1 (* Title: "Knowledge/rational-2.sml"
3 Use is subject to license terms.
6 "-----------------------------------------------------------------------------";
7 "-----------------------------------------------------------------------------";
8 "table of contents -----------------------------------------------------------";
9 "-----------------------------------------------------------------------------";
10 "-------- integration lev.1 fun factout_p_ -----------------------------------";
11 "-------- integration lev.1 fun cancel_p_ ------------------------------------";
12 "-------- integration lev.1 fun common_nominator_p_ --------------------------";
13 "-------- integration lev.1 fun add_fraction_p_ ------------------------------";
14 "Rfuns-------- and app_rev ...traced down from rewrite_set_ until prepats ---------";
15 "Rfuns-------- fun rewrite_set_ cancel_p downto fun gcd_poly ----------------------";
16 "-------- rls norm_Rational downto fun gcd_poly ------------------------------";
17 "Rfuns-------- rls norm_Rational downto fun add_fraction_p_ -----------------------";
18 "----------- rewrite_set_ Partial_Fractions norm_Rational --------------------------------------";
19 "----------- fun check_frac_sum with Free A and Const AA ---------------------------------------";
20 "-------- rewrite_set_ cancel_p from: Mathematik 1 Schalk Reniets Verlag -----";
21 "-------- rewrite_set_ add_fractions_p from: Mathematik 1 Schalk -------------";
22 "-------- integration lev.1 -- lev.5: cancel_p_ & add_fractions_p_ -----------";
23 "Rfuns-------- reverse rewrite ----------------------------------------------------";
24 "Rfuns-------- 'reverse-ruleset' cancel_p -----------------------------------------";
25 "-------- investigate rls norm_Rational --------------------------------------";
26 "-------- examples: rls norm_Rational ----------------------------------------";
27 "-------- rational numerals --------------------------------------------------";
28 "-------- examples cancellation from: Mathematik 1 Schalk --------------------";
29 "-------- examples common denominator from: Mathematik 1 Schalk --------------";
30 "-------- examples multiply and cancel from: Mathematik 1 Schalk -------------";
31 "-------- examples common denominator and multiplication from: Schalk --------";
32 "-------- examples double fractions from: Mathematik 1 Schalk ----------------";
33 "-------- me Schalk I No.186 -------------------------------------------------";
34 "-------- interSteps ..Simp_Rat_Double_No-1.xml ------------------------------";
35 "-------- interSteps ..Simp_Rat_Cancel_No-1.xml ------------------------------";
36 "-------- investigate rulesets for cancel_p ----------------------------------";
37 "-------- fun eval_get_denominator -------------------------------------------";
38 "-------- several errpats in complicated term --------------------------------";
39 "-------- WN1309xx non-terminating rls norm_Rational -------------------------";
40 "-----------------------------------------------------------------------------";
41 "-----------------------------------------------------------------------------";
44 "-------- integration lev.1 fun factout_p_ -----------------------------------";
45 "-------- integration lev.1 fun factout_p_ -----------------------------------";
46 "-------- integration lev.1 fun factout_p_ -----------------------------------";
47 val t = ParseC.parse_test @{context} "(x \<up> 2 + - 1*y \<up> 2) / (x \<up> 2 + - 1*x*y)"
48 val SOME (t', asm) = factout_p_ thy t;
49 if UnparseC.term @{context} t' = "(x + y) * (x + - 1 * y) / (x * (x + - 1 * y))"
50 then () else error ("factout_p_ term 1 changed: " ^ UnparseC.term @{context} t')
52 if UnparseC.terms @{context} asm = "[x \<noteq> 0, x + - 1 * y \<noteq> 0]"
53 then () else error "factout_p_ asm 1 changed"
55 val t = ParseC.parse_test @{context} "nothing + to_cancel ::real";
56 if NONE = factout_p_ thy t then () else error "factout_p_ doesn't report non-applicable";
58 val t = ParseC.parse_test @{context} "((3 * x \<up> 2 + 6 *x + 3) / (2*x + 2))";
59 val SOME (t', asm) = factout_p_ thy t;
60 if UnparseC.term @{context} t' = "(3 + 3 * x) * (1 + x) / (2 * (1 + x))" andalso
61 UnparseC.terms @{context} asm = "[1 + x \<noteq> 0]"
62 then () else error "factout_p_ 1 changed";
64 "-------- integration lev.1 fun cancel_p_ ------------------------------------";
65 "-------- integration lev.1 fun cancel_p_ ------------------------------------";
66 "-------- integration lev.1 fun cancel_p_ ------------------------------------";
67 val t = ParseC.parse_test @{context} "(x \<up> 2 + - 1*y \<up> 2) / (x \<up> 2 + - 1*x*y)"
68 val SOME (t', asm) = cancel_p_ thy t;
69 if (UnparseC.term @{context} t', UnparseC.terms @{context} asm) = ("(x + y) / x", "[x \<noteq> 0]")
70 then () else error ("cancel_p_ (t', asm) 1 changed: " ^ UnparseC.term @{context} t')
72 val t = ParseC.parse_test @{context} "nothing + to_cancel ::real";
73 if NONE = cancel_p_ thy t then () else error "cancel_p_ doesn't report non-applicable";
75 val t = ParseC.parse_test @{context} "((3 * x \<up> 2 + 6 *x + 3) / (2*x + 2))";
76 val SOME (t', asm) = cancel_p_ thy t;
77 if UnparseC.term @{context} t' = "(3 + 3 * x) / 2" andalso UnparseC.terms @{context} asm = "[]"
78 then () else error "cancel_p_ 1 changed";
80 "-------- integration lev.1 fun common_nominator_p_ --------------------------";
81 "-------- integration lev.1 fun common_nominator_p_ --------------------------";
82 "-------- integration lev.1 fun common_nominator_p_ --------------------------";
83 val t = ParseC.parse_test @{context} ("y / (a*x + b*x + c*x) " ^
87 val SOME (t', asm) = common_nominator_p_ thy t;
88 if UnparseC.term @{context} t' =
89 ("y * y / (x * ((a + b + c) * y)) " ^
90 (* n1 *d2'/ (c'* ( d1' *d2')) *)
91 "+ a * (a + b + c) / (x * ((a + b + c) * y))")
92 (* n2 * d1' / (c'* ( d1' *d2')) *)
93 then () else error "common_nominator_p_ term 1 changed";
94 if UnparseC.terms @{context} asm = "[a + b + c \<noteq> 0, y \<noteq> 0, x \<noteq> 0]"
95 then () else error "common_nominator_p_ asm 1 changed"
97 "-------- example in mail Nipkow";
98 val t = ParseC.parse_test @{context} "x/(x \<up> 2 + - 1*y \<up> 2) + y/(x \<up> 2 + - 1*x*y)";
99 val SOME (t', asm) = common_nominator_p_ thy t;
100 if UnparseC.term @{context} t' =
101 "x * x / ((x + - 1 * y) * ((x + y) * x)) +\ny * (x + y) / ((x + - 1 * y) * ((x + y) * x))"
102 then () else error "common_nominator_p_ term 2 changed"
104 if UnparseC.terms @{context} asm = "[x + y \<noteq> 0, x \<noteq> 0, x + - 1 * y \<noteq> 0]"
105 then () else error "common_nominator_p_ asm 2 changed"
107 "-------- example: applicable tested by SML code";
108 val t = ParseC.parse_test @{context} "nothing / to_add";
109 if NONE = common_nominator_p_ thy t then () else error "common_nominator_p_ term 3 changed";
111 val t = ParseC.parse_test @{context} "((x + (- 1)) / (x + 1)) + ((x + 1) / (x + (- 1)))";
112 val SOME (t', asm) = common_nominator_p_ thy t;
113 if UnparseC.term @{context} t' =
114 "(x + - 1) * (- 1 + x) / ((1 + x) * (- 1 + x)) +\n(x + 1) * (1 + x) / ((1 + x) * (- 1 + x))"
115 andalso UnparseC.terms @{context} asm = "[1 + x \<noteq> 0, - 1 + x \<noteq> 0]"
116 then () else error "common_nominator_p_ 3 changed";
118 "-------- integration lev.1 fun add_fraction_p_ ------------------------------";
119 "-------- integration lev.1 fun add_fraction_p_ ------------------------------";
120 "-------- integration lev.1 fun add_fraction_p_ ------------------------------";
121 val t = ParseC.parse_test @{context} "((x + (- 1)) / (x + 1)) + ((x + 1) / (x + (- 1)))";
122 val SOME (t', asm) = add_fraction_p_ thy t;
123 if UnparseC.term @{context} t' = "(2 + 2 * x \<up> 2) / (- 1 + x \<up> 2)"
124 then () else error "add_fraction_p_ 3 changed";
126 if UnparseC.terms @{context} asm = "[- 1 + x \<up> 2 \<noteq> 0]"
127 then () else error "add_fraction_p_ 3 changed";
129 val t = ParseC.parse_test @{context} "nothing / to_add";
130 if NONE = add_fraction_p_ thy t then () else error "add_fraction_p_ term 3 changed";
132 val t = ParseC.parse_test @{context} "((x + (- 1)) / (x + 1)) + ((x + 1) / (x + (- 1)))";
133 val SOME (t', asm) = add_fraction_p_ thy t;
134 if UnparseC.term @{context} t' = "(2 + 2 * x \<up> 2) / (- 1 + x \<up> 2)" andalso
135 UnparseC.terms @{context} asm = "[- 1 + x \<up> 2 \<noteq> 0]"
136 then () else error "add_fraction_p_ 3 changed";
138 "-------- and app_rev ...traced down from rewrite_set_ until prepats ---------";
139 "-------- and app_rev ...traced down from rewrite_set_ until prepats ---------";
140 "-------- and app_rev ...traced down from rewrite_set_ until prepats ---------";
141 (* trace down until prepats are evaluated
142 (which does not to work, because substitution is not done -- compare rew_sub!);
143 keep this sequence for the case, factout_p, cancel_p, common_nominator_p, add_fraction_p
144 (again) get prepat = [] changed to <>[]. *)
145 val t = ParseC.parse_test @{context} "(x \<up> 2 + - 1*y \<up> 2) / (x \<up> 2 + - 1*x*y)";
147 (*rewrite_set_ @{theory Isac_Knowledge} true cancel t = NONE; !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!*)
148 "~~~~~ fun rewrite_set_, args:"; val (thy, bool, rls, term) = (thy, false, cancel_p, t);
149 "~~~~~ fun rewrite__set_, args:"; val (thy, i, _, _, (rrls as Rrls _), t) =
150 (thy, 1, bool, [], rls, term);
151 (*val (t', asm, rew) = app_rev thy (i+1) rrls t; rew = false!!!!!!!!!!!!!!!!!!!!!*)
152 "~~~~~ and app_rev, args:"; val (thy, i, rrls, t) = (thy, (i+1), rrls, t);
153 fun chk_prepat thy asm_rls [] t = true
154 | chk_prepat thy asm_rls prepat t =
156 fun chk (pres, pat) =
158 val subst: Type.tyenv * Envir.tenv =
159 Pattern.match thy (pat, t) (Vartab.empty, Vartab.empty)
161 snd (eval__true ctxt (i + 1) (map (Envir.subst_term subst) pres) [] asm_rls)
162 end) handle Pattern.MATCH => false
163 fun scan_ f [] = false (*scan_ NEVER called by []*)
164 | scan_ f (pp::pps) =
165 if f pp then true else scan_ f pps;
166 in scan_ chk prepat end;
167 (* apply the normal_form of a rev-set *)
168 fun app_rev' thy (Rrls{asm_rls,prepat,program=Rfuns{normal_form,...},...}) t =
169 if chk_prepat thy asm_rls prepat t
170 then ((*tracing("### app_rev': t = "^UnparseC.term @{context} t);*) normal_form t)
172 (* val opt = app_rev' thy rrls t ..NONE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!*)
173 "~~~~~ and app_rev', args:"; val (thy, (Rrls{asm_rls,prepat,program=Rfuns{normal_form,...},...}), t) =
175 (* chk_prepat thy asm_rls prepat t = false!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!*)
176 (* app_sub thy i rrls t = false!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!*)
177 "~~~~~ fun chk_prepat, args:"; val (thy, asm_rls, prepat, t) = (thy, asm_rls, prepat, t);
178 fun chk (pres, pat) =
180 val subst: Type.tyenv * Envir.tenv =
181 Pattern.match thy (pat, t) (Vartab.empty, Vartab.empty)
183 snd (eval__true ctxt (i + 1) (map (Envir.subst_term subst) pres) [] asm_rls)
184 end) handle Pattern.MATCH => false
185 fun scan_ f [] = false (*scan_ NEVER called by []*)
186 | scan_ f (pp::pps) =
187 if f pp then true else scan_ f pps;
189 (*========== inhibit exn WN130823: prepat is empty ====================================
190 (* scan_ chk prepat = false!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!*)
191 "~~~~~ fun , args:"; val (f, (pp::pps)) = (chk, prepat);
193 val ([t1, t2], t) = pp;
194 UnparseC.term @{context} t1 = "?r is_expanded";
195 UnparseC.term @{context} t2 = "?s is_expanded";
196 UnparseC.term @{context} t = "?r / ?s";
197 (* f pp = false!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!*)
198 "~~~~~ fun chk, args:"; val (pres, pat) = (pp);
199 val subst: Type.tyenv * Envir.tenv =
200 Pattern.match thy (pat, t) (Vartab.empty, Vartab.empty)
202 ({}, {(("r", 0), ("real", Var (("r", 0), "real"))),
203 (("s", 0), ("real", Var (("s", 0), "real")))}*)
205 snd (eval__true thy (i + 1) (map (Envir.subst_term subst) pres) [] asm_rls)
206 "~~~~~ fun eval__true, args:"; val (thy, i, asms, bdv, rls) =
207 (thy, (i + 1), (map (Envir.subst_term subst) pres), [], asm_rls);
208 UnparseC.terms @{context} asms; (* = "[\"?r is_expanded\",\"?s is_expanded\"]"*)
209 asms = [@{term True}] orelse asms = []; (* = false*)
210 asms = [@{term False}] ; (* = false*)
211 "~~~~~ fun chk, args:"; val (indets, (a::asms)) = ([], asms);
212 bdv (*= []: _a list*);
213 val bdv : Subst.T = [];
214 rewrite__set_ thy (i+1) false;
215 UnparseC.term @{context} a = "?r is_expanded"; (*hier m"usste doch der Numerator eingesetzt sein ??????????????*)
216 val SOME (Const (\<^const_name>\<open>False\<close>, _), []) = rewrite__set_ thy (i+1) false bdv rls a
217 ============ inhibit exn WN130823: prepat is empty ===================================*)
219 "-------- fun rewrite_set_ cancel_p downto fun gcd_poly ----------------------";
220 "-------- fun rewrite_set_ cancel_p downto fun gcd_poly ----------------------";
221 "-------- fun rewrite_set_ cancel_p downto fun gcd_poly ----------------------";
222 val t = ParseC.parse_test @{context} "(12 * x * y) / (8 * y \<up> 2 )";
223 (* "-------- example 187a": exception Div raised...
224 val SOME (t', asm) = rewrite_set_ thy false cancel_p t;*)
225 val t = ParseC.parse_test @{context} "(8 * x \<up> 2 * y * z ) / (18 * x * y \<up> 2 * z )";
226 (* "-------- example 187b": doesn't terminate...
227 val SOME (t', asm) = rewrite_set_ thy false cancel_p t;*)
228 val t = ParseC.parse_test @{context} "(9 * x \<up> 5 * y \<up> 2 * z \<up> 4) / (15 * x \<up> 6 * y \<up> 3 * z )";
229 (* "-------- example 187c": doesn't terminate...
230 val SOME (t', asm) = rewrite_set_ thy false cancel_p t;*)
231 "~~~~~ fun rewrite_set_, args:"; val (thy, bool, rls, term) = (@{theory Isac_Knowledge}, false, cancel_p, t);
232 (* WN130827: exception Div raised...
233 rewrite__set_ thy 1 bool [] rls term
235 "~~~~~ and rewrite__set_, args:"; val (thy, i, _, _, (rrls as Rrls _), t) =
236 (thy, 1, bool, [], rls, term);
237 (* WN130827: exception Div raised...
238 val (t', asm, rew) = app_rev thy (i+1) rrls t
240 "~~~~~ fun app_rev, args:"; val (thy, i, rrls, t) = (thy, (i+1), rrls, t);
241 (* WN130827: exception Div raised...
242 val opt = app_rev' thy rrls t
244 "~~~~~ fun app_rev', args:"; val (thy, (Rrls{asm_rls,prepat,program=Rfuns{normal_form,...},...}), t) =
246 chk_prepat thy asm_rls prepat t = true;
247 (* WN130827: exception Div raised...
250 (* lookup Rational.thy, cancel_p: normal_form = cancel_p_ thy*)
251 "~~~~~ fun cancel_p_, args:"; val (t) = (t);
252 val opt = check_fraction t;
253 val SOME (numerator, denominator) = opt
254 val vs = TermC.vars_of t
255 val baseT = type_of numerator
256 val expT = HOLogic.realT
257 val (SOME a, SOME b) = (poly_of_term vs numerator, poly_of_term vs denominator);
258 (*"-------- example 187a": exception Div raised...
259 val a = [(12, [1, 1])]: poly
260 val b = [(8, [0, 2])]: poly
261 val ((a', b'), c) = gcd_poly a b
263 (* "-------- example 187b": doesn't terminate...
264 val a = [(8, [2, 1, 1])]: poly
265 val b = [(18, [1, 2, 1])]: poly
266 val ((a', b'), c) = gcd_poly a b
268 (* "-------- example 187c": doesn't terminate...
269 val a = [(9, [5, 2, 4])]: poly
270 val b = [(15, [6, 3, 1])]: poly
271 val ((a', b'), c) = gcd_poly a b
274 "-------- rls norm_Rational downto fun gcd_poly ------------------------------";
275 "-------- rls norm_Rational downto fun gcd_poly ------------------------------";
276 "-------- rls norm_Rational downto fun gcd_poly ------------------------------";
277 val t = ParseC.parse_test @{context} "(x \<up> 2 - 4)*(3 - y) / ((y \<up> 2 - 9)*(2+x))";
278 (* trace_rewrite stops with ...: (and then jEdit hangs)..
279 rewrite_set_ thy false norm_Rational t;
281 ### rls: cancel_p on: (- 12 + 4 * y + 3 * x \<up> 2 + - 1 * (x \<up> 2 * y)) /
282 (- 18 + -9 * x + 2 * y \<up> 2 + x * y \<up> 2)
284 val t = ParseC.parse_test @{context} (*copy from above: "::real" is not required due to " \<up> "*)
285 ("(- 12 + 4 * y + 3 * x \<up> 2 + - 1 * (x \<up> 2 * y)) /" ^
286 "(- 18 + -9 * x + 2 * y \<up> 2 + x * y \<up> 2)");
288 exception Div raised*)
290 "~~~~~ fun cancel_p_, args:"; val (t) = (t);
291 val opt = check_fraction t;
292 val SOME (numerator, denominator) = opt
293 val vs = TermC.vars_of t
294 val baseT = type_of numerator
295 val expT = HOLogic.realT;
296 (*default_print_depth 3; 999*)
297 val (SOME a, SOME b) = (poly_of_term vs numerator, poly_of_term vs denominator);
298 (*default_print_depth 3; 999*)
299 (* does not terminate instead of returning ?:
300 val ((a', b'), c) = gcd_poly a b
301 val a = [(~12, [0, 0]), (3, [2, 0]), (4, [0, 1]), (~1, [2, 1])]: poly
302 val b = [(~18, [0, 0]), (~9, [1, 0]), (2, [0, 2]), (1, [1, 2])]: poly
305 "-------- rls norm_Rational downto fun add_fraction_p_ -----------------------";
306 "-------- rls norm_Rational downto fun add_fraction_p_ -----------------------";
307 "-------- rls norm_Rational downto fun add_fraction_p_ -----------------------";
308 val thy = @{theory Isac_Knowledge};
309 "----- SK060904- 2a non-termination of add_fraction_p_";
310 val t = ParseC.parse_test @{context} (" (a + b * x) / (a + - 1 * (b * x)) + " ^
311 " (- 1 * a + b * x) / (a + b * x) ");
312 (* rewrite_set_ thy false norm_Rational t
313 exception Div raised*)
314 (* rewrite_set_ thy false add_fractions_p t;
315 exception Div raised*)
316 "~~~~~ fun rewrite_set_, args:"; val (thy, bool, rls, term) =
317 (@{theory Isac_Knowledge}, false, add_fractions_p, t);
318 "~~~~~ and rewrite__set_, args:"; val (thy, i, _, _, (rrls as Rrls _), t) =
319 (thy, 1, bool, [], rls, term);
320 (* app_rev thy (i+1) rrls t;
321 exception Div raised*)
322 "~~~~~ and app_rev, args:"; val (thy, i, rrls, t) = (thy, (i+1), rrls, t);
323 fun chk_prepat thy asm_rls [] t = true
324 | chk_prepat thy asm_rls prepat t =
326 fun chk (pres, pat) =
328 val subst: Type.tyenv * Envir.tenv =
329 Pattern.match thy (pat, t) (Vartab.empty, Vartab.empty)
331 snd (eval__true ctxt (i + 1) (map (Envir.subst_term subst) pres) [] asm_rls)
332 end) handle Pattern.MATCH => false
333 fun scan_ f [] = false (*scan_ NEVER called by []*)
334 | scan_ f (pp::pps) =
335 if f pp then true else scan_ f pps;
336 in scan_ chk prepat end;
337 (* apply the normal_form of a rev-set *)
338 fun app_rev' thy (Rrls{asm_rls,prepat,program=Rfuns{normal_form,...},...}) t =
339 if chk_prepat thy asm_rls prepat t
340 then ((*tracing("### app_rev': t = "^UnparseC.term @{context} t);*) normal_form t)
342 (* val opt = app_rev' thy rrls t;
343 exception Div raised*)
344 (* val opt = app_rev' thy rrls t;
345 exception Div raised*)
346 "~~~~~ and app_rev', args:"; val (thy, (Rrls{asm_rls,prepat,program=Rfuns{normal_form,...},...}), t) =
348 chk_prepat thy asm_rls prepat t = true = true;
350 exception Div raised*)
351 (* lookup Rational.thy, val add_fractions_p: normal_form = add_fraction_p_ thy*)
352 (*add_fraction_p_ thy t
353 exception Div raised*)
354 "~~~~~ fun add_fraction_p_, args:"; val ((_: theory), t) = (thy, t);
355 val SOME ((n1, d1), (n2, d2)) = check_frac_sum t;
356 UnparseC.term @{context} n1; UnparseC.term @{context} d1; UnparseC.term @{context} n2; UnparseC.term @{context} d2;
357 val vs = TermC.vars_of t;
358 (*default_print_depth 3; 999*)
359 val (SOME _, SOME a, SOME _, SOME b) =
360 (poly_of_term vs n1, poly_of_term vs d1, poly_of_term vs n2, poly_of_term vs d2);
361 (*default_print_depth 3; 999*)
363 val a = [(1, [1, 0, 0]), (~1, [0, 1, 1])]: poly
364 val b = [(1, [1, 0, 0]), (1, [0, 1, 1])]: poly
365 val ((a', b'), c) = gcd_poly a b
368 "----------- fun check_frac_sum with Free A and Const AA ---------------------------------------";
369 "----------- fun check_frac_sum with Free A and Const AA ---------------------------------------";
370 "----------- fun check_frac_sum with Free A and Const AA ---------------------------------------";
371 val thy = @{theory Isac_Knowledge(*Partial_Fractions*)}
372 val ctxt = Proof_Context.init_global thy;
374 (*---------- (1) with Free A, B ----------------------------------------------------------------*)
375 val t = (the o (ParseC.term_opt ctxt)) "3 = A / 2 + A / 4 + (B / 2 + - 1 * B / (2::real))";
376 (* required for applying thms in rewriting \<up> ^*)
377 (* we get details from here..*)
379 val SOME (t', _) = Rewrite.rewrite_set_ ctxt true add_fractions_p t;
381 add_fractions_p on: 3 = A / 2 + A / 4 + (B / 2 + - 1 * B / 2) --> 3 = A / 2 + A / 4 + 0 / 2 *)
382 (* |||||||||||||||||||||||||||||||||||| *)
384 val t = (the o (ParseC.term_opt ctxt))(* ||||||||||||||||||||||||| GUESS 1 GUESS 1 GUESS 1 GUESS 1 *)
385 "A / 2 + A / 4 + (B / 2 + - 1 * B / (2::real))";
386 "~~~~~ fun add_fraction_p_ , ad-hoc args:"; val (t) = (t);
387 val NONE = (*case*) check_frac_sum t (*of*)
390 add_fractions_p on: 3 = A / 2 + A / 4 + (B / 2 + - 1 * B / 2) --> 3 = A / 2 + A / 4 + 0 / 2 *)
391 (* |||||||||||||||||||||||||||| *)
392 val t = (the o (ParseC.term_opt ctxt))(* ||||||||||||||||||||||||| GUESS 2 GUESS 2 GUESS 2 GUESS 2 *)
393 "A / 4 + (B / 2 + - 1 * B / (2::real))";
394 "~~~~~ fun add_fraction_p_ , ad-hoc args:"; val (t) = (t);
395 val SOME ((n1, d1), (n2, d2)) = (*case*) check_frac_sum t (*of*);
396 (*+*)if (UnparseC.term @{context} n1, UnparseC.term @{context} d1) = ("A" , "4") andalso
397 (*+*) (UnparseC.term @{context} n2, UnparseC.term @{context} d2) = ("B / 2 + - 1 * B / 2", "1")
398 (*+*)then () else error "check_frac_sum (A / 4 + (B / 2 + - 1 * B / (2::real))) changed";
400 val vs = TermC.vars_of t;
401 val (SOME [(1, [1, 0])], SOME [(4, [0, 0])], NONE, SOME [(1, [0, 0])]) =
402 (*case*) (poly_of_term vs n1, poly_of_term vs d1, poly_of_term vs n2, poly_of_term vs d2) (*of*);
404 "~~~~~ fun poly_of_term , args:"; val (vs, t) = (vs, n1);
405 val SOME [(1, [xxx, 0])] = SOME [monom_of_term vs (1, replicate (length vs) 0) t];
406 (*+*)if xxx = 1 then () else error "monom_of_term changed"
408 "~~~~~ fun monom_of_term , args:"; val (vs, (c, es), (Free (id, _))) =
409 (vs, (1, replicate (length vs) 0), t);
410 case vs of [Free ("A", _), Free ("B", _)] =>
411 if c = 1 andalso id = "A"
412 then () else error "monom_of_term Free changed 1"
413 | _ => error "monom_of_term Free changed 2";
415 (*---------- (2) with Const AA, BB --------------------------------------------------------------*)
416 val t = (the o (ParseC.term_opt ctxt)) "3 = AA / 2 + AA / 4 + (BB / 2 + - 1 * BB / 2)";
418 (* we get details from here..*)
420 val SOME (t', _) = Rewrite.rewrite_set_ ctxt true add_fractions_p t;
422 add_fractions_p on: 3 = A / 2 + A / 4 + (B / 2 + - 1 * B / 2) --> 3 = A / 2 + A / 4 + 0 / 2 *)
423 (* |||||||||||||||||||||||||||||||||||| *)
424 val t = (the o (ParseC.term_opt ctxt))(* ||||||||||||||||||||||||| *)
425 "AA / 2 + AA / 4 + (BB / 2 + - 1 * BB / 2)";
426 "~~~~~ fun add_fraction_p_ , ad-hoc args:"; val (t) = (t);
427 val NONE = (*case*) check_frac_sum t (*of*)
430 add_fractions_p on: 3 = A / 2 + A / 4 + (B / 2 + - 1 * B / 2) --> 3 = A / 2 + A / 4 + 0 / 2 *)
431 (* |||||||||||||||||||||||||||| *)
432 val t = ParseC.parse_test @{context} (* ||||||||||||||||||||||||| *)
433 "AA / 4 + (BB / 2 + - 1 * BB / 2)";
434 "~~~~~ fun add_fraction_p_ , ad-hoc args:"; val (t) = (t);
435 val SOME ((n1, d1), (n2, d2)) = (*case*) check_frac_sum t (*of*);
436 (*+*)if (UnparseC.term @{context} n1, UnparseC.term @{context} d1) = ("AA" , "4") andalso
437 (*+*) (UnparseC.term @{context} n2, UnparseC.term @{context} d2) = ("BB / 2 + - 1 * BB / 2", "1")
438 (*+*)then () else error "check_frac_sum (AA / 4 + (BB / 2 + - 1 * BB / 2)) changed";
440 val vs = TermC.vars_of t;
441 val (SOME [(1, [1, 0])], SOME [(4, [0, 0])], NONE, SOME [(1, [0, 0])]) =
442 (*case*) (poly_of_term vs n1, poly_of_term vs d1, poly_of_term vs n2, poly_of_term vs d2) (*of*);
443 "~~~~~ fun poly_of_term , args:"; val (vs, t) = (vs, n1);
444 val SOME [(1, [1, 0])] = SOME [monom_of_term vs (1, replicate (length vs) 0) t];
446 "~~~~~ fun monom_of_term , args:"; val (vs, (c, es), (Const (id, _))) =
447 (vs, (1, replicate (length vs) 0), t);
448 case vs of [Const (\<^const_name>\<open>AA\<close>, _), Const (\<^const_name>\<open>BB\<close>, _)] =>
449 if c = 1 andalso id = "Partial_Fractions.AA"
450 then () else error "monom_of_term Const changed 1"
451 | _ => error "monom_of_term Const changed 2";
454 "-------- rewrite_set_ cancel_p from: Mathematik 1 Schalk Reniets Verlag -----";
455 "-------- rewrite_set_ cancel_p from: Mathematik 1 Schalk Reniets Verlag -----";
456 "-------- rewrite_set_ cancel_p from: Mathematik 1 Schalk Reniets Verlag -----";
457 val thy = @{theory "Rational"};
459 val t = ParseC.parse_test @{context} "(2 + -3 * x) / 9";
460 if NONE = rewrite_set_ ctxt false cancel_p t then ()
461 else error "rewrite_set_ cancel_p must return NONE, if the term cannot be cancelled";
463 "-------- example 186a";
464 val t = ParseC.parse_test @{context} "(14 * x * y) / (x * y)";
465 is_expanded (ParseC.parse_test @{context} "14 * x * y");
466 is_expanded (ParseC.parse_test @{context} "x * y");
467 val SOME (t', asm) = rewrite_set_ ctxt false cancel_p t;
468 if (UnparseC.term @{context} t', UnparseC.terms @{context} asm) = ("14 / 1", "[]")
469 then () else error "rational.sml cancel Schalk 186a";
471 "-------- example 186b";
472 val t = ParseC.parse_test @{context} "(60 * a * b) / ( 15 * a * b )";
473 val SOME (t', asm) = rewrite_set_ ctxt false cancel_p t;
474 if (UnparseC.term @{context} t', UnparseC.terms @{context} asm) = ("4 / 1", "[]")
475 then () else error "rational.sml cancel Schalk 186b";
477 "-------- example 186c";
478 val t = ParseC.parse_test @{context} "(144 * a \<up> 2 * b * c) / (12 * a * b * c)";
479 val SOME (t', asm) = rewrite_set_ ctxt false cancel_p t;
480 if (UnparseC.term @{context} t', UnparseC.terms @{context} asm) = ("12 * a / 1", "[]")
481 then () else error "rational.sml cancel Schalk 186c";
483 (* !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! exception Div raised !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
484 see --- fun rewrite_set_ downto fun gcd_poly ---
485 "-------- example 187a";
486 val t = ParseC.parse_test @{context} "(12 * x * y) / (8 * y \<up> 2 )";
487 val SOME (t', asm) = rewrite_set_ ctxt false cancel_p t;
488 if (UnparseC.term @{context} t', UnparseC.terms @{context} asm) = ("3 * x / (2 * y)", "[\"4 * y ~= 0\"]")
489 then () else error "rational.sml cancel Schalk 187a";
492 (* doesn't terminate !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
493 see --- fun rewrite_set_ downto fun gcd_poly ---
494 "-------- example 187b";
495 val t = ParseC.parse_test @{context} "(8 * x \<up> 2 * y * z ) / (18 * x * y \<up> 2 * z )";
496 val SOME (t', asm) = rewrite_set_ ctxt false cancel_p t;
497 if (UnparseC.term @{context} t', UnparseC.terms @{context} asm) = ("4 * x / (9 * y)", "[\"2 * (z * (y * x)) ~= 0\"]")
498 then () else error "rational.sml cancel Schalk 187b";
501 (* doesn't terminate !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
502 see --- fun rewrite_set_ downto fun gcd_poly ---
503 "-------- example 187c";
504 val t = ParseC.parse_test @{context} "(9 * x \<up> 5 * y \<up> 2 * z \<up> 4) / (15 * x \<up> 6 * y \<up> 3 * z )";
505 val SOME (t', asm) = rewrite_set_ ctxt false cancel_p t;
506 if (UnparseC.term @{context} t', UnparseC.terms @{context} asm) =
507 ("3 * z \<up> 3 / (5 * (y * x))", "[\"3 * (z * (y \<up> 2 * x \<up> 5)) ~= 0\"]")
508 then () else error "rational.sml cancel Schalk 187c";
511 "-------- example 188a";
512 val t = ParseC.parse_test @{context} "(-8 + 8 * x) / (-9 + 9 * x)";
513 is_expanded (ParseC.parse_test @{context} "8 * x + -8");
514 val SOME (t', asm) = rewrite_set_ ctxt false cancel_p t;
515 if (UnparseC.term @{context} t', UnparseC.terms @{context} asm) = ("8 / 9", "[]")
516 then () else error "rational.sml cancel Schalk 188a";
518 val t = ParseC.parse_test @{context} "(8*((- 1) + x))/(9*((- 1) + x))";
519 val SOME (t, _) = rewrite_set_ ctxt false make_polynomial t;
520 if (UnparseC.term @{context} t', UnparseC.terms @{context} asm) = ("8 / 9", "[]")
521 then () else error "rational.sml cancel Schalk make_polynomial 1";
523 "-------- example 188b";
524 val t = ParseC.parse_test @{context} "(- 15 + 5 * x) / (- 18 + 6 * x)";
525 val SOME (t', asm) = rewrite_set_ ctxt false cancel_p t;
526 if (UnparseC.term @{context} t', UnparseC.terms @{context} asm) = ("5 / 6", "[]")
527 then () else error "rational.sml cancel Schalk 188b";
529 "-------- example 188c";
530 val t = ParseC.parse_test @{context} "(a + - 1 * b) / (b + - 1 * a)";
531 val SOME (t', asm) = rewrite_set_ ctxt false cancel_p t;
532 if (UnparseC.term @{context} t', UnparseC.terms @{context} asm) = ("- 1 / 1", "[]")
533 then () else error "rational.sml cancel Schalk 188c";
535 is_expanded (ParseC.parse_test @{context} "a + - 1 * b") = true;
536 val t = ParseC.parse_test @{context} "((- 1)*(b + (- 1) * a))/(1*(b + (- 1) * a))";
537 val SOME (t', asm) = rewrite_set_ ctxt false make_polynomial t;
538 if (UnparseC.term @{context} t', UnparseC.terms @{context} asm) = ("(a + - 1 * b) / (- 1 * a + b)", "[]")
539 then () else error "rational.sml cancel Schalk make_polynomial 2";
541 "-------- example 190a";
542 val t = ParseC.parse_test @{context} "( 27 * a \<up> 3 + 9 * a \<up> 2 + 3 * a + 1 ) / ( 27 * a \<up> 3 + 18 * a \<up> 2 + 3 * a )";
543 val SOME (t', asm) = rewrite_set_ ctxt false cancel_p t;
544 if (UnparseC.term @{context} t', UnparseC.terms @{context} asm) =
545 ("(1 + 9 * a \<up> 2) / (3 * a + 9 * a \<up> 2)", "[3 * a + 9 * a \<up> 2 \<noteq> 0]")
546 then () else error "rational.sml cancel Schalk 190a";
548 "-------- example 190c";
549 val t = ParseC.parse_test @{context} "((1 + 9 * a \<up> 2)*(1 + 3 * a))/((3 * a + 9 * a \<up> 2)*(1 + 3 * a))";
550 val SOME (t', asm) = rewrite_set_ ctxt false make_polynomial t;
551 if (UnparseC.term @{context} t', UnparseC.terms @{context} asm) =
552 ("(1 + 3 * a + 9 * a \<up> 2 + 27 * a \<up> 3) /\n(3 * a + 18 * a \<up> 2 + 27 * a \<up> 3)", "[]")
553 then () else error "rational.sml make_polynomial Schalk 190c";
555 "-------- example 191a";
556 val t = ParseC.parse_test @{context} "( x \<up> 2 + - 1 * y \<up> 2 ) / ( x + y )";
557 is_expanded (ParseC.parse_test @{context} "x \<up> 2 + - 1 * y \<up> 2") = false; (*!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!*)
558 is_expanded (ParseC.parse_test @{context} "x + y") = true;
559 val SOME (t', asm) = rewrite_set_ ctxt false cancel_p t;
560 if (UnparseC.term @{context} t', UnparseC.terms @{context} asm) = ("(x + - 1 * y) / 1", "[]")
561 then () else error "rational.sml make_polynomial Schalk 191a";
563 "-------- example 191b";
564 val t = ParseC.parse_test @{context} "((x + (- 1) * y)*(x + y))/((1)*(x + y))";
565 val SOME (t', asm) = rewrite_set_ ctxt false make_polynomial t;
566 if (UnparseC.term @{context} t', UnparseC.terms @{context} asm) = ("(x \<up> 2 + - 1 * y \<up> 2) / (x + y)", "[]")
567 then () else error "rational.sml make_polynomial Schalk 191b";
569 "-------- example 191c";
570 val t = ParseC.parse_test @{context} "( 9 * x \<up> 2 + -30 * x + 25 ) / ( 9 * x \<up> 2 + - 25 )";
571 is_expanded (ParseC.parse_test @{context} "9 * x \<up> 2 + -30 * x + 25") = true;
572 is_expanded (ParseC.parse_test @{context} "25 + -30*x + 9*x \<up> 2") = true;
573 is_expanded (ParseC.parse_test @{context} "- 25 + 9*x \<up> 2") = true;
575 val t = ParseC.parse_test @{context} "(((-5) + 3 * x)*((-5) + 3 * x))/((5 + 3 * x)*((-5) + 3 * x))";
576 val SOME (t', asm) = rewrite_set_ ctxt false make_polynomial t;
577 if (UnparseC.term @{context} t', UnparseC.terms @{context} asm) =
578 ("(25 + - 30 * x + 9 * x \<up> 2) / (- 25 + 9 * x \<up> 2)", "[]")
579 then () else error "rational.sml make_polynomial Schalk 191c";
581 "-------- example 192b";
582 val t = ParseC.parse_test @{context} "( 7 * x \<up> 3 + - 1 * x \<up> 2 * y ) / ( 7 * x * y \<up> 2 + - 1 * y \<up> 3 )";
583 val SOME (t', asm) = rewrite_set_ ctxt false cancel_p t;
584 if (UnparseC.term @{context} t', UnparseC.terms @{context} asm) = ("x \<up> 2 / y \<up> 2", "[y \<up> 2 \<noteq> 0]")
585 then () else error "rational.sml cancel_p Schalk 192b";
587 val t = ParseC.parse_test @{context} "((x \<up> 2)*(7 * x + (- 1) * y))/((y \<up> 2)*(7 * x + (- 1) * y))";
588 val SOME (t', asm) = rewrite_set_ ctxt false make_polynomial t;
589 if (UnparseC.term @{context} t', UnparseC.terms @{context} asm) =
590 ("(7 * x \<up> 3 + - 1 * x \<up> 2 * y) /\n(7 * x * y \<up> 2 + - 1 * y \<up> 3)", "[]")
591 then () else error "rational.sml make_polynomial Schalk 192b";
593 val t = ParseC.parse_test @{context} "((x \<up> 2)*(7 * x + (- 1) * y))/((y \<up> 2)*(7 * x + (- 1) * y))";
594 val SOME (t', asm) = rewrite_set_ ctxt false make_polynomial t;
595 if (UnparseC.term @{context} t', UnparseC.terms @{context} asm) =
596 ("(7 * x \<up> 3 + - 1 * x \<up> 2 * y) /\n(7 * x * y \<up> 2 + - 1 * y \<up> 3)", "[]")
597 then () else error "rational.sml make_polynomial Schalk WN050929 not working";
599 "-------- example 193a";
600 val t = ParseC.parse_test @{context} "( x \<up> 2 + -6 * x + 9 ) / ( x \<up> 2 + -9 )";
601 val SOME (t', asm) = rewrite_set_ ctxt false cancel_p t;
602 if (UnparseC.term @{context} t', UnparseC.terms @{context} asm) = ("(- 3 + x) / (3 + x)", "[3 + x \<noteq> 0]")
603 then () else error "rational.sml cancel_p Schalk 193a";
605 "-------- example 193b";
606 val t = ParseC.parse_test @{context} "( x \<up> 2 + -8 * x + 16 ) / ( 2 * x \<up> 2 + -32 )";
607 val SOME (t', asm) = rewrite_set_ ctxt false cancel_p t;
608 if (UnparseC.term @{context} t', UnparseC.terms @{context} asm) = ("(- 4 + x) / (8 + 2 * x)", "[8 + 2 * x \<noteq> 0]")
609 then () else error "rational.sml cancel_p Schalk 193b";
611 "-------- example 193c";
612 val t = ParseC.parse_test @{context} "( 2 * x + -50 * x \<up> 3 ) / ( 25 * x \<up> 2 + - 10 * x + 1 )";
613 val SOME (t', asm) = rewrite_set_ ctxt false cancel_p t;
614 if (UnparseC.term @{context} t', UnparseC.terms @{context} asm) =
615 ("(2 * x + 10 * x \<up> 2) / (1 + - 5 * x)", "[1 + - 5 * x \<noteq> 0]")
616 then () else error "rational.sml cancel_p Schalk 193c";
618 (*WN: improved with new numerals*)
619 val t = ParseC.parse_test @{context} "(- 25 + 9*x \<up> 2)/(5 + 3*x)";
620 val SOME (t', asm) = rewrite_set_ ctxt false cancel_p t;
621 if (UnparseC.term @{context} t', UnparseC.terms @{context} asm) =
622 ("(- 5 + 3 * x) / 1", "[]")
623 then () else error "rational.sml cancel WN 1";
625 "-------- example heuberger";
626 val t = ParseC.parse_test @{context} ("(x \<up> 4 + x * y + x \<up> 3 * y + y \<up> 2) / " ^
627 "(x + 5 * x \<up> 2 + y + 5 * x * y + x \<up> 2 * y \<up> 3 + x * y \<up> 4)");
628 val SOME (t', asm) = rewrite_set_ ctxt false cancel_p t;
629 if (UnparseC.term @{context} t', UnparseC.terms @{context} asm) =
630 ("(x \<up> 3 + y) / (1 + 5 * x + x * y \<up> 3)", "[1 + 5 * x + x * y \<up> 3 \<noteq> 0]")
631 then () else error "rational.sml cancel_p heuberger";
633 "-------- rewrite_set_ add_fractions_p from: Mathematik 1 Schalk -------------";
634 "-------- rewrite_set_ add_fractions_p from: Mathematik 1 Schalk -------------";
635 "-------- rewrite_set_ add_fractions_p from: Mathematik 1 Schalk -------------";
636 (*deleted example 204 ... 236b at update Isabelle2012-->2013*)
638 "-------- integration lev.1 -- lev.5: cancel_p_ & add_fractions_p_ -----------";
639 "-------- integration lev.1 -- lev.5: cancel_p_ & add_fractions_p_ -----------";
640 "-------- integration lev.1 -- lev.5: cancel_p_ & add_fractions_p_ -----------";
641 val t = ParseC.parse_test @{context} ("123 = (a*x)/(b*x) + (c*x)/(d*x) + (e*x)/(f*x::real)");
642 "-------- gcd_poly integration level 1: works on exact term";
643 if NONE = cancel_p_ thy t then () else error "cancel_p_ works on exact fraction";
644 if NONE = add_fraction_p_ thy t then () else error "add_fraction_p_ works on exact fraction";
646 "-------- gcd_poly integration level 2: picks out ONE appropriate subterm";
647 val SOME (t', asm) = rewrite_set_ ctxt false cancel_p t;
648 if UnparseC.term @{context} t' = "123 = a * x / (b * x) + c * x / (d * x) + e / f"
649 then () else error "level 2, rewrite_set_ cancel_p: changed";
650 val SOME (t', asm) = rewrite_set_ ctxt false add_fractions_p t;
651 if UnparseC.term @{context} t' = "123 = (b * c * x + a * d * x) / (b * d * x) + e * x / (f * x)"
652 then () else error "level 2, rewrite_set_ add_fractions_p: changed";
654 "-------- gcd_poly integration level 3: rewrites all appropriate subterms";
655 val SOME (t', asm) = rewrite_set_ ctxt false cancel_p_rls t;
656 if UnparseC.term @{context} t' = "123 = a / b + c / d + e / f"
657 then () else error "level 3, rewrite_set_ cancel_p_rls: changed";
658 val SOME (t', asm) = rewrite_set_ ctxt false add_fractions_p_rls t; (*CREATE add_fractions_p_rls*)
659 if UnparseC.term @{context} t' = "123 = (b * d * e * x + b * c * f * x + a * d * f * x) / (b * d * f * x)"
660 then () else error "level 3, rewrite_set_ add_fractions_p_rls: changed";
662 "-------- gcd_poly integration level 4: iteration cancel_p -- add_fraction_p";
663 (* simpler variant *)
664 val testrls = Rule_Set.append_rules "testrls" Rule_Set.empty [Rls_ cancel_p, Rls_ add_fractions_p]
665 val SOME (t', asm) = rewrite_set_ ctxt false testrls t;
666 (*Rewrite.trace_on := false; (*true false*)
667 # rls: testrls on: 123 = a * x / (b * x) + c * x / (d * x) + e * x / (f * x)
668 ## rls: cancel_p on: 123 = a * x / (b * x) + c * x / (d * x) + e * x / (f * x)
669 ## rls: add_fractions_p on: 123 = a * x / (b * x) + c * x / (d * x) + e / f
670 ## rls: cancel_p on: 123 = (b * c * x + a * d * x) / (b * d * x) + e / f
671 ## rls: add_fractions_p on: 123 = (b * c + a * d) / (b * d) + e / f
672 ## rls: cancel_p on: 123 = (b * d * e + b * c * f + a * d * f) / (b * d * f)
673 ## rls: add_fractions_p on: 123 = (b * d * e + b * c * f + a * d * f) / (b * d * f) *)
674 if UnparseC.term @{context} t' = "123 = (b * d * e + b * c * f + a * d * f) / (b * d * f)"
675 then () else error "level 4, rewrite_set_ *_p: changed";
677 (* complicated variant *)
678 val testrls_rls = Rule_Set.append_rules "testrls_rls" Rule_Set.empty [Rls_ cancel_p_rls, Rls_ add_fractions_p_rls];
679 val SOME (t', asm) = rewrite_set_ ctxt false testrls_rls t;
680 (*# rls: testrls_rls on: 123 = a * x / (b * x) + c * x / (d * x) + e * x / (f * x)
681 ## rls: cancel_p_rls on: 123 = a * x / (b * x) + c * x / (d * x) + e * x / (f * x)
682 ### rls: cancel_p on: 123 = a * x / (b * x) + c * x / (d * x) + e * x / (f * x)
683 ### rls: cancel_p on: 123 = a * x / (b * x) + c * x / (d * x) + e / f
684 ### rls: cancel_p on: 123 = a * x / (b * x) + c / d + e / f
685 ### rls: cancel_p on: 123 = a / b + c / d + e / f
686 ## rls: add_fractions_p_rls on: 123 = a / b + c / d + e / f
687 ### rls: add_fractions_p on: 123 = a / b + c / d + e / f
688 ### rls: add_fractions_p on: 123 = (b * c + a * d) / (b * d) + e / f
689 ### rls: add_fractions_p on: 123 = (b * d * e + b * c * f + a * d * f) / (b * d * f)
690 ## rls: cancel_p_rls on: 123 = (b * d * e + b * c * f + a * d * f) / (b * d * f)
691 ### rls: cancel_p on: 123 = (b * d * e + b * c * f + a * d * f) / (b * d * f)
692 ## rls: add_fractions_p_rls on: 123 = (b * d * e + b * c * f + a * d * f) / (b * d * f)
693 ### rls: add_fractions_p on: 123 = (b * d * e + b * c * f + a * d * f) / (b * d * f) *)
694 if UnparseC.term @{context} t' = "123 = (b * d * e + b * c * f + a * d * f) / (b * d * f)"
695 then () else error "level 4, rewrite_set_ *_p_rls: changed"
697 "-------- gcd_poly integration level 5: cancel_p & add_fraction_p within norm_Rational";
698 val SOME (t', asm) = rewrite_set_ ctxt false norm_Rational t;
699 if UnparseC.term @{context} t' = "123 = (a * d * f + b * c * f + b * d * e) / (b * d * f)"
700 then () else error "level 5, rewrite_set_ norm_Rational: changed"
702 "-------- reverse rewrite ----------------------------------------------------";
703 "-------- reverse rewrite ----------------------------------------------------";
704 "-------- reverse rewrite ----------------------------------------------------";
705 (** the term for which reverse rewriting is demonstrated **)
706 val t = ParseC.parse_test @{context} "(9 + - 1 * x \<up> 2) / (9 + 6 * x + x \<up> 2)";
707 val Rrls {program = Rfuns {init_state = ini, locate_rule = loc,
708 next_rule = nex, normal_form = nor, ...},...} = cancel_p;
710 (** normal_form produces the result in ONE step **)
711 val SOME (t', _) = nor t;
712 if UnparseC.term @{context} t' = "(3 + - 1 * x) / (3 + x)" then ()
713 else error "rational.sml normal_form (9 - x \<up> 2) / (9 - 6 * x + x \<up> 2)";
715 (** initialize the interpreter state used by the 'me' **)
716 val (t, _, revsets, _) = ini t;
718 if length (hd revsets) = 11 then () else error "length of revset changed";
719 if (revsets |> nth 1 |> nth 1 |> Rule.id) =
720 (@{thm realpow_twoI} |> Thm.get_name_hint |> ThmC.cut_longid)
721 then () else error "first element of revset changed";
723 (revsets |> nth 1 |> nth 1 |> Rule.to_string ctxt) = "Thm (\"realpow_twoI\", ?r1 \<up> 2 = ?r1 * ?r1)" andalso
724 (revsets |> nth 1 |> nth 2 |> Rule.to_string ctxt) = "Thm (\"#: 9 = 3 \<up> 2\", 9 = 3 \<up> 2)" andalso
725 (revsets |> nth 1 |> nth 3 |> Rule.to_string ctxt) = "Thm (\"#: 6 * x = 2 * (3 * x)\", 6 * x = 2 * (3 * x))"
727 (revsets |> nth 1 |> nth 4 |> Rule.to_string ctxt) = "Thm (\"#: - 3 * x = - 1 * (3 * x)\", - 3 * x = - 1 * (3 * x))"
729 (revsets |> nth 1 |> nth 5 |> Rule.to_string ctxt) = "Thm (\"#: 9 = 3 * 3\", 9 = 3 * 3)" andalso
730 (revsets |> nth 1 |> nth 6 |> Rule.to_string ctxt) = "Rls_ (\"sym_order_mult_rls_\")" andalso
731 (revsets |> nth 1 |> nth 7 |> Rule.to_string ctxt) =
732 "Thm (\"sym_mult.assoc\", ?a * (?b * ?c) = ?a * ?b * ?c)"
733 then () else error "first 7 elements in revset changed"
735 (** find the rule 'r' to apply to term 't' **)
736 (*/------- WN1309: since cancel_ (accepted "-" between monomials) has been replaced by cancel_p_
737 for Isabelle2013, we don't get a working revset, but non-termination:
739 val SOME (r as (Thm (str, thm))) = nex revsets t;
741 ((3 * 3 + - 1 * x * x) / (3 * 3 + 2 * 3 * x + x * x),
742 Rls_ ("sym_order_mult_rls_"), ((3 * 3 + - 1 * (x * x)) / (3 * 3 + 2 * (3 * x) + x * x), []))", "
743 ((3 * 3 + - 1 * (x * x)) / (3 * 3 + 2 * (3 * x) + x * x),
744 Thm ("sym_mult.assoc", ""), ((3 * 3 + - 1 * (x * x)) / (3 * 3 + 2 * 3 * x + x * x), []))", "
745 ((3 * 3 + - 1 * (x * x)) / (3 * 3 + 2 * 3 * x + x * x),
746 Thm ("sym_mult.assoc", ""), ((3 * 3 + - 1 * x * x) / (3 * 3 + 2 * 3 * x + x * x), []))", "
747 ((3 * 3 + - 1 * x * x) / (3 * 3 + 2 * 3 * x + x * x), Rls_ ("sym_order_mult_rls_"), ((3 * 3 + - 1 * (x * x)) / (3 * 3 + 2 * (3 * x) + x * x), []))", "
750 Thm ("sym_#mult_2_3", "6 = 2 * 3")
751 ### Isabelle2009- 2 for cancel_ (not cancel_p_):
752 if str = "sym_#power_Float ((3,0), (0,0)) __ ((2,0), (0,0))"
753 andalso ThmC.string_of_thm thm =
754 (string_of_thm (Thm.make_thm @{theory "Isac_Knowledge"}
755 (Trueprop $ (ParseC.parse_test ctxt "9 = 3 \<up> 2"))) then ()
756 else error "rational.sml next_rule (9 - x \<up> 2) / (9 - 6 * x + x \<up> 2)";
757 \---------------------------------------------------------------------------------------/*)
759 (** check, if the rule 'r' applied by the user to 't' belongs to the ruleset;
760 if the rule is OK, the term resulting from applying the rule is returned,too;
761 there might be several rule applications inbetween,
762 which are listed after the head in reverse order **)
763 (*/-------------------------------------------- Isabelle2013: this gives "error id_of_thm";
764 we don't repair this, because interaction within "reverse rewriting" never worked properly:
766 val (r, (t, asm))::_ = loc revsets t r;
767 if UnparseC.term @{context} t = "(9 - x \<up> 2) / (3 \<up> 2 + 6 * x + x \<up> 2)" andalso asm = []
768 then () else error "rational.sml locate_rule (9 - x \<up> 2) / (9 - 6 * x + x \<up> 2)";
770 (* find the next rule to apply *)
771 val SOME (r as (Thm (str, thm))) = nex revsets t;
772 if str = "sym_#power_Float ((3,0), (0,0)) __ ((2,0), (0,0))" andalso
773 ThmC.string_of_thm thm = (string_of_thm (ThmC_Def.make_thm @{theory "Isac_Knowledge"}
774 (Trueprop $ (ParseC.parse_test ctxt "9 = 3 \<up> 2"))) then ()
775 else error "rational.sml next_rule (9 - x \<up> 2) / (9 - 6 * x + x \<up> 2)";
777 (*check the next rule*)
778 val (r, (t, asm)) :: _ = loc revsets t r;
779 if UnparseC.term @{context} t = "(3 \<up> 2 - x \<up> 2) / (3 \<up> 2 + 6 * x + x \<up> 2)" then ()
780 else error "rational.sml locate_rule (9 - x \<up> 2) / (9 - 6 * x + x \<up> 2) II";
782 (*find and check the next rules, rewrite*)
783 val SOME r = nex revsets t;
784 val (r,(t,asm))::_ = loc revsets t r;
785 if UnparseC.term @{context} t = "(3 \<up> 2 - x \<up> 2) / (3 \<up> 2 + 2 * 3 * x + x \<up> 2)" then ()
786 else error "rational.sml locate_rule II";
788 val SOME r = nex revsets t;
789 val (r,(t,asm))::_ = loc revsets t r;
790 if UnparseC.term @{context} t = "(3 - x) * (3 + x) / (3 \<up> 2 + 2 * 3 * x + x \<up> 2)" then ()
791 else error "rational.sml next_rule II";
793 val SOME r = nex revsets t;
794 val (r,(t,asm))::_ = loc revsets t r;
795 if UnparseC.term @{context} t = "(3 - x) * (3 + x) / ((3 + x) * (3 + x))" then ()
796 else error "rational.sml next_rule III";
798 val SOME r = nex revsets t;
799 val (r, (t, asm)) :: _ = loc revsets t r;
800 val ss = UnparseC.term @{context} t;
801 if ss = "(3 - x) / (3 + x)" andalso UnparseC.terms @{context} asm = "[\"3 + x ~= 0\"]" then ()
802 else error "rational.sml: new behav. in rev-set cancel";
803 \--------------------------------------------------------------------------------------/*)
805 "-------- 'reverse-ruleset' cancel_p -----------------------------------------";
806 "-------- 'reverse-ruleset' cancel_p -----------------------------------------";
807 "-------- 'reverse-ruleset' cancel_p -----------------------------------------";
808 (*WN130909: the example below shows, why "reverse rewriting" only worked for
811 (*the term for which reverse rewriting is demonstrated*)
812 val t = ParseC.parse_test @{context} "(9 + (- 1)*x \<up> 2) / (9 + ((-6)*x + x \<up> 2))";
813 val Rrls {program=Rfuns {init_state=ini,locate_rule=loc,
814 next_rule=nex,normal_form=nor,...},...} = cancel_p;
816 (*normal_form produces the result in ONE step*)
817 val SOME (t', _) = nor t;
818 if UnparseC.term @{context} t' = "(3 + x) / (3 + - 1 * x)"
819 then () else error "cancel_p normal_form CHANGED";;
821 (*initialize the interpreter state used by the 'me'*)
822 val SOME (t', asm) = cancel_p_ thy t;
823 if (UnparseC.term @{context} t', UnparseC.terms @{context} asm) =
824 ("(3 + x) / (3 + - 1 * x)", "[3 + - 1 * x \<noteq> 0]")
825 then () else error "cancel_p CHANGED";;
827 val (t,_,revsets,_) = ini t;
829 (* WN.10.10.02: dieser Fall terminiert nicht
830 (make_polynomial enth"alt zu viele rules)
831 WN060823 'init_state' requires rewriting on specified location in the term
832 default_print_depth 99; Rfuns; default_print_depth 3;
833 WN060831 cycling "sym_order_mult_rls_" "sym_mult.assoc"
834 as was with make_polynomial before ?!?* )
836 val SOME r = nex revsets t;
837 eq_Thm (r, Thm ("sym_#power_Float ((3,0), (0,0)) __ ((2,0), (0,0))",
838 mk_thm thy "9 = 3 \<up> 2"));
839 ( *WN060831 *** id_of_thm
840 Exception- ERROR raised ...
841 val (r,(t,asm))::_ = loc revsets t r;
842 UnparseC.term @{context} t;
844 val SOME r = nex revsets t;
845 val (r,(t,asm))::_ = loc revsets t r;
846 UnparseC.term @{context} t;
849 "-------- examples: rls norm_Rational ----------------------------------------";
850 "-------- examples: rls norm_Rational ----------------------------------------";
851 "-------- examples: rls norm_Rational ----------------------------------------";
852 val t = ParseC.parse_test @{context} "Not (6*x is_atom)";
853 val SOME (t',_) = rewrite_set_ ctxt false powers_erls t; UnparseC.term @{context} t';
855 val t = ParseC.parse_test @{context} "1 < 2";
856 val SOME (t',_) = rewrite_set_ ctxt false powers_erls t; UnparseC.term @{context} t';
859 val t = ParseC.parse_test @{context} "(6*x) \<up> 2";
860 val SOME (t',_) = rewrite_ ctxt Rewrite_Ord.function_empty powers_erls false @{thm realpow_def_atom} t;
861 if UnparseC.term @{context} t' = "6 * x * (6 * x) \<up> (2 + - 1)" then ()
862 else error "rational.sml powers_erls (6*x) \<up> 2";
864 val t = ParseC.parse_test @{context} "- 1 * (- 2 * (5 / 2 * (13 * x / 2)))";
865 val SOME (t',_) = rewrite_set_ ctxt false norm_Rational t; UnparseC.term @{context} t';
866 if UnparseC.term @{context} t' = "65 * x / 2" then () else error "rational.sml 4";
868 val t = ParseC.parse_test @{context} "1 - ((13*x)/2 - 5/2) \<up> 2";
869 val SOME (t',_) = rewrite_set_ ctxt false norm_Rational t; UnparseC.term @{context} t';
870 if UnparseC.term @{context} t' = "(- 21 + 130 * x + - 169 * x \<up> 2) / 4" then ()
871 else error "rational.sml 5";
873 (*SRAM Schalk I, p.92 Nr. 609a*)
874 val t = ParseC.parse_test @{context} "2*(3 - x/5)/3 - 4*(1 - x/3) - x/3 - 2*(x/2 - 1/4)/27 +5/54";
875 val SOME (t',_) = rewrite_set_ ctxt false norm_Rational t; UnparseC.term @{context} t';
876 if UnparseC.term @{context} t' = "(- 255 + 112 * x) / 135" then ()
877 else error "rational.sml 6";
879 (*SRAM Schalk I, p.92 Nr. 610c*)
880 val t = ParseC.parse_test @{context} "((x- 1)/(x+1) + 1) / ((x- 1)/(x+1) - (x+1)/(x- 1)) - 2";
881 val SOME (t',_) = rewrite_set_ ctxt false norm_Rational t; UnparseC.term @{context} t';
882 if UnparseC.term @{context} t' = "(3 + x) / - 2" then () else error "rational.sml 7";
884 (*SRAM Schalk I, p.92 Nr. 476a*)
885 val t = ParseC.parse_test @{context} "(x \<up> 2/(1 - x \<up> 2) + 1)/(x/(1 - x) + 1) * (1 + x)";
886 (*. a/b : c/d translated to a/b * d/c .*)
887 val SOME (t',_) = rewrite_set_ ctxt false norm_Rational t; UnparseC.term @{context} t';
888 if UnparseC.term @{context} t' = "1" then () else error "rational.sml 8";
890 (*Schalk I, p.92 Nr. 472a*)
891 val t = ParseC.parse_test @{context} "((8*x \<up> 2 - 32*y \<up> 2)/(2*x + 4*y))/((4*x - 8*y)/(x + y))";
892 val SOME (t',_) = rewrite_set_ ctxt false norm_Rational t; UnparseC.term @{context} t';
893 if UnparseC.term @{context} t' = "x + y" then () else error "rational.sml p.92 Nr. 472a";
895 (*Schalk I, p.70 Nr. 480b: SEE rational.sml --- nonterminating rls norm_Rational ---*)
897 (*WN130910 add_fractions_p exception Div raised + history:
898 ### WN.2.6.03 from rlang.sml 56a
899 val t = ParseC.parse_test @{context} "(a + b * x) / (a + - 1 * (b * x)) + (- 1 * a + b * x) / (a + b * x) = 4 * (a * b) / (a \<up> 2 + - 1 * b \<up> 2)";
900 val NONE = rewrite_set_ ctxt false add_fractions_p t;
902 THE ERROR ALREADY OCCURS IN THIS PART:
903 val t = ParseC.parse_test @{context} "(a + b * x) / (a + - 1 * (b * x)) + (- 1 * a + b * x) / (a + b * x)";
904 val NONE = add_fraction_p_ ctxt t;
906 SEE Test_Some.thy: section {* add_fractions_p downto exception Div raised ===
909 "-------- rational numerals --------------------------------------------------";
910 "-------- rational numerals --------------------------------------------------";
911 "-------- rational numerals --------------------------------------------------";
912 (*SRA Schalk I, p.40 Nr. 164b *)
913 val t = ParseC.parse_test @{context} "(47/6 - 76/9 + 13/4)/(35/12)";
914 val SOME (t, _) = rewrite_set_ ctxt false norm_Rational t;
915 if UnparseC.term @{context} t = "19 / 21" then ()
916 else error "rational.sml: diff.behav. in norm_Rational_mg 1";
918 (*SRA Schalk I, p.40 Nr. 166a *)
919 val t = ParseC.parse_test @{context} "((5/4)/(4+22/7) + 37/20)*(110/3 - 110/9 * 23/11)";
920 val SOME (t, _) = rewrite_set_ ctxt false norm_Rational t;
921 if UnparseC.term @{context} t = "45 / 2" then ()
922 else error "rational.sml: diff.behav. in norm_Rational_mg 2";
924 "-------- examples cancellation from: Mathematik 1 Schalk --------------------";
925 "-------- examples cancellation from: Mathematik 1 Schalk --------------------";
926 "-------- examples cancellation from: Mathematik 1 Schalk --------------------";
928 val t = ParseC.parse_test @{context} "((1 + 9*a \<up> 2) * (1 + 3*a)) / ((3*a + 9*a \<up> 2) * (1 + 3*a))";
929 val SOME (t, _) = rewrite_set_ ctxt false norm_Rational t;
930 if UnparseC.term @{context} t = "(1 + 9 * a \<up> 2) / (3 * a + 9 * a \<up> 2)"
931 then () else error "rational.sml: diff.behav. in norm_Rational_mg 3";
934 val t = ParseC.parse_test @{context} "(x \<up> 2 * (7*x + (- 1)*y)) / (y \<up> 2 * (7*x + (- 1)*y))";
935 val SOME (t, _) = rewrite_set_ ctxt false norm_Rational t;
936 if UnparseC.term @{context} t = "x \<up> 2 / y \<up> 2"
937 then () else error "rational.sml: diff.behav. in norm_Rational_mg 4";
939 (*SRC Schalk I, p.66 Nr. 379c *)
940 val t = ParseC.parse_test @{context} "(a - b)/(b - a)";
941 val SOME (t, _) = rewrite_set_ ctxt false norm_Rational t;
942 if UnparseC.term @{context} t = "- 1"
943 then () else error "rational.sml: diff.behav. in norm_Rational_mg 5";
945 (*SRC Schalk I, p.66 Nr. 380b *)
946 val t = ParseC.parse_test @{context} "15*(3*x + 3) * (4*x + 9) / (12*(2*x + 7) * (5*x + 5))";
947 val SOME (t, _) = rewrite_set_ ctxt false norm_Rational t;
948 if UnparseC.term @{context} t = "(27 + 12 * x) / (28 + 8 * x)"
949 then () else error "rational.sml: diff.behav. in norm_Rational_mg 6";
952 val t = ParseC.parse_test @{context} "((1 + 9*a \<up> 2) * (1 + 3*a)) / ((3*a + 9*a \<up> 2) * (1 + 3 * a))";
953 val SOME (t, _) = rewrite_set_ ctxt false norm_Rational t;
954 if UnparseC.term @{context} t = "(1 + 9 * a \<up> 2) / (3 * a + 9 * a \<up> 2)"
955 then () else error "rational.sml: diff.behav. in norm_Rational_mg 3";
958 val t = ParseC.parse_test @{context} "(x \<up> 2 * (7*x + (- 1)*y)) / (y \<up> 2 * (7*x + (- 1)*y))";
959 val SOME (t, _) = rewrite_set_ ctxt false norm_Rational t;
960 if UnparseC.term @{context} t = "x \<up> 2 / y \<up> 2"
961 then () else error "rational.sml: diff.behav. in norm_Rational_mg 4";
963 (*SRC Schalk I, p.66 Nr. 379c *)
964 val t = ParseC.parse_test @{context} "(a - b) / (b - a)";
965 val SOME (t, _) = rewrite_set_ ctxt false norm_Rational t;
966 if UnparseC.term @{context} t = "- 1"
967 then () else error "rational.sml: diff.behav. in norm_Rational_mg 5";
969 (*SRC Schalk I, p.66 Nr. 380b *)
970 val t = ParseC.parse_test @{context} "15*(3*x + 3) * (4*x + 9) / (12*(2*x + 7) * (5*x + 5))";
971 val SOME (t, _) = rewrite_set_ ctxt false norm_Rational t;
972 if UnparseC.term @{context} t = "(27 + 12 * x) / (28 + 8 * x)"
973 then () else error "rational.sml: diff.behav. in norm_Rational_mg 6";
975 (* extreme example from somewhere *)
976 val t = ParseC.parse_test @{context}
977 ("(a \<up> 4 * x + - 1*a \<up> 4 * y + 4*a \<up> 3 * b * x + -4*a \<up> 3 * b * y + " ^
978 "6*a \<up> 2 * b \<up> 2 * x + -6*a \<up> 2 * b \<up> 2 * y + 4*a * b \<up> 3 * x + -4*a * b \<up> 3 * y + " ^
979 "b \<up> 4 * x + - 1*b \<up> 4 * y) " ^
980 " / (a \<up> 2 * x \<up> 3 + -3*a \<up> 2 * x \<up> 2 * y + 3*a \<up> 2 * x * y \<up> 2 + - 1*a \<up> 2 * y \<up> 3 + " ^
981 "2*a * b * x \<up> 3 + -6*a * b * x \<up> 2 * y + 6*a * b * x * y \<up> 2 + - 2*a * b * y \<up> 3 + " ^
982 "b \<up> 2 * x \<up> 3 + -3*b \<up> 2 * x \<up> 2 * y + 3*b \<up> 2 * x * y \<up> 2 + - 1*b \<up> 2 * y \<up> 3)")
983 val SOME (t, _) = rewrite_set_ ctxt false cancel_p t;
984 if UnparseC.term @{context} t = "(a \<up> 2 + 2 * a * b + b \<up> 2) / (x \<up> 2 + - 2 * x * y + y \<up> 2)"
985 then () else error "with Isabelle2002: NONE -- now SOME changed";
987 (*Schalk I, p.66 Nr. 381a *)
988 (* ATTENTION: here the rls is very slow. In Isabelle2002 this required 2 min *)
989 val t = ParseC.parse_test @{context} "18*(a + b) \<up> 3 * (a - b) \<up> 2 / (72*(a - b) \<up> 3 * (a + b) \<up> 2)";
990 val SOME (t, _) = rewrite_set_ ctxt false norm_Rational t;
991 if UnparseC.term @{context} t = "(a + b) / (4 * a + - 4 * b)"
992 then () else error "rational.sml: diff.behav. in norm_Rational_mg 8";
994 (*SRC Schalk I, p.66 Nr. 381b *)
995 val t = ParseC.parse_test @{context} "(4*x \<up> 2 - 20*x + 25) / (2*x - 5) \<up> 3";
996 val SOME (t, _) = rewrite_set_ ctxt false norm_Rational t;
997 if UnparseC.term @{context} t = "1 / (- 5 + 2 * x)"
998 then () else error "rational.sml: diff.behav. in norm_Rational_mg 9";
1000 (*SRC Schalk I, p.66 Nr. 381c *)
1001 val t = ParseC.parse_test @{context} "(27*a \<up> 3 + 9*a \<up> 2+3*a+1) / (27*a \<up> 3 + 18*a \<up> 2+3*a)";
1002 val SOME (t, _) = rewrite_set_ ctxt false norm_Rational t;
1003 if UnparseC.term @{context} t = "(1 + 9 * a \<up> 2) / (3 * a + 9 * a \<up> 2)"
1004 then () else error "rational.sml: diff.behav. in norm_Rational_mg 10";
1006 (*SRC Schalk I, p.66 Nr. 383a *)
1007 val t = ParseC.parse_test @{context} "(5*a \<up> 2 - 5*a*b) / (a - b) \<up> 2";
1008 val SOME (t, _) = rewrite_set_ ctxt false norm_Rational t;
1009 if UnparseC.term @{context} t = "- 5 * a / (- 1 * a + b)"
1010 then () else error "rational.sml: diff.behav. in norm_Rational_mg 11";
1012 "----- NOT TERMINATING ?: worked before 0707xx";
1013 val t = ParseC.parse_test @{context} "(a \<up> 2 - 1)*(b + 1) / ((b \<up> 2 - 1)*(a+1))";
1014 (* WN130911 "exception Div raised" by
1015 cancel_p_ thy (ParseC.parse_test @{context} ("(- 1 + - 1 * b + a \<up> 2 + a \<up> 2 * b) /" ^
1016 "(- 1 + - 1 * a + b \<up> 2 + a * b \<up> 2)"))
1018 val SOME (t, _) = rewrite_set_ ctxt false norm_Rational t;
1019 if UnparseC.term @{context} t = "(1 + - 1 * a) / (1 + - 1 * b)" then ()
1020 else error "rational.sml MG tests 3e";
1023 "-------- examples common denominator from: Mathematik 1 Schalk --------------";
1024 "-------- examples common denominator from: Mathematik 1 Schalk --------------";
1025 "-------- examples common denominator from: Mathematik 1 Schalk --------------";
1026 (*SRA Schalk I, p.67 Nr. 403a *)
1027 val t = ParseC.parse_test @{context} "4/x - 3/y - 1";
1028 val SOME (t, _) = rewrite_set_ ctxt false norm_Rational t;
1029 if UnparseC.term @{context} t = "(- 3 * x + 4 * y + - 1 * x * y) / (x * y)"
1030 then () else error "rational.sml: diff.behav. in norm_Rational_mg 12";
1032 val t = ParseC.parse_test @{context} "(2*a+3*b)/(b*c) + (3*c+a)/(a*c) - (2*a \<up> 2+3*b*c)/(a*b*c)";
1033 val SOME (t, _) = rewrite_set_ ctxt false norm_Rational t;
1034 if UnparseC.term @{context} t = "4 / c"
1035 then () else error "rational.sml: diff.behav. in norm_Rational_mg 13";
1037 (*SRA Schalk I, p.67 Nr. 410b *)
1038 val t = ParseC.parse_test @{context} "1/(x+1) + 1/(x+2) - 2/(x+3)";
1039 (* WN130911 non-termination due to non-termination of
1040 cancel_p_ thy (ParseC.parse_test @{context} "(5 + 3 * x) / (6 + 11 * x + 6 * x \<up> 2 + x \<up> 3)")
1042 val SOME (t, _) = rewrite_set_ ctxt false norm_Rational t;
1043 if UnparseC.term @{context} t = "(5 + 3 * x) / (6 + 11 * x + 6 * x \<up> 2 + x \<up> 3)"
1044 then () else error "rational.sml: diff.behav. in norm_Rational_mg 14";
1047 (*SRA Schalk I, p.67 Nr. 413b *)
1048 val t = ParseC.parse_test @{context} "(1 + x)/(1 - x) - (1 - x)/(1 + x) + 2*x/(1 - x \<up> 2)";
1049 val SOME (t, _) = rewrite_set_ ctxt false norm_Rational t;
1050 if UnparseC.term @{context} t = "6 * x / (1 + - 1 * x \<up> 2)"
1051 then () else error "rational.sml: diff.behav. in norm_Rational_mg 15";
1053 (*SRA Schalk I, p.68 Nr. 414a *)
1054 val t = ParseC.parse_test @{context} "(x + 2)/(x - 1) + (x - 3)/(x - 2) - (x + 1)/((x - 1)*(x - 2))";
1055 val SOME (t, _) = rewrite_set_ ctxt false norm_Rational t;
1056 if UnparseC.term @{context} t ="(- 2 + - 5 * x + 2 * x \<up> 2) / (2 + - 3 * x + x \<up> 2)"
1057 then () else error "rational.sml: diff.behav. in norm_Rational_mg 16";
1059 (*SRA Schalk I, p.68 Nr. 428b *)
1060 val t = ParseC.parse_test @{context}
1061 "1/(a - b) \<up> 2 + 1/(a + b) \<up> 2 - 2/(a \<up> 2 - b \<up> 2) - 4*(b \<up> 2 - 1)/(a \<up> 2 - b \<up> 2) \<up> 2";
1062 (* WN130911 non-termination due to non-termination of
1063 cancel_p_ thy (ParseC.parse_test @{context} "(4 + -4 * b \<up> 2) / (a \<up> 4 + - 2 * (a \<up> 2 * b \<up> 2) + b \<up> 4)")
1065 val SOME (t, _) = rewrite_set_ ctxt false norm_Rational t;
1066 if UnparseC.term @{context} t = "4 / (a \<up> 4 + - 2 * a \<up> 2 * b \<up> 2 + b \<up> 4)"
1067 then () else error "rational.sml: diff.behav. in norm_Rational_mg 18";
1070 (*SRA Schalk I, p.68 Nr. 430b *)
1071 val t = ParseC.parse_test @{context}
1072 "a \<up> 2/(a - 3*b) - 108*a*b \<up> 3/((a+3*b)*(a \<up> 2 - 9*b \<up> 2)) - 9*b \<up> 2*(a - 3*b)/(a+3*b) \<up> 2";
1073 val SOME (t, _) = rewrite_set_ ctxt false norm_Rational t;
1074 if UnparseC.term @{context} t = "a + 3 * b"
1075 then () else error "rational.sml: diff.behav. in norm_Rational_mg 19";
1077 (*SRA Schalk I, p.68 Nr. 432 *)
1078 val t = ParseC.parse_test @{context}
1079 ("(a \<up> 2 + a*b) / (a \<up> 2 - b \<up> 2) - (b \<up> 2 - a*b) / (b \<up> 2 - a \<up> 2) + " ^
1080 "a \<up> 2*(a - b) / (a \<up> 3 - a \<up> 2*b) - 2*a*(a \<up> 2 - b \<up> 2) / (a \<up> 3 - a*b \<up> 2) - " ^
1081 "2*b \<up> 2 / (a \<up> 2 - b \<up> 2)");
1082 val SOME (t, _) = rewrite_set_ ctxt false norm_Rational t;
1083 if UnparseC.term @{context} t = (*"0" ..isabisac15 | Isabelle2017..*) "0 / (a \<up> 2 + - 1 * b \<up> 2)"
1084 then () else error "rational.sml: diff.behav. in norm_Rational_mg 20";
1087 val t = ParseC.parse_test @{context} "3*a / (a*b) + x/y";
1088 val SOME (t, _) = rewrite_set_ ctxt false norm_Rational t;
1089 if UnparseC.term @{context} t = "(3 * y + b * x) / (b * y)"
1090 then () else error "rational.sml: diff.behav. in norm_Rational_mg 21";
1093 "-------- examples multiply and cancel from: Mathematik 1 Schalk -------------";
1094 "-------- examples multiply and cancel from: Mathematik 1 Schalk -------------";
1095 "-------- examples multiply and cancel from: Mathematik 1 Schalk -------------";
1096 (*------- SRM Schalk I, p.68 Nr. 436a *)
1097 val t = ParseC.parse_test @{context} "3*(x+y) / (15*(x - y)) * 25*(x - y) \<up> 2 / (18*(x + y) \<up> 2)";
1098 val SOME (t, _) = rewrite_set_ ctxt false norm_Rational t;
1099 if UnparseC.term @{context} t = "(- 5 * x + 5 * y) / (- 18 * x + - 18 * y)"
1100 then () else error "rational.sml: diff.behav. in norm_Rational_mg 22";
1102 (*------- SRM.test Schalk I, p.68 Nr. 436b *)
1103 val t = ParseC.parse_test @{context} "5*a*(a - b) \<up> 2*(a + b) \<up> 3/(7*b*(a - b) \<up> 3) * 7*b/(a + b) \<up> 3";
1104 val SOME (t, _) = rewrite_set_ ctxt false norm_Rational t;
1105 if UnparseC.term @{context} t = "5 * a / (a + - 1 * b)"
1106 then () else error "rational.sml: diff.behav. in norm_Rational_mg 23";
1108 (*------- Schalk I, p.68 Nr. 437a *)
1109 val t = ParseC.parse_test @{context} "(3*a - 4*b) / (4*c+3*e) * (3*a+4*b)/(9*a \<up> 2 - 16*b \<up> 2)";
1110 (* raises an exception for unclear reasons:
1111 val SOME (t, _) = rewrite_set_ ctxt false norm_Rational t;
1113 ### rls: cancel_p on: (9 * a \<up> 2 + - 16 * b \<up> 2) / (4 * c + 3 * e) /
1114 (9 * a \<up> 2 + - 16 * b \<up> 2)
1115 exception Div raised
1118 val t = ParseC.parse_test @{context}
1119 ("(9 * a \<up> 2 + - 16 * b \<up> 2) / (4 * c + 3 * e) /" ^
1120 "(9 * a \<up> 2 + - 16 * b \<up> 2)");
1121 NONE = cancel_p_ thy t;
1123 if UnparseC.term @{context} t = "1 / (4 * c + 3 * e)" then ()
1124 else error "rational.sml: diff.behav. in norm_Rational_mg 24";
1127 "----- S.K. corrected non-termination 060904";
1128 val t = ParseC.parse_test @{context} "(3*a - 4*b) * (3*a+4*b)/((4*c+3*e)*(9*a \<up> 2 - 16*b \<up> 2))";
1129 val SOME (t, _) = rewrite_set_ ctxt false make_polynomial t;
1130 if UnparseC.term @{context} t =
1131 "(9 * a \<up> 2 + - 16 * b \<up> 2) /\n(36 * a \<up> 2 * c + 27 * a \<up> 2 * e + - 64 * b \<up> 2 * c +\n - 48 * b \<up> 2 * e)"
1132 then () else error "rational.sml: S.K.8..corrected 060904-6";
1134 "----- S.K. corrected non-termination of cancel_p_";
1135 val t'' = ParseC.parse_test @{context} ("(9 * a \<up> 2 + - 16 * b \<up> 2) /" ^
1136 "(36 * a \<up> 2 * c + (27 * a \<up> 2 * e + (-64 * b \<up> 2 * c + -48 * b \<up> 2 * e)))");
1137 (* /--- DOES NOT TERMINATE AT TRANSITION isabisac15 --> Isabelle2017 --------------------------\
1138 val SOME (t',_) = rewrite_set_ ctxt false cancel_p t'';
1139 if UnparseC.term @{context} t' = "1 / (4 * c + 3 * e)"
1140 then () else error "rational.sml: diff.behav. in cancel_p S.K.8";
1141 \--- DOES NOT TERMINATE AT TRANSITION isabisac15 --> Isabelle2017 --------------------------/*)
1143 (*------- Schalk I, p.68 Nr. 437b*)
1144 val t = ParseC.parse_test @{context} "(a + b)/(x \<up> 2 - y \<up> 2) * ((x - y) \<up> 2/(a \<up> 2 - b \<up> 2))";
1145 (*val SOME (t, _) = rewrite_set_ ctxt false norm_Rational t;
1147 #### rls: cancel_p on: (a * x \<up> 2 + - 2 * (a * (x * y)) + a * y \<up> 2 + b * x \<up> 2 +
1148 - 2 * (b * (x * y)) +
1150 (a \<up> 2 * x \<up> 2 + - 1 * (a \<up> 2 * y \<up> 2) + - 1 * (b \<up> 2 * x \<up> 2) +
1151 b \<up> 2 * y \<up> 2)
1152 exception Div raised
1155 (*------- SRM Schalk I, p.68 Nr. 438a *)
1156 val t = ParseC.parse_test @{context} "x*y / (x*y - y \<up> 2) * (x \<up> 2 - x*y)";
1157 val SOME (t, _) = rewrite_set_ ctxt false norm_Rational t;
1158 if UnparseC.term @{context} t = "x \<up> 2"
1159 then () else error "rational.sml: diff.behav. in norm_Rational_mg 24";
1161 (*------- SRM Schalk I, p.68 Nr. 439b *)
1162 val t = ParseC.parse_test @{context} "(4*x \<up> 2 + 4*x + 1) * ((x \<up> 2 - 2*x \<up> 3) / (4*x \<up> 2 + 2*x))";
1163 val SOME (t, _) = rewrite_set_ ctxt false norm_Rational t;
1164 if UnparseC.term @{context} t = "(x + - 4 * x \<up> 3) / 2"
1165 then () else error "rational.sml: diff.behav. in norm_Rational_mg 25";
1167 (*------- SRM Schalk I, p.68 Nr. 440a *)
1168 val t = ParseC.parse_test @{context} "(x \<up> 2 - 2*x) / (x \<up> 2 - 3*x) * (x - 3) \<up> 2 / (x \<up> 2 - 4)";
1169 val SOME (t, _) = rewrite_set_ ctxt false norm_Rational t;
1170 if UnparseC.term @{context} t = "(- 3 + x) / (2 + x)"
1171 then () else error "rational.sml: diff.behav. in norm_Rational_mg 26";
1173 "----- Schalk I, p.68 Nr. 440b SK11 works since 0707xx";
1174 val t = ParseC.parse_test @{context} "(a \<up> 3 - 9*a) / (a \<up> 3*b - a*b \<up> 3) * (a \<up> 2*b + a*b \<up> 2) / (a+3)";
1175 (* WN130911 non-termination for unclear reasons:
1176 val SOME (t, _) = rewrite_set_ ctxt false norm_Rational t;
1178 ... ENDS WITH THIS TRACE:
1180 ### rls: cancel_p on: (-9 * (a \<up> 3 * b) + -9 * (a \<up> 2 * b \<up> 2) + a \<up> 5 * b +
1181 a \<up> 4 * b \<up> 2) /
1182 (a \<up> 3 * b + - 1 * (a * b \<up> 3)) /
1184 BUT THIS IS CORRECTLY RECOGNISED
1185 val t = ParseC.parse_test @{context}
1186 ("(-9 * (a \<up> 3 * b) + -9 * (a \<up> 2 * b \<up> 2) + a \<up> 5 * b + a \<up> 4 * b \<up> 2) /" ^
1187 "(a \<up> 3 * b + - 1 * (a * b \<up> 3)) / (3 + (a::real))");
1189 NONE = cancel_p_ thy t;
1191 if UnparseC.term @{context} t = "(-3 * a + a \<up> 2) / (a + - 1 * b)" then ()
1192 else error "rational.sml: diff.behav. in norm_Rational 27";
1195 "----- SK12 works since 0707xx";
1196 val t = ParseC.parse_test @{context} "(a \<up> 3 - 9*a) * (a \<up> 2*b+a*b \<up> 2) / ((a \<up> 3*b - a*b \<up> 3) * (a+3))";
1197 (* WN130911 non-termination due to non-termination of
1198 cancel_p_ thy (ParseC.parse_test @{context} "(4 + -4 * b \<up> 2) / (a \<up> 4 + - 2 * (a \<up> 2 * b \<up> 2) + b \<up> 4)")
1200 val SOME (t, _) = rewrite_set_ ctxt false norm_Rational t;
1201 if UnparseC.term @{context} t' = "(-3 * a + a \<up> 2) / (a + - 1 * b)" then ()
1202 else error "rational.sml: diff.behav. in norm_Rational 28";
1205 "-------- examples common denominator and multiplication from: Schalk --------";
1206 "-------- examples common denominator and multiplication from: Schalk --------";
1207 "-------- examples common denominator and multiplication from: Schalk --------";
1208 (*------- SRAM Schalk I, p.69 Nr. 441b *)
1209 val t = ParseC.parse_test @{context} "(4*a/3 + 3*b \<up> 2/a \<up> 3 + b/(4*a))*(4*b/(3*a))";
1210 val SOME (t, _) = rewrite_set_ ctxt false norm_Rational t;
1211 if UnparseC.term @{context} t = "(36 * b \<up> 3 + 3 * a \<up> 2 * b \<up> 2 + 16 * a \<up> 4 * b) /\n(9 * a \<up> 4)"
1212 then () else error "rational.sml: diff.behav. in norm_Rational_mg 28";
1214 (*------- SRAM Schalk I, p.69 Nr. 442b *)
1215 val t = ParseC.parse_test @{context} ("(15*a \<up> 2/x \<up> 3 - 5*b \<up> 4/x \<up> 2 + 25*c \<up> 2/x) * " ^
1216 "(x \<up> 3/(5*a*b \<up> 3*c \<up> 3)) + 1/c \<up> 3 * (b*x/a - 3*a/b \<up> 3)");
1217 val SOME (t, _) = rewrite_set_ ctxt false norm_Rational t;
1218 if UnparseC.term @{context} t = "5 * x \<up> 2 / (a * b \<up> 3 * c)"
1219 then () else error "rational.sml: diff.behav. in norm_Rational_mg 29";
1221 (*------- SRAM Schalk I, p.69 Nr. 443b *)
1222 val t = ParseC.parse_test @{context} "(a/2 + b/3) * (b/3 - a/2)";
1223 val SOME (t, _) = rewrite_set_ ctxt false norm_Rational t;
1224 if UnparseC.term @{context} t = "(- 9 * a \<up> 2 + 4 * b \<up> 2) / 36"
1225 then () else error "rational.sml: diff.behav. in norm_Rational_mg 30";
1227 (*------- SRAM Schalk I, p.69 Nr. 445b *)
1228 val t = ParseC.parse_test @{context} "(a \<up> 2/9 + 2*a/(3*b) + 4/b \<up> 2)*(a/3 - 2/b) + 8/b \<up> 3";
1229 val SOME (t, _) = rewrite_set_ ctxt false norm_Rational t;
1230 if UnparseC.term @{context} t = "a \<up> 3 / 27"
1231 then () else error "rational.sml: diff.behav. in norm_Rational_mg 31";
1233 (*------- SRAM Schalk I, p.69 Nr. 446b *)
1234 val t = ParseC.parse_test @{context} "(x/(5*x + 4*y) - y/(5*x - 4*y) + 1)*(25*x \<up> 2 - 16*y \<up> 2)";
1235 val SOME (t, _) = rewrite_set_ ctxt false norm_Rational t;
1236 if UnparseC.term @{context} t = (*"30 * x \<up> 2 + -9 * x * y + - 20 * y \<up> 2" ..isabisac15 | Isabelle2017..*)
1237 "(- 30 * x \<up> 2 + 9 * x * y + 20 * y \<up> 2) / - 1"
1238 then () else error "rational.sml: diff.behav. in norm_Rational_mg 32";
1240 (*------- SRAM Schalk I, p.69 Nr. 449a *)(*Achtung: rechnet ca 8 Sekunden*)
1241 val t = ParseC.parse_test @{context}
1242 "(2*x \<up> 2/(3*y)+x/y \<up> 2)*(4*x \<up> 4/(9*y \<up> 2)+x \<up> 2/y \<up> 4)*(2*x \<up> 2/(3*y) - x/y \<up> 2)";
1243 val SOME (t, _) = rewrite_set_ ctxt false norm_Rational t;
1244 if UnparseC.term @{context} t = "(- 81 * x \<up> 4 + 16 * x \<up> 8 * y \<up> 4) / (81 * y \<up> 8)"
1245 then () else error "rational.sml: diff.behav. in norm_Rational_mg 33";
1247 (*------- SRAM Schalk I, p.69 Nr. 450a *)
1248 val t = ParseC.parse_test @{context}
1249 "(4*x/(3*y)+2*y/(3*x)) \<up> 2 - (2*y/(3*x) - 2*x/y)*(2*y/(3*x)+2*x/y)";
1250 val SOME (t, _) = rewrite_set_ ctxt false norm_Rational t;
1251 if UnparseC.term @{context} t = "(52 * x \<up> 2 + 16 * y \<up> 2) / (9 * y \<up> 2)"
1252 then () else error "rational.sml: diff.behav. in norm_Rational_mg 34";
1254 (*------- SRAM Schalk I, p.69 Nr. 442b --- abgewandelt*)
1255 val t = ParseC.parse_test @{context}
1256 ("(15*a \<up> 4/(a*x \<up> 3) - 5*a*((b \<up> 4 - 5*c \<up> 2*x) / x \<up> 2)) * " ^
1257 "(x \<up> 3/(5*a*b \<up> 3*c \<up> 3)) + a/c \<up> 3 * (x*(b/a) - 3*b*(a/b \<up> 4))");
1258 val SOME (t, _) = rewrite_set_ ctxt false norm_Rational t;
1259 if UnparseC.term @{context} t = "5 * x \<up> 2 / (b \<up> 3 * c)"
1260 then () else error "rational.sml: diff.behav. in norm_Rational_mg 53";
1263 "-------- examples double fractions from: Mathematik 1 Schalk ----------------";
1264 "-------- examples double fractions from: Mathematik 1 Schalk ----------------";
1265 "-------- examples double fractions from: Mathematik 1 Schalk ----------------";
1266 "----- SRD Schalk I, p.69 Nr. 454b";
1267 val t = ParseC.parse_test @{context} "((2 - x)/(2*a)) / (2*a/(x - 2))";
1268 val SOME (t, _) = rewrite_set_ ctxt false norm_Rational t;
1269 if UnparseC.term @{context} t = "(- 4 + 4 * x + - 1 * x \<up> 2) / (4 * a \<up> 2)"
1270 then () else error "rational.sml: diff.behav. in norm_Rational_mg 35";
1272 "----- SRD Schalk I, p.69 Nr. 455a";
1273 val t = ParseC.parse_test @{context} "(a \<up> 2 + 1)/(a \<up> 2 - 1) / ((a+1)/(a - 1))";
1274 val SOME (t, _) = rewrite_set_ ctxt false norm_Rational t;
1275 if UnparseC.term @{context} t = "(1 + a \<up> 2) / (1 + 2 * a + a \<up> 2)" then ()
1276 else error "rational.sml: diff.behav. in norm_Rational_mg 36";
1278 "----- Schalk I, p.69 Nr. 455b";
1279 val t = ParseC.parse_test @{context} "(x \<up> 2 - 4)/(y \<up> 2 - 9)/((2+x)/(3 - y))";
1280 (* WN130911 non-termination due to non-termination of
1281 cancel_p_ thy (ParseC.parse_test @{context} ("(- 12 + 4 * y + 3 * x \<up> 2 + - 1 * (x \<up> 2 * y)) /" ^
1282 "(- 18 + -9 * x + 2 * y \<up> 2 + x * y \<up> 2)"))
1284 val SOME (t, _) = rewrite_set_ ctxt false norm_Rational t;
1285 if UnparseC.term @{context} t = "(2 + - 1 * x) / (3 + y)" then ()
1286 else error "rational.sml: diff.behav. in norm_Rational_mg 37";
1289 "----- SK060904- 1a non-termination of cancel_p_ ?: worked before 0707xx";
1290 val t = ParseC.parse_test @{context} "(x \<up> 2 - 4)*(3 - y) / ((y \<up> 2 - 9)*(2+x))";
1291 (* WN130911 non-termination due to non-termination of
1292 cancel_p_ thy (ParseC.parse_test @{context} ("(- 12 + 4 * y + 3 * x \<up> 2 + - 1 * (x \<up> 2 * y)) /" ^
1293 "(- 18 + -9 * x + 2 * y \<up> 2 + x * y \<up> 2)"))
1295 val SOME (t, _) = rewrite_set_ ctxt false norm_Rational t;
1296 if UnparseC.term @{context} t = "(2 + - 1 * x) / (3 + y)" then ()
1297 else error "rational.sml: diff.behav. in norm_Rational_mg 37b";
1300 "----- ?: worked before 0707xx";
1301 val t = ParseC.parse_test @{context} "(3 + - 1 * y) / (-9 + y \<up> 2)";
1302 val SOME (t, _) = rewrite_set_ ctxt false norm_Rational t;
1303 if UnparseC.term @{context} t = "- 1 / (3 + y)"
1304 then () else error "rational.sml: - 1 / (3 + y) norm_Rational";
1306 "----- SRD Schalk I, p.69 Nr. 456b";
1307 val t = ParseC.parse_test @{context} "(b \<up> 3 - b \<up> 2) / (b \<up> 2+b) / (b \<up> 2 - 1)";
1308 val SOME (t, _) = rewrite_set_ ctxt false norm_Rational t;
1309 if UnparseC.term @{context} t = "b / (1 + 2 * b + b \<up> 2)"
1310 then () else error "rational.sml: diff.behav. in norm_Rational_mg 38";
1312 "----- SRD Schalk I, p.69 Nr. 457b";
1313 val t = ParseC.parse_test @{context} "(16*a \<up> 2 - 9*b \<up> 2)/(2*a+3*a*b) / ((4*a+3*b)/(4*a \<up> 2 - 9*a \<up> 2*b \<up> 2))";
1314 val SOME (t, _) = rewrite_set_ ctxt false norm_Rational t;
1315 if UnparseC.term @{context} t = "8 * a \<up> 2 + - 6 * a * b + - 12 * a \<up> 2 * b + 9 * a * b \<up> 2"
1316 then () else error "rational.sml: diff.behav. in norm_Rational_mg 39";
1318 "----- Schalk I, p.69 Nr. 458b works since 0707";
1319 val t = ParseC.parse_test @{context} "(2*a \<up> 2*x - a \<up> 2) / (a*x - b*x) / (b \<up> 2*(2*x - 1) / (x*(a - b)))";
1320 (*val SOME (t, _) = rewrite_set_ ctxt false norm_Rational t;
1322 ### rls: cancel_p on: (- 1 * a \<up> 2 + 2 * (a \<up> 2 * x)) / (a * x + - 1 * (b * x)) /
1323 ((- 1 * b \<up> 2 + 2 * (b \<up> 2 * x)) / (a * x + - 1 * (b * x)))
1324 exception Div raised
1327 val t = ParseC.parse_test @{context}
1328 ("(- 1 * a \<up> 2 + 2 * (a \<up> 2 * x)) / (a * x + - 1 * (b * x)) /" ^
1329 "((- 1 * b \<up> 2 + 2 * (b \<up> 2 * x)) / (a * x + - 1 * (b * x)))");
1330 NONE = cancel_p_ thy t;
1332 if UnparseC.term @{context} t = "a \<up> 2 / b \<up> 2" then ()
1333 else error "rational.sml: diff.behav. in norm_Rational_mg 39b";
1336 "----- SRD Schalk I, p.69 Nr. 459b";
1337 val t = ParseC.parse_test @{context} "(a \<up> 2 - b \<up> 2)/(a*b) / (4*(a+b) \<up> 2/a)";
1338 val SOME (t, _) = rewrite_set_ ctxt false norm_Rational t;
1339 if UnparseC.term @{context} t = "(a + - 1 * b) / (4 * a * b + 4 * b \<up> 2)" then ()
1340 else error "rational.sml: diff.behav. in norm_Rational_mg 41";
1342 "----- Schalk I, p.69 Nr. 460b nonterm.SK";
1343 val t = ParseC.parse_test @{context} "(9*(x \<up> 2 - 8*x + 16) / (4*(y \<up> 2 - 2*y + 1))) / ((3*x - 12) / (16*y - 16))";
1344 (*val SOME (t, _) = rewrite_set_ ctxt false norm_Rational t;
1345 exception Div raised
1348 val t = ParseC.parse_test @{context}
1349 ("(144 + -72 * x + 9 * x \<up> 2) / (4 + -8 * y + 4 * y \<up> 2) /" ^
1350 "((- 12 + 3 * x) / (- 16 + 16 * y))");
1351 NONE = cancel_p_ thy t;
1353 if UnparseC.term @{context} t = !!!!!!!!!!!!!!!!!!!!!!!!!
1354 then () else error "rational.sml: diff.behav. in norm_Rational_mg 42";
1357 "----- some variant of the above; was non-terminating before";
1358 val t = ParseC.parse_test @{context} "9*(x \<up> 2 - 8*x+16)*(16*y - 16)/(4*(y \<up> 2 - 2*y+1)*(3*x - 12))";
1359 val SOME (t , _) = rewrite_set_ ctxt false norm_Rational t;
1360 if UnparseC.term @{context} t = "(48 + - 12 * x) / (1 + - 1 * y)"
1361 then () else error "some variant of the above; was non-terminating before";
1363 "----- SRD Schalk I, p.70 Nr. 472a";
1364 val t = ParseC.parse_test @{context} ("((8*x \<up> 2 - 32*y \<up> 2) / (2*x + 4*y)) / ((4*x - 8*y) / (x + y))");
1365 val SOME (t, _) = rewrite_set_ ctxt false norm_Rational t;
1366 if UnparseC.term @{context} t = "x + y"
1367 then () else error "rational.sml: diff.behav. in norm_Rational_mg 43";
1369 "----- Schalk I, p.70 Nr. 478b ----- Rechenzeit: 5 sec";
1370 val t = ParseC.parse_test @{context} ("(a - (a*b + b \<up> 2)/(a+b))/(b+(a - b)/(1+(a+b)/(a - b))) / " ^
1371 "((a - a \<up> 2/(a+b))/(a+(a*b)/(a - b)))");
1372 val SOME (t, _) = rewrite_set_ ctxt false norm_Rational t;
1373 if UnparseC.term @{context} t = "(2 * a \<up> 3 + 2 * a \<up> 2 * b) / (a \<up> 2 * b + b \<up> 3)"
1374 then () else error "rational.sml: diff.behav. in norm_Rational_mg 51";
1376 (*SRD Schalk I, p.69 Nr. 461a *)
1377 val t = ParseC.parse_test @{context} "(2/(x+3) + 2/(x - 3)) / (8*x/(x \<up> 2 - 9))";
1378 val SOME (t, _) = rewrite_set_ ctxt false norm_Rational t;
1379 if UnparseC.term @{context} t = "1 / 2"
1380 then () else error "rational.sml: diff.behav. in norm_Rational_mg 44";
1382 (*SRD Schalk I, p.69 Nr. 464b *)
1383 val t = ParseC.parse_test @{context} "(a - a/(a - 2)) / (a + a/(a - 2))";
1384 val SOME (t, _) = rewrite_set_ ctxt false norm_Rational t;
1385 if UnparseC.term @{context} t = "(- 3 + a) / (- 1 + a)"
1386 then () else error "rational.sml: diff.behav. in norm_Rational_mg 45";
1388 (*SRD Schalk I, p.69 Nr. 465b *)
1389 val t = ParseC.parse_test @{context} "((x+3*y)/9 + (4*y \<up> 2 - 9*z \<up> 2)/(16*x)) / (x/9 + y/6 + z/4)";
1390 (* WN130911 non-termination due to non-termination of
1391 cancel_p_ thy (ParseC.parse_test @{context}
1392 ("("(576 * x \<up> 2 + 1728 * (x * y) + 1296 * y \<up> 2 + - 2916 * z \<up> 2) /" ^
1393 "(576 * x \<up> 2 + 864 * (x * y) + 1296 * (x * z))"))
1395 val SOME (t, _) = rewrite_set_ ctxt false norm_Rational t;
1396 if UnparseC.term @{context} t = "(4 * x + 6 * y + -9 * z) / (4 * x)"
1397 then () else error "rational.sml: diff.behav. in norm_Rational_mg 46";
1400 (*SRD Schalk I, p.69 Nr. 466b *)
1401 val t = ParseC.parse_test @{context} "((1 - 7*(x - 2)/(x \<up> 2 - 4)) / (6/(x+2))) / (3/(x+5)+30/(x \<up> 2 - 25))";
1402 val SOME (t, _) = rewrite_set_ ctxt false norm_Rational t;
1403 if UnparseC.term @{context} t = "(25 + - 10 * x + x \<up> 2) / 18"
1404 then () else error "rational.sml: diff.behav. in norm_Rational_mg 47";
1406 (*SRD Schalk I, p.70 Nr. 469 *)
1407 val t = ParseC.parse_test @{context} ("3*b \<up> 2 / (4*a \<up> 2 - 8*a*b + 4*b \<up> 2) / " ^
1408 "(a / (a \<up> 2*b - b \<up> 3) + (a - b) / (4*a*b \<up> 2 + 4*b \<up> 3) - 1 / (4*b \<up> 2))");
1409 val SOME (t, _) = rewrite_set_ ctxt false norm_Rational t;
1410 if UnparseC.term @{context} t = "- 3 * b \<up> 3 / (- 2 * a + 2 * b)"
1411 then () else error "rational.sml: diff.behav. in norm_Rational_mg 48";
1414 "-------- me Schalk I No.186 -------------------------------------------------";
1415 "-------- me Schalk I No.186 -------------------------------------------------";
1416 "-------- me Schalk I No.186 -------------------------------------------------";
1417 val fmz = ["Term ((14 * x * y) / ( x * y ))", "normalform N"];
1419 ("Rational",["rational", "simplification"],
1420 ["simplification", "of_rationals"]);
1421 val p = e_pos'; val c = [];
1422 val (p,_,f,nxt,_,pt) = Test_Code.init_calc @{context} [(fmz, (dI',pI',mI'))];
1423 val (p,_,f,nxt,_,pt) = me nxt p c pt;
1424 val (p,_,f,nxt,_,pt) = me nxt p c pt;
1425 val (p,_,f,nxt,_,pt) = me nxt p c pt;
1426 val (p,_,f,nxt,_,pt) = me nxt p c pt;
1427 val (p,_,f,nxt,_,pt) = me nxt p c pt;
1428 val (p,_,f,nxt,_,pt) = me nxt p c pt;
1429 val (p,_,f,nxt,_,pt) = me nxt p c pt;
1430 val (p,_,f,nxt,_,pt) = me nxt p c pt; f2str f;
1431 val (p,_,f,nxt,_,pt) = me nxt p c pt; f2str f;
1432 val (p,_,f,nxt,_,pt) = me nxt p c pt; f2str f;(*++ for explicit script*)
1433 val (p,_,f,nxt,_,pt) = me nxt p c pt; f2str f;(*++ for explicit script*)
1434 case (f2str f, nxt) of
1435 ("14", End_Proof') => ()
1436 | _ => error "rational.sml diff.behav. in me Schalk I No.186";
1439 "-------- interSteps ..Simp_Rat_Double_No- 1.xml ------------------------------";
1440 "-------- interSteps ..Simp_Rat_Double_No- 1.xml ------------------------------";
1441 "-------- interSteps ..Simp_Rat_Double_No- 1.xml ------------------------------";
1443 CalcTree @{context} [(["Term (((2 - x)/(2*a)) / (2*a/(x - 2)))", "normalform N"],
1444 ("Rational", ["rational", "simplification"], ["simplification", "of_rationals"]))];
1447 autoCalculate 1 CompleteCalc;
1448 val ((pt, p), _) = States.get_calc 1;
1450 Test_Tool.show_pt pt;
1452 (([], Frm), Simplify ((2 - x) / (2 * a) / (2 * a / (x - 2)))),
1453 (([1], Frm), (2 - x) / (2 * a) / (2 * a / (x - 2))),
1454 (([1], Res), (2 + - 1 * x) / (2 * a) / (2 * a / (x + - 1 * 2))),
1455 (([2], Res), (2 + - 1 * x) / (2 * a) / (2 * a / (- 2 + x))),
1456 (([3], Res), (2 + - 1 * x) * (- 2 + x) / (2 * a * (2 * a))),
1457 (([4], Res), (-4 + 4 * x + - 1 * x \<up> 2) / (4 * a \<up> 2)),
1458 (([], Res), (-4 + 4 * x + - 1 * x \<up> 2) / (4 * a \<up> 2))]
1460 interSteps 1 ([1], Res);
1461 val ((pt, p), _) = States.get_calc 1;
1462 (*Test_Tool.show_pt pt;
1464 (([], Frm), Simplify ((2 - x) / (2 * a) / (2 * a / (x - 2)))),
1465 (([1], Frm), (2 - x) / (2 * a) / (2 * a / (x - 2))),
1466 (([1,1], Frm), (2 - x) / (2 * a) / (2 * a / (x - 2))),
1467 (([1,1], Res), (2 - x) / (2 * a) / (2 * a / (x + - 1 * 2))),
1468 (([1,2], Res), (2 + - 1 * x) / (2 * a) / (2 * a / (x + - 1 * 2))),
1469 (([1], Res), (2 + - 1 * x) / (2 * a) / (2 * a / (x + - 1 * 2))),
1470 (([2], Res), (2 + - 1 * x) / (2 * a) / (2 * a / (- 2 + x))),
1471 (([3], Res), (2 + - 1 * x) * (- 2 + x) / (2 * a * (2 * a))),
1472 (([4], Res), (-4 + 4 * x + - 1 * x \<up> 2) / (4 * a \<up> 2)),
1473 (([], Res), (-4 + 4 * x + - 1 * x \<up> 2) / (4 * a \<up> 2))]
1475 val (t, asm) = get_obj g_result pt [1, 1];
1476 if UnparseC.term @{context} t = "(2 - x) / (2 * a) / (2 * a / (x + - 1 * 2))" andalso UnparseC.terms @{context} asm = "[]"
1477 then () else error "2nd interSteps ..Simp_Rat_Double_No- 1 changed on [1, 1]";
1478 val (t, asm) = get_obj g_result pt [1, 2];
1479 if UnparseC.term @{context} t = "(2 + - 1 * x) / (2 * a) / (2 * a / (x + - 1 * 2))" andalso UnparseC.terms @{context} asm = "[]"
1480 then () else error "3rd interSteps ..Simp_Rat_Double_No- 1 changed on [1, 2]";
1484 "-------- interSteps ..Simp_Rat_Cancel_No- 1.xml ------------------------------";
1485 "-------- interSteps ..Simp_Rat_Cancel_No- 1.xml ------------------------------";
1486 "-------- interSteps ..Simp_Rat_Cancel_No- 1.xml ------------------------------";
1488 CalcTree @{context} [(["Term ((a \<up> 2 + - 1*b \<up> 2) / (a \<up> 2 + - 2*a*b + b \<up> 2))", "normalform N"],
1489 ("Rational", ["rational", "simplification"], ["simplification", "of_rationals"]))];
1492 autoCalculate 1 CompleteCalc;
1493 val ((pt, p), _) = States.get_calc 1;
1494 (*Test_Tool.show_pt pt;
1496 (([], Frm), Simplify ((a \<up> 2 + - 1 * b \<up> 2) / (a \<up> 2 + - 2 * a * b + b \<up> 2))),
1497 (([1], Frm), (a \<up> 2 + - 1 * b \<up> 2) / (a \<up> 2 + - 2 * a * b + b \<up> 2)),
1498 (([1], Res), (a \<up> 2 + - 1 * b \<up> 2) / (a \<up> 2 + - 2 * (a * b) + b \<up> 2)),
1499 (([2], Res), (a + b) / (a + - 1 * b)),
1500 (([], Res), (a + b) / (a + - 1 * b))]
1502 interSteps 1 ([2], Res);
1503 val ((pt, p), _) = States.get_calc 1;
1504 (*Test_Tool.show_pt pt;
1506 (([], Frm), Simplify ((a \<up> 2 + - 1 * b \<up> 2) / (a \<up> 2 + - 2 * a * b + b \<up> 2))),
1507 (([1], Frm), (a \<up> 2 + - 1 * b \<up> 2) / (a \<up> 2 + - 2 * a * b + b \<up> 2)),
1508 (([1], Res), (a \<up> 2 + - 1 * b \<up> 2) / (a \<up> 2 + - 2 * (a * b) + b \<up> 2)),
1509 (([2,1], Frm), (a \<up> 2 + - 1 * b \<up> 2) / (a \<up> 2 + - 2 * (a * b) + b \<up> 2)),
1510 (([2,1], Res), (a + b) / (a + - 1 * b)),
1511 (([2], Res), (a + b) / (a + - 1 * b)),
1512 (([], Res), (a + b) / (a + - 1 * b))]
1514 interSteps 1 ([2,1],Res);
1515 val ((pt, p), _) = States.get_calc 1;
1516 (*Test_Tool.show_pt pt;
1518 (([], Frm), Simplify ((a \<up> 2 + - 1 * b \<up> 2) / (a \<up> 2 + - 2 * a * b + b \<up> 2))),
1519 (([1], Frm), (a \<up> 2 + - 1 * b \<up> 2) / (a \<up> 2 + - 2 * a * b + b \<up> 2)),
1520 (([1], Res), (a \<up> 2 + - 1 * b \<up> 2) / (a \<up> 2 + - 2 * (a * b) + b \<up> 2)),
1521 (([2,1], Frm), (a \<up> 2 + - 1 * b \<up> 2) / (a \<up> 2 + - 2 * (a * b) + b \<up> 2)),
1522 (([2,1,1], Frm), (a \<up> 2 + - 1 * b \<up> 2) / (a \<up> 2 + - 2 * (a * b) + b \<up> 2)),
1523 (([2,1,1], Res), (a \<up> 2 + - 1 * (a * b) + a * b + - 1 * b \<up> 2) /
1524 (a \<up> 2 + - 2 * (a * b) + 1 * b \<up> 2)),
1525 (([2,1,2], Res), (a \<up> 2 + - 1 * (a * b) + a * b + - 1 * b \<up> 2) /
1526 (a \<up> 2 + - 2 * (a * b) + - 1 \<up> 2 * b \<up> 2)),
1527 (([2,1,3], Res), (a \<up> 2 + - 1 * (a * b) + a * b + - 1 * b \<up> 2) /
1528 (a \<up> 2 + - 2 * (a * b) + (- 1 * b) \<up> 2)),
1529 (([2,1,4], Res), (a * a + - 1 * (a * b) + a * b + - 1 * b \<up> 2) /
1530 (a \<up> 2 + - 2 * (a * b) + (- 1 * b) \<up> 2)),
1531 (([2,1,5], Res), (a * a + - 1 * (a * b) + a * b + - 1 * (b * b)) /
1532 (a \<up> 2 + - 2 * (a * b) + (- 1 * b) \<up> 2)),
1533 (([2,1,6], Res), (a * a + - 1 * (a * b) + a * b + - 1 * (b * b)) /
1534 (a \<up> 2 + - 1 * (2 * (a * b)) + (- 1 * b) \<up> 2)),
1535 (([2,1,7], Res), (a * a + a * (- 1 * b) + (b * a + b * (- 1 * b))) /
1536 (a \<up> 2 + 2 * (a * (- 1 * b)) + (- 1 * b) \<up> 2)),
1537 (([2,1,8], Res), (a * a + a * (- 1 * b) + (b * a + b * (- 1 * b))) /
1538 (a \<up> 2 + 2 * a * (- 1 * b) + (- 1 * b) \<up> 2)),
1539 (([2,1,9], Res), (a * (a + - 1 * b) + (b * a + b * (- 1 * b))) /
1540 (a \<up> 2 + 2 * a * (- 1 * b) + (- 1 * b) \<up> 2)),
1541 (([2,1,10], Res), (a * (a + - 1 * b) + b * (a + - 1 * b)) /
1542 (a \<up> 2 + 2 * a * (- 1 * b) + (- 1 * b) \<up> 2)),
1543 (([2,1,11], Res), (a + b) * (a + - 1 * b) / (a \<up> 2 + 2 * a * (- 1 * b) + (- 1 * b) \<up> 2)),
1544 (([2,1,12], Res), (a + b) * (a + - 1 * b) / ((a + - 1 * b) * (a + - 1 * b))),
1545 (([2,1,13], Res), (a + b) / (a + - 1 * b)),
1546 (([2,1], Res), (a + b) / (a + - 1 * b)),
1547 (([2], Res), (a + b) / (a + - 1 * b)),
1548 (([], Res), (a + b) / (a + - 1 * b))]
1550 val newnds = children (get_nd pt [2,1]) (*see "fun detailrls"*);
1551 if length newnds = 13 then () else error "rational.sml: interSteps cancel_p rev_rew_p";
1553 val p = ([2,1,9],Res);
1555 val (_, tac, _) = ME_Misc.pt_extract ctxt (pt, p);
1556 case tac of SOME (Rewrite ("sym_distrib_left", _)) => ()
1557 | _ => error "rational.sml: getTactic, sym_real_plus_binom_times1";
1560 "-------- investigate rulesets for cancel_p ----------------------------------";
1561 "-------- investigate rulesets for cancel_p ----------------------------------";
1562 "-------- investigate rulesets for cancel_p ----------------------------------";
1563 val thy = @{theory "Rational"};
1564 val t = ParseC.parse_test @{context} "(a \<up> 2 + - 1*b \<up> 2) / (a \<up> 2 + - 2*a*b + b \<up> 2)";
1565 val tt = ParseC.parse_test @{context} "(1 * a + 1 * b) * (1 * a + - 1 * b)"(*numerator only*);
1567 "----- with rewrite_set_";
1568 val SOME (tt',asm) = rewrite_set_ ctxt false make_polynomial tt;
1569 if UnparseC.term @{context} tt'= "a \<up> 2 + - 1 * b \<up> 2" then () else error "rls chancel_p 1";
1570 val tt = ParseC.parse_test @{context} "((1 * a + - 1 * b) * (1 * a + - 1 * b))"(*denominator only*);
1571 val SOME (tt',asm) = rewrite_set_ ctxt false make_polynomial tt;
1572 if UnparseC.term @{context} tt' = "a \<up> 2 + - 2 * a * b + b \<up> 2" then () else error "rls chancel_p 2";
1574 "----- with Derive.do_one; WN1130912 not investigated further, will be discontinued";
1575 val SOME (tt, _) = factout_p_ thy t;
1576 if UnparseC.term @{context} tt = "(a + b) * (a + - 1 * b) / ((a + - 1 * b) * (a + - 1 * b))"
1577 then () else error "rls chancel_p 3";
1579 "--- with simpler ruleset";
1580 val {rules, rew_ord= (_, ro), ...} = Rule_Set.rep (get_rls @{context} "rev_rew_p");
1581 val der = Derive.do_one ctxt Atools_erls rules ro NONE tt;
1582 if length der = 12 then () else error "WN1130912 rls chancel_p 4";
1583 (*default_print_depth 99;*) writeln (Derive.deriv2str ctxt der); (*default_print_depth 3;*)
1585 (*default_print_depth 99;*) map ((UnparseC.term ctxt) o #1) der; (*default_print_depth 3;*)
1586 "...,(- 1 * b \<up> 2 + a \<up> 2) / (- 2 * (a * b) + a \<up> 2 + (- 1 * b) \<up> 2) ]";
1587 (*default_print_depth 99;*) map ((Rule.to_string ctxt) o #2) der; (*default_print_depth 3;*)
1588 (*default_print_depth 99;*) map ((UnparseC.term ctxt) o #1 o #3) der; (*default_print_depth 3;*)
1590 val der = Derive.do_one ctxt Atools_erls rules ro NONE
1591 (ParseC.parse_test @{context} "(1 * a + 1 * b) * (1 * a + - 1 * b)");
1592 (*default_print_depth 99;*) writeln (Derive.deriv2str ctxt der); (*default_print_depth 3;*)
1594 val {rules, rew_ord=(_,ro),...} = Rule_Set.rep (get_rls @{context} "rev_rew_p");
1595 val der = Derive.do_one ctxt Atools_erls rules ro NONE
1596 (ParseC.parse_test @{context} "(1 * a + - 1 * b) * (1 * a + - 1 * b)");
1597 (*default_print_depth 99;*) writeln (Derive.deriv2str ctxt der); (*default_print_depth 3;*)
1598 (*default_print_depth 99;*) map ((UnparseC.term ctxt) o #1) der; (*default_print_depth 3;*)
1599 (*WN060829 ...postponed*)
1602 "-------- fun eval_get_denominator -------------------------------------------";
1603 "-------- fun eval_get_denominator -------------------------------------------";
1604 "-------- fun eval_get_denominator -------------------------------------------";
1605 val thy = @{theory Isac_Knowledge};
1606 val ctxt = Proof_Context.init_global thy;
1607 val t = ParseC.parse_test ctxt "get_denominator ((a +x)/b)";
1608 val SOME (_, t') = eval_get_denominator "" 0 t ctxt;
1609 if UnparseC.term @{context} t' = "get_denominator ((a + x) / b) = b"
1610 then () else error "get_denominator ((a + x) / b) = b"
1613 "-------- several errpats in complicated term --------------------------------";
1614 "-------- several errpats in complicated term --------------------------------";
1615 "-------- several errpats in complicated term --------------------------------";
1616 (*WN12xxxx TODO: instead of Gabriella's example here (27.Jul.12) find a simpler one
1617 WN130912: kept this test, although not clear what for*)
1619 CalcTree @{context} [(["Term ((5*b + 25)/(a^2 - b^2) * (a - b)/(5*b))", "normalform N"],
1620 ("Rational", ["rational", "simplification"], ["simplification", "of_rationals"]))];
1623 autoCalculate 1 CompleteCalc;
1624 val ((pt, p), _) = States.get_calc 1;
1625 (*Test_Tool.show_pt pt;
1627 (([], Frm), Simplify ((5 * b + 25) / (a \<up> 2 - b \<up> 2) * (a - b) / (5 * b))),
1628 (([1], Frm), (5 * b + 25) / (a \<up> 2 - b \<up> 2) * (a - b) / (5 * b)),
1629 (([1], Res), (5 * b + 25) / (a \<up> 2 + - 1 * b \<up> 2) * (a + - 1 * b) / (5 * b)),
1630 (([2], Res), (5 * b + 25) * (a + - 1 * b) / (a \<up> 2 + - 1 * b \<up> 2) / (5 * b)),
1631 (([3], Res), (25 * a + - 25 * b + 5 * (a * b) + -5 * b \<up> 2) / (a \<up> 2 + - 1 * b \<up> 2) /
1633 (([4], Res), (25 + 5 * b) / (a + b) / (5 * b)),
1634 (([5], Res), (25 + 5 * b) / ((a + b) * (5 * b))),
1635 (([6], Res), (25 + 5 * b) / (5 * (a * b) + 5 * b \<up> 2)),
1636 (([7], Res), (5 + b) / (a * b + b \<up> 2)),
1637 (([], Res), (5 + b) / (a * b + b \<up> 2))] *)
1640 "-------- WN1309xx non-terminating rls norm_Rational -------------------------";
1641 "-------- WN1309xx non-terminating rls norm_Rational -------------------------";
1642 "-------- WN1309xx non-terminating rls norm_Rational -------------------------";
1643 (*------- Schalk I, p.70 Nr. 480b; a/b : c/d translated to a/b * d/c*)
1644 val t = ParseC.parse_test @{context}
1645 ("((12*x*y / (9*x \<up> 2 - y \<up> 2)) / (1 / (3*x - y) \<up> 2 - 1 / (3*x + y) \<up> 2)) * " ^
1646 "((1/(x - 5*y) \<up> 2 - 1/(x + 5*y) \<up> 2) / (20*x*y / (x \<up> 2 - 25*y \<up> 2)))");
1648 (*1st factor separately simplified *)
1649 val t = ParseC.parse_test @{context} "((12*x*y / (9*x \<up> 2 - y \<up> 2)) / (1 / (3*x - y) \<up> 2 - 1 / (3*x + y) \<up> 2))";
1650 val SOME (t', _) = rewrite_set_ ctxt false norm_Rational t;
1651 if UnparseC.term @{context} t' = "(- 9 * x \<up> 2 + y \<up> 2) / - 1" then () else error "Nr. 480b lhs changed";
1652 (*2nd factor separately simplified *)
1653 val t = ParseC.parse_test @{context} "((1/(x - 5*y) \<up> 2 - 1/(x + 5*y) \<up> 2) / (20*x*y / (x \<up> 2 - 25*y \<up> 2)))";
1654 val SOME (t',_) = rewrite_set_ ctxt false norm_Rational t; UnparseC.term @{context} t';
1655 if UnparseC.term @{context} t' = "- 1 / (- 1 * x \<up> 2 + 25 * y \<up> 2)" then () else error "Nr. 480b rhs changed";
1657 "-------- Schalk I, p.70 Nr. 477a: terms are exploding ?!?";
1658 val t = ParseC.parse_test @{context} ("b*y/(b - 2*y)/((b \<up> 2 - y \<up> 2)/(b+2*y)) /" ^
1659 "(b \<up> 2*y + b*y \<up> 2) * (a+x) \<up> 2 / ((b \<up> 2 - 4*y \<up> 2) * (a+2*x) \<up> 2)");
1660 (*val SOME (t',_) = rewrite_set_ ctxt false norm_Rational t;
1662 ### rls: cancel_p on: (a \<up> 2 * (b * y) + 2 * (a * (b * (x * y))) + b * (x \<up> 2 * y)) /
1664 ((b \<up> 2 + - 1 * y \<up> 2) / (b + 2 * y)) /
1665 (b \<up> 2 * y + b * y \<up> 2) /
1666 (a \<up> 2 * b \<up> 2 + -4 * (a \<up> 2 * y \<up> 2) + 4 * (a * (b \<up> 2 * x)) +
1667 - 16 * (a * (x * y \<up> 2)) +
1668 4 * (b \<up> 2 * x \<up> 2) +
1669 - 16 * (x \<up> 2 * y \<up> 2))
1670 exception Div raised
1673 val t = ParseC.parse_test @{context}
1674 ("(a \<up> 2 * (b * y) + 2 * (a * (b * (x * y))) + b * (x \<up> 2 * y)) /" ^
1676 "((b \<up> 2 + - 1 * y \<up> 2) / (b + 2 * y)) /" ^
1677 "(b \<up> 2 * y + b * y \<up> 2) /" ^
1678 "(a \<up> 2 * b \<up> 2 + -4 * (a \<up> 2 * y \<up> 2) + 4 * (a * (b \<up> 2 * x)) +" ^
1679 "- 16 * (a * (x * y \<up> 2)) +" ^
1680 "4 * (b \<up> 2 * x \<up> 2) +" ^
1681 "- 16 * (x \<up> 2 * y \<up> 2))");
1682 NONE = cancel_p_ thy t;
1685 (*------- Schalk I, p.70 Nr. 476b in 2003 this worked using 10 sec. *)
1686 val t = ParseC.parse_test @{context}
1687 ("((a \<up> 2 - b \<up> 2)/(2*a*b) + 2*a*b/(a \<up> 2 - b \<up> 2)) / ((a \<up> 2 + b \<up> 2)/(2*a*b) + 1) / " ^
1688 "((a \<up> 2 + b \<up> 2) \<up> 2 / (a + b) \<up> 2)");
1689 (* Rewrite.trace_on := true; (*true false*)
1690 rewrite_set_ ctxt false norm_Rational t;
1692 #### rls: cancel_p on: (2 * (a \<up> 7 * b) + 4 * (a \<up> 6 * b \<up> 2) + 6 * (a \<up> 5 * b \<up> 3) +
1693 8 * (a \<up> 4 * b \<up> 4) +
1694 6 * (a \<up> 3 * b \<up> 5) +
1695 4 * (a \<up> 2 * b \<up> 6) +
1696 2 * (a * b \<up> 7)) /
1697 (2 * (a \<up> 9 * b) + 4 * (a \<up> 8 * b \<up> 2) +
1698 2 * (2 * (a \<up> 7 * b \<up> 3)) +
1699 4 * (a \<up> 6 * b \<up> 4) +
1700 -4 * (a \<up> 4 * b \<up> 6) +
1701 -4 * (a \<up> 3 * b \<up> 7) +
1702 -4 * (a \<up> 2 * b \<up> 8) +
1703 - 2 * (a * b \<up> 9))
1705 if UnparseC.term @{context} t = "1 / (a \<up> 2 + - 1 * b \<up> 2)" then ()
1706 else error "rational.sml: diff.behav. in norm_Rational_mg 49";
1709 "-------- Schalk I, p.70 Nr. 480a: terms are exploding ?!?";
1710 val t = ParseC.parse_test @{context} ("(1/x + 1/y + 1/z) / (1/x - 1/y - 1/z) / " ^
1711 "(2*x \<up> 2 / (x \<up> 2 - z \<up> 2) / (x / (x + z) + x / (x - z)))");
1712 (* Rewrite.trace_on := true; (*true false*)
1713 rewrite_set_ ctxt false norm_Rational t;
1715 #### rls: cancel_p on: (2 * (x \<up> 6 * (y \<up> 2 * z)) + 2 * (x \<up> 6 * (y * z \<up> 2)) +
1716 2 * (x \<up> 5 * (y \<up> 2 * z \<up> 2)) +
1717 - 2 * (x \<up> 4 * (y \<up> 2 * z \<up> 3)) +
1718 - 2 * (x \<up> 4 * (y * z \<up> 4)) +
1719 - 2 * (x \<up> 3 * (y \<up> 2 * z \<up> 4))) /
1720 (- 2 * (x \<up> 6 * (y \<up> 2 * z)) + - 2 * (x \<up> 6 * (y * z \<up> 2)) +
1721 2 * (x \<up> 5 * (y \<up> 2 * z \<up> 2)) +
1722 2 * (x \<up> 4 * (y \<up> 2 * z \<up> 3)) +
1723 2 * (x \<up> 4 * (y * z \<up> 4)) +
1724 - 2 * (x \<up> 3 * (y \<up> 2 * z \<up> 4)))
1727 "-------- Schalk I, p.60 Nr. 215d: terms are exploding, internal loop does not terminate";
1728 val t = ParseC.parse_test @{context} "(a-b) \<up> 3 * (x+y) \<up> 4 / ((x+y) \<up> 2 * (a-b) \<up> 5)";
1729 (* Kein Wunder, denn Z???ler und Nenner extra als Polynom dargestellt ergibt:
1731 val t = ParseC.parse_test @{context} "(a-b) \<up> 3 * (x+y) \<up> 4";
1732 val SOME (t, _) = rewrite_set_ ctxt false norm_Rational t;
1733 UnparseC.term @{context} t;
1734 "a \<up> 3 * x \<up> 4 + 4 * a \<up> 3 * x \<up> 3 * y +6 * a \<up> 3 * x \<up> 2 * y \<up> 2 +4 * a \<up> 3 * x * y \<up> 3 +a \<up> 3 * y \<up> 4 +-3 * a \<up> 2 * b * x \<up> 4 +- 12 * a \<up> 2 * b * x \<up> 3 * y +- 18 * a \<up> 2 * b * x \<up> 2 * y \<up> 2 +- 12 * a \<up> 2 * b * x * y \<up> 3 +-3 * a \<up> 2 * b * y \<up> 4 +3 * a * b \<up> 2 * x \<up> 4 +12 * a * b \<up> 2 * x \<up> 3 * y +18 * a * b \<up> 2 * x \<up> 2 * y \<up> 2 +12 * a * b \<up> 2 * x * y \<up> 3 +3 * a * b \<up> 2 * y \<up> 4 +- 1 * b \<up> 3 * x \<up> 4 +-4 * b \<up> 3 * x \<up> 3 * y +-6 * b \<up> 3 * x \<up> 2 * y \<up> 2 +-4 * b \<up> 3 * x * y \<up> 3 +- 1 * b \<up> 3 * y \<up> 4";
1735 val t = ParseC.parse_test @{context} "((x+y) \<up> 2 * (a-b) \<up> 5)";
1736 val SOME (t, _) = rewrite_set_ ctxt false norm_Rational t;
1737 UnparseC.term @{context} t;
1738 "a \<up> 5 * x \<up> 2 + 2 * a \<up> 5 * x * y + a \<up> 5 * y \<up> 2 +-5 * a \<up> 4 * b * x \<up> 2 +- 10 * a \<up> 4 * b * x * y +-5 * a \<up> 4 * b * y \<up> 2 +10 * a \<up> 3 * b \<up> 2 * x \<up> 2 +20 * a \<up> 3 * b \<up> 2 * x * y +10 * a \<up> 3 * b \<up> 2 * y \<up> 2 +- 10 * a \<up> 2 * b \<up> 3 * x \<up> 2 +- 20 * a \<up> 2 * b \<up> 3 * x * y +- 10 * a \<up> 2 * b \<up> 3 * y \<up> 2 +5 * a * b \<up> 4 * x \<up> 2 +10 * a * b \<up> 4 * x * y +5 * a * b \<up> 4 * y \<up> 2 +- 1 * b \<up> 5 * x \<up> 2 +- 2 * b \<up> 5 * x * y +- 1 * b \<up> 5 * y \<up> 2";
1740 anscheinend macht dem Rechner das Krzen diese Bruches keinen Spass mehr ...*)
1742 "-------- Schalk I, p.70 Nr. 480b: terms are exploding, Rewrite.trace_on stops at";
1743 val t = ParseC.parse_test @{context} ("((12*x*y/(9*x \<up> 2 - y \<up> 2))/" ^
1744 "(1/(3*x - y) \<up> 2 - 1/(3*x + y) \<up> 2)) *" ^
1745 "(1/(x - 5*y) \<up> 2 - 1/(x + 5*y) \<up> 2)/" ^
1746 "(20*x*y/(x \<up> 2 - 25*y \<up> 2))");
1747 (*val SOME (t, _) = rewrite_set_ ctxt false norm_Rational t;
1749 #### rls: cancel_p on: (19440 * (x \<up> 8 * y \<up> 2) + -490320 * (x \<up> 6 * y \<up> 4) +
1750 108240 * (x \<up> 4 * y \<up> 6) +
1751 -6000 * (x \<up> 2 * y \<up> 8)) /
1752 (2160 * (x \<up> 8 * y \<up> 2) + - 108240 * (x \<up> 6 * y \<up> 4) +
1753 1362000 * (x \<up> 4 * y \<up> 6) +
1754 - 150000 * (x \<up> 2 * y \<up> 8))