1 #include "common.h"
2 using namespace std;
3
4 // the following headers are private...
5
6
7 #include "polys/monomials/ring.h"
8 #include "polys/monomials/p_polys.h"
9
10 #include "polys/simpleideals.h"
11
12 #if 0 //ifdef HAVE_FACTORY
13 #include "polys/clapsing.h"
14 #include "factory/factory.h"
15 #endif
16
17
18 #define TRANSEXT_PRIVATES
19
20 #include "polys/ext_fields/algext.h"
21 #include "polys/ext_fields/transext.h"
22
23
24 class MyGlobalPrintingFixture : public GlobalPrintingFixture
25 {
26 public:
setUpWorld()27 virtual bool setUpWorld()
28 {
29
30 GlobalPrintingFixture::setUpWorld();
31
32
33 //TS_ASSERT_EQUALS( nRegister( n_Zp, npInitChar), n_Zp );
34 //TS_ASSERT_EQUALS( nRegister( n_GF, nfInitChar), n_GF );
35 //TS_ASSERT_EQUALS( nRegister( n_R, nrInitChar), n_R );
36 //TS_ASSERT_EQUALS( nRegister( n_Q, nlInitChar), n_Q );
37 //TS_ASSERT_EQUALS( nRegister( n_R, nrInitChar), n_R );
38
39 #ifdef HAVE_RINGS
40 //TS_ASSERT_EQUALS( nRegister( n_Z, nrzInitChar), n_Z ); // these are UNusable at the moment!
41 #endif
42
43 return true;
44 }
45 };
46
47
48 //
49 // We can rely on this file being included exactly once
50 // and declare this global variable in the header file.
51 //
52 static MyGlobalPrintingFixture globalPrintingFixture;
53
54
55 namespace
56 {
57
PrintRing(const ring r)58 void PrintRing(const ring r)
59 {
60 rWrite(r); PrintLn();
61 #ifdef RDEBUG
62 rDebugPrint(r); PrintLn();
63 #endif
64 }
65
_2S(poly a,const ring r)66 static inline std::string _2S(poly a, const ring r)
67 {
68 p_Test(a,r);
69
70 StringSetS("");
71 p_Write(a, r);
72
73 std::stringstream ss;
74 {
75 char* s = StringEndS(); ss << s; omFree(s);
76 }
77
78 return ss.str();
79 }
80
81 static inline void PrintSized(/*const*/ poly a, const ring r, BOOLEAN eoln = TRUE)
82 {
83 std::clog << _2S(a, r) << ", of size: " << p_Size(a, r);
84
85 if( eoln )
86 std::clog << std::endl;
87 }
88
Delete(poly & p,const ring r)89 static inline void Delete(poly &p, const ring r)
90 {
91 if( p != NULL )
92 p_Delete(&p, r);
93
94 p = NULL;
95 }
96
TestSum(const ring r,const int N)97 void TestSum(const ring r, const int N)
98 {
99 TS_ASSERT_DIFFERS( r , NULLp);
100 TS_ASSERT_DIFFERS( r->cf, NULLp);
101
102
103 clog << ( _2S("TEST: sum[0..") + _2S(N) + "]: ");
104 clog << endl;
105
106 assume( N > 0 ); // just for now...
107
108 const int ssss = (N * (N+1)) / 2;
109
110 poly sum1 = p_ISet(ssss, r);
111 clog<< "poly(N*(N+1)/2) (int: " << ssss << "): "; PrintSized(sum1, r);
112
113 poly s=NULL, ss=NULL, i=NULL, res=NULL;
114
115 s = p_ISet(N , r);
116 i = p_ISet(N+1, r);
117
118 i = p_Mult_q(s, i, r); s = NULL;
119
120 clog<< "poly(N)*poly(N+1): (int: "<< N*(N+1) << "): "; PrintSized(i, r);
121
122 number t = n_Init(2, r->cf);
123 clog<< "number(2): "; PrintSized(t, r->cf);
124
125 if( !n_IsZero( t, r->cf) )
126 {
127 if( i != NULL )
128 {
129 number ii = p_GetCoeff(i, r);
130 clog<< "number(poly(N)*poly(N+1)): "; PrintSized(ii, r->cf);
131
132 #ifdef HAVE_RINGS
133 TS_ASSERT( n_DivBy(ii, t, r->cf) );
134 #endif
135 res = p_Div_nn(i, t, r); i = NULL;
136 }
137
138
139
140 clog<< "(poly(N)*poly(N+1))/number(2): "; PrintSized(res, r);
141 poly d = p_Sub(p_Copy(res, r), p_Copy(sum1, r), r);
142
143 if( d != NULL )
144 TS_ASSERT( n_IsZeroDivisor(p_GetCoeff(d, r), r->cf) );
145
146 Delete(d, r);
147
148 if( n_GetChar(r->cf) == 0 )
149 {
150 TS_ASSERT( p_EqualPolys(sum1, res, r) );
151 TS_ASSERT( p_EqualPolys(res, sum1, r) );
152 }
153 } else
154 TS_ASSERT_EQUALS( n_GetChar(r->cf), 2);
155
156 n_Delete(&t, r->cf);
157
158
159 s = NULL;
160 ss = NULL;
161 for( int k = N; k >= 0; k-- )
162 {
163 i = p_ISet(k, r);
164 s = p_Add_q(s, i, r); // s += i
165
166 i = p_Neg( p_ISet(k, r), r );
167 ss = p_Add_q(ss, i, r); // ss -= i
168 }
169
170 clog<< "ss(-sum): "; PrintSized(ss, r);
171
172 ss = p_Neg(ss, r); // ss = -ss
173
174 clog<< "real sum : "; PrintSized(s, r);
175 clog<< "real sum(--): "; PrintSized(ss, r);
176
177 TS_ASSERT( p_EqualPolys(s, ss, r) );
178 TS_ASSERT( p_EqualPolys(ss, s, r) );
179
180 // TODO(somebody, fix the delete method!);
181
182 Delete(sum1, r);
183 Delete(res, r);
184
185 Delete(s, r);
186 Delete(ss, r);
187
188 clog << ( " >>> TEST DONE!" );
189 clog << endl;
190
191 }
192
Test(const ring r)193 void Test(const ring r)
194 {
195 if( r == NULL )
196 TS_FAIL("Could not get needed ring");
197 else
198 {
199 TestSum( r, 10 );
200 TestSum( r, 100 );
201 TestSum( r, 101 );
202 TestSum( r, 1001 );
203 TestSum( r, 9000 );
204 }
205 }
206
207 }
208
209 class PolysTestSuite : public CxxTest::TestSuite
210 {
211 private:
212 /* replaces p by p + c * var(i)^exp (in-place);
213 expects exp >= 0 */
plusTerm(poly & p,int c,int i,int exp,const ring r)214 void plusTerm(poly &p, int c, int i, int exp, const ring r)
215 {
216 poly t = p_ISet(c, r);
217 if (exp > 0) { p_SetExp(t, i, exp, r); p_Setm(t, r); }
218 p = p_Add_q(p, t, r);
219 }
220 /* assumes that r is over Q;
221 replaces p by p + c1 / c2 * var(i)^exp (in-place);
222 expects exp >= 0, and c2 != 0 */
plusTermOverQ(poly & p,int c1,int c2,int i,int exp,const ring r)223 void plusTermOverQ(poly &p, int c1, int c2, int i, int exp, const ring r)
224 {
225 number c1AsN = n_Init(c1, r->cf);
226 number c2AsN = n_Init(c2, r->cf);
227 number c = n_Div(c1AsN, c2AsN, r->cf);
228 poly t = p_ISet(1, r); p_SetCoeff(t, c, r);
229 if (exp > 0) { p_SetExp(t, i, exp, r); p_Setm(t, r); }
230 p = p_Add_q(p, t, r);
231 }
232 /* assumes r to represent Q(x)[y], for some variable names x and y;
233 replaces p by p + (c1 * 1000000 + c2) * x^xExp * y^yExp (in-place);
234 expects xExp, yExp >= 0 */
specialPlusTerm(poly & p,int c1,int c2,int sign,int xExp,int yExp,const ring r)235 void specialPlusTerm(poly &p, int c1, int c2, int sign,
236 int xExp, int yExp, const ring r)
237 {
238 poly c1p = p_ISet(c1, r->cf->extRing);
239 poly c2p = p_ISet(c2, r->cf->extRing);
240 poly c3p = p_ISet(1000000, r->cf->extRing);
241 poly xterm = p_Mult_q(c1p, c3p, r->cf->extRing);
242 xterm = p_Add_q(xterm, c2p, r->cf->extRing);
243 if (sign == -1) xterm = p_Neg(xterm, r->cf->extRing);
244 if (xExp > 0)
245 {
246 p_SetExp(xterm, 1, xExp, r->cf->extRing);
247 p_Setm(xterm, r->cf->extRing);
248 }
249 number xtermAsN = toFractionNumber(xterm, r->cf);
250 poly yterm = p_ISet(1, r);
251 if (yExp > 0)
252 {
253 p_SetExp(yterm, 1, yExp, r);
254 p_Setm(yterm, r);
255 }
256 p_SetCoeff(yterm, xtermAsN, r);
257 p = p_Add_q(p, yterm, r);
258 }
259 /* defines a special test polynomial in Q(x)[y], for some variable
260 names x and y, by excessively using specialPlusTerm */
specialPoly(poly & p,const ring r)261 void specialPoly(poly &p, const ring r)
262 {
263 p = NULL;
264 specialPlusTerm(p, 0, 1, 1, 0, 17, r);
265 specialPlusTerm(p, 0, 1, -1, 15, 16, r);
266 specialPlusTerm(p, 0, 2, -1, 14, 16, r);
267 specialPlusTerm(p, 0, 3, -1, 13, 16, r);
268 specialPlusTerm(p, 0, 4, -1, 12, 16, r);
269 specialPlusTerm(p, 0, 5, -1, 11, 16, r);
270 specialPlusTerm(p, 0, 6, -1, 10, 16, r);
271 specialPlusTerm(p, 0, 7, -1, 9, 16, r);
272 specialPlusTerm(p, 0, 8, -1, 8, 16, r);
273 specialPlusTerm(p, 0, 9, -1, 7, 16, r);
274 specialPlusTerm(p, 0, 10, -1, 6, 16, r);
275 specialPlusTerm(p, 0, 11, -1, 5, 16, r);
276 specialPlusTerm(p, 0, 12, -1, 4, 16, r);
277 specialPlusTerm(p, 0, 13, -1, 3, 16, r);
278 specialPlusTerm(p, 0, 14, -1, 2, 16, r);
279 specialPlusTerm(p, 0, 15, -1, 1, 16, r);
280 specialPlusTerm(p, 0, 16, -1, 0, 16, r);
281 specialPlusTerm(p, 0, 1, 1, 29, 15, r);
282 specialPlusTerm(p, 0, 3, 1, 28, 15, r);
283 specialPlusTerm(p, 0, 7, 1, 27, 15, r);
284 specialPlusTerm(p, 0, 13, 1, 26, 15, r);
285 specialPlusTerm(p, 0, 22, 1, 25, 15, r);
286 specialPlusTerm(p, 0, 34, 1, 24, 15, r);
287 specialPlusTerm(p, 0, 50, 1, 23, 15, r);
288 specialPlusTerm(p, 0, 70, 1, 22, 15, r);
289 specialPlusTerm(p, 0, 95, 1, 21, 15, r);
290 specialPlusTerm(p, 0, 125, 1, 20, 15, r);
291 specialPlusTerm(p, 0, 161, 1, 19, 15, r);
292 specialPlusTerm(p, 0, 203, 1, 18, 15, r);
293 specialPlusTerm(p, 0, 252, 1, 17, 15, r);
294 specialPlusTerm(p, 0, 308, 1, 16, 15, r);
295 specialPlusTerm(p, 0, 372, 1, 15, 15, r);
296 specialPlusTerm(p, 0, 428, 1, 14, 15, r);
297 specialPlusTerm(p, 0, 476, 1, 13, 15, r);
298 specialPlusTerm(p, 0, 515, 1, 12, 15, r);
299 specialPlusTerm(p, 0, 545, 1, 11, 15, r);
300 specialPlusTerm(p, 0, 565, 1, 10, 15, r);
301 specialPlusTerm(p, 0, 575, 1, 9, 15, r);
302 specialPlusTerm(p, 0, 574, 1, 8, 15, r);
303 specialPlusTerm(p, 0, 562, 1, 7, 15, r);
304 specialPlusTerm(p, 0, 538, 1, 6, 15, r);
305 specialPlusTerm(p, 0, 502, 1, 5, 15, r);
306 specialPlusTerm(p, 0, 453, 1, 4, 15, r);
307 specialPlusTerm(p, 0, 391, 1, 3, 15, r);
308 specialPlusTerm(p, 0, 315, 1, 2, 15, r);
309 specialPlusTerm(p, 0, 225, 1, 1, 15, r);
310 specialPlusTerm(p, 0, 120, 1, 0, 15, r);
311 specialPlusTerm(p, 0, 1, -1, 42, 14, r);
312 specialPlusTerm(p, 0, 4, -1, 41, 14, r);
313 specialPlusTerm(p, 0, 11, -1, 40, 14, r);
314 specialPlusTerm(p, 0, 25, -1, 39, 14, r);
315 specialPlusTerm(p, 0, 50, -1, 38, 14, r);
316 specialPlusTerm(p, 0, 91, -1, 37, 14, r);
317 specialPlusTerm(p, 0, 155, -1, 36, 14, r);
318 specialPlusTerm(p, 0, 250, -1, 35, 14, r);
319 specialPlusTerm(p, 0, 386, -1, 34, 14, r);
320 specialPlusTerm(p, 0, 575, -1, 33, 14, r);
321 specialPlusTerm(p, 0, 831, -1, 32, 14, r);
322 specialPlusTerm(p, 0, 1170, -1, 31, 14, r);
323 specialPlusTerm(p, 0, 1611, -1, 30, 14, r);
324 specialPlusTerm(p, 0, 2175, -1, 29, 14, r);
325 specialPlusTerm(p, 0, 2871, -1, 28, 14, r);
326 specialPlusTerm(p, 0, 3710, -1, 27, 14, r);
327 specialPlusTerm(p, 0, 4690, -1, 26, 14, r);
328 specialPlusTerm(p, 0, 5810, -1, 25, 14, r);
329 specialPlusTerm(p, 0, 7056, -1, 24, 14, r);
330 specialPlusTerm(p, 0, 8414, -1, 23, 14, r);
331 specialPlusTerm(p, 0, 9856, -1, 22, 14, r);
332 specialPlusTerm(p, 0, 11354, -1, 21, 14, r);
333 specialPlusTerm(p, 0, 12865, -1, 20, 14, r);
334 specialPlusTerm(p, 0, 14345, -1, 19, 14, r);
335 specialPlusTerm(p, 0, 15735, -1, 18, 14, r);
336 specialPlusTerm(p, 0, 16974, -1, 17, 14, r);
337 specialPlusTerm(p, 0, 17985, -1, 16, 14, r);
338 specialPlusTerm(p, 0, 18689, -1, 15, 14, r);
339 specialPlusTerm(p, 0, 18990, -1, 14, 14, r);
340 specialPlusTerm(p, 0, 18909, -1, 13, 14, r);
341 specialPlusTerm(p, 0, 18465, -1, 12, 14, r);
342 specialPlusTerm(p, 0, 17689, -1, 11, 14, r);
343 specialPlusTerm(p, 0, 16610, -1, 10, 14, r);
344 specialPlusTerm(p, 0, 15270, -1, 9, 14, r);
345 specialPlusTerm(p, 0, 13709, -1, 8, 14, r);
346 specialPlusTerm(p, 0, 11980, -1, 7, 14, r);
347 specialPlusTerm(p, 0, 10135, -1, 6, 14, r);
348 specialPlusTerm(p, 0, 8239, -1, 5, 14, r);
349 specialPlusTerm(p, 0, 6356, -1, 4, 14, r);
350 specialPlusTerm(p, 0, 4564, -1, 3, 14, r);
351 specialPlusTerm(p, 0, 2940, -1, 2, 14, r);
352 specialPlusTerm(p, 0, 1575, -1, 1, 14, r);
353 specialPlusTerm(p, 0, 560, -1, 0, 14, r);
354 specialPlusTerm(p, 0, 1, 1, 54, 13, r);
355 specialPlusTerm(p, 0, 5, 1, 53, 13, r);
356 specialPlusTerm(p, 0, 16, 1, 52, 13, r);
357 specialPlusTerm(p, 0, 41, 1, 51, 13, r);
358 specialPlusTerm(p, 0, 92, 1, 50, 13, r);
359 specialPlusTerm(p, 0, 187, 1, 49, 13, r);
360 specialPlusTerm(p, 0, 353, 1, 48, 13, r);
361 specialPlusTerm(p, 0, 628, 1, 47, 13, r);
362 specialPlusTerm(p, 0, 1065, 1, 46, 13, r);
363 specialPlusTerm(p, 0, 1735, 1, 45, 13, r);
364 specialPlusTerm(p, 0, 2732, 1, 44, 13, r);
365 specialPlusTerm(p, 0, 4177, 1, 43, 13, r);
366 specialPlusTerm(p, 0, 6225, 1, 42, 13, r);
367 specialPlusTerm(p, 0, 9056, 1, 41, 13, r);
368 specialPlusTerm(p, 0, 12882, 1, 40, 13, r);
369 specialPlusTerm(p, 0, 17939, 1, 39, 13, r);
370 specialPlusTerm(p, 0, 24481, 1, 38, 13, r);
371 specialPlusTerm(p, 0, 32771, 1, 37, 13, r);
372 specialPlusTerm(p, 0, 43075, 1, 36, 13, r);
373 specialPlusTerm(p, 0, 55639, 1, 35, 13, r);
374 specialPlusTerm(p, 0, 70682, 1, 34, 13, r);
375 specialPlusTerm(p, 0, 88372, 1, 33, 13, r);
376 specialPlusTerm(p, 0, 108804, 1, 32, 13, r);
377 specialPlusTerm(p, 0, 131974, 1, 31, 13, r);
378 specialPlusTerm(p, 0, 157756, 1, 30, 13, r);
379 specialPlusTerm(p, 0, 185860, 1, 29, 13, r);
380 specialPlusTerm(p, 0, 215806, 1, 28, 13, r);
381 specialPlusTerm(p, 0, 246985, 1, 27, 13, r);
382 specialPlusTerm(p, 0, 278631, 1, 26, 13, r);
383 specialPlusTerm(p, 0, 309893, 1, 25, 13, r);
384 specialPlusTerm(p, 0, 339819, 1, 24, 13, r);
385 specialPlusTerm(p, 0, 367427, 1, 23, 13, r);
386 specialPlusTerm(p, 0, 391701, 1, 22, 13, r);
387 specialPlusTerm(p, 0, 411675, 1, 21, 13, r);
388 specialPlusTerm(p, 0, 426428, 1, 20, 13, r);
389 specialPlusTerm(p, 0, 435181, 1, 19, 13, r);
390 specialPlusTerm(p, 0, 437306, 1, 18, 13, r);
391 specialPlusTerm(p, 0, 432423, 1, 17, 13, r);
392 specialPlusTerm(p, 0, 420422, 1, 16, 13, r);
393 specialPlusTerm(p, 0, 401575, 1, 15, 13, r);
394 specialPlusTerm(p, 0, 376559, 1, 14, 13, r);
395 specialPlusTerm(p, 0, 346582, 1, 13, 13, r);
396 specialPlusTerm(p, 0, 312861, 1, 12, 13, r);
397 specialPlusTerm(p, 0, 276645, 1, 11, 13, r);
398 specialPlusTerm(p, 0, 239149, 1, 10, 13, r);
399 specialPlusTerm(p, 0, 201578, 1, 9, 13, r);
400 specialPlusTerm(p, 0, 165048, 1, 8, 13, r);
401 specialPlusTerm(p, 0, 130611, 1, 7, 13, r);
402 specialPlusTerm(p, 0, 99177, 1, 6, 13, r);
403 specialPlusTerm(p, 0, 71526, 1, 5, 13, r);
404 specialPlusTerm(p, 0, 48230, 1, 4, 13, r);
405 specialPlusTerm(p, 0, 29666, 1, 3, 13, r);
406 specialPlusTerm(p, 0, 15925, 1, 2, 13, r);
407 specialPlusTerm(p, 0, 6825, 1, 1, 13, r);
408 specialPlusTerm(p, 0, 1820, 1, 0, 13, r);
409 specialPlusTerm(p, 0, 1, -1, 65, 12, r);
410 specialPlusTerm(p, 0, 6, -1, 64, 12, r);
411 specialPlusTerm(p, 0, 22, -1, 63, 12, r);
412 specialPlusTerm(p, 0, 63, -1, 62, 12, r);
413 specialPlusTerm(p, 0, 155, -1, 61, 12, r);
414 specialPlusTerm(p, 0, 343, -1, 60, 12, r);
415 specialPlusTerm(p, 0, 701, -1, 59, 12, r);
416 specialPlusTerm(p, 0, 1345, -1, 58, 12, r);
417 specialPlusTerm(p, 0, 2451, -1, 57, 12, r);
418 specialPlusTerm(p, 0, 4278, -1, 56, 12, r);
419 specialPlusTerm(p, 0, 7198, -1, 55, 12, r);
420 specialPlusTerm(p, 0, 11733, -1, 54, 12, r);
421 specialPlusTerm(p, 0, 18589, -1, 53, 12, r);
422 specialPlusTerm(p, 0, 28699, -1, 52, 12, r);
423 specialPlusTerm(p, 0, 43265, -1, 51, 12, r);
424 specialPlusTerm(p, 0, 63799, -1, 50, 12, r);
425 specialPlusTerm(p, 0, 92152, -1, 49, 12, r);
426 specialPlusTerm(p, 0, 130543, -1, 48, 12, r);
427 specialPlusTerm(p, 0, 181565, -1, 47, 12, r);
428 specialPlusTerm(p, 0, 248179, -1, 46, 12, r);
429 specialPlusTerm(p, 0, 333673, -1, 45, 12, r);
430 specialPlusTerm(p, 0, 441596, -1, 44, 12, r);
431 specialPlusTerm(p, 0, 575643, -1, 43, 12, r);
432 specialPlusTerm(p, 0, 739501, -1, 42, 12, r);
433 specialPlusTerm(p, 0, 936619, -1, 41, 12, r);
434 specialPlusTerm(p, 1, 170014, -1, 40, 12, r);
435 specialPlusTerm(p, 1, 441997, -1, 39, 12, r);
436 specialPlusTerm(p, 1, 753919, -1, 38, 12, r);
437 specialPlusTerm(p, 2, 105911, -1, 37, 12, r);
438 specialPlusTerm(p, 2, 496652, -1, 36, 12, r);
439 specialPlusTerm(p, 2, 923127, -1, 35, 12, r);
440 specialPlusTerm(p, 3, 380499, -1, 34, 12, r);
441 specialPlusTerm(p, 3, 861979, -1, 33, 12, r);
442 specialPlusTerm(p, 4, 358819, -1, 32, 12, r);
443 specialPlusTerm(p, 4, 860402, -1, 31, 12, r);
444 specialPlusTerm(p, 5, 354477, -1, 30, 12, r);
445 specialPlusTerm(p, 5, 827501, -1, 29, 12, r);
446 specialPlusTerm(p, 6, 265239, -1, 28, 12, r);
447 specialPlusTerm(p, 6, 653507, -1, 27, 12, r);
448 specialPlusTerm(p, 6, 978743, -1, 26, 12, r);
449 specialPlusTerm(p, 7, 228746, -1, 25, 12, r);
450 specialPlusTerm(p, 7, 393190, -1, 24, 12, r);
451 specialPlusTerm(p, 7, 464241, -1, 23, 12, r);
452 specialPlusTerm(p, 7, 436963, -1, 22, 12, r);
453 specialPlusTerm(p, 7, 309763, -1, 21, 12, r);
454 specialPlusTerm(p, 7, 84549, -1, 20, 12, r);
455 specialPlusTerm(p, 6, 766941, -1, 19, 12, r);
456 specialPlusTerm(p, 6, 366119, -1, 18, 12, r);
457 specialPlusTerm(p, 5, 894636, -1, 17, 12, r);
458 specialPlusTerm(p, 5, 367870, -1, 16, 12, r);
459 specialPlusTerm(p, 4, 803365, -1, 15, 12, r);
460 specialPlusTerm(p, 4, 219710, -1, 14, 12, r);
461 specialPlusTerm(p, 3, 635296, -1, 13, 12, r);
462 specialPlusTerm(p, 3, 66522, -1, 12, 12, r);
463 specialPlusTerm(p, 2, 527597, -1, 11, 12, r);
464 specialPlusTerm(p, 2, 30222, -1, 10, 12, r);
465 specialPlusTerm(p, 1, 583491, -1, 9, 12, r);
466 specialPlusTerm(p, 1, 193660, -1, 8, 12, r);
467 specialPlusTerm(p, 0, 864214, -1, 7, 12, r);
468 specialPlusTerm(p, 0, 595790, -1, 6, 12, r);
469 specialPlusTerm(p, 0, 386386, -1, 5, 12, r);
470 specialPlusTerm(p, 0, 231504, -1, 4, 12, r);
471 specialPlusTerm(p, 0, 124579, -1, 3, 12, r);
472 specialPlusTerm(p, 0, 57330, -1, 2, 12, r);
473 specialPlusTerm(p, 0, 20475, -1, 1, 12, r);
474 specialPlusTerm(p, 0, 4368, -1, 0, 12, r);
475 specialPlusTerm(p, 0, 1, 1, 75, 11, r);
476 specialPlusTerm(p, 0, 7, 1, 74, 11, r);
477 specialPlusTerm(p, 0, 29, 1, 73, 11, r);
478 specialPlusTerm(p, 0, 92, 1, 72, 11, r);
479 specialPlusTerm(p, 0, 247, 1, 71, 11, r);
480 specialPlusTerm(p, 0, 590, 1, 70, 11, r);
481 specialPlusTerm(p, 0, 1292, 1, 69, 11, r);
482 specialPlusTerm(p, 0, 2643, 1, 68, 11, r);
483 specialPlusTerm(p, 0, 5116, 1, 67, 11, r);
484 specialPlusTerm(p, 0, 9457, 1, 66, 11, r);
485 specialPlusTerm(p, 0, 16810, 1, 65, 11, r);
486 specialPlusTerm(p, 0, 28874, 1, 64, 11, r);
487 specialPlusTerm(p, 0, 48105, 1, 63, 11, r);
488 specialPlusTerm(p, 0, 77963, 1, 62, 11, r);
489 specialPlusTerm(p, 0, 123209, 1, 61, 11, r);
490 specialPlusTerm(p, 0, 190245, 1, 60, 11, r);
491 specialPlusTerm(p, 0, 287494, 1, 59, 11, r);
492 specialPlusTerm(p, 0, 425804, 1, 58, 11, r);
493 specialPlusTerm(p, 0, 618866, 1, 57, 11, r);
494 specialPlusTerm(p, 0, 883609, 1, 56, 11, r);
495 specialPlusTerm(p, 1, 240541, 1, 55, 11, r);
496 specialPlusTerm(p, 1, 713978, 1, 54, 11, r);
497 specialPlusTerm(p, 2, 332107, 1, 53, 11, r);
498 specialPlusTerm(p, 3, 126867, 1, 52, 11, r);
499 specialPlusTerm(p, 4, 133571, 1, 51, 11, r);
500 specialPlusTerm(p, 5, 390227, 1, 50, 11, r);
501 specialPlusTerm(p, 6, 936520, 1, 49, 11, r);
502 specialPlusTerm(p, 8, 812464, 1, 48, 11, r);
503 specialPlusTerm(p, 11, 56669, 1, 47, 11, r);
504 specialPlusTerm(p, 13, 704280, 1, 46, 11, r);
505 specialPlusTerm(p, 16, 784594, 1, 45, 11, r);
506 specialPlusTerm(p, 20, 318470, 1, 44, 11, r);
507 specialPlusTerm(p, 24, 315607, 1, 43, 11, r);
508 specialPlusTerm(p, 28, 771888, 1, 42, 11, r);
509 specialPlusTerm(p, 33, 666946, 1, 41, 11, r);
510 specialPlusTerm(p, 38, 962309, 1, 40, 11, r);
511 specialPlusTerm(p, 44, 600023, 1, 39, 11, r);
512 specialPlusTerm(p, 50, 502149, 1, 38, 11, r);
513 specialPlusTerm(p, 56, 571139, 1, 37, 11, r);
514 specialPlusTerm(p, 62, 691244, 1, 36, 11, r);
515 specialPlusTerm(p, 68, 730935, 1, 35, 11, r);
516 specialPlusTerm(p, 74, 546533, 1, 34, 11, r);
517 specialPlusTerm(p, 79, 986722, 1, 33, 11, r);
518 specialPlusTerm(p, 84, 898120, 1, 32, 11, r);
519 specialPlusTerm(p, 89, 131550, 1, 31, 11, r);
520 specialPlusTerm(p, 92, 548805, 1, 30, 11, r);
521 specialPlusTerm(p, 95, 29441, 1, 29, 11, r);
522 specialPlusTerm(p, 96, 477351, 1, 28, 11, r);
523 specialPlusTerm(p, 96, 826185, 1, 27, 11, r);
524 specialPlusTerm(p, 96, 43174, 1, 26, 11, r);
525 specialPlusTerm(p, 94, 131647, 1, 25, 11, r);
526 specialPlusTerm(p, 91, 131660, 1, 24, 11, r);
527 specialPlusTerm(p, 87, 119171, 1, 23, 11, r);
528 specialPlusTerm(p, 82, 203392, 1, 22, 11, r);
529 specialPlusTerm(p, 76, 522667, 1, 21, 11, r);
530 specialPlusTerm(p, 70, 238707, 1, 20, 11, r);
531 specialPlusTerm(p, 63, 529796, 1, 19, 11, r);
532 specialPlusTerm(p, 56, 582713, 1, 18, 11, r);
533 specialPlusTerm(p, 49, 584249, 1, 17, 11, r);
534 specialPlusTerm(p, 42, 712395, 1, 16, 11, r);
535 specialPlusTerm(p, 36, 128059, 1, 15, 11, r);
536 specialPlusTerm(p, 29, 967652, 1, 14, 11, r);
537 specialPlusTerm(p, 24, 337808, 1, 13, 11, r);
538 specialPlusTerm(p, 19, 312634, 1, 12, 11, r);
539 specialPlusTerm(p, 14, 935096, 1, 11, 11, r);
540 specialPlusTerm(p, 11, 218988, 1, 10, 11, r);
541 specialPlusTerm(p, 8, 151858, 1, 9, 11, r);
542 specialPlusTerm(p, 5, 698407, 1, 8, 11, r);
543 specialPlusTerm(p, 3, 804801, 1, 7, 11, r);
544 specialPlusTerm(p, 2, 403115, 1, 6, 11, r);
545 specialPlusTerm(p, 1, 416415, 1, 5, 11, r);
546 specialPlusTerm(p, 0, 763763, 1, 4, 11, r);
547 specialPlusTerm(p, 0, 365365, 1, 3, 11, r);
548 specialPlusTerm(p, 0, 147147, 1, 2, 11, r);
549 specialPlusTerm(p, 0, 45045, 1, 1, 11, r);
550 specialPlusTerm(p, 0, 8008, 1, 0, 11, r);
551 specialPlusTerm(p, 0, 1, -1, 84, 10, r);
552 specialPlusTerm(p, 0, 8, -1, 83, 10, r);
553 specialPlusTerm(p, 0, 37, -1, 82, 10, r);
554 specialPlusTerm(p, 0, 129, -1, 81, 10, r);
555 specialPlusTerm(p, 0, 376, -1, 80, 10, r);
556 specialPlusTerm(p, 0, 966, -1, 79, 10, r);
557 specialPlusTerm(p, 0, 2258, -1, 78, 10, r);
558 specialPlusTerm(p, 0, 4902, -1, 77, 10, r);
559 specialPlusTerm(p, 0, 10025, -1, 76, 10, r);
560 specialPlusTerm(p, 0, 19511, -1, 75, 10, r);
561 specialPlusTerm(p, 0, 36402, -1, 74, 10, r);
562 specialPlusTerm(p, 0, 65457, -1, 73, 10, r);
563 specialPlusTerm(p, 0, 113910, -1, 72, 10, r);
564 specialPlusTerm(p, 0, 192472, -1, 71, 10, r);
565 specialPlusTerm(p, 0, 316620, -1, 70, 10, r);
566 specialPlusTerm(p, 0, 508215, -1, 69, 10, r);
567 specialPlusTerm(p, 0, 797473, -1, 68, 10, r);
568 specialPlusTerm(p, 1, 225306, -1, 67, 10, r);
569 specialPlusTerm(p, 1, 846017, -1, 66, 10, r);
570 specialPlusTerm(p, 2, 730299, -1, 65, 10, r);
571 specialPlusTerm(p, 3, 968427, -1, 64, 10, r);
572 specialPlusTerm(p, 5, 673536, -1, 63, 10, r);
573 specialPlusTerm(p, 7, 984777, -1, 62, 10, r);
574 specialPlusTerm(p, 11, 70116, -1, 61, 10, r);
575 specialPlusTerm(p, 15, 128465, -1, 60, 10, r);
576 specialPlusTerm(p, 20, 390819, -1, 59, 10, r);
577 specialPlusTerm(p, 27, 120017, -1, 58, 10, r);
578 specialPlusTerm(p, 35, 608761, -1, 57, 10, r);
579 specialPlusTerm(p, 46, 175479, -1, 56, 10, r);
580 specialPlusTerm(p, 59, 157726, -1, 55, 10, r);
581 specialPlusTerm(p, 74, 902862, -1, 54, 10, r);
582 specialPlusTerm(p, 93, 755945, -1, 53, 10, r);
583 specialPlusTerm(p, 116, 44932, -1, 52, 10, r);
584 specialPlusTerm(p, 142, 63382, -1, 51, 10, r);
585 specialPlusTerm(p, 172, 51120, -1, 50, 10, r);
586 specialPlusTerm(p, 206, 173563, -1, 49, 10, r);
587 specialPlusTerm(p, 244, 500607, -1, 48, 10, r);
588 specialPlusTerm(p, 286, 986083, -1, 47, 10, r);
589 specialPlusTerm(p, 333, 449096, -1, 46, 10, r);
590 specialPlusTerm(p, 383, 558571, -1, 45, 10, r);
591 specialPlusTerm(p, 436, 822461, -1, 44, 10, r);
592 specialPlusTerm(p, 492, 582939, -1, 43, 10, r);
593 specialPlusTerm(p, 550, 18832, -1, 42, 10, r);
594 specialPlusTerm(p, 608, 156141, -1, 41, 10, r);
595 specialPlusTerm(p, 665, 887167, -1, 40, 10, r);
596 specialPlusTerm(p, 721, 997807, -1, 39, 10, r);
597 specialPlusTerm(p, 775, 202852, -1, 38, 10, r);
598 specialPlusTerm(p, 824, 187996, -1, 37, 10, r);
599 specialPlusTerm(p, 867, 657138, -1, 36, 10, r);
600 specialPlusTerm(p, 904, 382945, -1, 35, 10, r);
601 specialPlusTerm(p, 933, 258541, -1, 34, 10, r);
602 specialPlusTerm(p, 953, 347368, -1, 33, 10, r);
603 specialPlusTerm(p, 963, 928871, -1, 32, 10, r);
604 specialPlusTerm(p, 964, 536834, -1, 31, 10, r);
605 specialPlusTerm(p, 954, 987850, -1, 30, 10, r);
606 specialPlusTerm(p, 935, 397536, -1, 29, 10, r);
607 specialPlusTerm(p, 906, 183073, -1, 28, 10, r);
608 specialPlusTerm(p, 868, 50862, -1, 27, 10, r);
609 specialPlusTerm(p, 821, 970338, -1, 26, 10, r);
610 specialPlusTerm(p, 769, 135827, -1, 25, 10, r);
611 specialPlusTerm(p, 710, 918057, -1, 24, 10, r);
612 specialPlusTerm(p, 648, 808233, -1, 23, 10, r);
613 specialPlusTerm(p, 584, 357073, -1, 22, 10, r);
614 specialPlusTerm(p, 519, 112032, -1, 21, 10, r);
615 specialPlusTerm(p, 454, 555728, -1, 20, 10, r);
616 specialPlusTerm(p, 392, 49009, -1, 19, 10, r);
617 specialPlusTerm(p, 332, 781273, -1, 18, 10, r);
618 specialPlusTerm(p, 277, 731388, -1, 17, 10, r);
619 specialPlusTerm(p, 227, 641117, -1, 16, 10, r);
620 specialPlusTerm(p, 183, 2853, -1, 15, 10, r);
621 specialPlusTerm(p, 144, 62127, -1, 14, 10, r);
622 specialPlusTerm(p, 110, 834647, -1, 13, 10, r);
623 specialPlusTerm(p, 83, 135184, -1, 12, 10, r);
624 specialPlusTerm(p, 60, 614741, -1, 11, 10, r);
625 specialPlusTerm(p, 42, 799119, -1, 10, 10, r);
626 specialPlusTerm(p, 29, 127956, -1, 9, 10, r);
627 specialPlusTerm(p, 18, 992545, -1, 8, 10, r);
628 specialPlusTerm(p, 11, 771474, -1, 7, 10, r);
629 specialPlusTerm(p, 6, 862141, -1, 6, 10, r);
630 specialPlusTerm(p, 3, 707704, -1, 5, 10, r);
631 specialPlusTerm(p, 1, 817816, -1, 4, 10, r);
632 specialPlusTerm(p, 0, 782782, -1, 3, 10, r);
633 specialPlusTerm(p, 0, 280280, -1, 2, 10, r);
634 specialPlusTerm(p, 0, 75075, -1, 1, 10, r);
635 specialPlusTerm(p, 0, 11440, -1, 0, 10, r);
636 specialPlusTerm(p, 0, 1, 1, 92, 9, r);
637 specialPlusTerm(p, 0, 9, 1, 91, 9, r);
638 specialPlusTerm(p, 0, 46, 1, 90, 9, r);
639 specialPlusTerm(p, 0, 175, 1, 89, 9, r);
640 specialPlusTerm(p, 0, 551, 1, 88, 9, r);
641 specialPlusTerm(p, 0, 1517, 1, 87, 9, r);
642 specialPlusTerm(p, 0, 3775, 1, 86, 9, r);
643 specialPlusTerm(p, 0, 8677, 1, 85, 9, r);
644 specialPlusTerm(p, 0, 18703, 1, 84, 9, r);
645 specialPlusTerm(p, 0, 38212, 1, 83, 9, r);
646 specialPlusTerm(p, 0, 74581, 1, 82, 9, r);
647 specialPlusTerm(p, 0, 139877, 1, 81, 9, r);
648 specialPlusTerm(p, 0, 253243, 1, 80, 9, r);
649 specialPlusTerm(p, 0, 444211, 1, 79, 9, r);
650 specialPlusTerm(p, 0, 757189, 1, 78, 9, r);
651 specialPlusTerm(p, 1, 257386, 1, 77, 9, r);
652 specialPlusTerm(p, 2, 38445, 1, 76, 9, r);
653 specialPlusTerm(p, 3, 232029, 1, 75, 9, r);
654 specialPlusTerm(p, 5, 19547, 1, 74, 9, r);
655 specialPlusTerm(p, 7, 646140, 1, 73, 9, r);
656 specialPlusTerm(p, 11, 436924, 1, 72, 9, r);
657 specialPlusTerm(p, 16, 815312, 1, 71, 9, r);
658 specialPlusTerm(p, 24, 323016, 1, 70, 9, r);
659 specialPlusTerm(p, 34, 641066, 1, 69, 9, r);
660 specialPlusTerm(p, 48, 610873, 1, 68, 9, r);
661 specialPlusTerm(p, 67, 254061, 1, 67, 9, r);
662 specialPlusTerm(p, 91, 789450, 1, 66, 9, r);
663 specialPlusTerm(p, 123, 645277, 1, 65, 9, r);
664 specialPlusTerm(p, 164, 464508, 1, 64, 9, r);
665 specialPlusTerm(p, 216, 101017, 1, 63, 9, r);
666 specialPlusTerm(p, 280, 604281, 1, 62, 9, r);
667 specialPlusTerm(p, 360, 190441, 1, 61, 9, r);
668 specialPlusTerm(p, 457, 197865, 1, 60, 9, r);
669 specialPlusTerm(p, 574, 25922, 1, 59, 9, r);
670 specialPlusTerm(p, 713, 56365, 1, 58, 9, r);
671 specialPlusTerm(p, 876, 557703, 1, 57, 9, r);
672 specialPlusTerm(p, 1066, 573992, 1, 56, 9, r);
673 specialPlusTerm(p, 1284, 800887, 1, 55, 9, r);
674 specialPlusTerm(p, 1532, 453056, 1, 54, 9, r);
675 specialPlusTerm(p, 1810, 128450, 1, 53, 9, r);
676 specialPlusTerm(p, 2117, 675954, 1, 52, 9, r);
677 specialPlusTerm(p, 2454, 73820, 1, 51, 9, r);
678 specialPlusTerm(p, 2817, 326941, 1, 50, 9, r);
679 specialPlusTerm(p, 3204, 391243, 1, 49, 9, r);
680 specialPlusTerm(p, 3611, 133043, 1, 48, 9, r);
681 specialPlusTerm(p, 4032, 330356, 1, 47, 9, r);
682 specialPlusTerm(p, 4461, 721846, 1, 46, 9, r);
683 specialPlusTerm(p, 4892, 107024, 1, 45, 9, r);
684 specialPlusTerm(p, 5315, 498836, 1, 44, 9, r);
685 specialPlusTerm(p, 5723, 326840, 1, 43, 9, r);
686 specialPlusTerm(p, 6106, 686025, 1, 42, 9, r);
687 specialPlusTerm(p, 6456, 623000, 1, 41, 9, r);
688 specialPlusTerm(p, 6764, 448368, 1, 40, 9, r);
689 specialPlusTerm(p, 7022, 61523, 1, 39, 9, r);
690 specialPlusTerm(p, 7222, 273135, 1, 38, 9, r);
691 specialPlusTerm(p, 7359, 108966, 1, 37, 9, r);
692 specialPlusTerm(p, 7428, 79054, 1, 36, 9, r);
693 specialPlusTerm(p, 7426, 396980, 1, 35, 9, r);
694 specialPlusTerm(p, 7353, 135921, 1, 34, 9, r);
695 specialPlusTerm(p, 7209, 310506, 1, 33, 9, r);
696 specialPlusTerm(p, 6997, 877688, 1, 32, 9, r);
697 specialPlusTerm(p, 6723, 653256, 1, 31, 9, r);
698 specialPlusTerm(p, 6393, 146079, 1, 30, 9, r);
699 specialPlusTerm(p, 6014, 316858, 1, 29, 9, r);
700 specialPlusTerm(p, 5596, 273275, 1, 28, 9, r);
701 specialPlusTerm(p, 5148, 917160, 1, 27, 9, r);
702 specialPlusTerm(p, 4682, 563401, 1, 26, 9, r);
703 specialPlusTerm(p, 4207, 550601, 1, 25, 9, r);
704 specialPlusTerm(p, 3733, 862769, 1, 24, 9, r);
705 specialPlusTerm(p, 3270, 780702, 1, 23, 9, r);
706 specialPlusTerm(p, 2826, 579105, 1, 22, 9, r);
707 specialPlusTerm(p, 2408, 283186, 1, 21, 9, r);
708 specialPlusTerm(p, 2021, 494926, 1, 20, 9, r);
709 specialPlusTerm(p, 1670, 295297, 1, 19, 9, r);
710 specialPlusTerm(p, 1357, 224099, 1, 18, 9, r);
711 specialPlusTerm(p, 1083, 335088, 1, 17, 9, r);
712 specialPlusTerm(p, 848, 318658, 1, 16, 9, r);
713 specialPlusTerm(p, 650, 680536, 1, 15, 9, r);
714 specialPlusTerm(p, 487, 961232, 1, 14, 9, r);
715 specialPlusTerm(p, 356, 978589, 1, 13, 9, r);
716 specialPlusTerm(p, 254, 74425, 1, 12, 9, r);
717 specialPlusTerm(p, 175, 348338, 1, 11, 9, r);
718 specialPlusTerm(p, 116, 865243, 1, 10, 9, r);
719 specialPlusTerm(p, 74, 831757, 1, 9, 9, r);
720 specialPlusTerm(p, 45, 737406, 1, 8, 9, r);
721 specialPlusTerm(p, 26, 458575, 1, 7, 9, r);
722 specialPlusTerm(p, 14, 324310, 1, 6, 9, r);
723 specialPlusTerm(p, 7, 145853, 1, 5, 9, r);
724 specialPlusTerm(p, 3, 212352, 1, 4, 9, r);
725 specialPlusTerm(p, 1, 257828, 1, 3, 9, r);
726 specialPlusTerm(p, 0, 405405, 1, 2, 9, r);
727 specialPlusTerm(p, 0, 96525, 1, 1, 9, r);
728 specialPlusTerm(p, 0, 12870, 1, 0, 9, r);
729 specialPlusTerm(p, 0, 1, -1, 99, 8, r);
730 specialPlusTerm(p, 0, 10, -1, 98, 8, r);
731 specialPlusTerm(p, 0, 56, -1, 97, 8, r);
732 specialPlusTerm(p, 0, 231, -1, 96, 8, r);
733 specialPlusTerm(p, 0, 782, -1, 95, 8, r);
734 specialPlusTerm(p, 0, 2299, -1, 94, 8, r);
735 specialPlusTerm(p, 0, 6074, -1, 93, 8, r);
736 specialPlusTerm(p, 0, 14751, -1, 92, 8, r);
737 specialPlusTerm(p, 0, 33445, -1, 91, 8, r);
738 specialPlusTerm(p, 0, 71586, -1, 90, 8, r);
739 specialPlusTerm(p, 0, 145843, -1, 89, 8, r);
740 specialPlusTerm(p, 0, 284605, -1, 88, 8, r);
741 specialPlusTerm(p, 0, 534639, -1, 87, 8, r);
742 specialPlusTerm(p, 0, 970707, -1, 86, 8, r);
743 specialPlusTerm(p, 1, 709091, -1, 85, 8, r);
744 specialPlusTerm(p, 2, 926134, -1, 84, 8, r);
745 specialPlusTerm(p, 4, 883022, -1, 83, 8, r);
746 specialPlusTerm(p, 7, 958118, -1, 82, 8, r);
747 specialPlusTerm(p, 12, 688161, -1, 81, 8, r);
748 specialPlusTerm(p, 19, 819543, -1, 80, 8, r);
749 specialPlusTerm(p, 30, 370620, -1, 79, 8, r);
750 specialPlusTerm(p, 45, 705588, -1, 78, 8, r);
751 specialPlusTerm(p, 67, 619803, -1, 77, 8, r);
752 specialPlusTerm(p, 98, 435565, -1, 76, 8, r);
753 specialPlusTerm(p, 141, 106293, -1, 75, 8, r);
754 specialPlusTerm(p, 199, 325748, -1, 74, 8, r);
755 specialPlusTerm(p, 277, 637550, -1, 73, 8, r);
756 specialPlusTerm(p, 381, 538692, -1, 72, 8, r);
757 specialPlusTerm(p, 517, 569184, -1, 71, 8, r);
758 specialPlusTerm(p, 693, 378528, -1, 70, 8, r);
759 specialPlusTerm(p, 917, 758545, -1, 69, 8, r);
760 specialPlusTerm(p, 1200, 631327, -1, 68, 8, r);
761 specialPlusTerm(p, 1552, 980935, -1, 67, 8, r);
762 specialPlusTerm(p, 1986, 718008, -1, 66, 8, r);
763 specialPlusTerm(p, 2514, 467898, -1, 65, 8, r);
764 specialPlusTerm(p, 3149, 275373, -1, 64, 8, r);
765 specialPlusTerm(p, 3904, 222333, -1, 63, 8, r);
766 specialPlusTerm(p, 4791, 959202, -1, 62, 8, r);
767 specialPlusTerm(p, 5824, 155954, -1, 61, 8, r);
768 specialPlusTerm(p, 7010, 884530, -1, 60, 8, r);
769 specialPlusTerm(p, 8359, 950639, -1, 59, 8, r);
770 specialPlusTerm(p, 9876, 199091, -1, 58, 8, r);
771 specialPlusTerm(p, 11560, 822647, -1, 57, 8, r);
772 specialPlusTerm(p, 13410, 709233, -1, 56, 8, r);
773 specialPlusTerm(p, 15417, 866033, -1, 55, 8, r);
774 specialPlusTerm(p, 17568, 960466, -1, 54, 8, r);
775 specialPlusTerm(p, 19845, 17463, -1, 53, 8, r);
776 specialPlusTerm(p, 22221, 309147, -1, 52, 8, r);
777 specialPlusTerm(p, 24667, 467342, -1, 51, 8, r);
778 specialPlusTerm(p, 27147, 841107, -1, 50, 8, r);
779 specialPlusTerm(p, 29622, 110916, -1, 49, 8, r);
780 specialPlusTerm(p, 32046, 158421, -1, 48, 8, r);
781 specialPlusTerm(p, 34373, 176970, -1, 47, 8, r);
782 specialPlusTerm(p, 36554, 993654, -1, 46, 8, r);
783 specialPlusTerm(p, 38543, 559373, -1, 45, 8, r);
784 specialPlusTerm(p, 40292, 550458, -1, 44, 8, r);
785 specialPlusTerm(p, 41759, 14716, -1, 43, 8, r);
786 specialPlusTerm(p, 42904, 987186, -1, 42, 8, r);
787 specialPlusTerm(p, 43698, 997388, -1, 41, 8, r);
788 specialPlusTerm(p, 44117, 391022, -1, 40, 8, r);
789 specialPlusTerm(p, 44145, 394986, -1, 39, 8, r);
790 specialPlusTerm(p, 43777, 865188, -1, 38, 8, r);
791 specialPlusTerm(p, 43019, 670206, -1, 37, 8, r);
792 specialPlusTerm(p, 41885, 681598, -1, 36, 8, r);
793 specialPlusTerm(p, 40400, 361216, -1, 35, 8, r);
794 specialPlusTerm(p, 38596, 956954, -1, 34, 8, r);
795 specialPlusTerm(p, 36516, 339240, -1, 33, 8, r);
796 specialPlusTerm(p, 34205, 530818, -1, 32, 8, r);
797 specialPlusTerm(p, 31715, 999202, -1, 31, 8, r);
798 specialPlusTerm(p, 29101, 795368, -1, 30, 8, r);
799 specialPlusTerm(p, 26417, 630514, -1, 29, 8, r);
800 specialPlusTerm(p, 23716, 985664, -1, 28, 8, r);
801 specialPlusTerm(p, 21050, 345182, -1, 27, 8, r);
802 specialPlusTerm(p, 18463, 636290, -1, 26, 8, r);
803 specialPlusTerm(p, 15996, 940992, -1, 25, 8, r);
804 specialPlusTerm(p, 13683, 529134, -1, 24, 8, r);
805 specialPlusTerm(p, 11549, 242308, -1, 23, 8, r);
806 specialPlusTerm(p, 9612, 238032, -1, 22, 8, r);
807 specialPlusTerm(p, 7883, 84208, -1, 21, 8, r);
808 specialPlusTerm(p, 6365, 175366, -1, 20, 8, r);
809 specialPlusTerm(p, 5055, 425826, -1, 19, 8, r);
810 specialPlusTerm(p, 3945, 181834, -1, 18, 8, r);
811 specialPlusTerm(p, 3021, 285630, -1, 17, 8, r);
812 specialPlusTerm(p, 2267, 219328, -1, 16, 8, r);
813 specialPlusTerm(p, 1664, 257320, -1, 15, 8, r);
814 specialPlusTerm(p, 1192, 561524, -1, 14, 8, r);
815 specialPlusTerm(p, 832, 164102, -1, 13, 8, r);
816 specialPlusTerm(p, 563, 796684, -1, 12, 8, r);
817 specialPlusTerm(p, 369, 542514, -1, 11, 8, r);
818 specialPlusTerm(p, 233, 304720, -1, 10, 8, r);
819 specialPlusTerm(p, 141, 98386, -1, 9, 8, r);
820 specialPlusTerm(p, 81, 180528, -1, 8, 8, r);
821 specialPlusTerm(p, 44, 38137, -1, 7, 8, r);
822 specialPlusTerm(p, 22, 259094, -1, 6, 8, r);
823 specialPlusTerm(p, 10, 314447, -1, 5, 8, r);
824 specialPlusTerm(p, 4, 281420, -1, 4, 8, r);
825 specialPlusTerm(p, 1, 537107, -1, 3, 8, r);
826 specialPlusTerm(p, 0, 450450, -1, 2, 8, r);
827 specialPlusTerm(p, 0, 96525, -1, 1, 8, r);
828 specialPlusTerm(p, 0, 11440, -1, 0, 8, r);
829 specialPlusTerm(p, 0, 1, 1, 105, 7, r);
830 specialPlusTerm(p, 0, 11, 1, 104, 7, r);
831 specialPlusTerm(p, 0, 67, 1, 103, 7, r);
832 specialPlusTerm(p, 0, 298, 1, 102, 7, r);
833 specialPlusTerm(p, 0, 1080, 1, 101, 7, r);
834 specialPlusTerm(p, 0, 3379, 1, 100, 7, r);
835 specialPlusTerm(p, 0, 9453, 1, 99, 7, r);
836 specialPlusTerm(p, 0, 24196, 1, 98, 7, r);
837 specialPlusTerm(p, 0, 57569, 1, 97, 7, r);
838 specialPlusTerm(p, 0, 128787, 1, 96, 7, r);
839 specialPlusTerm(p, 0, 273231, 1, 95, 7, r);
840 specialPlusTerm(p, 0, 553438, 1, 94, 7, r);
841 specialPlusTerm(p, 1, 75997, 1, 93, 7, r);
842 specialPlusTerm(p, 2, 16735, 1, 92, 7, r);
843 specialPlusTerm(p, 3, 657192, 1, 91, 7, r);
844 specialPlusTerm(p, 6, 436037, 1, 90, 7, r);
845 specialPlusTerm(p, 11, 19717, 1, 89, 7, r);
846 specialPlusTerm(p, 18, 397189, 1, 88, 7, r);
847 specialPlusTerm(p, 30, 3973, 1, 87, 7, r);
848 specialPlusTerm(p, 47, 880870, 1, 86, 7, r);
849 specialPlusTerm(p, 74, 872383, 1, 85, 7, r);
850 specialPlusTerm(p, 114, 869036, 1, 84, 7, r);
851 specialPlusTerm(p, 173, 96283, 1, 83, 7, r);
852 specialPlusTerm(p, 256, 450472, 1, 82, 7, r);
853 specialPlusTerm(p, 373, 879259, 1, 81, 7, r);
854 specialPlusTerm(p, 536, 799939, 1, 80, 7, r);
855 specialPlusTerm(p, 759, 544391, 1, 79, 7, r);
856 specialPlusTerm(p, 1059, 813880, 1, 78, 7, r);
857 specialPlusTerm(p, 1459, 121011, 1, 77, 7, r);
858 specialPlusTerm(p, 1983, 190069, 1, 76, 7, r);
859 specialPlusTerm(p, 2662, 281192, 1, 75, 7, r);
860 specialPlusTerm(p, 3531, 398853, 1, 74, 7, r);
861 specialPlusTerm(p, 4630, 341477, 1, 73, 7, r);
862 specialPlusTerm(p, 6003, 547268, 1, 72, 7, r);
863 specialPlusTerm(p, 7699, 692101, 1, 71, 7, r);
864 specialPlusTerm(p, 9770, 999253, 1, 70, 7, r);
865 specialPlusTerm(p, 12272, 228155, 1, 69, 7, r);
866 specialPlusTerm(p, 15259, 320516, 1, 68, 7, r);
867 specialPlusTerm(p, 18787, 697047, 1, 67, 7, r);
868 specialPlusTerm(p, 22910, 216326, 1, 66, 7, r);
869 specialPlusTerm(p, 27674, 828551, 1, 65, 7, r);
870 specialPlusTerm(p, 33121, 980096, 1, 64, 7, r);
871 specialPlusTerm(p, 39281, 848637, 1, 63, 7, r);
872 specialPlusTerm(p, 46171, 511745, 1, 62, 7, r);
873 specialPlusTerm(p, 53792, 172793, 1, 61, 7, r);
874 specialPlusTerm(p, 62126, 584715, 1, 60, 7, r);
875 specialPlusTerm(p, 71136, 823074, 1, 59, 7, r);
876 specialPlusTerm(p, 80762, 563409, 1, 58, 7, r);
877 specialPlusTerm(p, 90920, 12755, 1, 57, 7, r);
878 specialPlusTerm(p, 101501, 630586, 1, 56, 7, r);
879 specialPlusTerm(p, 112376, 750037, 1, 55, 7, r);
880 specialPlusTerm(p, 123393, 176185, 1, 54, 7, r);
881 specialPlusTerm(p, 134379, 795971, 1, 53, 7, r);
882 specialPlusTerm(p, 145150, 185558, 1, 52, 7, r);
883 specialPlusTerm(p, 155507, 148257, 1, 51, 7, r);
884 specialPlusTerm(p, 165248, 62169, 1, 50, 7, r);
885 specialPlusTerm(p, 174170, 864688, 1, 49, 7, r);
886 specialPlusTerm(p, 182080, 454274, 1, 48, 7, r);
887 specialPlusTerm(p, 188795, 252141, 1, 47, 7, r);
888 specialPlusTerm(p, 194153, 640367, 1, 46, 7, r);
889 specialPlusTerm(p, 198019, 981033, 1, 45, 7, r);
890 specialPlusTerm(p, 200289, 925212, 1, 44, 7, r);
891 specialPlusTerm(p, 200894, 741748, 1, 43, 7, r);
892 specialPlusTerm(p, 199804, 433264, 1, 42, 7, r);
893 specialPlusTerm(p, 197029, 459520, 1, 41, 7, r);
894 specialPlusTerm(p, 192620, 953188, 1, 40, 7, r);
895 specialPlusTerm(p, 186669, 386562, 1, 39, 7, r);
896 specialPlusTerm(p, 179301, 725204, 1, 38, 7, r);
897 specialPlusTerm(p, 170677, 181240, 1, 37, 7, r);
898 specialPlusTerm(p, 160981, 751274, 1, 36, 7, r);
899 specialPlusTerm(p, 150421, 786460, 1, 35, 7, r);
900 specialPlusTerm(p, 139216, 891710, 1, 34, 7, r);
901 specialPlusTerm(p, 127592, 483930, 1, 33, 7, r);
902 specialPlusTerm(p, 115772, 353582, 1, 32, 7, r);
903 specialPlusTerm(p, 103971, 568098, 1, 31, 7, r);
904 specialPlusTerm(p, 92390, 30732, 1, 30, 7, r);
905 specialPlusTerm(p, 81206, 964790, 1, 29, 7, r);
906 specialPlusTerm(p, 70576, 534794, 1, 28, 7, r);
907 specialPlusTerm(p, 60624, 746714, 1, 27, 7, r);
908 specialPlusTerm(p, 51447, 694586, 1, 26, 7, r);
909 specialPlusTerm(p, 43111, 145244, 1, 25, 7, r);
910 specialPlusTerm(p, 35651, 383472, 1, 24, 7, r);
911 specialPlusTerm(p, 29077, 179220, 1, 23, 7, r);
912 specialPlusTerm(p, 23372, 689230, 1, 22, 7, r);
913 specialPlusTerm(p, 18501, 69995, 1, 21, 7, r);
914 specialPlusTerm(p, 14408, 558395, 1, 20, 7, r);
915 specialPlusTerm(p, 11028, 771237, 1, 19, 7, r);
916 specialPlusTerm(p, 8286, 985223, 1, 18, 7, r);
917 specialPlusTerm(p, 6104, 182964, 1, 17, 7, r);
918 specialPlusTerm(p, 4400, 686554, 1, 16, 7, r);
919 specialPlusTerm(p, 3099, 245270, 1, 15, 7, r);
920 specialPlusTerm(p, 2127, 493720, 1, 14, 7, r);
921 specialPlusTerm(p, 1419, 747120, 1, 13, 7, r);
922 specialPlusTerm(p, 918, 147362, 1, 12, 7, r);
923 specialPlusTerm(p, 573, 212794, 1, 11, 7, r);
924 specialPlusTerm(p, 343, 872738, 1, 10, 7, r);
925 specialPlusTerm(p, 197, 84030, 1, 9, 7, r);
926 specialPlusTerm(p, 107, 132168, 1, 8, 7, r);
927 specialPlusTerm(p, 54, 719808, 1, 7, 7, r);
928 specialPlusTerm(p, 25, 940200, 1, 6, 7, r);
929 specialPlusTerm(p, 11, 223212, 1, 5, 7, r);
930 specialPlusTerm(p, 4, 327323, 1, 4, 7, r);
931 specialPlusTerm(p, 1, 434433, 1, 3, 7, r);
932 specialPlusTerm(p, 0, 385385, 1, 2, 7, r);
933 specialPlusTerm(p, 0, 75075, 1, 1, 7, r);
934 specialPlusTerm(p, 0, 8008, 1, 0, 7, r);
935 specialPlusTerm(p, 0, 1, -1, 110, 6, r);
936 specialPlusTerm(p, 0, 12, -1, 109, 6, r);
937 specialPlusTerm(p, 0, 79, -1, 108, 6, r);
938 specialPlusTerm(p, 0, 377, -1, 107, 6, r);
939 specialPlusTerm(p, 0, 1457, -1, 106, 6, r);
940 specialPlusTerm(p, 0, 4836, -1, 105, 6, r);
941 specialPlusTerm(p, 0, 14282, -1, 104, 6, r);
942 specialPlusTerm(p, 0, 38408, -1, 103, 6, r);
943 specialPlusTerm(p, 0, 95585, -1, 102, 6, r);
944 specialPlusTerm(p, 0, 222755, -1, 101, 6, r);
945 specialPlusTerm(p, 0, 490512, -1, 100, 6, r);
946 specialPlusTerm(p, 1, 27858, -1, 99, 6, r);
947 specialPlusTerm(p, 2, 61348, -1, 98, 6, r);
948 specialPlusTerm(p, 3, 974921, -1, 97, 6, r);
949 specialPlusTerm(p, 7, 398548, -1, 96, 6, r);
950 specialPlusTerm(p, 13, 335851, -1, 95, 6, r);
951 specialPlusTerm(p, 23, 342939, -1, 94, 6, r);
952 specialPlusTerm(p, 39, 772696, -1, 93, 6, r);
953 specialPlusTerm(p, 66, 100395, -1, 92, 6, r);
954 specialPlusTerm(p, 107, 347509, -1, 91, 6, r);
955 specialPlusTerm(p, 170, 620609, -1, 90, 6, r);
956 specialPlusTerm(p, 265, 780891, -1, 89, 6, r);
957 specialPlusTerm(p, 406, 256761, -1, 88, 6, r);
958 specialPlusTerm(p, 610, 6662, -1, 87, 6, r);
959 specialPlusTerm(p, 900, 631638, -1, 86, 6, r);
960 specialPlusTerm(p, 1308, 626820, -1, 85, 6, r);
961 specialPlusTerm(p, 1872, 748088, -1, 84, 6, r);
962 specialPlusTerm(p, 2641, 454830, -1, 83, 6, r);
963 specialPlusTerm(p, 3674, 372459, -1, 82, 6, r);
964 specialPlusTerm(p, 5043, 699859, -1, 81, 6, r);
965 specialPlusTerm(p, 6835, 468267, -1, 80, 6, r);
966 specialPlusTerm(p, 9150, 540598, -1, 79, 6, r);
967 specialPlusTerm(p, 12105, 225506, -1, 78, 6, r);
968 specialPlusTerm(p, 15831, 370284, -1, 77, 6, r);
969 specialPlusTerm(p, 20475, 792894, -1, 76, 6, r);
970 specialPlusTerm(p, 26198, 917672, -1, 75, 6, r);
971 specialPlusTerm(p, 33172, 493074, -1, 74, 6, r);
972 specialPlusTerm(p, 41576, 294268, -1, 73, 6, r);
973 specialPlusTerm(p, 51593, 749027, -1, 72, 6, r);
974 specialPlusTerm(p, 63406, 472134, -1, 71, 6, r);
975 specialPlusTerm(p, 77187, 750422, -1, 70, 6, r);
976 specialPlusTerm(p, 93095, 85649, -1, 69, 6, r);
977 specialPlusTerm(p, 111261, 972846, -1, 68, 6, r);
978 specialPlusTerm(p, 131789, 163843, -1, 67, 6, r);
979 specialPlusTerm(p, 154735, 735031, -1, 66, 6, r);
980 specialPlusTerm(p, 180110, 340164, -1, 65, 6, r);
981 specialPlusTerm(p, 207863, 78032, -1, 64, 6, r);
982 specialPlusTerm(p, 237878, 436148, -1, 63, 6, r);
983 specialPlusTerm(p, 269969, 780853, -1, 62, 6, r);
984 specialPlusTerm(p, 303875, 847919, -1, 61, 6, r);
985 specialPlusTerm(p, 339259, 643405, -1, 60, 6, r);
986 specialPlusTerm(p, 375710, 91709, -1, 59, 6, r);
987 specialPlusTerm(p, 412746, 667621, -1, 58, 6, r);
988 specialPlusTerm(p, 449827, 124838, -1, 57, 6, r);
989 specialPlusTerm(p, 486358, 289884, -1, 56, 6, r);
990 specialPlusTerm(p, 521709, 734617, -1, 55, 6, r);
991 specialPlusTerm(p, 555229, 980825, -1, 54, 6, r);
992 specialPlusTerm(p, 586264, 736452, -1, 53, 6, r);
993 specialPlusTerm(p, 614176, 524327, -1, 52, 6, r);
994 specialPlusTerm(p, 638364, 950461, -1, 51, 6, r);
995 specialPlusTerm(p, 658286, 778382, -1, 50, 6, r);
996 specialPlusTerm(p, 673474, 935703, -1, 49, 6, r);
997 specialPlusTerm(p, 683555, 584035, -1, 48, 6, r);
998 specialPlusTerm(p, 688262, 435939, -1, 47, 6, r);
999 specialPlusTerm(p, 687447, 601958, -1, 46, 6, r);
1000 specialPlusTerm(p, 681088, 393321, -1, 45, 6, r);
1001 specialPlusTerm(p, 669289, 685002, -1, 44, 6, r);
1002 specialPlusTerm(p, 652281, 650056, -1, 43, 6, r);
1003 specialPlusTerm(p, 630412, 897910, -1, 42, 6, r);
1004 specialPlusTerm(p, 604139, 273828, -1, 41, 6, r);
1005 specialPlusTerm(p, 574008, 790372, -1, 40, 6, r);
1006 specialPlusTerm(p, 540643, 351434, -1, 39, 6, r);
1007 specialPlusTerm(p, 504718, 83850, -1, 38, 6, r);
1008 specialPlusTerm(p, 466939, 201686, -1, 37, 6, r);
1009 specialPlusTerm(p, 428021, 387818, -1, 36, 6, r);
1010 specialPlusTerm(p, 388665, 682772, -1, 35, 6, r);
1011 specialPlusTerm(p, 349538, 822179, -1, 34, 6, r);
1012 specialPlusTerm(p, 311254, 865006, -1, 33, 6, r);
1013 specialPlusTerm(p, 274359, 811613, -1, 32, 6, r);
1014 specialPlusTerm(p, 239319, 732987, -1, 31, 6, r);
1015 specialPlusTerm(p, 206512, 732148, -1, 30, 6, r);
1016 specialPlusTerm(p, 176224, 848533, -1, 29, 6, r);
1017 specialPlusTerm(p, 148649, 810169, -1, 28, 6, r);
1018 specialPlusTerm(p, 123892, 349306, -1, 27, 6, r);
1019 specialPlusTerm(p, 101974, 636229, -1, 26, 6, r);
1020 specialPlusTerm(p, 82845, 261439, -1, 25, 6, r);
1021 specialPlusTerm(p, 66390, 113996, -1, 24, 6, r);
1022 specialPlusTerm(p, 52444, 464455, -1, 23, 6, r);
1023 specialPlusTerm(p, 40805, 563557, -1, 22, 6, r);
1024 specialPlusTerm(p, 31245, 109466, -1, 21, 6, r);
1025 specialPlusTerm(p, 23521, 11382, -1, 20, 6, r);
1026 specialPlusTerm(p, 17387, 978784, -1, 19, 6, r);
1027 specialPlusTerm(p, 12606, 585145, -1, 18, 6, r);
1028 specialPlusTerm(p, 8950, 583389, -1, 17, 6, r);
1029 specialPlusTerm(p, 6212, 378502, -1, 16, 6, r);
1030 specialPlusTerm(p, 4206, 681655, -1, 15, 6, r);
1031 specialPlusTerm(p, 2772, 472065, -1, 14, 6, r);
1032 specialPlusTerm(p, 1773, 471986, -1, 13, 6, r);
1033 specialPlusTerm(p, 1097, 393517, -1, 12, 6, r);
1034 specialPlusTerm(p, 654, 242447, -1, 11, 6, r);
1035 specialPlusTerm(p, 373, 966384, -1, 10, 6, r);
1036 specialPlusTerm(p, 203, 716799, -1, 9, 6, r);
1037 specialPlusTerm(p, 104, 963287, -1, 8, 6, r);
1038 specialPlusTerm(p, 50, 659180, -1, 7, 6, r);
1039 specialPlusTerm(p, 22, 613305, -1, 6, 6, r);
1040 specialPlusTerm(p, 9, 176167, -1, 5, 6, r);
1041 specialPlusTerm(p, 3, 303300, -1, 4, 6, r);
1042 specialPlusTerm(p, 1, 17016, -1, 3, 6, r);
1043 specialPlusTerm(p, 0, 252252, -1, 2, 6, r);
1044 specialPlusTerm(p, 0, 45045, -1, 1, 6, r);
1045 specialPlusTerm(p, 0, 4368, -1, 0, 6, r);
1046 specialPlusTerm(p, 0, 1, 1, 114, 5, r);
1047 specialPlusTerm(p, 0, 13, 1, 113, 5, r);
1048 specialPlusTerm(p, 0, 92, 1, 112, 5, r);
1049 specialPlusTerm(p, 0, 469, 1, 111, 5, r);
1050 specialPlusTerm(p, 0, 1926, 1, 110, 5, r);
1051 specialPlusTerm(p, 0, 6756, 1, 109, 5, r);
1052 specialPlusTerm(p, 0, 20972, 1, 108, 5, r);
1053 specialPlusTerm(p, 0, 58978, 1, 107, 5, r);
1054 specialPlusTerm(p, 0, 152775, 1, 106, 5, r);
1055 specialPlusTerm(p, 0, 369050, 1, 105, 5, r);
1056 specialPlusTerm(p, 0, 839288, 1, 104, 5, r);
1057 specialPlusTerm(p, 1, 810449, 1, 103, 5, r);
1058 specialPlusTerm(p, 3, 726832, 1, 102, 5, r);
1059 specialPlusTerm(p, 7, 357527, 1, 101, 5, r);
1060 specialPlusTerm(p, 13, 988283, 1, 100, 5, r);
1061 specialPlusTerm(p, 25, 701547, 1, 99, 5, r);
1062 specialPlusTerm(p, 45, 773588, 1, 98, 5, r);
1063 specialPlusTerm(p, 79, 222619, 1, 97, 5, r);
1064 specialPlusTerm(p, 133, 546121, 1, 96, 5, r);
1065 specialPlusTerm(p, 219, 688458, 1, 95, 5, r);
1066 specialPlusTerm(p, 353, 280515, 1, 94, 5, r);
1067 specialPlusTerm(p, 556, 190572, 1, 93, 5, r);
1068 specialPlusTerm(p, 858, 418990, 1, 92, 5, r);
1069 specialPlusTerm(p, 1300, 357646, 1, 91, 5, r);
1070 specialPlusTerm(p, 1935, 417677, 1, 90, 5, r);
1071 specialPlusTerm(p, 2833, 5498, 1, 89, 5, r);
1072 specialPlusTerm(p, 4081, 797160, 1, 88, 5, r);
1073 specialPlusTerm(p, 5793, 225338, 1, 87, 5, r);
1074 specialPlusTerm(p, 8105, 52608, 1, 86, 5, r);
1075 specialPlusTerm(p, 11184, 860904, 1, 85, 5, r);
1076 specialPlusTerm(p, 15233, 242543, 1, 84, 5, r);
1077 specialPlusTerm(p, 20486, 436025, 1, 83, 5, r);
1078 specialPlusTerm(p, 27218, 113560, 1, 82, 5, r);
1079 specialPlusTerm(p, 35740, 941, 1, 81, 5, r);
1080 specialPlusTerm(p, 46400, 998184, 1, 80, 5, r);
1081 specialPlusTerm(p, 59584, 475380, 1, 79, 5, r);
1082 specialPlusTerm(p, 75703, 446044, 1, 78, 5, r);
1083 specialPlusTerm(p, 95193, 372588, 1, 77, 5, r);
1084 specialPlusTerm(p, 118502, 436837, 1, 76, 5, r);
1085 specialPlusTerm(p, 146079, 212557, 1, 75, 5, r);
1086 specialPlusTerm(p, 178357, 804753, 1, 74, 5, r);
1087 specialPlusTerm(p, 215740, 667987, 1, 73, 5, r);
1088 specialPlusTerm(p, 258579, 477117, 1, 72, 5, r);
1089 specialPlusTerm(p, 307154, 590636, 1, 71, 5, r);
1090 specialPlusTerm(p, 361653, 809467, 1, 70, 5, r);
1091 specialPlusTerm(p, 422151, 281668, 1, 69, 5, r);
1092 specialPlusTerm(p, 488587, 524562, 1, 68, 5, r);
1093 specialPlusTerm(p, 560751, 619043, 1, 67, 5, r);
1094 specialPlusTerm(p, 638266, 666013, 1, 66, 5, r);
1095 specialPlusTerm(p, 720579, 573693, 1, 65, 5, r);
1096 specialPlusTerm(p, 806956, 161270, 1, 64, 5, r);
1097 specialPlusTerm(p, 896482, 416756, 1, 63, 5, r);
1098 specialPlusTerm(p, 988072, 536828, 1, 62, 5, r);
1099 specialPlusTerm(p, 1080484, 109735, 1, 61, 5, r);
1100 specialPlusTerm(p, 1172340, 489345, 1, 60, 5, r);
1101 specialPlusTerm(p, 1262160, 63390, 1, 59, 5, r);
1102 specialPlusTerm(p, 1348391, 759522, 1, 58, 5, r);
1103 specialPlusTerm(p, 1429455, 778912, 1, 57, 5, r);
1104 specialPlusTerm(p, 1503788, 220123, 1, 56, 5, r);
1105 specialPlusTerm(p, 1569887, 977111, 1, 55, 5, r);
1106 specialPlusTerm(p, 1626364, 84113, 1, 54, 5, r);
1107 specialPlusTerm(p, 1671981, 553512, 1, 53, 5, r);
1108 specialPlusTerm(p, 1705703, 722632, 1, 52, 5, r);
1109 specialPlusTerm(p, 1726729, 198623, 1, 51, 5, r);
1110 specialPlusTerm(p, 1734521, 667786, 1, 50, 5, r);
1111 specialPlusTerm(p, 1728831, 111168, 1, 49, 5, r);
1112 specialPlusTerm(p, 1709705, 329909, 1, 48, 5, r);
1113 specialPlusTerm(p, 1677491, 113716, 1, 47, 5, r);
1114 specialPlusTerm(p, 1632824, 861010, 1, 46, 5, r);
1115 specialPlusTerm(p, 1576612, 953462, 1, 45, 5, r);
1116 specialPlusTerm(p, 1510002, 672602, 1, 44, 5, r);
1117 specialPlusTerm(p, 1434344, 893769, 1, 43, 5, r);
1118 specialPlusTerm(p, 1351150, 176624, 1, 42, 5, r);
1119 specialPlusTerm(p, 1262040, 169393, 1, 41, 5, r);
1120 specialPlusTerm(p, 1168696, 438727, 1, 40, 5, r);
1121 specialPlusTerm(p, 1072808, 918138, 1, 39, 5, r);
1122 specialPlusTerm(p, 976026, 132162, 1, 38, 5, r);
1123 specialPlusTerm(p, 879909, 204828, 1, 37, 5, r);
1124 specialPlusTerm(p, 785891, 410576, 1, 36, 5, r);
1125 specialPlusTerm(p, 695244, 690346, 1, 35, 5, r);
1126 specialPlusTerm(p, 609054, 157073, 1, 34, 5, r);
1127 specialPlusTerm(p, 528201, 178547, 1, 33, 5, r);
1128 specialPlusTerm(p, 453355, 178523, 1, 32, 5, r);
1129 specialPlusTerm(p, 384973, 865967, 1, 31, 5, r);
1130 specialPlusTerm(p, 323311, 212357, 1, 30, 5, r);
1131 specialPlusTerm(p, 268432, 169189, 1, 29, 5, r);
1132 specialPlusTerm(p, 220232, 868421, 1, 28, 5, r);
1133 specialPlusTerm(p, 178464, 887323, 1, 27, 5, r);
1134 specialPlusTerm(p, 142762, 89447, 1, 26, 5, r);
1135 specialPlusTerm(p, 112668, 572043, 1, 25, 5, r);
1136 specialPlusTerm(p, 87666, 348585, 1, 24, 5, r);
1137 specialPlusTerm(p, 67201, 559745, 1, 23, 5, r);
1138 specialPlusTerm(p, 50708, 221257, 1, 22, 5, r);
1139 specialPlusTerm(p, 37628, 764983, 1, 21, 5, r);
1140 specialPlusTerm(p, 27430, 891847, 1, 20, 5, r);
1141 specialPlusTerm(p, 19620, 514504, 1, 19, 5, r);
1142 specialPlusTerm(p, 13750, 807706, 1, 18, 5, r);
1143 specialPlusTerm(p, 9427, 591898, 1, 17, 5, r);
1144 specialPlusTerm(p, 6311, 440762, 1, 16, 5, r);
1145 specialPlusTerm(p, 4117, 20228, 1, 15, 5, r);
1146 specialPlusTerm(p, 2610, 233212, 1, 14, 5, r);
1147 specialPlusTerm(p, 1603, 763552, 1, 13, 5, r);
1148 specialPlusTerm(p, 951, 590329, 1, 12, 5, r);
1149 specialPlusTerm(p, 542, 988511, 1, 11, 5, r);
1150 specialPlusTerm(p, 296, 453834, 1, 10, 5, r);
1151 specialPlusTerm(p, 153, 899291, 1, 9, 5, r);
1152 specialPlusTerm(p, 75, 376496, 1, 8, 5, r);
1153 specialPlusTerm(p, 34, 484437, 1, 7, 5, r);
1154 specialPlusTerm(p, 14, 545453, 1, 6, 5, r);
1155 specialPlusTerm(p, 5, 557552, 1, 5, 5, r);
1156 specialPlusTerm(p, 1, 876238, 1, 4, 5, r);
1157 specialPlusTerm(p, 0, 539266, 1, 3, 5, r);
1158 specialPlusTerm(p, 0, 124215, 1, 2, 5, r);
1159 specialPlusTerm(p, 0, 20475, 1, 1, 5, r);
1160 specialPlusTerm(p, 0, 1820, 1, 0, 5, r);
1161 specialPlusTerm(p, 0, 1, -1, 117, 4, r);
1162 specialPlusTerm(p, 0, 14, -1, 116, 4, r);
1163 specialPlusTerm(p, 0, 106, -1, 115, 4, r);
1164 specialPlusTerm(p, 0, 575, -1, 114, 4, r);
1165 specialPlusTerm(p, 0, 2496, -1, 113, 4, r);
1166 specialPlusTerm(p, 0, 9192, -1, 112, 4, r);
1167 specialPlusTerm(p, 0, 29769, -1, 111, 4, r);
1168 specialPlusTerm(p, 0, 86862, -1, 110, 4, r);
1169 specialPlusTerm(p, 0, 232352, -1, 109, 4, r);
1170 specialPlusTerm(p, 0, 577237, -1, 108, 4, r);
1171 specialPlusTerm(p, 1, 345280, -1, 107, 4, r);
1172 specialPlusTerm(p, 2, 964694, -1, 106, 4, r);
1173 specialPlusTerm(p, 6, 218071, -1, 105, 4, r);
1174 specialPlusTerm(p, 12, 478024, -1, 104, 4, r);
1175 specialPlusTerm(p, 24, 64445, -1, 103, 4, r);
1176 specialPlusTerm(p, 44, 768554, -1, 102, 4, r);
1177 specialPlusTerm(p, 80, 598456, -1, 101, 4, r);
1178 specialPlusTerm(p, 140, 809905, -1, 100, 4, r);
1179 specialPlusTerm(p, 239, 293294, -1, 99, 4, r);
1180 specialPlusTerm(p, 396, 392192, -1, 98, 4, r);
1181 specialPlusTerm(p, 641, 228471, -1, 97, 4, r);
1182 specialPlusTerm(p, 1014, 602512, -1, 96, 4, r);
1183 specialPlusTerm(p, 1572, 522451, -1, 95, 4, r);
1184 specialPlusTerm(p, 2390, 392393, -1, 94, 4, r);
1185 specialPlusTerm(p, 3567, 854826, -1, 93, 4, r);
1186 specialPlusTerm(p, 5234, 236531, -1, 92, 4, r);
1187 specialPlusTerm(p, 7554, 490334, -1, 91, 4, r);
1188 specialPlusTerm(p, 10735, 458285, -1, 90, 4, r);
1189 specialPlusTerm(p, 15032, 207608, -1, 89, 4, r);
1190 specialPlusTerm(p, 20754, 112592, -1, 88, 4, r);
1191 specialPlusTerm(p, 28270, 278236, -1, 87, 4, r);
1192 specialPlusTerm(p, 38013, 830749, -1, 86, 4, r);
1193 specialPlusTerm(p, 50484, 542623, -1, 85, 4, r);
1194 specialPlusTerm(p, 66249, 223101, -1, 84, 4, r);
1195 specialPlusTerm(p, 85939, 295631, -1, 83, 4, r);
1196 specialPlusTerm(p, 110245, 8968, -1, 82, 4, r);
1197 specialPlusTerm(p, 139905, 793448, -1, 81, 4, r);
1198 specialPlusTerm(p, 175696, 382307, -1, 80, 4, r);
1199 specialPlusTerm(p, 218408, 471011, -1, 79, 4, r);
1200 specialPlusTerm(p, 268827, 883672, -1, 78, 4, r);
1201 specialPlusTerm(p, 327707, 449671, -1, 77, 4, r);
1202 specialPlusTerm(p, 395736, 57018, -1, 76, 4, r);
1203 specialPlusTerm(p, 473504, 629765, -1, 75, 4, r);
1204 specialPlusTerm(p, 561470, 59952, -1, 74, 4, r);
1205 specialPlusTerm(p, 659918, 392736, -1, 73, 4, r);
1206 specialPlusTerm(p, 768928, 797683, -1, 72, 4, r);
1207 specialPlusTerm(p, 888340, 40490, -1, 71, 4, r);
1208 specialPlusTerm(p, 1017721, 279436, -1, 70, 4, r);
1209 specialPlusTerm(p, 1156349, 33848, -1, 69, 4, r);
1210 specialPlusTerm(p, 1303192, 95883, -1, 68, 4, r);
1211 specialPlusTerm(p, 1456905, 975122, -1, 67, 4, r);
1212 specialPlusTerm(p, 1615838, 177110, -1, 66, 4, r);
1213 specialPlusTerm(p, 1778045, 228075, -1, 65, 4, r);
1214 specialPlusTerm(p, 1941321, 881690, -1, 64, 4, r);
1215 specialPlusTerm(p, 2103242, 399767, -1, 63, 4, r);
1216 specialPlusTerm(p, 2261213, 213104, -1, 62, 4, r);
1217 specialPlusTerm(p, 2412535, 672007, -1, 61, 4, r);
1218 specialPlusTerm(p, 2554477, 22053, -1, 60, 4, r);
1219 specialPlusTerm(p, 2684347, 224260, -1, 59, 4, r);
1220 specialPlusTerm(p, 2799578, 813532, -1, 58, 4, r);
1221 specialPlusTerm(p, 2897806, 685056, -1, 57, 4, r);
1222 specialPlusTerm(p, 2976944, 539523, -1, 56, 4, r);
1223 specialPlusTerm(p, 3035254, 721183, -1, 55, 4, r);
1224 specialPlusTerm(p, 3071408, 355156, -1, 54, 4, r);
1225 specialPlusTerm(p, 3084533, 29299, -1, 53, 4, r);
1226 specialPlusTerm(p, 3074245, 758101, -1, 52, 4, r);
1227 specialPlusTerm(p, 3040669, 588583, -1, 51, 4, r);
1228 specialPlusTerm(p, 2984432, 929416, -1, 50, 4, r);
1229 specialPlusTerm(p, 2906651, 466023, -1, 49, 4, r);
1230 specialPlusTerm(p, 2808893, 323361, -1, 48, 4, r);
1231 specialPlusTerm(p, 2693128, 909640, -1, 47, 4, r);
1232 specialPlusTerm(p, 2561667, 574760, -1, 46, 4, r);
1233 specialPlusTerm(p, 2417083, 807115, -1, 45, 4, r);
1234 specialPlusTerm(p, 2262136, 138608, -1, 44, 4, r);
1235 specialPlusTerm(p, 2099682, 206060, -1, 43, 4, r);
1236 specialPlusTerm(p, 1932593, 513922, -1, 42, 4, r);
1237 specialPlusTerm(p, 1763673, 355846, -1, 41, 4, r);
1238 specialPlusTerm(p, 1595581, 90061, -1, 40, 4, r);
1239 specialPlusTerm(p, 1430765, 545095, -1, 39, 4, r);
1240 specialPlusTerm(p, 1271409, 786637, -1, 38, 4, r);
1241 specialPlusTerm(p, 1119388, 838595, -1, 37, 4, r);
1242 specialPlusTerm(p, 976241, 261398, -1, 36, 4, r);
1243 specialPlusTerm(p, 843154, 789753, -1, 35, 4, r);
1244 specialPlusTerm(p, 720965, 560845, -1, 34, 4, r);
1245 specialPlusTerm(p, 610169, 859179, -1, 33, 4, r);
1246 specialPlusTerm(p, 510946, 796821, -1, 32, 4, r);
1247 specialPlusTerm(p, 423189, 960892, -1, 31, 4, r);
1248 specialPlusTerm(p, 346545, 808032, -1, 30, 4, r);
1249 specialPlusTerm(p, 280456, 472902, -1, 29, 4, r);
1250 specialPlusTerm(p, 224204, 680080, -1, 28, 4, r);
1251 specialPlusTerm(p, 176958, 593014, -1, 27, 4, r);
1252 specialPlusTerm(p, 137814, 680334, -1, 26, 4, r);
1253 specialPlusTerm(p, 105837, 4252, -1, 25, 4, r);
1254 specialPlusTerm(p, 80091, 710806, -1, 24, 4, r);
1255 specialPlusTerm(p, 59675, 899582, -1, 23, 4, r);
1256 specialPlusTerm(p, 43740, 445029, -1, 22, 4, r);
1257 specialPlusTerm(p, 31506, 709211, -1, 21, 4, r);
1258 specialPlusTerm(p, 22277, 407599, -1, 20, 4, r);
1259 specialPlusTerm(p, 15442, 151129, -1, 19, 4, r);
1260 specialPlusTerm(p, 10478, 380611, -1, 18, 4, r);
1261 specialPlusTerm(p, 6948, 530664, -1, 17, 4, r);
1262 specialPlusTerm(p, 4494, 312038, -1, 16, 4, r);
1263 specialPlusTerm(p, 2828, 990461, -1, 15, 4, r);
1264 specialPlusTerm(p, 1728, 477668, -1, 14, 4, r);
1265 specialPlusTerm(p, 1021, 949004, -1, 13, 4, r);
1266 specialPlusTerm(p, 582, 575810, -1, 12, 4, r);
1267 specialPlusTerm(p, 318, 823114, -1, 11, 4, r);
1268 specialPlusTerm(p, 166, 625848, -1, 10, 4, r);
1269 specialPlusTerm(p, 82, 629352, -1, 9, 4, r);
1270 specialPlusTerm(p, 38, 568972, -1, 8, 4, r);
1271 specialPlusTerm(p, 16, 773120, -1, 7, 4, r);
1272 specialPlusTerm(p, 6, 706050, -1, 6, 4, r);
1273 specialPlusTerm(p, 2, 420964, -1, 5, 4, r);
1274 specialPlusTerm(p, 0, 769496, -1, 4, 4, r);
1275 specialPlusTerm(p, 0, 207389, -1, 3, 4, r);
1276 specialPlusTerm(p, 0, 44590, -1, 2, 4, r);
1277 specialPlusTerm(p, 0, 6825, -1, 1, 4, r);
1278 specialPlusTerm(p, 0, 560, -1, 0, 4, r);
1279 specialPlusTerm(p, 0, 1, 1, 119, 3, r);
1280 specialPlusTerm(p, 0, 15, 1, 118, 3, r);
1281 specialPlusTerm(p, 0, 121, 1, 117, 3, r);
1282 specialPlusTerm(p, 0, 692, 1, 116, 3, r);
1283 specialPlusTerm(p, 0, 3136, 1, 115, 3, r);
1284 specialPlusTerm(p, 0, 11960, 1, 114, 3, r);
1285 specialPlusTerm(p, 0, 39853, 1, 113, 3, r);
1286 specialPlusTerm(p, 0, 119021, 1, 112, 3, r);
1287 specialPlusTerm(p, 0, 324469, 1, 111, 3, r);
1288 specialPlusTerm(p, 0, 818608, 1, 110, 3, r);
1289 specialPlusTerm(p, 1, 931746, 1, 109, 3, r);
1290 specialPlusTerm(p, 4, 299910, 1, 108, 3, r);
1291 specialPlusTerm(p, 9, 90121, 1, 107, 3, r);
1292 specialPlusTerm(p, 18, 353593, 1, 106, 3, r);
1293 specialPlusTerm(p, 35, 558983, 1, 105, 3, r);
1294 specialPlusTerm(p, 66, 370113, 1, 104, 3, r);
1295 specialPlusTerm(p, 119, 744513, 1, 103, 3, r);
1296 specialPlusTerm(p, 209, 439344, 1, 102, 3, r);
1297 specialPlusTerm(p, 356, 18067, 1, 101, 3, r);
1298 specialPlusTerm(p, 589, 452669, 1, 100, 3, r);
1299 specialPlusTerm(p, 952, 410212, 1, 99, 3, r);
1300 specialPlusTerm(p, 1504, 296795, 1, 98, 3, r);
1301 specialPlusTerm(p, 2326, 104760, 1, 97, 3, r);
1302 specialPlusTerm(p, 3526, 68612, 1, 96, 3, r);
1303 specialPlusTerm(p, 5246, 80850, 1, 95, 3, r);
1304 specialPlusTerm(p, 7668, 750896, 1, 94, 3, r);
1305 specialPlusTerm(p, 11024, 909967, 1, 93, 3, r);
1306 specialPlusTerm(p, 15601, 274876, 1, 92, 3, r);
1307 specialPlusTerm(p, 21747, 888690, 1, 91, 3, r);
1308 specialPlusTerm(p, 29884, 861708, 1, 90, 3, r);
1309 specialPlusTerm(p, 40507, 849459, 1, 89, 3, r);
1310 specialPlusTerm(p, 54191, 633482, 1, 88, 3, r);
1311 specialPlusTerm(p, 71591, 124221, 1, 87, 3, r);
1312 specialPlusTerm(p, 93439, 92109, 1, 86, 3, r);
1313 specialPlusTerm(p, 120539, 960778, 1, 85, 3, r);
1314 specialPlusTerm(p, 153759, 71799, 1, 84, 3, r);
1315 specialPlusTerm(p, 194006, 957680, 1, 83, 3, r);
1316 specialPlusTerm(p, 242218, 340335, 1, 82, 3, r);
1317 specialPlusTerm(p, 299325, 803637, 1, 81, 3, r);
1318 specialPlusTerm(p, 366228, 364763, 1, 80, 3, r);
1319 specialPlusTerm(p, 443755, 479465, 1, 79, 3, r);
1320 specialPlusTerm(p, 532627, 346793, 1, 78, 3, r);
1321 specialPlusTerm(p, 633412, 711280, 1, 77, 3, r);
1322 specialPlusTerm(p, 746485, 674616, 1, 76, 3, r);
1323 specialPlusTerm(p, 871983, 302274, 1, 75, 3, r);
1324 specialPlusTerm(p, 1009766, 21123, 1, 74, 3, r);
1325 specialPlusTerm(p, 1159382, 930867, 1, 73, 3, r);
1326 specialPlusTerm(p, 1320044, 177277, 1, 72, 3, r);
1327 specialPlusTerm(p, 1490602, 445312, 1, 71, 3, r);
1328 specialPlusTerm(p, 1669545, 418046, 1, 70, 3, r);
1329 specialPlusTerm(p, 1855000, 712658, 1, 69, 3, r);
1330 specialPlusTerm(p, 2044754, 355265, 1, 68, 3, r);
1331 specialPlusTerm(p, 2236283, 307760, 1, 67, 3, r);
1332 specialPlusTerm(p, 2426801, 935374, 1, 66, 3, r);
1333 specialPlusTerm(p, 2613321, 633418, 1, 65, 3, r);
1334 specialPlusTerm(p, 2792722, 150781, 1, 64, 3, r);
1335 specialPlusTerm(p, 2961832, 494671, 1, 63, 3, r);
1336 specialPlusTerm(p, 3117518, 715055, 1, 62, 3, r);
1337 specialPlusTerm(p, 3256775, 385842, 1, 61, 3, r);
1338 specialPlusTerm(p, 3376817, 256340, 1, 60, 3, r);
1339 specialPlusTerm(p, 3475167, 367466, 1, 59, 3, r);
1340 specialPlusTerm(p, 3549737, 930366, 1, 58, 3, r);
1341 specialPlusTerm(p, 3598900, 457938, 1, 57, 3, r);
1342 specialPlusTerm(p, 3621542, 18424, 1, 56, 3, r);
1343 specialPlusTerm(p, 3617105, 29495, 1, 55, 3, r);
1344 specialPlusTerm(p, 3585608, 705050, 1, 54, 3, r);
1345 specialPlusTerm(p, 3527651, 69853, 1, 53, 3, r);
1346 specialPlusTerm(p, 3444391, 326416, 1, 52, 3, r);
1347 specialPlusTerm(p, 3337513, 246817, 1, 51, 3, r);
1348 specialPlusTerm(p, 3209171, 120352, 1, 50, 3, r);
1349 specialPlusTerm(p, 3061920, 568442, 1, 49, 3, r);
1350 specialPlusTerm(p, 2898637, 197953, 1, 48, 3, r);
1351 specialPlusTerm(p, 2722426, 567254, 1, 47, 3, r);
1352 specialPlusTerm(p, 2536529, 259766, 1, 46, 3, r);
1353 specialPlusTerm(p, 2344224, 982535, 1, 45, 3, r);
1354 specialPlusTerm(p, 2148739, 529673, 1, 44, 3, r);
1355 specialPlusTerm(p, 1953158, 181630, 1, 43, 3, r);
1356 specialPlusTerm(p, 1760348, 671733, 1, 42, 3, r);
1357 specialPlusTerm(p, 1572896, 271477, 1, 41, 3, r);
1358 specialPlusTerm(p, 1393052, 863345, 1, 40, 3, r);
1359 specialPlusTerm(p, 1222701, 126910, 1, 39, 3, r);
1360 specialPlusTerm(p, 1063334, 204889, 1, 38, 3, r);
1361 specialPlusTerm(p, 916050, 483828, 1, 37, 3, r);
1362 specialPlusTerm(p, 781562, 458519, 1, 36, 3, r);
1363 specialPlusTerm(p, 660218, 83241, 1, 35, 3, r);
1364 specialPlusTerm(p, 552032, 571637, 1, 34, 3, r);
1365 specialPlusTerm(p, 456728, 306449, 1, 33, 3, r);
1366 specialPlusTerm(p, 373780, 366678, 1, 32, 3, r);
1367 specialPlusTerm(p, 302465, 169735, 1, 31, 3, r);
1368 specialPlusTerm(p, 241909, 847846, 1, 30, 3, r);
1369 specialPlusTerm(p, 191140, 212177, 1, 29, 3, r);
1370 specialPlusTerm(p, 149125, 480301, 1, 28, 3, r);
1371 specialPlusTerm(p, 114818, 324960, 1, 27, 3, r);
1372 specialPlusTerm(p, 87189, 215772, 1, 26, 3, r);
1373 specialPlusTerm(p, 65254, 442815, 1, 25, 3, r);
1374 specialPlusTerm(p, 48097, 606920, 1, 24, 3, r);
1375 specialPlusTerm(p, 34884, 715247, 1, 23, 3, r);
1376 specialPlusTerm(p, 24873, 316659, 1, 22, 3, r);
1377 specialPlusTerm(p, 17416, 339482, 1, 21, 3, r);
1378 specialPlusTerm(p, 11961, 450014, 1, 20, 3, r);
1379 specialPlusTerm(p, 8046, 834503, 1, 19, 3, r);
1380 specialPlusTerm(p, 5294, 325768, 1, 18, 3, r);
1381 specialPlusTerm(p, 3400, 757398, 1, 17, 3, r);
1382 specialPlusTerm(p, 2128, 345318, 1, 16, 3, r);
1383 specialPlusTerm(p, 1294, 781596, 1, 15, 3, r);
1384 specialPlusTerm(p, 763, 591975, 1, 14, 3, r);
1385 specialPlusTerm(p, 435, 169111, 1, 13, 3, r);
1386 specialPlusTerm(p, 238, 758463, 1, 12, 3, r);
1387 specialPlusTerm(p, 125, 551459, 1, 11, 3, r);
1388 specialPlusTerm(p, 62, 936621, 1, 10, 3, r);
1389 specialPlusTerm(p, 29, 876893, 1, 9, 3, r);
1390 specialPlusTerm(p, 13, 321355, 1, 8, 3, r);
1391 specialPlusTerm(p, 5, 520901, 1, 7, 3, r);
1392 specialPlusTerm(p, 2, 98067, 1, 6, 3, r);
1393 specialPlusTerm(p, 0, 717871, 1, 5, 3, r);
1394 specialPlusTerm(p, 0, 215565, 1, 4, 3, r);
1395 specialPlusTerm(p, 0, 54691, 1, 3, 3, r);
1396 specialPlusTerm(p, 0, 11025, 1, 2, 3, r);
1397 specialPlusTerm(p, 0, 1575, 1, 1, 3, r);
1398 specialPlusTerm(p, 0, 120, 1, 0, 3, r);
1399 specialPlusTerm(p, 0, 1, -1, 120, 2, r);
1400 specialPlusTerm(p, 0, 16, -1, 119, 2, r);
1401 specialPlusTerm(p, 0, 134, -1, 118, 2, r);
1402 specialPlusTerm(p, 0, 784, -1, 117, 2, r);
1403 specialPlusTerm(p, 0, 3602, -1, 116, 2, r);
1404 specialPlusTerm(p, 0, 13843, -1, 115, 2, r);
1405 specialPlusTerm(p, 0, 46286, -1, 114, 2, r);
1406 specialPlusTerm(p, 0, 138283, -1, 113, 2, r);
1407 specialPlusTerm(p, 0, 376259, -1, 112, 2, r);
1408 specialPlusTerm(p, 0, 945827, -1, 111, 2, r);
1409 specialPlusTerm(p, 2, 220933, -1, 110, 2, r);
1410 specialPlusTerm(p, 4, 914174, -1, 109, 2, r);
1411 specialPlusTerm(p, 10, 318553, -1, 108, 2, r);
1412 specialPlusTerm(p, 20, 680144, -1, 107, 2, r);
1413 specialPlusTerm(p, 39, 750869, -1, 106, 2, r);
1414 specialPlusTerm(p, 73, 579984, -1, 105, 2, r);
1415 specialPlusTerm(p, 131, 610793, -1, 104, 2, r);
1416 specialPlusTerm(p, 228, 154162, -1, 103, 2, r);
1417 specialPlusTerm(p, 384, 310996, -1, 102, 2, r);
1418 specialPlusTerm(p, 630, 410278, -1, 101, 2, r);
1419 specialPlusTerm(p, 1009, 15895, -1, 100, 2, r);
1420 specialPlusTerm(p, 1578, 532849, -1, 99, 2, r);
1421 specialPlusTerm(p, 2417, 410542, -1, 98, 2, r);
1422 specialPlusTerm(p, 3628, 897233, -1, 97, 2, r);
1423 specialPlusTerm(p, 5346, 245930, -1, 96, 2, r);
1424 specialPlusTerm(p, 7738, 209354, -1, 95, 2, r);
1425 specialPlusTerm(p, 11014, 592780, -1, 94, 2, r);
1426 specialPlusTerm(p, 15431, 562271, -1, 93, 2, r);
1427 specialPlusTerm(p, 21296, 336917, -1, 92, 2, r);
1428 specialPlusTerm(p, 28970, 832923, -1, 91, 2, r);
1429 specialPlusTerm(p, 38873, 781118, -1, 90, 2, r);
1430 specialPlusTerm(p, 51480, 814244, -1, 89, 2, r);
1431 specialPlusTerm(p, 67322, 22502, -1, 88, 2, r);
1432 specialPlusTerm(p, 86976, 510707, -1, 87, 2, r);
1433 specialPlusTerm(p, 111063, 562039, -1, 86, 2, r);
1434 specialPlusTerm(p, 140230, 123797, -1, 85, 2, r);
1435 specialPlusTerm(p, 175134, 479331, -1, 84, 2, r);
1436 specialPlusTerm(p, 216426, 154185, -1, 83, 2, r);
1437 specialPlusTerm(p, 264722, 317163, -1, 82, 2, r);
1438 specialPlusTerm(p, 320581, 169273, -1, 81, 2, r);
1439 specialPlusTerm(p, 384473, 53329, -1, 80, 2, r);
1440 specialPlusTerm(p, 456750, 250207, -1, 79, 2, r);
1441 specialPlusTerm(p, 537616, 638714, -1, 78, 2, r);
1442 specialPlusTerm(p, 627098, 568602, -1, 77, 2, r);
1443 specialPlusTerm(p, 725018, 414915, -1, 76, 2, r);
1444 specialPlusTerm(p, 830972, 332853, -1, 75, 2, r);
1445 specialPlusTerm(p, 944313, 704873, -1, 74, 2, r);
1446 specialPlusTerm(p, 1064143, 659019, -1, 73, 2, r);
1447 specialPlusTerm(p, 1189309, 837532, -1, 72, 2, r);
1448 specialPlusTerm(p, 1318414, 311129, -1, 71, 2, r);
1449 specialPlusTerm(p, 1449831, 176128, -1, 70, 2, r);
1450 specialPlusTerm(p, 1581733, 953526, -1, 69, 2, r);
1451 specialPlusTerm(p, 1712132, 450851, -1, 68, 2, r);
1452 specialPlusTerm(p, 1838918, 272730, -1, 67, 2, r);
1453 specialPlusTerm(p, 1959917, 700931, -1, 66, 2, r);
1454 specialPlusTerm(p, 2072950, 236513, -1, 65, 2, r);
1455 specialPlusTerm(p, 2175890, 732337, -1, 64, 2, r);
1456 specialPlusTerm(p, 2266732, 767744, -1, 63, 2, r);
1457 specialPlusTerm(p, 2343650, 748669, -1, 62, 2, r);
1458 specialPlusTerm(p, 2405058, 170088, -1, 61, 2, r);
1459 specialPlusTerm(p, 2449659, 560856, -1, 60, 2, r);
1460 specialPlusTerm(p, 2476493, 843437, -1, 59, 2, r);
1461 specialPlusTerm(p, 2484967, 174656, -1, 58, 2, r);
1462 specialPlusTerm(p, 2474873, 772785, -1, 57, 2, r);
1463 specialPlusTerm(p, 2446403, 758673, -1, 56, 2, r);
1464 specialPlusTerm(p, 2400137, 616515, -1, 55, 2, r);
1465 specialPlusTerm(p, 2337027, 481818, -1, 54, 2, r);
1466 specialPlusTerm(p, 2258366, 57059, -1, 53, 2, r);
1467 specialPlusTerm(p, 2165744, 506758, -1, 52, 2, r);
1468 specialPlusTerm(p, 2061001, 163040, -1, 51, 2, r);
1469 specialPlusTerm(p, 1946163, 254505, -1, 50, 2, r);
1470 specialPlusTerm(p, 1823384, 135692, -1, 49, 2, r);
1471 specialPlusTerm(p, 1694878, 629195, -1, 48, 2, r);
1472 specialPlusTerm(p, 1562859, 93097, -1, 47, 2, r);
1473 specialPlusTerm(p, 1429474, 696453, -1, 46, 2, r);
1474 specialPlusTerm(p, 1296756, 136371, -1, 45, 2, r);
1475 specialPlusTerm(p, 1166567, 679850, -1, 44, 2, r);
1476 specialPlusTerm(p, 1040567, 985354, -1, 43, 2, r);
1477 specialPlusTerm(p, 920180, 680239, -1, 42, 2, r);
1478 specialPlusTerm(p, 806575, 169521, -1, 41, 2, r);
1479 specialPlusTerm(p, 700657, 657865, -1, 40, 2, r);
1480 specialPlusTerm(p, 603071, 906907, -1, 39, 2, r);
1481 specialPlusTerm(p, 514208, 847321, -1, 38, 2, r);
1482 specialPlusTerm(p, 434223, 837763, -1, 37, 2, r);
1483 specialPlusTerm(p, 363060, 123557, -1, 36, 2, r);
1484 specialPlusTerm(p, 300476, 903127, -1, 35, 2, r);
1485 specialPlusTerm(p, 246080, 359923, -1, 34, 2, r);
1486 specialPlusTerm(p, 199356, 56374, -1, 33, 2, r);
1487 specialPlusTerm(p, 159701, 203700, -1, 32, 2, r);
1488 specialPlusTerm(p, 126455, 502830, -1, 31, 2, r);
1489 specialPlusTerm(p, 98929, 480219, -1, 30, 2, r);
1490 specialPlusTerm(p, 76429, 499829, -1, 29, 2, r);
1491 specialPlusTerm(p, 58278, 900847, -1, 28, 2, r);
1492 specialPlusTerm(p, 43834, 973084, -1, 27, 2, r);
1493 specialPlusTerm(p, 32501, 723962, -1, 26, 2, r);
1494 specialPlusTerm(p, 23738, 601098, -1, 25, 2, r);
1495 specialPlusTerm(p, 17065, 504721, -1, 24, 2, r);
1496 specialPlusTerm(p, 12064, 550062, -1, 23, 2, r);
1497 specialPlusTerm(p, 8379, 120417, -1, 22, 2, r);
1498 specialPlusTerm(p, 5710, 788839, -1, 21, 2, r);
1499 specialPlusTerm(p, 3814, 684934, -1, 20, 2, r);
1500 specialPlusTerm(p, 2493, 849460, -1, 19, 2, r);
1501 specialPlusTerm(p, 1593, 60962, -1, 18, 2, r);
1502 specialPlusTerm(p, 992, 543577, -1, 17, 2, r);
1503 specialPlusTerm(p, 601, 881264, -1, 16, 2, r);
1504 specialPlusTerm(p, 354, 378149, -1, 15, 2, r);
1505 specialPlusTerm(p, 202, 23344, -1, 14, 2, r);
1506 specialPlusTerm(p, 111, 145993, -1, 13, 2, r);
1507 specialPlusTerm(p, 58, 785390, -1, 12, 2, r);
1508 specialPlusTerm(p, 29, 753317, -1, 11, 2, r);
1509 specialPlusTerm(p, 14, 331491, -1, 10, 2, r);
1510 specialPlusTerm(p, 6, 525379, -1, 9, 2, r);
1511 specialPlusTerm(p, 2, 785083, -1, 8, 2, r);
1512 specialPlusTerm(p, 1, 102494, -1, 7, 2, r);
1513 specialPlusTerm(p, 0, 399235, -1, 6, 2, r);
1514 specialPlusTerm(p, 0, 129826, -1, 5, 2, r);
1515 specialPlusTerm(p, 0, 36944, -1, 4, 2, r);
1516 specialPlusTerm(p, 0, 8854, -1, 3, 2, r);
1517 specialPlusTerm(p, 0, 1680, -1, 2, 2, r);
1518 specialPlusTerm(p, 0, 225, -1, 1, 2, r);
1519 specialPlusTerm(p, 0, 16, -1, 0, 2, r);
1520 specialPlusTerm(p, 0, 1, 1, 120, 1, r);
1521 specialPlusTerm(p, 0, 15, 1, 119, 1, r);
1522 specialPlusTerm(p, 0, 119, 1, 118, 1, r);
1523 specialPlusTerm(p, 0, 664, 1, 117, 1, r);
1524 specialPlusTerm(p, 0, 2924, 1, 116, 1, r);
1525 specialPlusTerm(p, 0, 10813, 1, 115, 1, r);
1526 specialPlusTerm(p, 0, 34900, 1, 114, 1, r);
1527 specialPlusTerm(p, 0, 100913, 1, 113, 1, r);
1528 specialPlusTerm(p, 0, 266338, 1, 112, 1, r);
1529 specialPlusTerm(p, 0, 650658, 1, 111, 1, r);
1530 specialPlusTerm(p, 1, 487262, 1, 110, 1, r);
1531 specialPlusTerm(p, 3, 208036, 1, 109, 1, r);
1532 specialPlusTerm(p, 6, 574987, 1, 108, 1, r);
1533 specialPlusTerm(p, 12, 876702, 1, 107, 1, r);
1534 specialPlusTerm(p, 24, 210652, 1, 106, 1, r);
1535 specialPlusTerm(p, 43, 874857, 1, 105, 1, r);
1536 specialPlusTerm(p, 76, 893687, 1, 104, 1, r);
1537 specialPlusTerm(p, 130, 701986, 1, 103, 1, r);
1538 specialPlusTerm(p, 216, 8661, 1, 102, 1, r);
1539 specialPlusTerm(p, 347, 854815, 1, 101, 1, r);
1540 specialPlusTerm(p, 546, 871981, 1, 100, 1, r);
1541 specialPlusTerm(p, 840, 732790, 1, 99, 1, r);
1542 specialPlusTerm(p, 1265, 769513, 1, 98, 1, r);
1543 specialPlusTerm(p, 1868, 715733, 1, 97, 1, r);
1544 specialPlusTerm(p, 2708, 503701, 1, 96, 1, r);
1545 specialPlusTerm(p, 3858, 25899, 1, 95, 1, r);
1546 specialPlusTerm(p, 5405, 745562, 1, 94, 1, r);
1547 specialPlusTerm(p, 7457, 19331, 1, 93, 1, r);
1548 specialPlusTerm(p, 10134, 977992, 1, 92, 1, r);
1549 specialPlusTerm(p, 13580, 800674, 1, 91, 1, r);
1550 specialPlusTerm(p, 17953, 216130, 1, 90, 1, r);
1551 specialPlusTerm(p, 23427, 73737, 1, 89, 1, r);
1552 specialPlusTerm(p, 30190, 848078, 1, 88, 1, r);
1553 specialPlusTerm(p, 38442, 975195, 1, 87, 1, r);
1554 specialPlusTerm(p, 48386, 965771, 1, 86, 1, r);
1555 specialPlusTerm(p, 60225, 299589, 1, 85, 1, r);
1556 specialPlusTerm(p, 74152, 174574, 1, 84, 1, r);
1557 specialPlusTerm(p, 90345, 259476, 1, 83, 1, r);
1558 specialPlusTerm(p, 108956, 677797, 1, 82, 1, r);
1559 specialPlusTerm(p, 130103, 527156, 1, 81, 1, r);
1560 specialPlusTerm(p, 153858, 307693, 1, 80, 1, r);
1561 specialPlusTerm(p, 180239, 689955, 1, 79, 1, r);
1562 specialPlusTerm(p, 209204, 91832, 1, 78, 1, r);
1563 specialPlusTerm(p, 240638, 550997, 1, 77, 1, r);
1564 specialPlusTerm(p, 274355, 370450, 1, 76, 1, r);
1565 specialPlusTerm(p, 310088, 978041, 1, 75, 1, r);
1566 specialPlusTerm(p, 347495, 375766, 1, 74, 1, r);
1567 specialPlusTerm(p, 386154, 462530, 1, 73, 1, r);
1568 specialPlusTerm(p, 425575, 398166, 1, 72, 1, r);
1569 specialPlusTerm(p, 465205, 41801, 1, 71, 1, r);
1570 specialPlusTerm(p, 504439, 350762, 1, 70, 1, r);
1571 specialPlusTerm(p, 542637, 474944, 1, 69, 1, r);
1572 specialPlusTerm(p, 579138, 134521, 1, 68, 1, r);
1573 specialPlusTerm(p, 613277, 734909, 1, 67, 1, r);
1574 specialPlusTerm(p, 644409, 560477, 1, 66, 1, r);
1575 specialPlusTerm(p, 671923, 305201, 1, 65, 1, r);
1576 specialPlusTerm(p, 695264, 150336, 1, 64, 1, r);
1577 specialPlusTerm(p, 713950, 590364, 1, 63, 1, r);
1578 specialPlusTerm(p, 727590, 240796, 1, 62, 1, r);
1579 specialPlusTerm(p, 735892, 934219, 1, 61, 1, r);
1580 specialPlusTerm(p, 738680, 521142, 1, 60, 1, r);
1581 specialPlusTerm(p, 735892, 934219, 1, 59, 1, r);
1582 specialPlusTerm(p, 727590, 240796, 1, 58, 1, r);
1583 specialPlusTerm(p, 713950, 590364, 1, 57, 1, r);
1584 specialPlusTerm(p, 695264, 150336, 1, 56, 1, r);
1585 specialPlusTerm(p, 671923, 305201, 1, 55, 1, r);
1586 specialPlusTerm(p, 644409, 560477, 1, 54, 1, r);
1587 specialPlusTerm(p, 613277, 734909, 1, 53, 1, r);
1588 specialPlusTerm(p, 579138, 134521, 1, 52, 1, r);
1589 specialPlusTerm(p, 542637, 474944, 1, 51, 1, r);
1590 specialPlusTerm(p, 504439, 350762, 1, 50, 1, r);
1591 specialPlusTerm(p, 465205, 41801, 1, 49, 1, r);
1592 specialPlusTerm(p, 425575, 398166, 1, 48, 1, r);
1593 specialPlusTerm(p, 386154, 462530, 1, 47, 1, r);
1594 specialPlusTerm(p, 347495, 375766, 1, 46, 1, r);
1595 specialPlusTerm(p, 310088, 978041, 1, 45, 1, r);
1596 specialPlusTerm(p, 274355, 370450, 1, 44, 1, r);
1597 specialPlusTerm(p, 240638, 550997, 1, 43, 1, r);
1598 specialPlusTerm(p, 209204, 91832, 1, 42, 1, r);
1599 specialPlusTerm(p, 180239, 689955, 1, 41, 1, r);
1600 specialPlusTerm(p, 153858, 307693, 1, 40, 1, r);
1601 specialPlusTerm(p, 130103, 527156, 1, 39, 1, r);
1602 specialPlusTerm(p, 108956, 677797, 1, 38, 1, r);
1603 specialPlusTerm(p, 90345, 259476, 1, 37, 1, r);
1604 specialPlusTerm(p, 74152, 174574, 1, 36, 1, r);
1605 specialPlusTerm(p, 60225, 299589, 1, 35, 1, r);
1606 specialPlusTerm(p, 48386, 965771, 1, 34, 1, r);
1607 specialPlusTerm(p, 38442, 975195, 1, 33, 1, r);
1608 specialPlusTerm(p, 30190, 848078, 1, 32, 1, r);
1609 specialPlusTerm(p, 23427, 73737, 1, 31, 1, r);
1610 specialPlusTerm(p, 17953, 216130, 1, 30, 1, r);
1611 specialPlusTerm(p, 13580, 800674, 1, 29, 1, r);
1612 specialPlusTerm(p, 10134, 977992, 1, 28, 1, r);
1613 specialPlusTerm(p, 7457, 19331, 1, 27, 1, r);
1614 specialPlusTerm(p, 5405, 745562, 1, 26, 1, r);
1615 specialPlusTerm(p, 3858, 25899, 1, 25, 1, r);
1616 specialPlusTerm(p, 2708, 503701, 1, 24, 1, r);
1617 specialPlusTerm(p, 1868, 715733, 1, 23, 1, r);
1618 specialPlusTerm(p, 1265, 769513, 1, 22, 1, r);
1619 specialPlusTerm(p, 840, 732790, 1, 21, 1, r);
1620 specialPlusTerm(p, 546, 871981, 1, 20, 1, r);
1621 specialPlusTerm(p, 347, 854815, 1, 19, 1, r);
1622 specialPlusTerm(p, 216, 8661, 1, 18, 1, r);
1623 specialPlusTerm(p, 130, 701986, 1, 17, 1, r);
1624 specialPlusTerm(p, 76, 893687, 1, 16, 1, r);
1625 specialPlusTerm(p, 43, 874857, 1, 15, 1, r);
1626 specialPlusTerm(p, 24, 210652, 1, 14, 1, r);
1627 specialPlusTerm(p, 12, 876702, 1, 13, 1, r);
1628 specialPlusTerm(p, 6, 574987, 1, 12, 1, r);
1629 specialPlusTerm(p, 3, 208036, 1, 11, 1, r);
1630 specialPlusTerm(p, 1, 487262, 1, 10, 1, r);
1631 specialPlusTerm(p, 0, 650658, 1, 9, 1, r);
1632 specialPlusTerm(p, 0, 266338, 1, 8, 1, r);
1633 specialPlusTerm(p, 0, 100913, 1, 7, 1, r);
1634 specialPlusTerm(p, 0, 34900, 1, 6, 1, r);
1635 specialPlusTerm(p, 0, 10813, 1, 5, 1, r);
1636 specialPlusTerm(p, 0, 2924, 1, 4, 1, r);
1637 specialPlusTerm(p, 0, 664, 1, 3, 1, r);
1638 specialPlusTerm(p, 0, 119, 1, 2, 1, r);
1639 specialPlusTerm(p, 0, 15, 1, 1, 1, r);
1640 specialPlusTerm(p, 0, 1, 1, 0, 1, r);
1641 }
checkInverse(number n,const coeffs cf)1642 void checkInverse(number n, const coeffs cf)
1643 {
1644 clog << "n = "; p_Write((poly)n, cf->extRing);
1645 number n1 = n_Invers(n, cf);
1646 clog << "==> n^(-1) = "; p_Write((poly)n1, cf->extRing);
1647 number n2 = n_Mult(n, n1, cf);
1648 clog << "check: n * n^(-1) = "; p_Write((poly)n2, cf->extRing);
1649 TS_ASSERT( n_IsOne(n2, cf) );
1650 n_Delete(&n1, cf); n_Delete(&n2, cf);
1651 }
1652 /* to be used over a rational function field, only!
1653 assumes that cf represents a rational function field;
1654 uses p inside the resulting number (and not a copy of it!) */
toFractionNumber(poly p,const coeffs cf)1655 number toFractionNumber(poly p, const coeffs cf)
1656 {
1657 number n = n_Init(1, cf);
1658 fraction f = (fraction)n;
1659 p_Delete(&(f->numerator), cf->extRing);
1660 f->numerator = p;
1661 return n;
1662 }
TestArithCf(const coeffs r)1663 void TestArithCf(const coeffs r)
1664 {
1665 clog << ("TEST: Simple Arithmetics: ");
1666 clog << endl;
1667
1668 number two = n_Init(2, r);
1669
1670 number t = n_Init(1, r);
1671 n_InpAdd(t, t, r);
1672 TS_ASSERT( n_Equal(two, t, r) );
1673 n_Delete(&t, r);
1674
1675 if( getCoeffType(r) == n_Q )
1676 {
1677 number t = n_Init(1, r);
1678 n_InpAdd(t, t, r);
1679 TS_ASSERT( n_Equal(two, t, r) );
1680 n_Delete(&t, r);
1681 }
1682
1683 const int N = 66666;
1684
1685 number a = n_Init(N, r);
1686
1687 clog<< "a: "; PrintSized(a, r);
1688
1689 clog<< "two: "; PrintSized(two, r);
1690
1691 number aa0 = n_Init(N*2, r);
1692
1693 number aa = n_Add(a, a, r);
1694
1695 clog<< "aa = a + a: "; PrintSized(aa, r);
1696
1697 number aa2 = n_Mult(a, two, r);
1698
1699 clog<< "aa2 = a * 2: "; PrintSized(aa2, r);
1700
1701 number aa1 = n_Mult(two, a, r);
1702
1703 clog<< "aa1 = 2 * a: "; PrintSized(aa1, r);
1704
1705 n_Delete(&a, r);
1706 n_Delete(&two, r);
1707
1708 a = n_Sub( aa, aa1, r );
1709
1710 clog<< "a = aa - aa1: "; PrintSized(a, r);
1711
1712 TS_ASSERT( n_IsZero(a, r) );
1713
1714 n_Delete(&a, r);
1715
1716 a = n_Sub( aa, aa2, r );
1717
1718 clog<< "a = aa - aa2: "; PrintSized(a, r);
1719
1720 TS_ASSERT( n_IsZero(a, r) );
1721
1722 n_Delete(&a, r);
1723
1724 a = n_Sub( aa1, aa2, r );
1725
1726 clog<< "a = aa1 - aa2: "; PrintSized(a, r);
1727
1728 TS_ASSERT( n_IsZero(a, r) );
1729
1730 n_Delete(&a, r);
1731
1732 TS_ASSERT( n_Equal(aa, aa1, r) );
1733 TS_ASSERT( n_Equal(aa, aa2, r) );
1734 TS_ASSERT( n_Equal(aa1, aa2, r) );
1735
1736 TS_ASSERT( n_Equal(aa0, aa, r) );
1737 TS_ASSERT( n_Equal(aa0, aa1, r) );
1738 TS_ASSERT( n_Equal(aa0, aa2, r) );
1739
1740 n_Delete(&aa, r);
1741 n_Delete(&aa1, r);
1742 n_Delete(&aa2, r);
1743
1744 n_Delete(&aa0, r);
1745
1746 clog << ( " >>> TEST DONE!" );
1747 clog << endl;
1748 }
TestSumCf(const coeffs r,const unsigned long N)1749 void TestSumCf(const coeffs r, const unsigned long N)
1750 {
1751 clog << ( _2S("TEST: sum[0..") + _2S(N) + "]: ");
1752 clog << endl;
1753
1754 assume( N > 0 ); // just for now...
1755
1756 const unsigned long ssss = (N * (N+1)) / 2;
1757
1758 number sum1 = n_Init(ssss, r);
1759 clog<< "N*(N+1)/2 (int: " << ssss << "): "; PrintSized(sum1, r);
1760
1761 number s, ss, i, res;
1762
1763 s = n_Init(N , r);
1764 i = n_Init(N+1, r);
1765 n_InpMult(s, i, r);
1766 n_Delete(&i, r);
1767
1768 clog<< "N*(N+1): ("<< N*(N+1) << ")"; PrintSized(s, r);
1769
1770 i = n_Init(2, r);
1771 clog<< "2: "; PrintSized(i, r);
1772
1773 if( !n_IsZero( i, r) )
1774 {
1775 #ifdef HAVE_RINGS
1776 TS_ASSERT( n_DivBy(s, i, r) );
1777 #endif
1778
1779 res = n_Div(s, i, r);
1780
1781 clog<< "N*(N+1)/2: "; PrintSized(res, r);
1782
1783
1784 number d = n_Sub(res, sum1, r);
1785 TS_ASSERT( n_IsZeroDivisor(d, r) );
1786 n_Delete(&d, r);
1787
1788 if( n_GetChar(r) == 0 )
1789 {
1790 TS_ASSERT( n_Equal(sum1, res, r) );
1791 TS_ASSERT( n_Equal(res, sum1, r) );
1792 }
1793 } else
1794 TS_ASSERT_EQUALS( n_GetChar(r), 2);
1795
1796
1797 n_Delete(&s, r); n_Delete(&i, r);
1798
1799 n_Delete(&sum1, r); n_Delete(&res, r);
1800
1801
1802 s = n_Init(0 , r);
1803 ss = n_Init(0 , r);
1804 for( int k = N; k >= 0; k-- )
1805 {
1806 i = n_Init(k, r);
1807 n_InpAdd(s, i, r); // s += i
1808
1809 i = n_InpNeg(i, r);
1810 n_InpAdd(ss, i, r); // ss -= i
1811
1812 n_Delete(&i, r);
1813 }
1814 clog<< "ss: "; PrintSized(ss, r);
1815
1816 ss = n_InpNeg(ss, r); // ss = -ss
1817
1818 clog<< "real sum : "; PrintSized(s, r);
1819 clog<< "real sum(--): "; PrintSized(ss, r);
1820
1821 TS_ASSERT( n_Equal(s, ss, r) );
1822 TS_ASSERT( n_Equal(ss, s, r) );
1823
1824 n_Delete(&s, r);
1825 n_Delete(&ss, r);
1826
1827 clog << ( " >>> TEST DONE!" );
1828 clog << endl;
1829
1830 }
1831 public:
test_Z13_t()1832 void test_Z13_t()
1833 {
1834 clog << "Creating Z/13[t]: " << endl;
1835
1836 char* n[] = {(char*)"t"};
1837 ring r = rDefault( 13, 1, n);
1838 TS_ASSERT_DIFFERS( r, NULLp );
1839
1840 PrintRing(r);
1841
1842 TS_ASSERT( rField_is_Domain(r) );
1843 TS_ASSERT( !rField_is_Q(r) );
1844
1845 TS_ASSERT( rField_is_Zp(r) );
1846 TS_ASSERT( !rField_is_Zp(r, 11) );
1847 TS_ASSERT( rField_is_Zp(r, 13) );
1848
1849 TS_ASSERT_EQUALS( rVar(r), 1);
1850
1851 Test(r);
1852
1853 rDelete(r);
1854 }
1855
test_QQ_t()1856 void test_QQ_t()
1857 {
1858 clog << "Creating Q[s]: " << endl;
1859
1860 char* n[] = {(char*)"s"};
1861 ring r = rDefault( 0, 1, n);
1862 TS_ASSERT_DIFFERS( r, NULLp );
1863
1864 PrintRing(r);
1865
1866 TS_ASSERT( rField_is_Domain(r) );
1867 TS_ASSERT( rField_is_Q(r) );
1868
1869 TS_ASSERT( !rField_is_Zp(r) );
1870 TS_ASSERT( !rField_is_Zp(r, 11) );
1871
1872 TS_ASSERT_EQUALS( rVar(r), 1);
1873
1874 Test(r);
1875
1876 rDelete(r);
1877 }
1878
test_Z11_x_y_z()1879 void test_Z11_x_y_z()
1880 {
1881 clog << "Creating Z/11[x, y, z]: " << endl;
1882
1883 char* n[] = {(char*)"x", (char*)"y", (char*)"z"};
1884 ring r = rDefault( 11, 3, n);
1885 TS_ASSERT_DIFFERS( r, NULLp );
1886
1887 PrintRing(r);
1888
1889 TS_ASSERT( rField_is_Domain(r) );
1890 TS_ASSERT( !rField_is_Q(r) );
1891
1892 TS_ASSERT( rField_is_Zp(r) );
1893 TS_ASSERT( rField_is_Zp(r, 11) );
1894 TS_ASSERT( !rField_is_Zp(r, 13) );
1895
1896 TS_ASSERT_EQUALS( rVar(r), 3);
1897
1898 Test(r);
1899
1900 rDelete(r);
1901 }
test_QQ_x_y_z()1902 void test_QQ_x_y_z()
1903 {
1904 clog << "Creating QQ[x, y, z, u]: " << endl;
1905
1906 char* n[] = {(char*)"x", (char*)"y", (char*)"z", (char*)"u"};
1907 ring r = rDefault( 0, 4, n);
1908 TS_ASSERT_DIFFERS( r, NULLp );
1909
1910 PrintRing(r);
1911
1912 TS_ASSERT( rField_is_Domain(r) );
1913 TS_ASSERT( rField_is_Q(r) );
1914
1915 TS_ASSERT( !rField_is_Zp(r) );
1916 TS_ASSERT( !rField_is_Zp(r, 11) );
1917
1918 TS_ASSERT_EQUALS( rVar(r), 4);
1919
1920 Test(r);
1921
1922 rDelete(r);
1923 }
1924
1925
test_Z13_t_GF()1926 void test_Z13_t_GF()
1927 {
1928 clog << "Creating GF[t]: " << endl;
1929
1930 char* n[] = {(char*)"t"};
1931
1932 GFInfo param;
1933
1934 param.GFChar= 5;
1935 param.GFDegree= 2;
1936 param.GFPar_name= (const char*)"Q";
1937
1938 const coeffs cf = nInitChar( n_GF, ¶m );
1939
1940 if( cf == NULL )
1941 TS_FAIL("Could not get needed coeff. domain");
1942
1943 TS_ASSERT_DIFFERS( cf, NULLp );
1944
1945 ring r = rDefault( cf, 1, n); // now cf belongs to r!
1946 TS_ASSERT_DIFFERS( r, NULLp );
1947
1948 PrintRing(r);
1949
1950 TS_ASSERT( rField_is_Domain(r) );
1951 TS_ASSERT( !rField_is_Q(r) );
1952
1953 TS_ASSERT( !rField_is_Zp(r) );
1954 TS_ASSERT( !rField_is_Zp(r, 11) );
1955 TS_ASSERT( !rField_is_Zp(r, 13) );
1956 TS_ASSERT( rField_is_GF(r) );
1957
1958 TS_ASSERT( rField_is_GF(r, 5) );
1959 TS_ASSERT( !rField_is_GF(r, 25) );
1960
1961 TS_ASSERT_EQUALS( rVar(r), 1);
1962
1963 Test(r);
1964
1965 rDelete(r); // kills 'cf' as well!
1966 }
1967
test_Q_Ext_a()1968 void test_Q_Ext_a()
1969 {
1970 clog << "Start by creating Q[a]..." << endl;
1971
1972 char* n[] = {(char*)"a"};
1973 ring r = rDefault( 0, 1, n); // Q[a]
1974 TS_ASSERT_DIFFERS( r, NULLp );
1975
1976 PrintRing(r);
1977
1978 TS_ASSERT( rField_is_Domain(r) );
1979 TS_ASSERT( rField_is_Q(r) );
1980
1981 TS_ASSERT( !rField_is_Zp(r) );
1982 TS_ASSERT( !rField_is_Zp(r, 11) );
1983
1984 TS_ASSERT_EQUALS( rVar(r), 1);
1985
1986 poly minPoly = p_ISet(1, r); // minPoly = 1
1987 p_SetExp(minPoly, 1, 2, r); p_Setm(minPoly, r); // minPoly = a^2
1988 minPoly = p_Add_q(minPoly, p_ISet(1, r), r); // minPoly = a^2 + 1
1989 ideal minIdeal = idInit(1); // minIdeal = < 0 >
1990 minIdeal->m[0] = minPoly; // minIdeal = < a^2 + 1 >
1991
1992 n_coeffType type = nRegister(n_algExt, naInitChar);
1993 TS_ASSERT(type == n_algExt);
1994
1995 r->qideal = minIdeal;
1996 AlgExtInfo extParam;
1997 extParam.r = r;
1998
1999 clog << "Next create the extension field Q[a]/<a2+1>..." << endl;
2000
2001 const coeffs cf = nInitChar(type, &extParam); // Q[a]/<a2+1>
2002
2003 if( cf == NULL )
2004 TS_FAIL("Could not get needed coeff. domain");
2005
2006 TS_ASSERT_DIFFERS( cf->cfCoeffWrite, NULLp );
2007
2008 if( cf->cfCoeffWrite != NULL )
2009 {
2010 clog << "Coeff-domain: " << endl;
2011 n_CoeffWrite(cf); PrintLn();
2012 }
2013
2014 TS_ASSERT( nCoeff_is_algExt(cf) );
2015 TS_ASSERT( !nCoeff_is_transExt(cf) );
2016
2017 // some tests for the coefficient field represented by cf:
2018 TestArithCf(cf);
2019 TestSumCf(cf, 10);
2020 TestSumCf(cf, 100);
2021 TestSumCf(cf, 101);
2022 TestSumCf(cf, 1001);
2023 TestSumCf(cf, 2000);
2024
2025 clog << "Finally create the polynomial ring (Q[a]/<a2+1>)[x, y]..."
2026 << endl;
2027
2028 char* m[] = {(char*)"x", (char*)"y"};
2029 ring s = rDefault(cf, 2, m); // (Q[a]/<a2+1>)[x, y]
2030 TS_ASSERT_DIFFERS(s, NULLp);
2031
2032 PrintRing(s);
2033
2034 TS_ASSERT( rField_is_Domain(s) );
2035 TS_ASSERT( !rField_is_Q(s) );
2036 TS_ASSERT( !rField_is_Zp(s) );
2037 TS_ASSERT( !rField_is_Zp(s, 11) );
2038 TS_ASSERT( !rField_is_Zp(s, 13) );
2039 TS_ASSERT( !rField_is_GF(s) );
2040 TS_ASSERT( (s->cf->extRing!=NULL) );
2041 TS_ASSERT( !rField_is_GF(s, 25) );
2042 TS_ASSERT_EQUALS(rVar(s), 2);
2043
2044 Test(s);
2045
2046 clog << endl
2047 << "Now let's compute some inverses in Q[a]/<a^2+1>..."
2048 << endl;
2049
2050 poly u;
2051 u = NULL; plusTerm(u, 1, 1, 1, cf->extRing);
2052 plusTerm(u, 1, 1, 0, cf->extRing); // a + 1
2053 checkInverse((number)u, cf); p_Delete(&u, cf->extRing);
2054 u = NULL; plusTerm(u, 1, 1, 1, cf->extRing);
2055 plusTerm(u, -1, 1, 0, cf->extRing); // a - 1
2056 checkInverse((number)u, cf); p_Delete(&u, cf->extRing);
2057 u = NULL; plusTerm(u, 1, 1, 1, cf->extRing);
2058 plusTerm(u, 5, 1, 0, cf->extRing); // a + 5
2059 checkInverse((number)u, cf); p_Delete(&u, cf->extRing);
2060 u = NULL; plusTerm(u, 1, 1, 1, cf->extRing);
2061 plusTerm(u, -5, 1, 0, cf->extRing); // a - 5
2062 checkInverse((number)u, cf); p_Delete(&u, cf->extRing);
2063 u = NULL; plusTerm(u, 17, 1, 1, cf->extRing);
2064 plusTerm(u, 5, 1, 0, cf->extRing); // 17a + 5
2065 checkInverse((number)u, cf); p_Delete(&u, cf->extRing);
2066
2067 rDelete(s); // kills 'cf' and 'r' as well
2068 }
test_Q_Ext_b()2069 void test_Q_Ext_b()
2070 {
2071 clog << "Start by creating Q[b]..." << endl;
2072
2073 char* n[] = {(char*)"b"};
2074 ring r = rDefault( 0, 1, n); // Q[b]
2075 TS_ASSERT_DIFFERS( r, NULLp );
2076
2077 PrintRing(r);
2078
2079 TS_ASSERT( rField_is_Domain(r) );
2080 TS_ASSERT( rField_is_Q(r) );
2081
2082 TS_ASSERT( !rField_is_Zp(r) );
2083 TS_ASSERT( !rField_is_Zp(r, 11) );
2084
2085 TS_ASSERT_EQUALS( rVar(r), 1);
2086
2087 poly minPoly = p_ISet(1, r); // minPoly = 1
2088 p_SetExp(minPoly, 1, 7, r); p_Setm(minPoly, r); // minPoly = b^7
2089 minPoly = p_Add_q(minPoly, p_ISet(17, r), r); // minPoly = b^7 + 17
2090 ideal minIdeal = idInit(1); // minIdeal = < 0 >
2091 minIdeal->m[0] = minPoly; // minIdeal = < b^7 + 17 >
2092
2093 n_coeffType type = nRegister(n_algExt, naInitChar);
2094 TS_ASSERT(type == n_algExt);
2095
2096 r->qideal = minIdeal;
2097 AlgExtInfo extParam;
2098 extParam.r = r;
2099
2100 clog << "Next create the extension field Q[b]/<b^7+17>..." << endl;
2101
2102 const coeffs cf = nInitChar(type, &extParam); // Q[b]/<b^7+17>
2103
2104 if( cf == NULL )
2105 TS_FAIL("Could not get needed coeff. domain");
2106
2107 TS_ASSERT_DIFFERS( cf->cfCoeffWrite, NULLp );
2108
2109 if( cf->cfCoeffWrite != NULL )
2110 {
2111 clog << "Coeff-domain: " << endl;
2112 n_CoeffWrite(cf); PrintLn();
2113 }
2114
2115 TS_ASSERT( nCoeff_is_algExt(cf) );
2116 TS_ASSERT( !nCoeff_is_transExt(cf) );
2117
2118 // some tests for the coefficient field represented by cf:
2119 TestArithCf(cf);
2120 TestSumCf(cf, 10);
2121 TestSumCf(cf, 100);
2122 TestSumCf(cf, 101);
2123 TestSumCf(cf, 1001);
2124 TestSumCf(cf, 9000);
2125
2126 clog << "Finally create the polynomial ring (Q[b]/<b^7+17>)[u, v, w]..."
2127 << endl;
2128
2129 char* m[] = {(char*)"u", (char*)"v", (char*)"w"};
2130 ring s = rDefault(cf, 3, m); // (Q[b]/<b^7+17>)[u, v, w]
2131 TS_ASSERT_DIFFERS(s, NULLp);
2132
2133 PrintRing(s);
2134
2135 TS_ASSERT( rField_is_Domain(s) );
2136 TS_ASSERT( !rField_is_Q(s) );
2137 TS_ASSERT( !rField_is_Zp(s) );
2138 TS_ASSERT( !rField_is_Zp(s, 11) );
2139 TS_ASSERT( !rField_is_Zp(s, 13) );
2140 TS_ASSERT( !rField_is_GF(s) );
2141 TS_ASSERT( (s->cf->extRing!=NULL) );
2142 TS_ASSERT( !rField_is_GF(s, 25) );
2143 TS_ASSERT_EQUALS(rVar(s), 3);
2144
2145 Test(s);
2146
2147 clog << endl
2148 << "Now let's compute some inverses in Q[b]/<b^7+17>..."
2149 << endl;
2150
2151 poly u;
2152 u = NULL; plusTerm(u, 1, 1, 2, cf->extRing);
2153 plusTerm(u, 33, 1, 0, cf->extRing); // b^2 + 33
2154 checkInverse((number)u, cf); p_Delete(&u, cf->extRing);
2155 u = NULL; plusTerm(u, 1, 1, 5, cf->extRing);
2156 plusTerm(u, -137, 1, 0, cf->extRing); // b^5 - 137
2157 checkInverse((number)u, cf); p_Delete(&u, cf->extRing);
2158
2159 clog << endl
2160 << "Now let's check a gcd computation in Q[b]..."
2161 << endl;
2162
2163 poly v;
2164 v = NULL; plusTerm(v, 1, 1, 2, cf->extRing);
2165 plusTerm(v, 7, 1, 1, cf->extRing);
2166 plusTerm(v, 1, 1, 0, cf->extRing); // b^2 + 7b + 1
2167 number w = n_Mult((number)v, (number)v, cf); // (b^2 + 7b + 1)^2
2168 number y = n_Mult((number)v, (number)w, cf); // (b^2 + 7b + 1)^3
2169 p_Delete(&v, cf->extRing);
2170 v = NULL; plusTerm(v, 2, 1, 2, cf->extRing);
2171 plusTerm(v, -61, 1, 1, cf->extRing); // 2b^2 - 61b
2172 number z = n_Mult((number)w,
2173 (number)v, cf); // (b^2 + 7b + 1)^2 * (2b^2 - 61b)
2174 p_Delete(&v, cf->extRing);
2175
2176 clog << "z = "; p_Write((poly)z, cf->extRing);
2177 clog << "y = "; p_Write((poly)y, cf->extRing);
2178 number theGcd = n_Gcd(z, y, cf); // should yield w = (b^2 + 7b + 1)^2
2179 clog << "gcd(z, y) = "; p_Write((poly)theGcd, cf->extRing);
2180
2181 v = (poly)n_Sub(theGcd, w, cf);
2182 // TS_ASSERT( v == NULL );
2183 p_Delete(&v, cf->extRing);
2184
2185 clog << endl
2186 << "Now let's check an ext_gcd computation in Q[b]..."
2187 << endl;
2188
2189 poly zFactor; poly yFactor;
2190 poly ppp = p_ExtGcd((poly)z, zFactor, (poly)y, yFactor, cf->extRing);
2191 v = (poly)n_Sub(theGcd, (number)ppp, cf);
2192 // TS_ASSERT( v == NULL );
2193 p_Delete(&v, cf->extRing);
2194 clog << "z = "; p_Write((poly)z, cf->extRing);
2195 clog << "zFactor = "; p_Write(zFactor, cf->extRing);
2196 clog << "y = "; p_Write((poly)y, cf->extRing);
2197 clog << "yFactor = "; p_Write((poly)yFactor, cf->extRing);
2198 number v1 = n_Mult(z, (number)zFactor, cf);
2199 number v2 = n_Mult(y, (number)yFactor, cf);
2200 number v3 = n_Add(v1, v2, cf);
2201 clog << "z * zFactor + y * yFactor = "; p_Write((poly)v3, cf->extRing);
2202 clog << "gcd(z, y) = "; p_Write(ppp, cf->extRing);
2203 number v4 = n_Sub(v3, w, cf);
2204 TS_ASSERT( v4 == NULL );
2205
2206 p_Delete(&ppp, cf->extRing); p_Delete(&zFactor, cf->extRing);
2207 p_Delete(&yFactor, cf->extRing);
2208 n_Delete(&z, cf); n_Delete(&y, cf); n_Delete(&w, cf);
2209 n_Delete(&theGcd, cf); p_Delete(&v, cf->extRing); n_Delete(&v1, cf);
2210 n_Delete(&v2, cf); n_Delete(&v3, cf); n_Delete(&v4, cf);
2211
2212 rDelete(s); // kills 'cf' and 'r' as well
2213 }
test_Z_17_Ext_a()2214 void test_Z_17_Ext_a()
2215 {
2216 clog << "Start by creating Z_17[a]..." << endl;
2217
2218 char* n[] = {(char*)"a"};
2219 ring r = rDefault( 17, 1, n); // Z/17Z[a]
2220 TS_ASSERT_DIFFERS( r, NULLp );
2221
2222 PrintRing(r);
2223
2224 TS_ASSERT( rField_is_Domain(r) );
2225 TS_ASSERT( !rField_is_Q(r) );
2226
2227 TS_ASSERT( rField_is_Zp(r) );
2228 TS_ASSERT( rField_is_Zp(r, 17) );
2229
2230 TS_ASSERT_EQUALS( rVar(r), 1);
2231
2232 poly minPoly = p_ISet(1, r); // minPoly = 1
2233 p_SetExp(minPoly, 1, 2, r); p_Setm(minPoly, r); // minPoly = a^2
2234 minPoly = p_Add_q(minPoly, p_ISet(3, r), r); // minPoly = a^2 + 3
2235 ideal minIdeal = idInit(1); // minIdeal = < 0 >
2236 minIdeal->m[0] = minPoly; // minIdeal = < a^2 + 3 >
2237
2238 n_coeffType type = nRegister(n_algExt, naInitChar);
2239 TS_ASSERT(type == n_algExt);
2240
2241 r->qideal = minIdeal;
2242 AlgExtInfo extParam;
2243 extParam.r = r;
2244
2245 clog << "Next create the extension field Z_17[a]/<a^2+3>..." << endl;
2246
2247 const coeffs cf = nInitChar(type, &extParam); // Z_17[a]/<a^2+3>
2248
2249 if( cf == NULL )
2250 TS_FAIL("Could not get needed coeff. domain");
2251
2252 TS_ASSERT_DIFFERS( cf->cfCoeffWrite, NULLp );
2253
2254 if( cf->cfCoeffWrite != NULL )
2255 {
2256 clog << "Coeff-domain: " << endl;
2257 n_CoeffWrite(cf); PrintLn();
2258 }
2259
2260 TS_ASSERT( nCoeff_is_algExt(cf) );
2261 TS_ASSERT( !nCoeff_is_transExt(cf) );
2262
2263 // some tests for the coefficient field represented by cf:
2264 TestArithCf(cf);
2265 TestSumCf(cf, 10);
2266 TestSumCf(cf, 100);
2267 TestSumCf(cf, 101);
2268 TestSumCf(cf, 1001);
2269 TestSumCf(cf, 9000);
2270
2271 clog << "Finally create the polynomial ring (Z_17[a]/<a^2+3>)[u, v, w]..."
2272 << endl;
2273
2274 char* m[] = {(char*)"u", (char*)"v", (char*)"w"};
2275 ring s = rDefault(cf, 3, m); // (Z_17[a]/<a^2+3>)[u, v, w]
2276 TS_ASSERT_DIFFERS(s, NULLp);
2277
2278 PrintRing(s);
2279
2280 TS_ASSERT( rField_is_Domain(s) );
2281 TS_ASSERT( !rField_is_Q(s) );
2282 TS_ASSERT( !rField_is_Zp(s) );
2283 TS_ASSERT( !rField_is_Zp(s, 11) );
2284 TS_ASSERT( !rField_is_Zp(s, 17) );
2285 TS_ASSERT( !rField_is_GF(s) );
2286 TS_ASSERT( (s->cf->extRing!=NULL) );
2287 TS_ASSERT( !rField_is_GF(s, 25) );
2288 TS_ASSERT_EQUALS(rVar(s), 3);
2289
2290 Test(s);
2291
2292 rDelete(s); // kills 'cf' and 'r' as well
2293 }
test_Q_Ext_s_t()2294 void test_Q_Ext_s_t()
2295 {
2296 clog << "Start by creating Q[s, t]..." << endl;
2297
2298 char* n[] = {(char*)"s", (char*)"t"};
2299 ring r = rDefault( 0, 2, n); // Q[s, t]
2300 TS_ASSERT_DIFFERS( r, NULLp );
2301
2302 PrintRing(r);
2303
2304 TS_ASSERT( rField_is_Domain(r) );
2305 TS_ASSERT( rField_is_Q(r) );
2306
2307 TS_ASSERT( !rField_is_Zp(r) );
2308 TS_ASSERT( !rField_is_Zp(r, 17) );
2309
2310 TS_ASSERT_EQUALS( rVar(r), 2);
2311
2312 n_coeffType type = nRegister(n_transExt, ntInitChar);
2313 TS_ASSERT(type == n_transExt);
2314
2315 TransExtInfo extParam;
2316 extParam.r = r;
2317
2318 clog << "Next create the rational function field Q(s, t)..." << endl;
2319
2320 const coeffs cf = nInitChar(type, &extParam); // Q(s, t)
2321
2322 if( cf == NULL )
2323 TS_FAIL("Could not get needed coeff. domain");
2324
2325 TS_ASSERT_DIFFERS( cf->cfCoeffWrite, NULLp );
2326
2327 if( cf->cfCoeffWrite != NULL )
2328 {
2329 clog << "Coeff-domain: " << endl;
2330 n_CoeffWrite(cf); PrintLn();
2331 }
2332
2333 TS_ASSERT( !nCoeff_is_algExt(cf) );
2334 TS_ASSERT( nCoeff_is_transExt(cf) );
2335
2336 // some tests for the coefficient field represented by cf:
2337 TestArithCf(cf);
2338 TestSumCf(cf, 10);
2339 TestSumCf(cf, 100);
2340 TestSumCf(cf, 101);
2341 TestSumCf(cf, 1001);
2342 TestSumCf(cf, 9000);
2343
2344 clog << "Finally create the polynomial ring Q(s, t)[x, y, z]..."
2345 << endl;
2346
2347 char* m[] = {(char*)"x", (char*)"y", (char*)"z"};
2348 ring s = rDefault(cf, 3, m); // Q(s, t)[x, y, z]
2349 TS_ASSERT_DIFFERS(s, NULLp);
2350
2351 PrintRing(s);
2352
2353 TS_ASSERT( rField_is_Domain(s) );
2354 TS_ASSERT( !rField_is_Q(s) );
2355 TS_ASSERT( !rField_is_Zp(s) );
2356 TS_ASSERT( !rField_is_Zp(s, 11) );
2357 TS_ASSERT( !rField_is_Zp(s, 17) );
2358 TS_ASSERT( !rField_is_GF(s) );
2359 TS_ASSERT( (s->cf->extRing!=NULL) );
2360 TS_ASSERT( !rField_is_GF(s, 25) );
2361 TS_ASSERT_EQUALS(rVar(s), 3);
2362
2363 Test(s);
2364
2365 /* some special tests: */
2366 poly v1 = NULL;
2367 plusTerm(v1, 1, 1, 1, cf->extRing); // s
2368 plusTerm(v1, 1, 1, 0, cf->extRing); // s + 1
2369 poly v2 = NULL;
2370 plusTerm(v2, 1, 1, 1, cf->extRing); // s
2371 plusTerm(v2, 2, 2, 1, cf->extRing); // s + 2t
2372 poly v = p_Mult_q(v1, v2, cf->extRing); // (s + 1) * (s + 2t)
2373 number v_n = toFractionNumber(v, cf);
2374 PrintSized(v_n, cf);
2375 poly w1 = NULL;
2376 plusTerm(w1, 1, 1, 1, cf->extRing); // s
2377 plusTerm(w1, 1, 1, 0, cf->extRing); // s + 1
2378 poly w2 = NULL;
2379 plusTerm(w2, 3, 1, 1, cf->extRing); // 3s
2380 plusTerm(w2, -7, 2, 1, cf->extRing); // 3s - 7t
2381 poly w = p_Mult_q(w1, w2, cf->extRing); // (s + 1) * (3s - 7t)
2382 number w_n = toFractionNumber(w, cf);
2383 PrintSized(w_n, cf);
2384 number vOverW_n = n_Div(v_n, w_n, cf);
2385 PrintSized(vOverW_n, cf);
2386 number wOverV_n = n_Invers(vOverW_n, cf);
2387 PrintSized(wOverV_n, cf);
2388 number prod = n_Mult(vOverW_n, wOverV_n, cf);
2389 PrintSized(prod, cf);
2390 number tmp; number nn = n_Copy(vOverW_n, cf);
2391 for (int i = 1; i <= 6; i++)
2392 {
2393 tmp = n_Div(nn, v_n, cf);
2394 n_Delete(&nn, cf);
2395 nn = tmp;
2396 clog << i << ". "; PrintSized(nn, cf);
2397 }
2398
2399 n_Delete(&prod, cf); n_Delete(&nn, cf);
2400 n_Delete(&v_n, cf); n_Delete(&w_n, cf);
2401 n_Delete(&vOverW_n, cf); n_Delete(&wOverV_n, cf);
2402
2403 rDelete(s); // kills 'cf' and 'r' as well
2404 }
test_Q_Ext_Performance()2405 void test_Q_Ext_Performance()
2406 {
2407 clog << "Start by creating Q[q]..." << endl;
2408
2409 char* n[] = {(char*)"q"};
2410 ring r = rDefault( 0, 1, n); // Q[q]
2411 r->order[0] = ringorder_dp;
2412 TS_ASSERT_DIFFERS( r, NULLp );
2413
2414 PrintRing(r);
2415
2416 TS_ASSERT( rField_is_Domain(r) );
2417 TS_ASSERT( rField_is_Q(r) );
2418
2419 TS_ASSERT( !rField_is_Zp(r) );
2420 TS_ASSERT( !rField_is_Zp(r, 17) );
2421
2422 TS_ASSERT_EQUALS( rVar(r), 1);
2423
2424 n_coeffType type = nRegister(n_transExt, ntInitChar);
2425 TS_ASSERT(type == n_transExt);
2426
2427 TransExtInfo extParam;
2428 extParam.r = r;
2429
2430 clog << "Next create the rational function field Q(q)..." << endl;
2431
2432 const coeffs cf = nInitChar(type, &extParam); // Q(q)
2433
2434 if( cf == NULL )
2435 TS_FAIL("Could not get needed coeff. domain");
2436
2437 TS_ASSERT_DIFFERS( cf->cfCoeffWrite, NULLp );
2438
2439 if( cf->cfCoeffWrite != NULL )
2440 {
2441 clog << "Coeff-domain: " << endl;
2442 n_CoeffWrite(cf); PrintLn();
2443 }
2444
2445 TS_ASSERT( !nCoeff_is_algExt(cf) );
2446 TS_ASSERT( nCoeff_is_transExt(cf) );
2447
2448 // some tests for the coefficient field represented by cf:
2449 TestArithCf(cf);
2450 TestSumCf(cf, 10);
2451 TestSumCf(cf, 100);
2452 TestSumCf(cf, 101);
2453 TestSumCf(cf, 1001);
2454 TestSumCf(cf, 9000);
2455
2456 clog << "Finally create the polynomial ring Q(q)[t]..."
2457 << endl;
2458
2459 char* m[] = {(char*)"t"};
2460 ring s = rDefault(cf, 1, m); // Q(q)[t]
2461 s->order[0] = ringorder_dp;
2462 TS_ASSERT_DIFFERS(s, NULLp);
2463
2464 PrintRing(s);
2465
2466 TS_ASSERT( rField_is_Domain(s) );
2467 TS_ASSERT( !rField_is_Q(s) );
2468 TS_ASSERT( !rField_is_Zp(s) );
2469 TS_ASSERT( !rField_is_Zp(s, 11) );
2470 TS_ASSERT( !rField_is_Zp(s, 17) );
2471 TS_ASSERT( !rField_is_GF(s) );
2472 TS_ASSERT( (s->cf->extRing!=NULL) );
2473 TS_ASSERT( !rField_is_GF(s, 25) );
2474 TS_ASSERT_EQUALS(rVar(s), 1);
2475
2476 Test(s);
2477
2478 /* a special performance test: */
2479 poly entry = NULL;
2480 for (int ti = 0; ti <= 20; ti++)
2481 {
2482 for (int qi = 0; qi <= 100; qi++)
2483 {
2484 int c = rand() % 1000000;
2485 poly qterm = p_ISet(c, r); p_SetExp(qterm, 1, qi, r);
2486 p_Setm(qterm, r);
2487 number qtermAsN = toFractionNumber(qterm, cf);
2488 poly tterm = p_ISet(1, s); p_SetExp(tterm, 1, ti, s);
2489 p_Setm(tterm, r); p_SetCoeff(tterm, qtermAsN, s);
2490 entry = p_Add_q(entry, tterm, s);
2491 }
2492 }
2493 p_Write(entry, s);
2494 poly qfactor = p_ISet(1, r); p_SetExp(qfactor, 1, 66, r);
2495 p_Setm(qfactor, r); /* q^66 */
2496 number qfactorAsN = toFractionNumber(qfactor, cf);
2497 number uuu = n_Invers(qfactorAsN, cf); /* 1 / q^66 */
2498 poly factor = p_ISet(1, s); p_SetCoeff(factor, uuu, s); /* 1 / q^66 */
2499 p_Write(factor, s);
2500 clog << "starting multiplication..." << endl;
2501 poly theProduct = p_Mult_q(entry, factor, s);
2502 p_Write(theProduct, s);
2503 clog << "...ending multiplication" << endl;
2504 n_Delete(&qfactorAsN, cf); p_Delete(&theProduct, s);
2505
2506 /* a very special performance test: */
2507 specialPoly(entry, s);
2508 p_Write(entry, s);
2509 qfactor = p_ISet(1, r); p_SetExp(qfactor, 1, 66, r);
2510 p_Setm(qfactor, r); /* q^66 */
2511 qfactorAsN = toFractionNumber(qfactor, cf);
2512 uuu = n_Invers(qfactorAsN, cf); /* 1 / q^66 */
2513 factor = p_ISet(1, s); p_SetCoeff(factor, uuu, s); /* 1 / q^66 */
2514 p_Write(factor, s);
2515 clog << "starting very special multiplication..." << endl;
2516 /* The following multiplication + output of the product is very slow
2517 in the svn/trunk SINGULAR version; see trac ticket #308.
2518 Here, in the Spielwiese, the result is instantaneous. */
2519 theProduct = p_Mult_q(entry, factor, s);
2520 p_Write(theProduct, s);
2521 clog << "...ending very special multiplication" << endl;
2522 n_Delete(&qfactorAsN, cf); p_Delete(&theProduct, s);
2523
2524 rDelete(s); // kills 'cf' and 'r' as well
2525 }
test_Q_Ext_s_t_NestedFractions()2526 void test_Q_Ext_s_t_NestedFractions()
2527 {
2528 clog << "Start by creating Q[s, t]..." << endl;
2529
2530 char* n[] = {(char*)"s", (char*)"t"};
2531 ring r = rDefault( 0, 2, n); // Q[s, t]
2532 TS_ASSERT_DIFFERS( r, NULLp );
2533
2534 PrintRing(r);
2535
2536 TS_ASSERT( rField_is_Domain(r) );
2537 TS_ASSERT( rField_is_Q(r) );
2538
2539 TS_ASSERT( !rField_is_Zp(r) );
2540 TS_ASSERT( !rField_is_Zp(r, 17) );
2541
2542 TS_ASSERT_EQUALS( rVar(r), 2);
2543
2544 n_coeffType type = nRegister(n_transExt, ntInitChar);
2545 TS_ASSERT(type == n_transExt);
2546
2547 TransExtInfo extParam;
2548 extParam.r = r;
2549
2550 clog << "Next create the rational function field Q(s, t)..." << endl;
2551
2552 const coeffs cf = nInitChar(type, &extParam); // Q(s, t)
2553
2554 if( cf == NULL )
2555 TS_FAIL("Could not get needed coeff. domain");
2556
2557 TS_ASSERT_DIFFERS( cf->cfCoeffWrite, NULLp );
2558
2559 if( cf->cfCoeffWrite != NULL )
2560 {
2561 clog << "Coeff-domain: " << endl;
2562 n_CoeffWrite(cf); PrintLn();
2563 }
2564
2565 TS_ASSERT( !nCoeff_is_algExt(cf) );
2566 TS_ASSERT( nCoeff_is_transExt(cf) );
2567
2568 clog << "Finally create the polynomial ring Q(s, t)[x, y, z]..."
2569 << endl;
2570
2571 char* m[] = {(char*)"x", (char*)"y", (char*)"z"};
2572 ring s = rDefault(cf, 3, m); // Q(s, t)[x, y, z]
2573 TS_ASSERT_DIFFERS(s, NULLp);
2574
2575 PrintRing(s);
2576
2577 TS_ASSERT( rField_is_Domain(s) );
2578 TS_ASSERT( !rField_is_Q(s) );
2579 TS_ASSERT( !rField_is_Zp(s) );
2580 TS_ASSERT( !rField_is_Zp(s, 11) );
2581 TS_ASSERT( !rField_is_Zp(s, 17) );
2582 TS_ASSERT( !rField_is_GF(s) );
2583 TS_ASSERT( (s->cf->extRing!=NULL) );
2584 TS_ASSERT( !rField_is_GF(s, 25) );
2585 TS_ASSERT_EQUALS(rVar(s), 3);
2586
2587 /* test 1 for nested fractions, i.e. fractional coefficients: */
2588 poly v1 = NULL;
2589 plusTermOverQ(v1, 21, 2, 1, 1, cf->extRing); // 21/2*s
2590 plusTermOverQ(v1, 14, 3, 1, 0, cf->extRing); // 21/2*s + 14/3
2591 number v1_n = toFractionNumber(v1, cf);
2592 PrintSized(v1_n, cf);
2593 poly v2 = NULL;
2594 plusTermOverQ(v2, 7, 5, 1, 1, cf->extRing); // 7/5*s
2595 plusTermOverQ(v2, -49, 6, 2, 1, cf->extRing); // 7/5*s - 49/6*t
2596 number v2_n = toFractionNumber(v2, cf);
2597 PrintSized(v2_n, cf);
2598 number v3_n = n_Div(v1_n, v2_n, cf); // (45*s + 20) / (6s - 35*t)
2599 PrintSized(v3_n, cf);
2600 n_Delete(&v1_n, cf); n_Delete(&v2_n, cf); n_Delete(&v3_n, cf);
2601
2602 /* test 2 for nested fractions, i.e. fractional coefficients: */
2603 v1 = NULL;
2604 plusTermOverQ(v1, 1, 2, 1, 1, cf->extRing); // 1/2*s
2605 plusTermOverQ(v1, 1, 1, 1, 0, cf->extRing); // 1/2*s + 1
2606 v2 = NULL;
2607 plusTermOverQ(v2, 1, 1, 1, 1, cf->extRing); // s
2608 plusTermOverQ(v2, 2, 3, 2, 1, cf->extRing); // s + 2/3*t
2609 poly v3 = p_Mult_q(v1, v2, cf->extRing); // (1/2*s + 1) * (s + 2/3*t)
2610 number v_n = toFractionNumber(v3, cf);
2611 PrintSized(v_n, cf);
2612 poly w1 = NULL;
2613 plusTermOverQ(w1, 1, 2, 1, 1, cf->extRing); // 1/2*s
2614 plusTermOverQ(w1, 1, 1, 1, 0, cf->extRing); // 1/2*s + 1
2615 poly w2 = NULL;
2616 plusTermOverQ(w2, -7, 5, 1, 0, cf->extRing); // -7/5
2617 poly w3 = p_Mult_q(w1, w2, cf->extRing); // (1/2*s + 1) * (-7/5)
2618 number w_n = toFractionNumber(w3, cf);
2619 PrintSized(w_n, cf);
2620 number z_n = n_Div(v_n, w_n, cf); // -5/7*s - 10/21*t
2621 PrintSized(z_n, cf);
2622 n_Delete(&v_n, cf); n_Delete(&w_n, cf); n_Delete(&z_n, cf);
2623
2624 rDelete(s); // kills 'cf' and 'r' as well
2625 }
2626 };
2627
2628