successfull *************************";
987 (*WN.17.3.03 =========================================================vvv---*)
988 "-------- norm_Rational ---------------------------------";
989 "-------- norm_Rational ---------------------------------";
990 "-------- norm_Rational ---------------------------------";
991 val t = str2term "(3*x+5)/18 - x/2 - -(3*x - 2)/9 = 0";
992 val SOME (t',_) = rewrite_set_ thy false norm_Rational t; term2str t';
993 if term2str t' = "1 / 18 = 0" then () else error "rational.sml 1";
995 val t = str2term "(17*x - 51)/9 - (-(13*x - 3)/6) + 11 - (9*x - 7)/4 = 0";
996 val SOME (t',_) = rewrite_set_ thy false norm_Rational t; term2str t';
997 if term2str t' = "(237 + 65 * x) / 36 = 0" then ()
998 else error "rational.sml 2";
1000 val t = str2term "(1/2 + (5*x)/2)^^^2 - ((13*x)/2 - 5/2)^^^2 - (6*x)^^^2 + 29";
1001 val SOME (t',_) = rewrite_set_ thy false norm_Rational t; term2str t';
1002 if term2str t' = "23 + 35 * x + -72 * x ^^^ 2" then ()
1003 else error "rational.sml 3";
1005 (*trace_rewrite:=true;*)
1006 val t = str2term "Not (6*x is_atom)";
1007 val SOME (t',_) = rewrite_set_ thy false powers_erls t; term2str t';
1009 val t = str2term "1 < 2";
1010 val SOME (t',_) = rewrite_set_ thy false powers_erls t; term2str t';
1013 val t = str2term "(6*x)^^^2";
1014 val SOME (t',_) = rewrite_ thy dummy_ord powers_erls false
1015 (num_str @{thm realpow_def_atom}) t;
1016 if term2str t' = "6 * x * (6 * x) ^^^ (2 + -1)" then ()
1017 else error "rational.sml powers_erls (6*x)^^^2";
1019 val t = str2term "-1 * (-2 * (5 / 2 * (13 * x / 2)))";
1020 val SOME (t',_) = rewrite_set_ thy false norm_Rational t; term2str t';
1021 if term2str t' = "65 * x / 2" then () else error "rational.sml 4";
1023 val t = str2term "1 - ((13*x)/2 - 5/2)^^^2";
1024 val SOME (t',_) = rewrite_set_ thy false norm_Rational t; term2str t';
1025 (*bef.040209: if term2str t' = "(-21 + (130 * x + -169 * x ^^^ 2)) / 4"then()*)
1026 if term2str t' = "(-21 + 130 * x + -169 * x ^^^ 2) / 4" then ()
1027 else error "rational.sml 5";
1029 (*SRAM Schalk I, p.92 Nr. 609a*)
1030 val t = str2term "2*(3 - x/5)/3 - 4*(1 - x/3) - x/3 - 2*(x/2 - 1/4)/27 +5/54";
1031 val SOME (t',_) = rewrite_set_ thy false norm_Rational t; term2str t';
1032 if term2str t' = "(-255 + 112 * x) / 135" then ()
1033 else error "rational.sml 6";
1035 (*SRAM Schalk I, p.92 Nr. 610c*)
1036 val t = str2term "((x- 1)/(x+1) + 1) / ((x- 1)/(x+1) - (x+1)/(x- 1)) - 2";
1037 val SOME (t',_) = rewrite_set_ thy false norm_Rational t; term2str t';
1038 if term2str t' = "(-3 + -1 * x) / 2" then () else error "rational.sml 7";
1040 (*SRAM Schalk I, p.92 Nr. 476a*)
1041 val t = str2term "(x^^^2/(1 - x^^^2) + 1)/(x/(1 - x) + 1) * (1 + x)";
1042 (*. a/b : c/d translated to a/b * d/c .*)
1043 val SOME (t',_) = rewrite_set_ thy false norm_Rational t; term2str t';
1044 (*if term2str t' = "1 / 1" then () else error "rational.sml 8";3.6.03*)
1045 if term2str t' = "1" then () else error "rational.sml 8";
1047 (*............................vvv---TODO: sollte gehen mit poly_order *)
1048 (*Schalk I, p.92 Nr. 472a*)
1049 val t = str2term "((8*x^^^2 - 32*y^^^2)/(2*x + 4*y))/((4*x - 8*y)/(x + y))";
1050 val SOME (t',_) = rewrite_set_ thy false norm_Rational t; term2str t';
1051 if term2str t' = "x + y" then () else error "rational.sml p.92 Nr. 472a";
1053 (*Schalk I, p.70 Nr. 480b; a/b : c/d translated to a/b * d/c*)
1054 val t = str2term ("((12*x*y/(9*x^^^2 - y^^^2))/" ^
1055 "(1/(3*x - y)^^^2 - 1/(3*x + y)^^^2)) *" ^
1056 "(1/(x - 5*y)^^^2 - 1/(x + 5*y)^^^2)/" ^
1057 "(20*x*y/(x^^^2 - 25*y^^^2))");
1058 (*... nicht simpl, zerlegt ...*)
1059 val t = str2term ("((12*x*y/(9*x^^^2 - y^^^2))/" ^
1060 "(1/(3*x - y)^^^2 - 1/(3*x + y)^^^2))");
1061 val SOME (t',_) = rewrite_set_ thy false norm_Rational t; term2str t';
1062 "(-12 * (x * y ^^^ 3) + 108 * (x * (y * x ^^^ 2))) / (12 * (x * y))";
1063 (* ~~~~~~~~~~ poly_order notwendig!*)
1064 val t = str2term ("(1/(x - 5*y)^^^2 - 1/(x + 5*y)^^^2)/" ^
1065 "(20*x*y/(x^^^2 - 25*y^^^2))");
1066 val SOME (t',_) = rewrite_set_ thy false norm_Rational t; term2str t';
1067 if term2str t' = "1 / (x ^^^ 2 + -25 * y ^^^ 2)" then ()
1068 else error "rational.sml norm_Rational 1 / (x ^^^ 2 + -25 * y ^^^ 2)";
1070 "nonterm.SK6 ----- SK060904-2a non-termination of add_fraction_p_";
1071 (*WN.2.6.03 from rlang.sml 56a
1072 val t = str2term "(a + b * x) / (a + -1 * (b * x)) + (-1 * a + b * x) / (a + b * x) = 4 * (a * b) / (a ^^^ 2 + -1 * b ^^^ 2)";
1073 val NONE = rewrite_set_ thy false common_nominator_p t;
1075 WN060831 nonterm.SK7
1076 val t = str2term "(a + b * x) / (a + -1 * (b * x)) + (-1 * a + b * x) / (a + b * x)";
1077 val NONE = add_fraction_p_ thy t;
1081 (* ------------------------------------------------------------------- *)
1082 (*---------vvv------------ MG: ab 1.7.03 ----------------vvv-----------*)
1083 (* Simplifier fuer beliebige Buchterme *)
1084 (* ------------------------------------------------------------------- *)
1085 (*----------------------- norm_Rational_mg ----------------------------*)
1086 (* ------------------------------------------------------------------- *)
1088 "-------- numeral rationals -----------------------------";
1089 "-------- numeral rationals -----------------------------";
1090 "-------- numeral rationals -----------------------------";
1091 (*SRA Schalk I, p.40 Nr. 164b *)
1092 val t = str2term "(47/6 - 76/9 + 13/4)/(35/12)";
1093 val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
1095 if (term2str t) = "19 / 21" then ()
1096 else error "rational.sml: diff.behav. in norm_Rational_mg 1";
1098 (*SRA Schalk I, p.40 Nr. 166a *)
1099 val t = str2term "((5/4)/(4+22/7) + 37/20)*(110/3 - 110/9 * 23/11)";
1100 val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
1102 if (term2str t) = "45 / 2" then ()
1103 else error "rational.sml: diff.behav. in norm_Rational_mg 2";
1106 "-------- cancellation ----------------------------------";
1107 "-------- cancellation ----------------------------------";
1108 "-------- cancellation ----------------------------------";
1109 (* e190c Stefan K.*)
1111 "((1 + 9 * a ^^^ 2)*(1 + 3 * a))/((3 * a + 9 * a ^^^ 2)*(1 + 3 * a))";
1112 val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
1115 "(1 + 9 * a ^^^ 2) / (3 * a + 9 * a ^^^ 2)"
1117 else error "rational.sml: diff.behav. in norm_Rational_mg 3";
1119 (* e192b Stefan K.*)
1121 "((x ^^^ 2)*(7 * x + (-1) * y))/((y ^^^ 2)*(7 * x + (-1) * y))";
1122 val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
1127 else error "rational.sml: diff.behav. in norm_Rational_mg 4";
1129 (*SRC Schalk I, p.66 Nr. 379c *)
1132 val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
1137 else error "rational.sml: diff.behav. in norm_Rational_mg 5";
1139 (*SRC Schalk I, p.66 Nr. 380b *)
1141 "15*(3*x+3)*(4*x+9)/(12*(2*x+7)*(5*x+5))";
1142 val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
1145 "(27 + 12 * x) / (28 + 8 * x)"
1147 else error "rational.sml: diff.behav. in norm_Rational_mg 6";
1149 (*Schalk I, p.60 Nr. 215c *)
1150 (* Falsches Ergebnis: rechnet lange und cancel_p kann nicht weiter krzen!!!*)
1152 val t = str2term "(a+b)^^^4*(x - y)/((x - y)^^^3*(a+b)^^^2)";
1153 val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
1156 "(a ^^^ 4 * x + -1 * a ^^^ 4 * y + 4 * a ^^^ 3 * b * x + -4 * a ^^^ 3 * b * y + 6 * a ^^^ 2 * b ^^^ 2 * x + -6 * a ^^^ 2 * b ^^^ 2 * y + 4 * a * b ^^^ 3 * x + -4 * a * b ^^^ 3 * y + b ^^^ 4 * x + -1 * b ^^^ 4 * y) /(a ^^^ 2 * x ^^^ 3 + -3 * a ^^^ 2 * x ^^^ 2 * y + 3 * a ^^^ 2 * x * y ^^^ 2 + -1 * a ^^^ 2 * y ^^^ 3 + 2 * a * b * x ^^^ 3 + -6 * a * b * x ^^^ 2 * y + 6 * a * b * x * y ^^^ 2 + -2 * a * b * y ^^^ 3 + b ^^^ 2 * x ^^^ 3 + -3 * b ^^^ 2 * x ^^^ 2 * y + 3 * b ^^^ 2 * x * y ^^^ 2 + -1 * b ^^^ 2 * y ^^^ 3)"
1158 else error "rational.sml: diff.behav. in norm_Rational_mg 7";
1161 "(a ^^^ 4 * x + -1 * a ^^^ 4 * y + 4 * a ^^^ 3 * b * x + -4 * a ^^^ 3 * b * y + 6 * a ^^^ 2 * b ^^^ 2 * x + -6 * a ^^^ 2 * b ^^^ 2 * y + 4 * a * b ^^^ 3 * x + -4 * a * b ^^^ 3 * y + b ^^^ 4 * x + -1 * b ^^^ 4 * y) /(a ^^^ 2 * x ^^^ 3 + -3 * a ^^^ 2 * x ^^^ 2 * y + 3 * a ^^^ 2 * x * y ^^^ 2 + -1 * a ^^^ 2 * y ^^^ 3 + 2 * a * b * x ^^^ 3 + -6 * a * b * x ^^^ 2 * y + 6 * a * b * x * y ^^^ 2 + -2 * a * b * y ^^^ 3 + b ^^^ 2 * x ^^^ 3 + -3 * b ^^^ 2 * x ^^^ 2 * y + 3 * b ^^^ 2 * x * y ^^^ 2 + -1 * b ^^^ 2 * y ^^^ 3)"
1162 val SOME (t,_) = rewrite_set_ thy false cancel_p t;
1164 (* uncaught exception nonexhaustive binding failure
1165 raised at: stdIn:93.1-93.51 *)
1167 (*Schalk I, p.66 Nr. 381a *)
1168 (* ACHTUNG: rechnet ca. 2 Minuten !!! *)
1170 val t = str2term "18*(a+b)^^^3*(a - b)^^^2/(72*(a - b)^^^3*(a+b)^^^2)";
1171 val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
1174 "(a + b) / (4 * a + -4 * b)"
1175 then () else error "rational.sml: diff.behav. in norm_Rational_mg 8";
1178 (*SRC Schalk I, p.66 Nr. 381b *)
1180 "(4*x^^^2 - 20*x + 25)/(2*x - 5)^^^3";
1181 val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
1186 else error "rational.sml: diff.behav. in norm_Rational_mg 9";
1188 (*SRC Schalk I, p.66 Nr. 381c *)
1190 "(27*a^^^3+9*a^^^2+3*a+1)/(27*a^^^3+18*a^^^2+3*a)";
1191 val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
1194 "(1 + 9 * a ^^^ 2) / (3 * a + 9 * a ^^^ 2)"
1196 else error "rational.sml: diff.behav. in norm_Rational_mg 10";
1198 (*SRC Schalk I, p.66 Nr. 383a *)
1200 "(5*a^^^2 - 5*a*b)/(a - b)^^^2";
1201 val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
1204 "5 * a / (a + -1 * b)"
1206 else error "rational.sml: diff.behav. in norm_Rational_mg 11";
1209 "-------- common denominator ----------------------------";
1210 "-------- common denominator ----------------------------";
1211 "-------- common denominator ----------------------------";
1212 (*SRA Schalk I, p.67 Nr. 403a *)
1215 val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
1218 "(-3 * x + 4 * y + -1 * x * y) / (x * y)"
1220 else error "rational.sml: diff.behav. in norm_Rational_mg 12";
1222 (*SRA Schalk I, p.67 Nr. 407b *)
1224 "(2*a+3*b)/(b*c) + (3*c+a)/(a*c) - (2*a^^^2+3*b*c)/(a*b*c)";
1225 val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
1230 else error "rational.sml: diff.behav. in norm_Rational_mg 13";
1232 (*SRA Schalk I, p.67 Nr. 410b *)
1234 "1/(x+1) + 1/(x+2) - 2/(x+3)";
1235 val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
1238 "(5 + 3 * x) / (6 + 11 * x + 6 * x ^^^ 2 + x ^^^ 3)"
1240 else error "rational.sml: diff.behav. in norm_Rational_mg 14";
1242 (*SRA Schalk I, p.67 Nr. 413b *)
1244 "(1+x)/(1 - x) - (1 - x)/(1+x) + 2*x/(1 - x^^^2)";
1245 val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
1248 "6 * x / (1 + -1 * x ^^^ 2)"
1250 else error "rational.sml: diff.behav. in norm_Rational_mg 15";
1252 (*SRA Schalk I, p.68 Nr. 414a *)
1254 "(x + 2)/(x - 1) + (x - 3)/(x - 2) - (x + 1)/((x - 1)*(x - 2))";
1255 val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
1258 "(-2 + -5 * x + 2 * x ^^^ 2) / (2 + -3 * x + x ^^^ 2)"
1260 else error "rational.sml: diff.behav. in norm_Rational_mg 16";
1262 (*SRA Schalk I, p.68 Nr. 423a *)
1264 "(2*x+3*y)/x + (4*x^^^3 - x*y^^^2 - 3*y^^^3)/(x^^^3 - 2*x^^^2*y+x*y^^^2) - (5*x+6*y)/(x - y)";
1265 val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
1270 else error "rational.sml: diff.behav. in norm_Rational_mg 17";
1272 (*SRA Schalk I, p.68 Nr. 428b *)
1274 "1/(a - b)^^^2 + 1/(a+b)^^^2 - 2/(a^^^2 - b^^^2) - 4*(b^^^2 - 1)/(a^^^2 - b^^^2)^^^2";
1275 val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
1278 "4 / (a ^^^ 4 + -2 * a ^^^ 2 * b ^^^ 2 + b ^^^ 4)"
1280 else error "rational.sml: diff.behav. in norm_Rational_mg 18";
1282 (*SRA Schalk I, p.68 Nr. 430b *)
1284 "a^^^2/(a - 3*b) - 108*a*b^^^3/((a+3*b)*(a^^^2 - 9*b^^^2)) - 9*b^^^2*(a - 3*b)/(a+3*b)^^^2";
1285 val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
1290 else error "rational.sml: diff.behav. in norm_Rational_mg 19";
1293 (*SRA Schalk I, p.68 Nr. 432 *)
1295 "(a^^^2+a*b)/(a^^^2 - b^^^2) - (b^^^2 - a*b)/(b^^^2 - a^^^2) + a^^^2*(a - b)/(a^^^3 - a^^^2*b) - 2*a*(a^^^2 - b^^^2)/(a^^^3 - a*b^^^2) - 2*b^^^2/(a^^^2 - b^^^2)";
1296 val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
1301 else error "rational.sml: diff.behav. in norm_Rational_mg 20";
1306 val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
1309 "(3 * y + b * x) / (b * y)"
1311 else error "rational.sml: diff.behav. in norm_Rational_mg 21";
1314 "-------- multiply and cancel ---------------------------";
1315 "-------- multiply and cancel ---------------------------";
1316 "-------- multiply and cancel ---------------------------";
1317 (*SRM Schalk I, p.68 Nr. 436a *)
1319 "3*(x+y)/(15*(x - y)) * 25*(x - y)^^^2/(18*(x+y)^^^2)";
1320 val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
1323 "(5 * x + -5 * y) / (18 * x + 18 * y)"
1325 else error "rational.sml: diff.behav. in norm_Rational_mg 22";
1327 (*SRM.test Schalk I, p.68 Nr. 436b *)
1328 (*WN060420???MG3 crashes with method 'simplify' in
1329 IsacCore > Simplification > Rational Terms > Multiplication > No.2*)
1330 val t = str2term "5*a*(a - b)^^^2*(a + b)^^^3/(7*b*(a - b)^^^3) * 7*b/(a + b)^^^3";
1331 val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
1334 "5 * a / (a + -1 * b)"
1336 else error "rational.sml: diff.behav. in norm_Rational_mg 23";
1338 (*Schalk I, p.68 Nr. 437a *)
1339 val t = str2term "(3*a - 4*b)/(4*c+3*e) * (3*a+4*b)/(9*a^^^2 - 16*b^^^2)";
1340 val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
1341 if (term2str t) = "1 / (4 * c + 3 * e)" then ()
1342 else error "rational.sml: diff.behav. in norm_Rational_mg 24";
1344 "----- S.K. corrected non-termination 060904";
1345 val t = str2term "(3*a - 4*b) * (3*a+4*b)/((4*c+3*e)*(9*a^^^2 - 16*b^^^2))";
1346 val SOME (t',_) = rewrite_set_ thy false make_polynomial t;
1347 if term2str t' = "(9 * a ^^^ 2 + -16 * b ^^^ 2) /\n(36 * a ^^^ 2 * c + 27 * a ^^^ 2 * e + -64 * b ^^^ 2 * c +\n -48 * b ^^^ 2 * e)" then ()
1348 else error "rational.sml: S.K.8..corrected 060904-6";
1350 "----- S.K. corrected non-termination of cancel_p_";
1351 val t'' = str2term ("(9 * a ^^^ 2 + -16 * b ^^^ 2) /" ^
1352 "(36 * a^^^2 * c + (27 * a^^^2 * e + (-64 * b^^^2 * c + -48 * b^^^2 * e)))");
1353 val SOME (t',_) = rewrite_set_ thy false cancel_p t'';
1354 if term2str t' = "1 / (4 * c + 3 * e)" then ()
1355 else error "rational.sml: diff.behav. in cancel_p S.K.8";
1357 (*Schalk I, p.68 Nr. 437b *)
1358 (* nonterm.SK9 loops: cancel_p kann nicht weiter kuerzen!!! *)
1359 val t'' = str2term "(a + b)/(x^^^2 - y^^^2) * ((x - y)^^^2/(a^^^2 - b^^^2))";
1360 (* val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t'';
1363 "================delete===";
1364 (*a casual output from above*)
1366 "(a * x ^^^ 2 + -2 * a * x * y + a * y ^^^ 2 + b * x ^^^ 2 + -2 * b * x * y + b * y ^^^ 2) /(a ^^^ 2 * x ^^^ 2 + -1 * a ^^^ 2 * y ^^^ 2 + -1 * b ^^^ 2 * x ^^^ 2 + b ^^^ 2 * y ^^^ 2)";
1367 (* WN060831 nonterm.SK10
1368 val SOME (t,_) = rewrite_set_ thy false cancel_p t;
1372 (*SRM Schalk I, p.68 Nr. 438a *)
1374 "x*y/(x*y - y^^^2)*(x^^^2 - x*y)";
1375 val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
1380 else error "rational.sml: diff.behav. in norm_Rational_mg 24";
1382 (*SRM Schalk I, p.68 Nr. 439b *)
1384 "(4*x^^^2+4*x+1)*((x^^^2 - 2*x^^^3)/(4*x^^^2+2*x))";
1385 val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
1388 "(x + -4 * x ^^^ 3) / 2"
1390 else error "rational.sml: diff.behav. in norm_Rational_mg 25";
1392 (*SRM Schalk I, p.68 Nr. 440a *)
1394 "(x^^^2 - 2*x)/(x^^^2 - 3*x) * (x - 3)^^^2/(x^^^2 - 4)";
1395 val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
1398 "(-3 + x) / (2 + x)"
1400 else error "rational.sml: diff.behav. in norm_Rational_mg 26";
1402 "----- Schalk I, p.68 Nr. 440b SK11 works since 0707xx";
1404 "(a^^^3 - 9*a)/(a^^^3*b - a*b^^^3)*(a^^^2*b+a*b^^^2)/(a+3)";
1405 val SOME (t,_) = rewrite_set_ thy false norm_Rational t;
1406 if term2str t = "(-3 * a + a ^^^ 2) / (a + -1 * b)" then ()
1407 else error "rational.sml: diff.behav. in norm_Rational 27";
1409 "----- SK12 works since 0707xx";
1410 val t = str2term "(a^^^3 - 9*a)*(a^^^2*b+a*b^^^2)/((a^^^3*b - a*b^^^3)*(a+3))";
1411 val SOME (t',_) = rewrite_set_ thy false norm_Rational t; term2str t';
1412 if term2str t' = "(-3 * a + a ^^^ 2) / (a + -1 * b)" then ()
1413 else error "rational.sml: diff.behav. in norm_Rational 28";
1416 "-------- common denominator and multiplication ---------";
1417 "-------- common denominator and multiplication ---------";
1418 "-------- common denominator and multiplication ---------";
1419 (*SRAM Schalk I, p.69 Nr. 441b *)
1420 val t = str2term "(4*a/3 + 3*b^^^2/a^^^3 + b/(4*a))*(4*b/(3*a))";
1421 val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
1424 "(36 * b ^^^ 3 + 3 * a ^^^ 2 * b ^^^ 2 + 16 * a ^^^ 4 * b) / (9 * a ^^^ 4)"
1425 then () else error "rational.sml: diff.behav. in norm_Rational_mg 28";
1427 (*SRAM Schalk I, p.69 Nr. 442b *)
1428 val t = str2term "(15*a^^^2/x^^^3 - 5*b^^^4/x^^^2 + 25*c^^^2/x)*(x^^^3/(5*a*b^^^3*c^^^3)) + 1/c^^^3 * (b*x/a - 3*a/b^^^3)";
1429 val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
1432 "5 * x ^^^ 2 / (a * b ^^^ 3 * c)"
1433 then () else error "rational.sml: diff.behav. in norm_Rational_mg 29";
1435 (*SRAM Schalk I, p.69 Nr. 443b *)
1436 val t = str2term "(a/2 + b/3)*(b/3 - a/2)";
1437 val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
1440 "(-9 * a ^^^ 2 + 4 * b ^^^ 2) / 36"
1441 then () else error "rational.sml: diff.behav. in norm_Rational_mg 30";
1443 (*SRAM Schalk I, p.69 Nr. 445b *)
1444 val t = str2term "(a^^^2/9 + 2*a/(3*b) + 4/b^^^2)*(a/3 - 2/b) + 8/b^^^3";
1445 val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
1449 then () else error "rational.sml: diff.behav. in norm_Rational_mg 31";
1451 (*SRAM Schalk I, p.69 Nr. 446b *)
1452 val t = str2term "(x/(5*x + 4*y) - y/(5*x - 4*y) + 1)*(25*x^^^2 - 16*y^^^2)";
1453 val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
1456 "30 * x ^^^ 2 + -9 * x * y + -20 * y ^^^ 2"
1458 else error "rational.sml: diff.behav. in norm_Rational_mg 32";
1460 (*SRAM Schalk I, p.69 Nr. 449a *)(*Achtung: rechnet ca 8 Sekunden*)
1462 "(2*x^^^2/(3*y)+x/y^^^2)*(4*x^^^4/(9*y^^^2)+x^^^2/y^^^4)*(2*x^^^2/(3*y) - x/y^^^2)";
1463 val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
1465 if (term2str t) = "(-81 * x ^^^ 4 + 16 * x ^^^ 8 * y ^^^ 4) / (81 * y ^^^ 8)"
1466 then () else error "rational.sml: diff.behav. in norm_Rational_mg 33";
1469 (*SRAM Schalk I, p.69 Nr. 450a *)
1471 "(4*x/(3*y)+2*y/(3*x))^^^2 - (2*y/(3*x) - 2*x/y)*(2*y/(3*x)+2*x/y)";
1472 val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
1475 "(52 * x ^^^ 2 + 16 * y ^^^ 2) / (9 * y ^^^ 2)"
1477 else error "rational.sml: diff.behav. in norm_Rational_mg 34";
1480 "-------- double fractions ------------------------------";
1481 "-------- double fractions ------------------------------";
1482 "-------- double fractions ------------------------------";
1483 (*SRD Schalk I, p.69 Nr. 454b *)
1485 "((2 - x)/(2*a)) / (2*a/(x - 2))";
1486 val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
1489 "(-4 + 4 * x + -1 * x ^^^ 2) / (4 * a ^^^ 2)"
1491 else error "rational.sml: diff.behav. in norm_Rational_mg 35";
1493 (*SRD Schalk I, p.69 Nr. 455a *)
1495 "(a^^^2 + 1)/(a^^^2 - 1) / ((a+1)/(a - 1))";
1496 val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
1499 "(1 + a ^^^ 2) / (1 + 2 * a + a ^^^ 2)" then ()
1500 else error "rational.sml: diff.behav. in norm_Rational_mg 36";
1503 "----- Schalk I, p.69 Nr. 455b";
1504 val t = str2term "(x^^^2 - 4)/(y^^^2 - 9)/((2+x)/(3 - y))";
1505 val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
1506 if term2str t = "(2 + -1 * x) / (3 + y)" then ()
1507 else error "rational.sml: diff.behav. in norm_Rational_mg 37";
1509 "----- SK060904-1a non-termination of cancel_p_ ?: worked before 0707xx";
1510 val t = str2term "(x^^^2 - 4)*(3 - y)/((y^^^2 - 9)*(2+x))";
1511 val SOME (t,_) = rewrite_set_ thy false norm_Rational t;
1512 if term2str t = "(2 + -1 * x) / (3 + y)" then ()
1513 else error "rational.sml: diff.behav. in norm_Rational_mg 37b";
1515 "----- ?: worked before 0707xx";
1516 val t = str2term "(3 + -1 * y) / (-9 + y ^^^ 2)";
1517 val SOME (t,_) = rewrite_set_ thy false norm_Rational t;
1518 if term2str t = "-1 / (3 + y)" then ()
1519 else error "rational.sml: -1 / (3 + y) norm_Rational";
1521 (*SRD Schalk I, p.69 Nr. 456b *)
1523 "(b^^^3 - b^^^2)/(b^^^2+b)/(b^^^2 - 1)";
1524 val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
1526 if (term2str t) = "b / (1 + 2 * b + b ^^^ 2)" then ()
1527 else error "rational.sml: diff.behav. in norm_Rational_mg 38";
1529 (*SRD Schalk I, p.69 Nr. 457b *)
1531 "(16*a^^^2 - 9*b^^^2)/(2*a+3*a*b) / ((4*a+3*b)/(4*a^^^2 - 9*a^^^2*b^^^2))";
1532 val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
1535 "8 * a ^^^ 2 + -6 * a * b + -12 * a ^^^ 2 * b + 9 * a * b ^^^ 2"
1537 else error "rational.sml: diff.behav. in norm_Rational_mg 39";
1539 "----- Schalk I, p.69 Nr. 458b works since 0707";
1541 "(2*a^^^2*x - a^^^2)/(a*x - b*x) / (b^^^2*(2*x - 1)/(x*(a - b)))";
1542 val SOME (t,_) = rewrite_set_ thy false norm_Rational t;
1543 if term2str t = "a ^^^ 2 / b ^^^ 2" then ()
1544 else error "rational.sml: diff.behav. in norm_Rational_mg 39b";
1546 (*SRD Schalk I, p.69 Nr. 459b *)
1547 val t = str2term "(a^^^2 - b^^^2)/(a*b) / (4*(a+b)^^^2/a)";
1548 val SOME (t,_) = rewrite_set_ thy false norm_Rational t;
1549 if term2str t = "(a + -1 * b) / (4 * a * b + 4 * b ^^^ 2)" then ()
1550 else error "rational.sml: diff.behav. in norm_Rational_mg 41";
1553 (*Schalk I, p.69 Nr. 460b nonterm.SK
1555 "(9*(x^^^2 - 8*x+16)/(4*(y^^^2 - 2*y+1)))/((3*x - 12)/(16*y - 16))";
1556 val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
1559 else error "rational.sml: diff.behav. in norm_Rational_mg 42";
1562 "9*(x^^^2 - 8*x+16)*(16*y - 16)/(4*(y^^^2 - 2*y+1)*(3*x - 12))";
1563 val SOME (t',_) = rewrite_set_ thy false norm_Rational t;
1564 ... non terminating.
1565 val SOME (t',_) = rewrite_set_ thy false make_polynomial t;
1566 "(-2304 + 1152 * x + 2304 * y + -144 * x ^^^ 2 + -1152 * x * y + 144 * x ^^^ 2 * y) /(-48 + 12 * x + 96 * y + -24 * x * y + -48 * y ^^^ 2 + 12 * x * y ^^^ 2)";
1567 val SOME (t,_) = rewrite_set_ thy false cancel_p t';
1568 ... non terminating.*)
1570 (*SRD Schalk I, p.70 Nr. 472a *)
1571 val t = str2term ("((8*x^^^2 - 32*y^^^2)/(2*x + 4*y))/" ^
1572 "((4*x - 8*y)/(x + y))");
1573 val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
1578 else error "rational.sml: diff.behav. in norm_Rational_mg 43";
1581 (*----------------------------------------------------------------------*)
1582 (*---------------------- Einfache Dppelbrche --------------------------*)
1583 (*----------------------------------------------------------------------*)
1585 (*SRD Schalk I, p.69 Nr. 461a *)
1587 "(2/(x+3) + 2/(x - 3)) / (8*x/(x^^^2 - 9))";
1588 val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
1593 else error "rational.sml: diff.behav. in norm_Rational_mg 44";
1595 (*SRD Schalk I, p.69 Nr. 464b *)
1597 "(a - a/(a - 2)) / (a + a/(a - 2))";
1598 val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
1601 "(3 + -1 * a) / (1 + -1 * a)"
1603 else error "rational.sml: diff.behav. in norm_Rational_mg 45";
1605 (*SRD Schalk I, p.69 Nr. 465b *)
1607 "((x+3*y)/9 + (4*y^^^2 - 9*z^^^2)/(16*x)) /(x/9+y/6+z/4)";
1608 val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
1611 "(4 * x + 6 * y + -9 * z) / (4 * x)"
1613 else error "rational.sml: diff.behav. in norm_Rational_mg 46";
1615 (*SRD Schalk I, p.69 Nr. 466b *)
1617 "((1 - 7*(x - 2)/(x^^^2 - 4)) / (6/(x+2))) / (3/(x+5)+30/(x^^^2 - 25))";
1618 val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
1621 "(25 + -10 * x + x ^^^ 2) / 18"
1623 else error "rational.sml: diff.behav. in norm_Rational_mg 47";
1625 (*SRD Schalk I, p.70 Nr. 469 *)
1627 "3*b^^^2/(4*a^^^2 - 8*a*b + 4*b^^^2)/(a/(a^^^2*b - b^^^3) + (a - b)/(4*a*b^^^2+4*b^^^3) - 1/(4*b^^^2))";
1628 val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
1631 "3 * b ^^^ 3 / (2 * a + -2 * b)"
1633 else error "rational.sml: diff.behav. in norm_Rational_mg 48";
1635 (*----------------------------------------------------------------------*)
1636 (*---------------------- Mehrfache Dppelbrueche ------------------------*)
1637 (*----------------------------------------------------------------------*)
1639 (*SRD.test Schalk I, p.70 Nr. 476b *) (* Rechenzeit: 10 sec *)
1640 (*WN060419 crashes with method 'simplify' ????SK*)
1642 "((a^^^2 - b^^^2)/(2*a*b)+2*a*b/(a^^^2 - b^^^2))/((a^^^2+b^^^2)/(2*a*b)+1) / ((a^^^2+b^^^2)^^^2/(a+b)^^^2)";
1643 val SOME (t,_) = rewrite_set_ thy false norm_Rational t;
1644 if term2str t = "1 / (a ^^^ 2 + -1 * b ^^^ 2)" then ()
1645 else error "rational.sml: diff.behav. in norm_Rational_mg 49";
1647 "----- Schalk I, p.70 Nr. 477a";
1648 (* MG Achtung: terme explodieren; Bsp zu komplex;
1649 L???ung sollte (ziemlich grosser) Faktorisierter Ausdruck sein
1650 val t = str2term "b*y/(b - 2*y)/((b^^^2 - y^^^2)/(b+2*y)) /" ^
1651 "(b^^^2*y+b*y^^^2)*(a+x)^^^2/((b^^^2 - 4*y^^^2)*(a+2*x)^^^2)";
1652 val SOME (t',_) = rewrite_set_ thy false norm_Rational t;
1655 val t = str2term "b*y*(b+2*y)*(b^^^2 - 4*y^^^2)*(a+2*x)^^^2 / " ^
1656 "((b - 2*y)*(b^^^2 - y^^^2)*(b^^^2*y+b*y^^^2)*(a+x)^^^2)";
1657 val SOME (t,_) = rewrite_set_ thy false make_polynomial t;
1661 "----- Schalk I, p.70 Nr. 478b ----- Rechenzeit: 5 sec";
1662 val t = str2term ("(a - (a*b+b^^^2)/(a+b))/(b+(a - b)/(1+(a+b)/(a - b))) / " ^
1663 "((a - a^^^2/(a+b))/(a+(a*b)/(a - b)))");
1664 val SOME (t',_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
1666 "(2 * a ^^^ 3 + 2 * a ^^^ 2 * b) / (a ^^^ 2 * b + b ^^^ 3)"
1668 else error "rational.sml: diff.behav. in norm_Rational_mg 51";
1670 (* TODO.new_c:WN050820 STOP_REW_SUB introduced gave ...
1671 if term2str t' = "(a ^^^ 4 + -1 * a ^^^ 2 * b ^^^ 2) /(a * b * (b + (a * (a + -1 * b) + -1 * b * (a + -1 * b)) / (2 * a)) * (a + -1 * b))" then ()
1672 else error "rational.sml: works again";
1673 re-outcommented with TODO.new_c: cvs before 071227, 11:50*)
1677 (*Schalk I, p.70 Nr. 480a *)
1678 (* Achtung: rechnet ewig; cancel_p kann nicht krzen: WN060831 nonterm.SK00
1680 "(1/x+1/y+1/z)/(1/x - 1/y - 1/z) / (2*x^^^2/(x^^^2 - z^^^2)/(x/(x+z)+x/(x - z)))";
1681 val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
1686 else error "rational.sml: diff.behav. in norm_Rational_mg 52";
1688 (*MG Berechne Zwischenergebnisse: WN060831 nonterm.SK00*)
1690 "(1/x+1/y+1/z)/(1/x - 1/y - 1/z)";
1691 val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
1693 "(x ^^^ 2 * y ^^^ 2 * z + x ^^^ 2 * y * z ^^^ 2 + x * y ^^^ 2 * z ^^^ 2) /
1694 (-1 * x ^^^ 2 * y ^^^ 2 * z + -1 * x ^^^ 2 * y * z ^^^ 2 + x * y ^^^ 2 * z ^^^ 2)";
1696 "2*x^^^2/(x^^^2 - z^^^2)/(x/(x+z)+x/(x - z))";
1697 val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
1701 (* SK 1. Ausdruck kann nicht weiter gekrzt werden; cancel_p !!!*)
1702 ### rls: cancel_p on:
1703 (x ^^^ 2 * (y ^^^ 2 * z) + x ^^^ 2 * (y * z ^^^ 2) + x * (y ^^^ 2 * z ^^^ 2)) /
1704 (-1 * (x ^^^ 2 * (y ^^^ 2 * z)) + -1 * (x ^^^ 2 * (y * z ^^^ 2)) + x * (y ^^^ 2 * z ^^^ 2))
1705 GC #3.61.81.101.197.17503: (0 ms)
1706 *** RATIONALS_DIRECT_CANCEL_EXCEPTION: Invalid fraction
1709 "(x^^^2 * (y^^^2 * z) + x^^^2 * (y * z^^^2) + x * (y^^^2 * z^^^2)) / (-1 * (x^^^2 * (y^^^2 * z)) + -1 * (x^^^2 * (y * z^^^2)) + x * (y^^^2 * z^^^2))";
1710 val SOME (t,_) = rewrite_set_ thy false cancel_p t;
1712 (*uncaught exception nonexhaustive binding failure*)
1714 (* Das kann er aber krzen !!????: *)
1716 "(x^^^2 * (y^^^2 * z) + x * (y^^^2 * z^^^2)) / (-1 * (x^^^2 * (y * z^^^2)) + x * (y^^^2 * z^^^2))";
1717 val SOME (t,_) = rewrite_set_ thy false cancel_p t;
1719 "(-1 * (y * x) + -1 * (z * y)) / (1 * (z * x) + -1 * (z * y))";
1723 "-------- crucial examples ------------------------------";
1724 "-------- crucial examples ------------------------------";
1725 "-------- crucial examples ------------------------------";
1726 (*Schalk I, p.60 Nr. 215d *)
1727 (* Achtung: rechnet ewig ...
1728 val t = str2term "(a-b)^^^3 * (x+y)^^^4 / ((x+y)^^^2 * (a-b)^^^5)";
1729 val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
1730 term2str t; noterm.SK
1733 (* Kein Wunder, denn Z???ler und Nenner extra als Polynom dargestellt ergibt:*)
1735 val t = str2term "(a-b)^^^3 * (x+y)^^^4";
1736 val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
1738 "a^^^3 * x^^^4 + 4 * a^^^3 * x^^^3 * y +6 * a^^^3 * x^^^2 * y^^^2 +4 * a^^^3 * x * y^^^3 +a^^^3 * y^^^4 +-3 * a^^^2 * b * x^^^4 +-12 * a^^^2 * b * x^^^3 * y +-18 * a^^^2 * b * x^^^2 * y^^^2 +-12 * a^^^2 * b * x * y^^^3 +-3 * a^^^2 * b * y^^^4 +3 * a * b^^^2 * x^^^4 +12 * a * b^^^2 * x^^^3 * y +18 * a * b^^^2 * x^^^2 * y^^^2 +12 * a * b^^^2 * x * y^^^3 +3 * a * b^^^2 * y^^^4 +-1 * b^^^3 * x^^^4 +-4 * b^^^3 * x^^^3 * y +-6 * b^^^3 * x^^^2 * y^^^2 +-4 * b^^^3 * x * y^^^3 +-1 * b^^^3 * y^^^4";
1739 val t = str2term "((x+y)^^^2 * (a-b)^^^5)";
1740 val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
1742 "a^^^5 * x^^^2 + 2 * a^^^5 * x * y + a^^^5 * y^^^2 +-5 * a^^^4 * b * x^^^2 +-10 * a^^^4 * b * x * y +-5 * a^^^4 * b * y^^^2 +10 * a^^^3 * b^^^2 * x^^^2 +20 * a^^^3 * b^^^2 * x * y +10 * a^^^3 * b^^^2 * y^^^2 +-10 * a^^^2 * b^^^3 * x^^^2 +-20 * a^^^2 * b^^^3 * x * y +-10 * a^^^2 * b^^^3 * y^^^2 +5 * a * b^^^4 * x^^^2 +10 * a * b^^^4 * x * y +5 * a * b^^^4 * y^^^2 +-1 * b^^^5 * x^^^2 +-2 * b^^^5 * x * y +-1 * b^^^5 * y^^^2";
1744 (*anscheinend macht dem Rechner das Krzen diese Bruches keinen Spass mehr ...*)
1746 (*--------------------------------------------------------------------*)
1747 (*Schalk I, p.70 Nr. 480b
1748 val t = str2term "((12*x*y/(9*x^^^2 - y^^^2))/" ^
1749 "(1/(3*x - y)^^^2 - 1/(3*x + y)^^^2)) *" ^
1750 "(1/(x - 5*y)^^^2 - 1/(x + 5*y)^^^2)/" ^
1751 "(20*x*y/(x^^^2 - 25*y^^^2))";
1752 val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
1754 Kann nicht weiter vereinfacht werden !!!!?? *)
1756 (*--------------------------------------------------------------------*)
1757 "---- MGs test set";
1758 val t = str2term " (1 + x^^^5) / (y + x) + x^^^3 / x ";
1759 val SOME (t,_) = rewrite_set_ thy false common_nominator_p t;
1760 if term2str t = "(1 + x ^^^ 3 + x ^^^ 5 + y * x ^^^ 2) / (x + y)" then()
1763 (*--------------------------------------------------------------------*)
1764 (* cancel_p liefert nicht immer Polynomnormalform (2): WN060831???SK3b
1765 ---> Sortierung FALSCH !! *)
1766 val t = str2term "b^^^3 * a^^^5/a ";
1767 val SOME (t,_) = rewrite_set_ thy false cancel_p t;
1769 "1 * (a^^^4 * b^^^3) / 1"; (*OK*)
1771 val t = str2term "b^^^3 * a^^^5/b ";
1772 val SOME (t,_) = rewrite_set_ thy false cancel_p t;
1774 "1 * (b^^^2 * a^^^5) / 1"; (*cancel_p sortiert hier falsch um!*)
1776 (* Problem liegt NICHT bei ord_make_polynomial! (siehe folgende Bsple) *)
1778 val x = str2term "x"; val bdv = str2term "bdv";
1779 val t1 = str2term "b^^^2 * a^^^5";
1780 val t2 = str2term "a^^^5 * b^^^2 ";
1781 ord_make_polynomial false Rational.thy [(x,bdv)] (t1,t2); (*false*)
1783 (* ==> "b^^^2 * a^^^5" > "a^^^5 * b^^^2 " ... OK!*)
1785 (*--------------------------------------------------------------------*)
1786 (* cancel_p liefert nicht immer Polynomnormalform (2): WN060831???SK3c
1787 ---> erzeugt berflssige "1 * ..."
1789 val t = str2term "-1 / (3 + y)";
1791 val SOME (t,_) = rewrite_set_ thy false cancel_p t;
1794 (********* Das ist das PROBLEM !!!!!!!??? *******************)
1795 (* -1 im Z???ler der Angabe verursacht das Problem !*)
1798 (* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - *)
1799 "----- MGs test set";
1800 val t = str2term "(a^^^2 + -1)/(a+1)";
1801 val SOME (t',_) = rewrite_set_ thy false cancel_p t;
1802 if term2str t' = "(-1 + a) / 1" then ()
1803 else error "rational.sml MG tests 3d";
1805 "----- NOT TERMINATING ?: worked before 0707xx";
1806 val t = str2term "(a^^^2 - 1)*(b + 1) / ((b^^^2 - 1)*(a+1))";
1807 val SOME (t'',_) = rewrite_set_ thy false norm_Rational t;
1808 if term2str t'' = "(1 + -1 * a) / (1 + -1 * b)" then ()
1809 else error "rational.sml MG tests 3e";
1811 "----- corrected SK060905";
1812 val t = str2term "(4*x^^^2 - 20*x + 25)/(2*x - 5)^^^3";
1813 val SOME (t',_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
1814 if term2str t' = "-1 / (5 + -2 * x)" then ()
1815 else error "rational.sml corrected SK060905";
1818 "-------- examples for Stefan Karnels thesis ------------";
1819 "-------- examples for Stefan Karnels thesis ------------";
1820 "-------- examples for Stefan Karnels thesis ------------";
1821 (*SRAM Schalk I, p.69 Nr. 442b --- abgewandelt*)
1823 "(15*a^^^4/(a*x^^^3) - 5*a*((b^^^4 - 5*c^^^2*x)/x^^^2))*(x^^^3/(5*a*b^^^3*c^^^3)) + a/c^^^3 * (x*(b/a) - 3*b*(a/b^^^4))";
1824 val SOME (t,_) = rewrite_set_ thy false norm_Rational(*_mg*) t;
1827 "5 * x ^^^ 2 / (b ^^^ 3 * c)"
1829 else error "rational.sml: diff.behav. in norm_Rational_mg 53";
1832 "-------- me Schalk I No.186 ----------------------------";
1833 "-------- me Schalk I No.186 ----------------------------";
1834 "-------- me Schalk I No.186 ----------------------------";
1835 val fmz = ["Term ((14 * x * y) / ( x * y ))",
1838 ("Rational",["rational","simplification"],
1839 ["simplification","of_rationals"]);
1840 val p = e_pos'; val c = [];
1841 (*========== inhibit exn =======================================================
1842 val (p,_,f,nxt,_,pt) = CalcTreeTEST [(fmz, (dI',pI',mI'))];
1843 val (p,_,f,nxt,_,pt) = me nxt p c pt;
1844 val (p,_,f,nxt,_,pt) = me nxt p c pt;
1845 val (p,_,f,nxt,_,pt) = me nxt p c pt;
1846 val (p,_,f,nxt,_,pt) = me nxt p c pt;
1847 val (p,_,f,nxt,_,pt) = me nxt p c pt;
1848 val (p,_,f,nxt,_,pt) = me nxt p c pt;
1849 val (p,_,f,nxt,_,pt) = me nxt p c pt;
1850 val (p,_,f,nxt,_,pt) = me nxt p c pt; f2str f;
1851 val (p,_,f,nxt,_,pt) = me nxt p c pt; f2str f;
1852 val (p,_,f,nxt,_,pt) = me nxt p c pt; f2str f;(*++ for explicit script*)
1853 val (p,_,f,nxt,_,pt) = me nxt p c pt; f2str f;(*++ for explicit script*)
1854 case (f2str f, nxt) of
1855 ("14", ("End_Proof'", _)) => ()
1856 | _ => error "rational.sml diff.behav. in me Schalk I No.186";
1859 "-------- interSteps ..Simp_Rat_Double_No-1.xml ---------";
1860 "-------- interSteps ..Simp_Rat_Double_No-1.xml ---------";
1861 "-------- interSteps ..Simp_Rat_Double_No-1.xml ---------";
1864 [(["Term (((2 - x)/(2*a)) / (2*a/(x - 2)))", "normalform N"],
1865 ("Rational",["rational","simplification"],
1866 ["simplification","of_rationals"]))];
1869 autoCalculate 1 CompleteCalc;
1870 val ((pt,p),_) = get_calc 1; show_pt pt;
1872 interSteps 1 ([1],Res);
1873 val ((pt,p),_) = get_calc 1; show_pt pt;
1876 "-------- interSteps ..Simp_Rat_Cancel_No-1.xml ---------";
1877 "-------- interSteps ..Simp_Rat_Cancel_No-1.xml ---------";
1878 "-------- interSteps ..Simp_Rat_Cancel_No-1.xml ---------";
1881 [(["Term ((a^2 + -1*b^2) / (a^2 + -2*a*b + b^2))", "normalform N"],
1882 ("Rational",["rational","simplification"],
1883 ["simplification","of_rationals"]))];
1886 autoCalculate 1 CompleteCalc;
1887 val ((pt,p),_) = get_calc 1; show_pt pt;
1888 (*with explicit script done already... and removed [1,..] at below...
1889 interSteps 1 ([1],Res);
1890 val ((pt,p),_) = get_calc 1; show_pt pt;
1892 interSteps 1 ([2],Res);
1893 val ((pt,p),_) = get_calc 1; show_pt pt;
1895 interSteps 1 ([2,1],Res);
1896 val ((pt,p),_) = get_calc 1; show_pt pt;
1897 val newnds = children (get_nd pt [2,1]) (*see "fun detailrls"*);
1898 (*if length newnds = 12 then () WN060905*)
1899 if length newnds = 13 then ()
1900 else error "rational.sml: interSteps cancel_p rev_rew_p";
1902 val p = ([2,1,9],Res);
1904 val (_, tac, _) = pt_extract (pt, p);
1905 (*case tac of SOME (Rewrite ("sym_real_plus_binom_times1", _)) => ()
1907 case tac of SOME (Rewrite ("sym_real_add_mult_distrib2", _)) => ()
1908 | _ => error "rational.sml: getTactic, sym_real_plus_binom_times1";
1911 "-------- investigate rulesets for cancel_p -------------";
1912 "-------- investigate rulesets for cancel_p -------------";
1913 "-------- investigate rulesets for cancel_p -------------";
1914 val thy = Rational.thy;
1915 "---------------- (a^^^2 + -1*b^^^2) / (a^^^2 + -2*a*b + b^^^2)";
1916 val t = str2term "(a^^^2 + -1*b^^^2) / (a^^^2 + -2*a*b + b^^^2)";
1917 val tt = str2term "(1 * a + 1 * b) * (1 * a + -1 * b)"(*numerator only*);
1918 "----- with rewrite_set_";
1919 val SOME (tt',asm) = rewrite_set_ thy false make_polynomial tt;
1920 term2str tt'= "a ^^^ 2 + -1 * b ^^^ 2" (*true*);
1921 val tt = str2term "((1 * a + -1 * b) * (1 * a + -1 * b))"(*denominator only*);
1922 val SOME (tt',asm) = rewrite_set_ thy false make_polynomial tt;
1923 term2str tt' = "a ^^^ 2 + -2 * a * b + b ^^^ 2" (*true*);
1925 "----- with make_deriv";
1926 val SOME (tt, _) = factout_p_ thy t; term2str tt =
1927 "(1 * a + 1 * b) * (1 * a + -1 * b) / ((1 * a + -1 * b) * (1 * a + -1 * b))";
1929 "--- with ruleset as before 060829";
1930 val {rules, rew_ord=(_,ro),...} =
1931 rep_rls (assoc_rls "make_polynomial");
1932 val der = make_deriv thy Atools_erls rules ro NONE tt;
1933 print_depth 99; map (term2str o #1) der; print_depth 3;
1934 print_depth 99; map (rule2str o #2) der; print_depth 3;
1935 ... did not terminate*)
1936 "--- with simpler ruleset";
1937 val {rules, rew_ord=(_,ro),...} =
1938 rep_rls (assoc_rls "rev_rew_p");
1939 val der = make_deriv thy Atools_erls rules ro NONE tt;
1940 print_depth 99; writeln (deriv2str der); print_depth 3;
1942 print_depth 99; map (term2str o #1) der; print_depth 3;
1943 "...,(-1 * b ^^^ 2 + a ^^^ 2) / (-2 * (a * b) + a ^^^ 2 + (-1 * b) ^^^ 2) ]";
1944 print_depth 99; map (rule2str o #2) der; print_depth 3;
1945 print_depth 99; map (term2str o #1 o #3) der; print_depth 3;
1947 val der = make_deriv thy Atools_erls rules ro NONE
1948 (str2term "(1 * a + 1 * b) * (1 * a + -1 * b)");
1949 print_depth 99; writeln (deriv2str der); print_depth 3;
1951 val {rules, rew_ord=(_,ro),...} =
1952 rep_rls (assoc_rls "rev_rew_p");
1953 val der = make_deriv thy Atools_erls rules ro NONE
1954 (str2term "(1 * a + -1 * b) * (1 * a + -1 * b)");
1955 print_depth 99; writeln (deriv2str der); print_depth 3;
1956 print_depth 99; map (term2str o #1) der; print_depth 3;
1957 (*WN060829 ...postponed*)
1960 "-------- investigate format of factout_ and factout_p_ -";
1961 "-------- investigate format of factout_ and factout_p_ -";
1962 "-------- investigate format of factout_ and factout_p_ -";
1963 val {rules, rew_ord = (_,ro),...} = rep_rls (assoc_rls "make_polynomial");
1964 val (thy, eval_rls) = (Rational.thy, Atools_erls)(*see 'fun init_state'*);
1965 val Rrls {scr = Rfuns {init_state,...},...} = assoc_rls "cancel_p";
1967 "----- see Rational.ML, local cancel_p, fun init_state";
1968 val t = str2term "(a^^^2 + (-1)*b^^^2) / (a^^^2 + (-2)*a*b + b^^^2)";
1969 val SOME (t',_) = factout_p_ thy t; term2str t';
1971 val rtas = reverse_deriv thy eval_rls rules ro NONE t';
1972 writeln(trtas2str rst);
1976 "----- see Rational.ML, local cancel_p, fun init_state";
1977 val t = str2term "a^^^2 / a";
1978 val SOME (t',_) = factout_p_ thy t;
1979 term2str t' = "a * a / (1 * a)" (*true*);
1980 (*... can be canceled with
1981 real_mult_div_cancel2 ?k ~= 0 ==> ?m * ?k / (?n * ?k) = ?m / ?n"*)
1982 (* sml/ME/rewtools.sml:
1983 val rtas = reverse_deriv thy Atools_erls rules ro NONE t';
1984 writeln (deri2str rtas);
1989 "-------- SK 060904 ----------------------------------------------";
1990 "----- order on polynomials -- input + output";
1991 val thy = theory "Isac";
1992 val t = str2term "(a + -1 * b) / (-1 * a + b)";
1993 val SOME (t', _) = factout_p_ thy t; term2str t';
1994 val SOME (t', _) = cancel_p_ thy t; term2str t';
1996 val t = str2term "a*b*c*d / (d*e*f*g)";
1997 val SOME (t', _) = cancel_p_ thy t; term2str t';
1999 val t = str2term "a*(b*(c*d)) / (b*(e*(f*g)))";
2000 val SOME (t', _) = cancel_p_ thy t; term2str t';
2003 "----- SK060904-1a non-termination of cancel_p_ ? worked before 0707xx";
2004 val t = str2term "(x^^^2 - 4)*(3 - y) / ((y^^^2 - 9)*(2+x))";
2005 val SOME (t',_) = rewrite_set_ thy false norm_Rational t;
2006 if term2str t' = "(2 + -1 * x) / (3 + y)" then ()
2007 else error "rational.sml SK060904-1a worked since 0707xx";
2009 "----- SK060904-1b non-termination of cancel_p_ ... worked before 0707xx";
2010 val t = str2term "(9 * a ^^^ 2 + -16 * b ^^^ 2) /" ^
2011 "(36 * a^^^2 * c + (27 * a^^^2 * e + (-64 * b^^^2 * c + -48 * b^^^2 * e)))";
2012 val SOME (t',_) = cancel_p_ thy t;
2013 if term2str t' = "1 / (4 * c + 3 * e)" then ()
2014 else error "rational.sml SK060904-1b";
2017 "----- SK060904-2a non-termination of add_fraction_p_";
2018 val t = str2term " (a + b * x) / (a + -1 * (b * x)) + " ^
2019 " (-1 * a + b * x) / (a + b * x) ";
2021 val SOME (t',_) = rewrite_set_ thy false common_nominator_p t;
2023 common_nominator_p_ thy t;
2024 " (a + b * x)*(a + b * x) / ((a + -1 * (b * x))*(a + -1 * (b * x))) + " ^
2025 " (-1 * a + b * x)*(a + -1 * (b * x)) / ((a + b * x)*(-1 * a + b * x)) ";
2027 add_fraction_p_ thy t;
2028 " ((a + b * x)*(a + b * x) + (-1 * a + b * x)*(a + -1 * (b * x))) /" ^
2029 " ((a + b * x)*(-1 * a + b * x)) ";
2033 "-------- how to stepwise construct Scripts -------------";
2034 "-------- how to stepwise construct Scripts -------------";
2035 "-------- how to stepwise construct Scripts -------------";
2036 val thy = (theory "Rational");
2038 val p1 = parse thy (
2039 "Script SimplifyScript (t_t::real) = " ^
2040 " (Rewrite_Set discard_minus False " ^
2043 (*required (): (Rewrite_Set discard_minus False)*)
2044 val p2 = parse thy (
2045 "Script SimplifyScript (t_t::real) = " ^
2046 " (Rewrite_Set discard_minus False " ^
2049 val p3 = parse thy (
2050 "Script SimplifyScript (t_t::real) = " ^
2051 " ((Rewrite_Set discard_minus False) " ^
2054 val p4 = parse thy (
2055 "Script SimplifyScript (t_t::real) = " ^
2056 " ((Rewrite_Set discard_minus False) " ^
2059 val p5 = parse thy (
2060 "Script SimplifyScript (t_t::real) = " ^
2061 " ((Try (Rewrite_Set discard_minus False) " ^
2062 " Try (Rewrite_Set discard_parentheses False)) " ^
2065 val p6 = parse thy (
2066 "Script SimplifyScript (t_t::real) = " ^
2067 " ((Try (Rewrite_Set discard_minus False) @@ " ^
2068 " Try (Rewrite_Set rat_mult_poly False) @@ " ^
2069 " Try (Rewrite_Set make_rat_poly_with_parentheses False) @@ " ^
2070 " Try (Rewrite_Set cancel_p_rls False) @@ " ^
2072 " ((Try (Rewrite_Set common_nominator_p_rls False) @@ " ^
2073 " Try (Rewrite_Set rat_mult_div_pow False) @@ " ^
2074 " Try (Rewrite_Set make_rat_poly_with_parentheses False) @@" ^
2075 " Try (Rewrite_Set cancel_p_rls False) @@ " ^
2076 " Try (Rewrite_Set rat_reduce_1 False)))) @@ " ^
2077 " Try (Rewrite_Set discard_parentheses False)) " ^
2081 ============ inhibit exn =====================================================*)
2083 (*-.-.-.-.-.-isolate response.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.
2084 -.-.-.-.-.-.-isolate response.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.*)