Context Navigation

source: git/libpolys/tests/polys_test.h @ 2d3091c

fieker-DuValspielwiese

Last change on this file since 2d3091c was 2d3091c, checked in by Frank Seelisch <seelisch@…>, 13 years ago
test for trac ticket #308 with new implementation (result is instantaneous)
Property mode set to `100644`
File size: 97.0 KB

Line
1	#include "config.h"
2
3	#include "common.h"
4	using namespace std;
5
6	// the following headers are private...
7	#include <coeffs/longrat.h>
8	#include <coeffs/gnumpfl.h>
9	#include <coeffs/gnumpc.h>
10	#include <coeffs/shortfl.h>
11	#include <coeffs/ffields.h>
12	#include <coeffs/modulop.h>
13	#include <coeffs/rmodulon.h>
14	#include <coeffs/rmodulo2m.h>
15	#include <coeffs/rintegers.h>
16
17	#include <polys/ext_fields/algext.h>
18	#include <polys/ext_fields/transext.h>
19	#include <polys/monomials/ring.h>
20	#include <polys/monomials/p_polys.h>
21
22	#include <polys/simpleideals.h>
23
24	#if 0 //ifdef HAVE_FACTORY
25	#include <polys/clapsing.h>
26	#include <factory/factory.h>
27	#endif
28
29	class MyGlobalPrintingFixture : public GlobalPrintingFixture
30	{
31	public:
32	virtual bool setUpWorld()
33	{
34
35	GlobalPrintingFixture::setUpWorld();
36
37
38	//TS_ASSERT_EQUALS( nRegister( n_Zp, npInitChar), n_Zp );
39	//TS_ASSERT_EQUALS( nRegister( n_GF, nfInitChar), n_GF );
40	//TS_ASSERT_EQUALS( nRegister( n_R, nrInitChar), n_R );
41	//TS_ASSERT_EQUALS( nRegister( n_Q, nlInitChar), n_Q );
42	//TS_ASSERT_EQUALS( nRegister( n_R, nrInitChar), n_R );
43
44	#ifdef HAVE_RINGS
45	//TS_ASSERT_EQUALS( nRegister( n_Z, nrzInitChar), n_Z ); // these are UNusable at the moment!
46	#endif
47
48	return true;
49	}
50	};
51
52
53	//
54	// We can rely on this file being included exactly once
55	// and declare this global variable in the header file.
56	//
57	static MyGlobalPrintingFixture globalPrintingFixture;
58
59
60	namespace
61	{
62
63	void PrintRing(const ring r)
64	{
65	rWrite(r); PrintLn();
66	#ifdef RDEBUG
67	rDebugPrint(r); PrintLn();
68	#endif
69	}
70
71	static inline std::string _2S(poly a, const ring r)
72	{
73	p_Test(a,r);
74
75	StringSetS("");
76	p_Write(a, r);
77
78	const char* s = StringAppendS("");
79
80	std::stringstream ss; ss << s;
81
82	StringSetS("");
83	return ss.str();
84	}
85
86	static inline void PrintSized(/const/ poly a, const ring r, BOOLEAN eoln = TRUE)
87	{
88	std::clog << _2S(a, r) << ", of size: " << p_Size(a, r);
89
90	if( eoln )
91	std::clog << std::endl;
92	}
93
94	static inline void Delete(poly &p, const ring r)
95	{
96	if( p != NULL )
97	p_Delete(&p, r);
98
99	p = NULL;
100	}
101
102	void TestSum(const ring r, const int N)
103	{
104	TS_ASSERT_DIFFERS( r , NULLp);
105	TS_ASSERT_DIFFERS( r->cf, NULLp);
106
107
108	clog << ( _2S("TEST: sum[0..") + _2S(N) + "]: ");
109	clog << endl;
110
111	assume( N > 0 ); // just for now...
112
113	const int ssss = (N * (N+1)) / 2;
114
115	poly sum1 = p_ISet(ssss, r);
116	clog<< "poly(N*(N+1)/2) (int: " << ssss << "): "; PrintSized(sum1, r);
117
118	poly s=NULL, ss=NULL, i=NULL, res=NULL;
119
120	s = p_ISet(N , r);
121	i = p_ISet(N+1, r);
122
123	i = p_Mult_q(s, i, r); s = NULL;
124
125	clog<< "poly(N)poly(N+1): (int: "<< N(N+1) << "): "; PrintSized(i, r);
126
127	number t = n_Init(2, r->cf);
128	clog<< "number(2): "; PrintSized(t, r->cf);
129
130	if( !n_IsZero( t, r->cf) )
131	{
132	if( i != NULL )
133	{
134	number ii = p_GetCoeff(i, r);
135	clog<< "number(poly(N)*poly(N+1)): "; PrintSized(ii, r->cf);
136
137	#ifdef HAVE_RINGS
138	TS_ASSERT( n_DivBy(ii, t, r->cf) );
139	#endif
140	res = p_Div_nn(i, t, r); i = NULL;
141	}
142
143
144
145	clog<< "(poly(N)*poly(N+1))/number(2): "; PrintSized(res, r);
146	poly d = p_Sub(p_Copy(res, r), p_Copy(sum1, r), r);
147
148	if( d != NULL )
149	TS_ASSERT( n_IsZeroDivisor(p_GetCoeff(d, r), r->cf) );
150
151	Delete(d, r);
152
153	if( n_GetChar(r->cf) == 0 )
154	{
155	TS_ASSERT( p_EqualPolys(sum1, res, r) );
156	TS_ASSERT( p_EqualPolys(res, sum1, r) );
157	}
158	} else
159	TS_ASSERT_EQUALS( n_GetChar(r->cf), 2);
160
161	n_Delete(&t, r->cf);
162
163
164	s = NULL;
165	ss = NULL;
166	for( int k = N; k >= 0; k-- )
167	{
168	i = p_ISet(k, r);
169	s = p_Add_q(s, i, r); // s += i
170
171	i = p_Neg( p_ISet(k, r), r );
172	ss = p_Add_q(ss, i, r); // ss -= i
173	}
174
175	clog<< "ss(-sum): "; PrintSized(ss, r);
176
177	ss = p_Neg(ss, r); // ss = -ss
178
179	clog<< "real sum : "; PrintSized(s, r);
180	clog<< "real sum(--): "; PrintSized(ss, r);
181
182	TS_ASSERT( p_EqualPolys(s, ss, r) );
183	TS_ASSERT( p_EqualPolys(ss, s, r) );
184
185	TODO(somebody, fix the delete method!);
186
187	Delete(sum1, r);
188	Delete(res, r);
189
190	Delete(s, r);
191	Delete(ss, r);
192
193	clog << ( " >>> TEST DONE!" );
194	clog << endl;
195
196	}
197
198	void Test(const ring r)
199	{
200	if( r == NULL )
201	TS_FAIL("Could not get needed ring");
202	else
203	{
204	TestSum( r, 10 );
205	TestSum( r, 100 );
206	TestSum( r, 101 );
207	TestSum( r, 1001 );
208	TestSum( r, 9000 );
209	}
210	}
211
212	}
213
214	class PolysTestSuite : public CxxTest::TestSuite
215	{
216	private:
217	/* replaces p by p + c * var(i)^exp (in-place);
218	expects exp >= 0 */
219	void plusTerm(poly &p, int c, int i, int exp, const ring r)
220	{
221	poly t = p_ISet(c, r);
222	if (exp > 0) { p_SetExp(t, i, exp, r); p_Setm(t, r); }
223	p = p_Add_q(p, t, r);
224	}
225	/* assumes r to represent Q(x)[y], for some variable names x and y;
226	replaces p by p + (c1 * 1000000 + c2) * x^xExp * y^yExp (in-place);
227	expects xExp, yExp >= 0 */
228	void specialPlusTerm(poly &p, int c1, int c2, int sign,
229	int xExp, int yExp, const ring r)
230	{
231	poly c1p = p_ISet(c1, r->cf->extRing);
232	poly c2p = p_ISet(c2, r->cf->extRing);
233	poly c3p = p_ISet(1000000, r->cf->extRing);
234	poly xterm = p_Mult_q(c1p, c3p, r->cf->extRing);
235	xterm = p_Add_q(xterm, c2p, r->cf->extRing);
236	if (sign == -1) xterm = p_Neg(xterm, r->cf->extRing);
237	if (xExp > 0)
238	{
239	p_SetExp(xterm, 1, xExp, r->cf->extRing);
240	p_Setm(xterm, r->cf->extRing);
241	}
242	number xtermAsN = toFractionNumber(xterm, r->cf);
243	poly yterm = p_ISet(1, r);
244	if (yExp > 0)
245	{
246	p_SetExp(yterm, 1, yExp, r);
247	p_Setm(yterm, r);
248	}
249	p_SetCoeff(yterm, xtermAsN, r);
250	p = p_Add_q(p, yterm, r);
251	}
252	/* defines a special test polynomial in Q(x)[y], for some variable
253	names x and y, by excessively using specialPlusTerm */
254	void specialPoly(poly &p, const ring r)
255	{
256	p = NULL;
257	specialPlusTerm(p, 0, 1, 1, 0, 17, r);
258	specialPlusTerm(p, 0, 1, -1, 15, 16, r);
259	specialPlusTerm(p, 0, 2, -1, 14, 16, r);
260	specialPlusTerm(p, 0, 3, -1, 13, 16, r);
261	specialPlusTerm(p, 0, 4, -1, 12, 16, r);
262	specialPlusTerm(p, 0, 5, -1, 11, 16, r);
263	specialPlusTerm(p, 0, 6, -1, 10, 16, r);
264	specialPlusTerm(p, 0, 7, -1, 9, 16, r);
265	specialPlusTerm(p, 0, 8, -1, 8, 16, r);
266	specialPlusTerm(p, 0, 9, -1, 7, 16, r);
267	specialPlusTerm(p, 0, 10, -1, 6, 16, r);
268	specialPlusTerm(p, 0, 11, -1, 5, 16, r);
269	specialPlusTerm(p, 0, 12, -1, 4, 16, r);
270	specialPlusTerm(p, 0, 13, -1, 3, 16, r);
271	specialPlusTerm(p, 0, 14, -1, 2, 16, r);
272	specialPlusTerm(p, 0, 15, -1, 1, 16, r);
273	specialPlusTerm(p, 0, 16, -1, 0, 16, r);
274	specialPlusTerm(p, 0, 1, 1, 29, 15, r);
275	specialPlusTerm(p, 0, 3, 1, 28, 15, r);
276	specialPlusTerm(p, 0, 7, 1, 27, 15, r);
277	specialPlusTerm(p, 0, 13, 1, 26, 15, r);
278	specialPlusTerm(p, 0, 22, 1, 25, 15, r);
279	specialPlusTerm(p, 0, 34, 1, 24, 15, r);
280	specialPlusTerm(p, 0, 50, 1, 23, 15, r);
281	specialPlusTerm(p, 0, 70, 1, 22, 15, r);
282	specialPlusTerm(p, 0, 95, 1, 21, 15, r);
283	specialPlusTerm(p, 0, 125, 1, 20, 15, r);
284	specialPlusTerm(p, 0, 161, 1, 19, 15, r);
285	specialPlusTerm(p, 0, 203, 1, 18, 15, r);
286	specialPlusTerm(p, 0, 252, 1, 17, 15, r);
287	specialPlusTerm(p, 0, 308, 1, 16, 15, r);
288	specialPlusTerm(p, 0, 372, 1, 15, 15, r);
289	specialPlusTerm(p, 0, 428, 1, 14, 15, r);
290	specialPlusTerm(p, 0, 476, 1, 13, 15, r);
291	specialPlusTerm(p, 0, 515, 1, 12, 15, r);
292	specialPlusTerm(p, 0, 545, 1, 11, 15, r);
293	specialPlusTerm(p, 0, 565, 1, 10, 15, r);
294	specialPlusTerm(p, 0, 575, 1, 9, 15, r);
295	specialPlusTerm(p, 0, 574, 1, 8, 15, r);
296	specialPlusTerm(p, 0, 562, 1, 7, 15, r);
297	specialPlusTerm(p, 0, 538, 1, 6, 15, r);
298	specialPlusTerm(p, 0, 502, 1, 5, 15, r);
299	specialPlusTerm(p, 0, 453, 1, 4, 15, r);
300	specialPlusTerm(p, 0, 391, 1, 3, 15, r);
301	specialPlusTerm(p, 0, 315, 1, 2, 15, r);
302	specialPlusTerm(p, 0, 225, 1, 1, 15, r);
303	specialPlusTerm(p, 0, 120, 1, 0, 15, r);
304	specialPlusTerm(p, 0, 1, -1, 42, 14, r);
305	specialPlusTerm(p, 0, 4, -1, 41, 14, r);
306	specialPlusTerm(p, 0, 11, -1, 40, 14, r);
307	specialPlusTerm(p, 0, 25, -1, 39, 14, r);
308	specialPlusTerm(p, 0, 50, -1, 38, 14, r);
309	specialPlusTerm(p, 0, 91, -1, 37, 14, r);
310	specialPlusTerm(p, 0, 155, -1, 36, 14, r);
311	specialPlusTerm(p, 0, 250, -1, 35, 14, r);
312	specialPlusTerm(p, 0, 386, -1, 34, 14, r);
313	specialPlusTerm(p, 0, 575, -1, 33, 14, r);
314	specialPlusTerm(p, 0, 831, -1, 32, 14, r);
315	specialPlusTerm(p, 0, 1170, -1, 31, 14, r);
316	specialPlusTerm(p, 0, 1611, -1, 30, 14, r);
317	specialPlusTerm(p, 0, 2175, -1, 29, 14, r);
318	specialPlusTerm(p, 0, 2871, -1, 28, 14, r);
319	specialPlusTerm(p, 0, 3710, -1, 27, 14, r);
320	specialPlusTerm(p, 0, 4690, -1, 26, 14, r);
321	specialPlusTerm(p, 0, 5810, -1, 25, 14, r);
322	specialPlusTerm(p, 0, 7056, -1, 24, 14, r);
323	specialPlusTerm(p, 0, 8414, -1, 23, 14, r);
324	specialPlusTerm(p, 0, 9856, -1, 22, 14, r);
325	specialPlusTerm(p, 0, 11354, -1, 21, 14, r);
326	specialPlusTerm(p, 0, 12865, -1, 20, 14, r);
327	specialPlusTerm(p, 0, 14345, -1, 19, 14, r);
328	specialPlusTerm(p, 0, 15735, -1, 18, 14, r);
329	specialPlusTerm(p, 0, 16974, -1, 17, 14, r);
330	specialPlusTerm(p, 0, 17985, -1, 16, 14, r);
331	specialPlusTerm(p, 0, 18689, -1, 15, 14, r);
332	specialPlusTerm(p, 0, 18990, -1, 14, 14, r);
333	specialPlusTerm(p, 0, 18909, -1, 13, 14, r);
334	specialPlusTerm(p, 0, 18465, -1, 12, 14, r);
335	specialPlusTerm(p, 0, 17689, -1, 11, 14, r);
336	specialPlusTerm(p, 0, 16610, -1, 10, 14, r);
337	specialPlusTerm(p, 0, 15270, -1, 9, 14, r);
338	specialPlusTerm(p, 0, 13709, -1, 8, 14, r);
339	specialPlusTerm(p, 0, 11980, -1, 7, 14, r);
340	specialPlusTerm(p, 0, 10135, -1, 6, 14, r);
341	specialPlusTerm(p, 0, 8239, -1, 5, 14, r);
342	specialPlusTerm(p, 0, 6356, -1, 4, 14, r);
343	specialPlusTerm(p, 0, 4564, -1, 3, 14, r);
344	specialPlusTerm(p, 0, 2940, -1, 2, 14, r);
345	specialPlusTerm(p, 0, 1575, -1, 1, 14, r);
346	specialPlusTerm(p, 0, 560, -1, 0, 14, r);
347	specialPlusTerm(p, 0, 1, 1, 54, 13, r);
348	specialPlusTerm(p, 0, 5, 1, 53, 13, r);
349	specialPlusTerm(p, 0, 16, 1, 52, 13, r);
350	specialPlusTerm(p, 0, 41, 1, 51, 13, r);
351	specialPlusTerm(p, 0, 92, 1, 50, 13, r);
352	specialPlusTerm(p, 0, 187, 1, 49, 13, r);
353	specialPlusTerm(p, 0, 353, 1, 48, 13, r);
354	specialPlusTerm(p, 0, 628, 1, 47, 13, r);
355	specialPlusTerm(p, 0, 1065, 1, 46, 13, r);
356	specialPlusTerm(p, 0, 1735, 1, 45, 13, r);
357	specialPlusTerm(p, 0, 2732, 1, 44, 13, r);
358	specialPlusTerm(p, 0, 4177, 1, 43, 13, r);
359	specialPlusTerm(p, 0, 6225, 1, 42, 13, r);
360	specialPlusTerm(p, 0, 9056, 1, 41, 13, r);
361	specialPlusTerm(p, 0, 12882, 1, 40, 13, r);
362	specialPlusTerm(p, 0, 17939, 1, 39, 13, r);
363	specialPlusTerm(p, 0, 24481, 1, 38, 13, r);
364	specialPlusTerm(p, 0, 32771, 1, 37, 13, r);
365	specialPlusTerm(p, 0, 43075, 1, 36, 13, r);
366	specialPlusTerm(p, 0, 55639, 1, 35, 13, r);
367	specialPlusTerm(p, 0, 70682, 1, 34, 13, r);
368	specialPlusTerm(p, 0, 88372, 1, 33, 13, r);
369	specialPlusTerm(p, 0, 108804, 1, 32, 13, r);
370	specialPlusTerm(p, 0, 131974, 1, 31, 13, r);
371	specialPlusTerm(p, 0, 157756, 1, 30, 13, r);
372	specialPlusTerm(p, 0, 185860, 1, 29, 13, r);
373	specialPlusTerm(p, 0, 215806, 1, 28, 13, r);
374	specialPlusTerm(p, 0, 246985, 1, 27, 13, r);
375	specialPlusTerm(p, 0, 278631, 1, 26, 13, r);
376	specialPlusTerm(p, 0, 309893, 1, 25, 13, r);
377	specialPlusTerm(p, 0, 339819, 1, 24, 13, r);
378	specialPlusTerm(p, 0, 367427, 1, 23, 13, r);
379	specialPlusTerm(p, 0, 391701, 1, 22, 13, r);
380	specialPlusTerm(p, 0, 411675, 1, 21, 13, r);
381	specialPlusTerm(p, 0, 426428, 1, 20, 13, r);
382	specialPlusTerm(p, 0, 435181, 1, 19, 13, r);
383	specialPlusTerm(p, 0, 437306, 1, 18, 13, r);
384	specialPlusTerm(p, 0, 432423, 1, 17, 13, r);
385	specialPlusTerm(p, 0, 420422, 1, 16, 13, r);
386	specialPlusTerm(p, 0, 401575, 1, 15, 13, r);
387	specialPlusTerm(p, 0, 376559, 1, 14, 13, r);
388	specialPlusTerm(p, 0, 346582, 1, 13, 13, r);
389	specialPlusTerm(p, 0, 312861, 1, 12, 13, r);
390	specialPlusTerm(p, 0, 276645, 1, 11, 13, r);
391	specialPlusTerm(p, 0, 239149, 1, 10, 13, r);
392	specialPlusTerm(p, 0, 201578, 1, 9, 13, r);
393	specialPlusTerm(p, 0, 165048, 1, 8, 13, r);
394	specialPlusTerm(p, 0, 130611, 1, 7, 13, r);
395	specialPlusTerm(p, 0, 99177, 1, 6, 13, r);
396	specialPlusTerm(p, 0, 71526, 1, 5, 13, r);
397	specialPlusTerm(p, 0, 48230, 1, 4, 13, r);
398	specialPlusTerm(p, 0, 29666, 1, 3, 13, r);
399	specialPlusTerm(p, 0, 15925, 1, 2, 13, r);
400	specialPlusTerm(p, 0, 6825, 1, 1, 13, r);
401	specialPlusTerm(p, 0, 1820, 1, 0, 13, r);
402	specialPlusTerm(p, 0, 1, -1, 65, 12, r);
403	specialPlusTerm(p, 0, 6, -1, 64, 12, r);
404	specialPlusTerm(p, 0, 22, -1, 63, 12, r);
405	specialPlusTerm(p, 0, 63, -1, 62, 12, r);
406	specialPlusTerm(p, 0, 155, -1, 61, 12, r);
407	specialPlusTerm(p, 0, 343, -1, 60, 12, r);
408	specialPlusTerm(p, 0, 701, -1, 59, 12, r);
409	specialPlusTerm(p, 0, 1345, -1, 58, 12, r);
410	specialPlusTerm(p, 0, 2451, -1, 57, 12, r);
411	specialPlusTerm(p, 0, 4278, -1, 56, 12, r);
412	specialPlusTerm(p, 0, 7198, -1, 55, 12, r);
413	specialPlusTerm(p, 0, 11733, -1, 54, 12, r);
414	specialPlusTerm(p, 0, 18589, -1, 53, 12, r);
415	specialPlusTerm(p, 0, 28699, -1, 52, 12, r);
416	specialPlusTerm(p, 0, 43265, -1, 51, 12, r);
417	specialPlusTerm(p, 0, 63799, -1, 50, 12, r);
418	specialPlusTerm(p, 0, 92152, -1, 49, 12, r);
419	specialPlusTerm(p, 0, 130543, -1, 48, 12, r);
420	specialPlusTerm(p, 0, 181565, -1, 47, 12, r);
421	specialPlusTerm(p, 0, 248179, -1, 46, 12, r);
422	specialPlusTerm(p, 0, 333673, -1, 45, 12, r);
423	specialPlusTerm(p, 0, 441596, -1, 44, 12, r);
424	specialPlusTerm(p, 0, 575643, -1, 43, 12, r);
425	specialPlusTerm(p, 0, 739501, -1, 42, 12, r);
426	specialPlusTerm(p, 0, 936619, -1, 41, 12, r);
427	specialPlusTerm(p, 1, 170014, -1, 40, 12, r);
428	specialPlusTerm(p, 1, 441997, -1, 39, 12, r);
429	specialPlusTerm(p, 1, 753919, -1, 38, 12, r);
430	specialPlusTerm(p, 2, 105911, -1, 37, 12, r);
431	specialPlusTerm(p, 2, 496652, -1, 36, 12, r);
432	specialPlusTerm(p, 2, 923127, -1, 35, 12, r);
433	specialPlusTerm(p, 3, 380499, -1, 34, 12, r);
434	specialPlusTerm(p, 3, 861979, -1, 33, 12, r);
435	specialPlusTerm(p, 4, 358819, -1, 32, 12, r);
436	specialPlusTerm(p, 4, 860402, -1, 31, 12, r);
437	specialPlusTerm(p, 5, 354477, -1, 30, 12, r);
438	specialPlusTerm(p, 5, 827501, -1, 29, 12, r);
439	specialPlusTerm(p, 6, 265239, -1, 28, 12, r);
440	specialPlusTerm(p, 6, 653507, -1, 27, 12, r);
441	specialPlusTerm(p, 6, 978743, -1, 26, 12, r);
442	specialPlusTerm(p, 7, 228746, -1, 25, 12, r);
443	specialPlusTerm(p, 7, 393190, -1, 24, 12, r);
444	specialPlusTerm(p, 7, 464241, -1, 23, 12, r);
445	specialPlusTerm(p, 7, 436963, -1, 22, 12, r);
446	specialPlusTerm(p, 7, 309763, -1, 21, 12, r);
447	specialPlusTerm(p, 7, 84549, -1, 20, 12, r);
448	specialPlusTerm(p, 6, 766941, -1, 19, 12, r);
449	specialPlusTerm(p, 6, 366119, -1, 18, 12, r);
450	specialPlusTerm(p, 5, 894636, -1, 17, 12, r);
451	specialPlusTerm(p, 5, 367870, -1, 16, 12, r);
452	specialPlusTerm(p, 4, 803365, -1, 15, 12, r);
453	specialPlusTerm(p, 4, 219710, -1, 14, 12, r);
454	specialPlusTerm(p, 3, 635296, -1, 13, 12, r);
455	specialPlusTerm(p, 3, 66522, -1, 12, 12, r);
456	specialPlusTerm(p, 2, 527597, -1, 11, 12, r);
457	specialPlusTerm(p, 2, 30222, -1, 10, 12, r);
458	specialPlusTerm(p, 1, 583491, -1, 9, 12, r);
459	specialPlusTerm(p, 1, 193660, -1, 8, 12, r);
460	specialPlusTerm(p, 0, 864214, -1, 7, 12, r);
461	specialPlusTerm(p, 0, 595790, -1, 6, 12, r);
462	specialPlusTerm(p, 0, 386386, -1, 5, 12, r);
463	specialPlusTerm(p, 0, 231504, -1, 4, 12, r);
464	specialPlusTerm(p, 0, 124579, -1, 3, 12, r);
465	specialPlusTerm(p, 0, 57330, -1, 2, 12, r);
466	specialPlusTerm(p, 0, 20475, -1, 1, 12, r);
467	specialPlusTerm(p, 0, 4368, -1, 0, 12, r);
468	specialPlusTerm(p, 0, 1, 1, 75, 11, r);
469	specialPlusTerm(p, 0, 7, 1, 74, 11, r);
470	specialPlusTerm(p, 0, 29, 1, 73, 11, r);
471	specialPlusTerm(p, 0, 92, 1, 72, 11, r);
472	specialPlusTerm(p, 0, 247, 1, 71, 11, r);
473	specialPlusTerm(p, 0, 590, 1, 70, 11, r);
474	specialPlusTerm(p, 0, 1292, 1, 69, 11, r);
475	specialPlusTerm(p, 0, 2643, 1, 68, 11, r);
476	specialPlusTerm(p, 0, 5116, 1, 67, 11, r);
477	specialPlusTerm(p, 0, 9457, 1, 66, 11, r);
478	specialPlusTerm(p, 0, 16810, 1, 65, 11, r);
479	specialPlusTerm(p, 0, 28874, 1, 64, 11, r);
480	specialPlusTerm(p, 0, 48105, 1, 63, 11, r);
481	specialPlusTerm(p, 0, 77963, 1, 62, 11, r);
482	specialPlusTerm(p, 0, 123209, 1, 61, 11, r);
483	specialPlusTerm(p, 0, 190245, 1, 60, 11, r);
484	specialPlusTerm(p, 0, 287494, 1, 59, 11, r);
485	specialPlusTerm(p, 0, 425804, 1, 58, 11, r);
486	specialPlusTerm(p, 0, 618866, 1, 57, 11, r);
487	specialPlusTerm(p, 0, 883609, 1, 56, 11, r);
488	specialPlusTerm(p, 1, 240541, 1, 55, 11, r);
489	specialPlusTerm(p, 1, 713978, 1, 54, 11, r);
490	specialPlusTerm(p, 2, 332107, 1, 53, 11, r);
491	specialPlusTerm(p, 3, 126867, 1, 52, 11, r);
492	specialPlusTerm(p, 4, 133571, 1, 51, 11, r);
493	specialPlusTerm(p, 5, 390227, 1, 50, 11, r);
494	specialPlusTerm(p, 6, 936520, 1, 49, 11, r);
495	specialPlusTerm(p, 8, 812464, 1, 48, 11, r);
496	specialPlusTerm(p, 11, 56669, 1, 47, 11, r);
497	specialPlusTerm(p, 13, 704280, 1, 46, 11, r);
498	specialPlusTerm(p, 16, 784594, 1, 45, 11, r);
499	specialPlusTerm(p, 20, 318470, 1, 44, 11, r);
500	specialPlusTerm(p, 24, 315607, 1, 43, 11, r);
501	specialPlusTerm(p, 28, 771888, 1, 42, 11, r);
502	specialPlusTerm(p, 33, 666946, 1, 41, 11, r);
503	specialPlusTerm(p, 38, 962309, 1, 40, 11, r);
504	specialPlusTerm(p, 44, 600023, 1, 39, 11, r);
505	specialPlusTerm(p, 50, 502149, 1, 38, 11, r);
506	specialPlusTerm(p, 56, 571139, 1, 37, 11, r);
507	specialPlusTerm(p, 62, 691244, 1, 36, 11, r);
508	specialPlusTerm(p, 68, 730935, 1, 35, 11, r);
509	specialPlusTerm(p, 74, 546533, 1, 34, 11, r);
510	specialPlusTerm(p, 79, 986722, 1, 33, 11, r);
511	specialPlusTerm(p, 84, 898120, 1, 32, 11, r);
512	specialPlusTerm(p, 89, 131550, 1, 31, 11, r);
513	specialPlusTerm(p, 92, 548805, 1, 30, 11, r);
514	specialPlusTerm(p, 95, 29441, 1, 29, 11, r);
515	specialPlusTerm(p, 96, 477351, 1, 28, 11, r);
516	specialPlusTerm(p, 96, 826185, 1, 27, 11, r);
517	specialPlusTerm(p, 96, 43174, 1, 26, 11, r);
518	specialPlusTerm(p, 94, 131647, 1, 25, 11, r);
519	specialPlusTerm(p, 91, 131660, 1, 24, 11, r);
520	specialPlusTerm(p, 87, 119171, 1, 23, 11, r);
521	specialPlusTerm(p, 82, 203392, 1, 22, 11, r);
522	specialPlusTerm(p, 76, 522667, 1, 21, 11, r);
523	specialPlusTerm(p, 70, 238707, 1, 20, 11, r);
524	specialPlusTerm(p, 63, 529796, 1, 19, 11, r);
525	specialPlusTerm(p, 56, 582713, 1, 18, 11, r);
526	specialPlusTerm(p, 49, 584249, 1, 17, 11, r);
527	specialPlusTerm(p, 42, 712395, 1, 16, 11, r);
528	specialPlusTerm(p, 36, 128059, 1, 15, 11, r);
529	specialPlusTerm(p, 29, 967652, 1, 14, 11, r);
530	specialPlusTerm(p, 24, 337808, 1, 13, 11, r);
531	specialPlusTerm(p, 19, 312634, 1, 12, 11, r);
532	specialPlusTerm(p, 14, 935096, 1, 11, 11, r);
533	specialPlusTerm(p, 11, 218988, 1, 10, 11, r);
534	specialPlusTerm(p, 8, 151858, 1, 9, 11, r);
535	specialPlusTerm(p, 5, 698407, 1, 8, 11, r);
536	specialPlusTerm(p, 3, 804801, 1, 7, 11, r);
537	specialPlusTerm(p, 2, 403115, 1, 6, 11, r);
538	specialPlusTerm(p, 1, 416415, 1, 5, 11, r);
539	specialPlusTerm(p, 0, 763763, 1, 4, 11, r);
540	specialPlusTerm(p, 0, 365365, 1, 3, 11, r);
541	specialPlusTerm(p, 0, 147147, 1, 2, 11, r);
542	specialPlusTerm(p, 0, 45045, 1, 1, 11, r);
543	specialPlusTerm(p, 0, 8008, 1, 0, 11, r);
544	specialPlusTerm(p, 0, 1, -1, 84, 10, r);
545	specialPlusTerm(p, 0, 8, -1, 83, 10, r);
546	specialPlusTerm(p, 0, 37, -1, 82, 10, r);
547	specialPlusTerm(p, 0, 129, -1, 81, 10, r);
548	specialPlusTerm(p, 0, 376, -1, 80, 10, r);
549	specialPlusTerm(p, 0, 966, -1, 79, 10, r);
550	specialPlusTerm(p, 0, 2258, -1, 78, 10, r);
551	specialPlusTerm(p, 0, 4902, -1, 77, 10, r);
552	specialPlusTerm(p, 0, 10025, -1, 76, 10, r);
553	specialPlusTerm(p, 0, 19511, -1, 75, 10, r);
554	specialPlusTerm(p, 0, 36402, -1, 74, 10, r);
555	specialPlusTerm(p, 0, 65457, -1, 73, 10, r);
556	specialPlusTerm(p, 0, 113910, -1, 72, 10, r);
557	specialPlusTerm(p, 0, 192472, -1, 71, 10, r);
558	specialPlusTerm(p, 0, 316620, -1, 70, 10, r);
559	specialPlusTerm(p, 0, 508215, -1, 69, 10, r);
560	specialPlusTerm(p, 0, 797473, -1, 68, 10, r);
561	specialPlusTerm(p, 1, 225306, -1, 67, 10, r);
562	specialPlusTerm(p, 1, 846017, -1, 66, 10, r);
563	specialPlusTerm(p, 2, 730299, -1, 65, 10, r);
564	specialPlusTerm(p, 3, 968427, -1, 64, 10, r);
565	specialPlusTerm(p, 5, 673536, -1, 63, 10, r);
566	specialPlusTerm(p, 7, 984777, -1, 62, 10, r);
567	specialPlusTerm(p, 11, 70116, -1, 61, 10, r);
568	specialPlusTerm(p, 15, 128465, -1, 60, 10, r);
569	specialPlusTerm(p, 20, 390819, -1, 59, 10, r);
570	specialPlusTerm(p, 27, 120017, -1, 58, 10, r);
571	specialPlusTerm(p, 35, 608761, -1, 57, 10, r);
572	specialPlusTerm(p, 46, 175479, -1, 56, 10, r);
573	specialPlusTerm(p, 59, 157726, -1, 55, 10, r);
574	specialPlusTerm(p, 74, 902862, -1, 54, 10, r);
575	specialPlusTerm(p, 93, 755945, -1, 53, 10, r);
576	specialPlusTerm(p, 116, 44932, -1, 52, 10, r);
577	specialPlusTerm(p, 142, 63382, -1, 51, 10, r);
578	specialPlusTerm(p, 172, 51120, -1, 50, 10, r);
579	specialPlusTerm(p, 206, 173563, -1, 49, 10, r);
580	specialPlusTerm(p, 244, 500607, -1, 48, 10, r);
581	specialPlusTerm(p, 286, 986083, -1, 47, 10, r);
582	specialPlusTerm(p, 333, 449096, -1, 46, 10, r);
583	specialPlusTerm(p, 383, 558571, -1, 45, 10, r);
584	specialPlusTerm(p, 436, 822461, -1, 44, 10, r);
585	specialPlusTerm(p, 492, 582939, -1, 43, 10, r);
586	specialPlusTerm(p, 550, 18832, -1, 42, 10, r);
587	specialPlusTerm(p, 608, 156141, -1, 41, 10, r);
588	specialPlusTerm(p, 665, 887167, -1, 40, 10, r);
589	specialPlusTerm(p, 721, 997807, -1, 39, 10, r);
590	specialPlusTerm(p, 775, 202852, -1, 38, 10, r);
591	specialPlusTerm(p, 824, 187996, -1, 37, 10, r);
592	specialPlusTerm(p, 867, 657138, -1, 36, 10, r);
593	specialPlusTerm(p, 904, 382945, -1, 35, 10, r);
594	specialPlusTerm(p, 933, 258541, -1, 34, 10, r);
595	specialPlusTerm(p, 953, 347368, -1, 33, 10, r);
596	specialPlusTerm(p, 963, 928871, -1, 32, 10, r);
597	specialPlusTerm(p, 964, 536834, -1, 31, 10, r);
598	specialPlusTerm(p, 954, 987850, -1, 30, 10, r);
599	specialPlusTerm(p, 935, 397536, -1, 29, 10, r);
600	specialPlusTerm(p, 906, 183073, -1, 28, 10, r);
601	specialPlusTerm(p, 868, 50862, -1, 27, 10, r);
602	specialPlusTerm(p, 821, 970338, -1, 26, 10, r);
603	specialPlusTerm(p, 769, 135827, -1, 25, 10, r);
604	specialPlusTerm(p, 710, 918057, -1, 24, 10, r);
605	specialPlusTerm(p, 648, 808233, -1, 23, 10, r);
606	specialPlusTerm(p, 584, 357073, -1, 22, 10, r);
607	specialPlusTerm(p, 519, 112032, -1, 21, 10, r);
608	specialPlusTerm(p, 454, 555728, -1, 20, 10, r);
609	specialPlusTerm(p, 392, 49009, -1, 19, 10, r);
610	specialPlusTerm(p, 332, 781273, -1, 18, 10, r);
611	specialPlusTerm(p, 277, 731388, -1, 17, 10, r);
612	specialPlusTerm(p, 227, 641117, -1, 16, 10, r);
613	specialPlusTerm(p, 183, 2853, -1, 15, 10, r);
614	specialPlusTerm(p, 144, 62127, -1, 14, 10, r);
615	specialPlusTerm(p, 110, 834647, -1, 13, 10, r);
616	specialPlusTerm(p, 83, 135184, -1, 12, 10, r);
617	specialPlusTerm(p, 60, 614741, -1, 11, 10, r);
618	specialPlusTerm(p, 42, 799119, -1, 10, 10, r);
619	specialPlusTerm(p, 29, 127956, -1, 9, 10, r);
620	specialPlusTerm(p, 18, 992545, -1, 8, 10, r);
621	specialPlusTerm(p, 11, 771474, -1, 7, 10, r);
622	specialPlusTerm(p, 6, 862141, -1, 6, 10, r);
623	specialPlusTerm(p, 3, 707704, -1, 5, 10, r);
624	specialPlusTerm(p, 1, 817816, -1, 4, 10, r);
625	specialPlusTerm(p, 0, 782782, -1, 3, 10, r);
626	specialPlusTerm(p, 0, 280280, -1, 2, 10, r);
627	specialPlusTerm(p, 0, 75075, -1, 1, 10, r);
628	specialPlusTerm(p, 0, 11440, -1, 0, 10, r);
629	specialPlusTerm(p, 0, 1, 1, 92, 9, r);
630	specialPlusTerm(p, 0, 9, 1, 91, 9, r);
631	specialPlusTerm(p, 0, 46, 1, 90, 9, r);
632	specialPlusTerm(p, 0, 175, 1, 89, 9, r);
633	specialPlusTerm(p, 0, 551, 1, 88, 9, r);
634	specialPlusTerm(p, 0, 1517, 1, 87, 9, r);
635	specialPlusTerm(p, 0, 3775, 1, 86, 9, r);
636	specialPlusTerm(p, 0, 8677, 1, 85, 9, r);
637	specialPlusTerm(p, 0, 18703, 1, 84, 9, r);
638	specialPlusTerm(p, 0, 38212, 1, 83, 9, r);
639	specialPlusTerm(p, 0, 74581, 1, 82, 9, r);
640	specialPlusTerm(p, 0, 139877, 1, 81, 9, r);
641	specialPlusTerm(p, 0, 253243, 1, 80, 9, r);
642	specialPlusTerm(p, 0, 444211, 1, 79, 9, r);
643	specialPlusTerm(p, 0, 757189, 1, 78, 9, r);
644	specialPlusTerm(p, 1, 257386, 1, 77, 9, r);
645	specialPlusTerm(p, 2, 38445, 1, 76, 9, r);
646	specialPlusTerm(p, 3, 232029, 1, 75, 9, r);
647	specialPlusTerm(p, 5, 19547, 1, 74, 9, r);
648	specialPlusTerm(p, 7, 646140, 1, 73, 9, r);
649	specialPlusTerm(p, 11, 436924, 1, 72, 9, r);
650	specialPlusTerm(p, 16, 815312, 1, 71, 9, r);
651	specialPlusTerm(p, 24, 323016, 1, 70, 9, r);
652	specialPlusTerm(p, 34, 641066, 1, 69, 9, r);
653	specialPlusTerm(p, 48, 610873, 1, 68, 9, r);
654	specialPlusTerm(p, 67, 254061, 1, 67, 9, r);
655	specialPlusTerm(p, 91, 789450, 1, 66, 9, r);
656	specialPlusTerm(p, 123, 645277, 1, 65, 9, r);
657	specialPlusTerm(p, 164, 464508, 1, 64, 9, r);
658	specialPlusTerm(p, 216, 101017, 1, 63, 9, r);
659	specialPlusTerm(p, 280, 604281, 1, 62, 9, r);
660	specialPlusTerm(p, 360, 190441, 1, 61, 9, r);
661	specialPlusTerm(p, 457, 197865, 1, 60, 9, r);
662	specialPlusTerm(p, 574, 25922, 1, 59, 9, r);
663	specialPlusTerm(p, 713, 56365, 1, 58, 9, r);
664	specialPlusTerm(p, 876, 557703, 1, 57, 9, r);
665	specialPlusTerm(p, 1066, 573992, 1, 56, 9, r);
666	specialPlusTerm(p, 1284, 800887, 1, 55, 9, r);
667	specialPlusTerm(p, 1532, 453056, 1, 54, 9, r);
668	specialPlusTerm(p, 1810, 128450, 1, 53, 9, r);
669	specialPlusTerm(p, 2117, 675954, 1, 52, 9, r);
670	specialPlusTerm(p, 2454, 73820, 1, 51, 9, r);
671	specialPlusTerm(p, 2817, 326941, 1, 50, 9, r);
672	specialPlusTerm(p, 3204, 391243, 1, 49, 9, r);
673	specialPlusTerm(p, 3611, 133043, 1, 48, 9, r);
674	specialPlusTerm(p, 4032, 330356, 1, 47, 9, r);
675	specialPlusTerm(p, 4461, 721846, 1, 46, 9, r);
676	specialPlusTerm(p, 4892, 107024, 1, 45, 9, r);
677	specialPlusTerm(p, 5315, 498836, 1, 44, 9, r);
678	specialPlusTerm(p, 5723, 326840, 1, 43, 9, r);
679	specialPlusTerm(p, 6106, 686025, 1, 42, 9, r);
680	specialPlusTerm(p, 6456, 623000, 1, 41, 9, r);
681	specialPlusTerm(p, 6764, 448368, 1, 40, 9, r);
682	specialPlusTerm(p, 7022, 61523, 1, 39, 9, r);
683	specialPlusTerm(p, 7222, 273135, 1, 38, 9, r);
684	specialPlusTerm(p, 7359, 108966, 1, 37, 9, r);
685	specialPlusTerm(p, 7428, 79054, 1, 36, 9, r);
686	specialPlusTerm(p, 7426, 396980, 1, 35, 9, r);
687	specialPlusTerm(p, 7353, 135921, 1, 34, 9, r);
688	specialPlusTerm(p, 7209, 310506, 1, 33, 9, r);
689	specialPlusTerm(p, 6997, 877688, 1, 32, 9, r);
690	specialPlusTerm(p, 6723, 653256, 1, 31, 9, r);
691	specialPlusTerm(p, 6393, 146079, 1, 30, 9, r);
692	specialPlusTerm(p, 6014, 316858, 1, 29, 9, r);
693	specialPlusTerm(p, 5596, 273275, 1, 28, 9, r);
694	specialPlusTerm(p, 5148, 917160, 1, 27, 9, r);
695	specialPlusTerm(p, 4682, 563401, 1, 26, 9, r);
696	specialPlusTerm(p, 4207, 550601, 1, 25, 9, r);
697	specialPlusTerm(p, 3733, 862769, 1, 24, 9, r);
698	specialPlusTerm(p, 3270, 780702, 1, 23, 9, r);
699	specialPlusTerm(p, 2826, 579105, 1, 22, 9, r);
700	specialPlusTerm(p, 2408, 283186, 1, 21, 9, r);
701	specialPlusTerm(p, 2021, 494926, 1, 20, 9, r);
702	specialPlusTerm(p, 1670, 295297, 1, 19, 9, r);
703	specialPlusTerm(p, 1357, 224099, 1, 18, 9, r);
704	specialPlusTerm(p, 1083, 335088, 1, 17, 9, r);
705	specialPlusTerm(p, 848, 318658, 1, 16, 9, r);
706	specialPlusTerm(p, 650, 680536, 1, 15, 9, r);
707	specialPlusTerm(p, 487, 961232, 1, 14, 9, r);
708	specialPlusTerm(p, 356, 978589, 1, 13, 9, r);
709	specialPlusTerm(p, 254, 74425, 1, 12, 9, r);
710	specialPlusTerm(p, 175, 348338, 1, 11, 9, r);
711	specialPlusTerm(p, 116, 865243, 1, 10, 9, r);
712	specialPlusTerm(p, 74, 831757, 1, 9, 9, r);
713	specialPlusTerm(p, 45, 737406, 1, 8, 9, r);
714	specialPlusTerm(p, 26, 458575, 1, 7, 9, r);
715	specialPlusTerm(p, 14, 324310, 1, 6, 9, r);
716	specialPlusTerm(p, 7, 145853, 1, 5, 9, r);
717	specialPlusTerm(p, 3, 212352, 1, 4, 9, r);
718	specialPlusTerm(p, 1, 257828, 1, 3, 9, r);
719	specialPlusTerm(p, 0, 405405, 1, 2, 9, r);
720	specialPlusTerm(p, 0, 96525, 1, 1, 9, r);
721	specialPlusTerm(p, 0, 12870, 1, 0, 9, r);
722	specialPlusTerm(p, 0, 1, -1, 99, 8, r);
723	specialPlusTerm(p, 0, 10, -1, 98, 8, r);
724	specialPlusTerm(p, 0, 56, -1, 97, 8, r);
725	specialPlusTerm(p, 0, 231, -1, 96, 8, r);
726	specialPlusTerm(p, 0, 782, -1, 95, 8, r);
727	specialPlusTerm(p, 0, 2299, -1, 94, 8, r);
728	specialPlusTerm(p, 0, 6074, -1, 93, 8, r);
729	specialPlusTerm(p, 0, 14751, -1, 92, 8, r);
730	specialPlusTerm(p, 0, 33445, -1, 91, 8, r);
731	specialPlusTerm(p, 0, 71586, -1, 90, 8, r);
732	specialPlusTerm(p, 0, 145843, -1, 89, 8, r);
733	specialPlusTerm(p, 0, 284605, -1, 88, 8, r);
734	specialPlusTerm(p, 0, 534639, -1, 87, 8, r);
735	specialPlusTerm(p, 0, 970707, -1, 86, 8, r);
736	specialPlusTerm(p, 1, 709091, -1, 85, 8, r);
737	specialPlusTerm(p, 2, 926134, -1, 84, 8, r);
738	specialPlusTerm(p, 4, 883022, -1, 83, 8, r);
739	specialPlusTerm(p, 7, 958118, -1, 82, 8, r);
740	specialPlusTerm(p, 12, 688161, -1, 81, 8, r);
741	specialPlusTerm(p, 19, 819543, -1, 80, 8, r);
742	specialPlusTerm(p, 30, 370620, -1, 79, 8, r);
743	specialPlusTerm(p, 45, 705588, -1, 78, 8, r);
744	specialPlusTerm(p, 67, 619803, -1, 77, 8, r);
745	specialPlusTerm(p, 98, 435565, -1, 76, 8, r);
746	specialPlusTerm(p, 141, 106293, -1, 75, 8, r);
747	specialPlusTerm(p, 199, 325748, -1, 74, 8, r);
748	specialPlusTerm(p, 277, 637550, -1, 73, 8, r);
749	specialPlusTerm(p, 381, 538692, -1, 72, 8, r);
750	specialPlusTerm(p, 517, 569184, -1, 71, 8, r);
751	specialPlusTerm(p, 693, 378528, -1, 70, 8, r);
752	specialPlusTerm(p, 917, 758545, -1, 69, 8, r);
753	specialPlusTerm(p, 1200, 631327, -1, 68, 8, r);
754	specialPlusTerm(p, 1552, 980935, -1, 67, 8, r);
755	specialPlusTerm(p, 1986, 718008, -1, 66, 8, r);
756	specialPlusTerm(p, 2514, 467898, -1, 65, 8, r);
757	specialPlusTerm(p, 3149, 275373, -1, 64, 8, r);
758	specialPlusTerm(p, 3904, 222333, -1, 63, 8, r);
759	specialPlusTerm(p, 4791, 959202, -1, 62, 8, r);
760	specialPlusTerm(p, 5824, 155954, -1, 61, 8, r);
761	specialPlusTerm(p, 7010, 884530, -1, 60, 8, r);
762	specialPlusTerm(p, 8359, 950639, -1, 59, 8, r);
763	specialPlusTerm(p, 9876, 199091, -1, 58, 8, r);
764	specialPlusTerm(p, 11560, 822647, -1, 57, 8, r);
765	specialPlusTerm(p, 13410, 709233, -1, 56, 8, r);
766	specialPlusTerm(p, 15417, 866033, -1, 55, 8, r);
767	specialPlusTerm(p, 17568, 960466, -1, 54, 8, r);
768	specialPlusTerm(p, 19845, 17463, -1, 53, 8, r);
769	specialPlusTerm(p, 22221, 309147, -1, 52, 8, r);
770	specialPlusTerm(p, 24667, 467342, -1, 51, 8, r);
771	specialPlusTerm(p, 27147, 841107, -1, 50, 8, r);
772	specialPlusTerm(p, 29622, 110916, -1, 49, 8, r);
773	specialPlusTerm(p, 32046, 158421, -1, 48, 8, r);
774	specialPlusTerm(p, 34373, 176970, -1, 47, 8, r);
775	specialPlusTerm(p, 36554, 993654, -1, 46, 8, r);
776	specialPlusTerm(p, 38543, 559373, -1, 45, 8, r);
777	specialPlusTerm(p, 40292, 550458, -1, 44, 8, r);
778	specialPlusTerm(p, 41759, 14716, -1, 43, 8, r);
779	specialPlusTerm(p, 42904, 987186, -1, 42, 8, r);
780	specialPlusTerm(p, 43698, 997388, -1, 41, 8, r);
781	specialPlusTerm(p, 44117, 391022, -1, 40, 8, r);
782	specialPlusTerm(p, 44145, 394986, -1, 39, 8, r);
783	specialPlusTerm(p, 43777, 865188, -1, 38, 8, r);
784	specialPlusTerm(p, 43019, 670206, -1, 37, 8, r);
785	specialPlusTerm(p, 41885, 681598, -1, 36, 8, r);
786	specialPlusTerm(p, 40400, 361216, -1, 35, 8, r);
787	specialPlusTerm(p, 38596, 956954, -1, 34, 8, r);
788	specialPlusTerm(p, 36516, 339240, -1, 33, 8, r);
789	specialPlusTerm(p, 34205, 530818, -1, 32, 8, r);
790	specialPlusTerm(p, 31715, 999202, -1, 31, 8, r);
791	specialPlusTerm(p, 29101, 795368, -1, 30, 8, r);
792	specialPlusTerm(p, 26417, 630514, -1, 29, 8, r);
793	specialPlusTerm(p, 23716, 985664, -1, 28, 8, r);
794	specialPlusTerm(p, 21050, 345182, -1, 27, 8, r);
795	specialPlusTerm(p, 18463, 636290, -1, 26, 8, r);
796	specialPlusTerm(p, 15996, 940992, -1, 25, 8, r);
797	specialPlusTerm(p, 13683, 529134, -1, 24, 8, r);
798	specialPlusTerm(p, 11549, 242308, -1, 23, 8, r);
799	specialPlusTerm(p, 9612, 238032, -1, 22, 8, r);
800	specialPlusTerm(p, 7883, 84208, -1, 21, 8, r);
801	specialPlusTerm(p, 6365, 175366, -1, 20, 8, r);
802	specialPlusTerm(p, 5055, 425826, -1, 19, 8, r);
803	specialPlusTerm(p, 3945, 181834, -1, 18, 8, r);
804	specialPlusTerm(p, 3021, 285630, -1, 17, 8, r);
805	specialPlusTerm(p, 2267, 219328, -1, 16, 8, r);
806	specialPlusTerm(p, 1664, 257320, -1, 15, 8, r);
807	specialPlusTerm(p, 1192, 561524, -1, 14, 8, r);
808	specialPlusTerm(p, 832, 164102, -1, 13, 8, r);
809	specialPlusTerm(p, 563, 796684, -1, 12, 8, r);
810	specialPlusTerm(p, 369, 542514, -1, 11, 8, r);
811	specialPlusTerm(p, 233, 304720, -1, 10, 8, r);
812	specialPlusTerm(p, 141, 98386, -1, 9, 8, r);
813	specialPlusTerm(p, 81, 180528, -1, 8, 8, r);
814	specialPlusTerm(p, 44, 38137, -1, 7, 8, r);
815	specialPlusTerm(p, 22, 259094, -1, 6, 8, r);
816	specialPlusTerm(p, 10, 314447, -1, 5, 8, r);
817	specialPlusTerm(p, 4, 281420, -1, 4, 8, r);
818	specialPlusTerm(p, 1, 537107, -1, 3, 8, r);
819	specialPlusTerm(p, 0, 450450, -1, 2, 8, r);
820	specialPlusTerm(p, 0, 96525, -1, 1, 8, r);
821	specialPlusTerm(p, 0, 11440, -1, 0, 8, r);
822	specialPlusTerm(p, 0, 1, 1, 105, 7, r);
823	specialPlusTerm(p, 0, 11, 1, 104, 7, r);
824	specialPlusTerm(p, 0, 67, 1, 103, 7, r);
825	specialPlusTerm(p, 0, 298, 1, 102, 7, r);
826	specialPlusTerm(p, 0, 1080, 1, 101, 7, r);
827	specialPlusTerm(p, 0, 3379, 1, 100, 7, r);
828	specialPlusTerm(p, 0, 9453, 1, 99, 7, r);
829	specialPlusTerm(p, 0, 24196, 1, 98, 7, r);
830	specialPlusTerm(p, 0, 57569, 1, 97, 7, r);
831	specialPlusTerm(p, 0, 128787, 1, 96, 7, r);
832	specialPlusTerm(p, 0, 273231, 1, 95, 7, r);
833	specialPlusTerm(p, 0, 553438, 1, 94, 7, r);
834	specialPlusTerm(p, 1, 75997, 1, 93, 7, r);
835	specialPlusTerm(p, 2, 16735, 1, 92, 7, r);
836	specialPlusTerm(p, 3, 657192, 1, 91, 7, r);
837	specialPlusTerm(p, 6, 436037, 1, 90, 7, r);
838	specialPlusTerm(p, 11, 19717, 1, 89, 7, r);
839	specialPlusTerm(p, 18, 397189, 1, 88, 7, r);
840	specialPlusTerm(p, 30, 3973, 1, 87, 7, r);
841	specialPlusTerm(p, 47, 880870, 1, 86, 7, r);
842	specialPlusTerm(p, 74, 872383, 1, 85, 7, r);
843	specialPlusTerm(p, 114, 869036, 1, 84, 7, r);
844	specialPlusTerm(p, 173, 96283, 1, 83, 7, r);
845	specialPlusTerm(p, 256, 450472, 1, 82, 7, r);
846	specialPlusTerm(p, 373, 879259, 1, 81, 7, r);
847	specialPlusTerm(p, 536, 799939, 1, 80, 7, r);
848	specialPlusTerm(p, 759, 544391, 1, 79, 7, r);
849	specialPlusTerm(p, 1059, 813880, 1, 78, 7, r);
850	specialPlusTerm(p, 1459, 121011, 1, 77, 7, r);
851	specialPlusTerm(p, 1983, 190069, 1, 76, 7, r);
852	specialPlusTerm(p, 2662, 281192, 1, 75, 7, r);
853	specialPlusTerm(p, 3531, 398853, 1, 74, 7, r);
854	specialPlusTerm(p, 4630, 341477, 1, 73, 7, r);
855	specialPlusTerm(p, 6003, 547268, 1, 72, 7, r);
856	specialPlusTerm(p, 7699, 692101, 1, 71, 7, r);
857	specialPlusTerm(p, 9770, 999253, 1, 70, 7, r);
858	specialPlusTerm(p, 12272, 228155, 1, 69, 7, r);
859	specialPlusTerm(p, 15259, 320516, 1, 68, 7, r);
860	specialPlusTerm(p, 18787, 697047, 1, 67, 7, r);
861	specialPlusTerm(p, 22910, 216326, 1, 66, 7, r);
862	specialPlusTerm(p, 27674, 828551, 1, 65, 7, r);
863	specialPlusTerm(p, 33121, 980096, 1, 64, 7, r);
864	specialPlusTerm(p, 39281, 848637, 1, 63, 7, r);
865	specialPlusTerm(p, 46171, 511745, 1, 62, 7, r);
866	specialPlusTerm(p, 53792, 172793, 1, 61, 7, r);
867	specialPlusTerm(p, 62126, 584715, 1, 60, 7, r);
868	specialPlusTerm(p, 71136, 823074, 1, 59, 7, r);
869	specialPlusTerm(p, 80762, 563409, 1, 58, 7, r);
870	specialPlusTerm(p, 90920, 12755, 1, 57, 7, r);
871	specialPlusTerm(p, 101501, 630586, 1, 56, 7, r);
872	specialPlusTerm(p, 112376, 750037, 1, 55, 7, r);
873	specialPlusTerm(p, 123393, 176185, 1, 54, 7, r);
874	specialPlusTerm(p, 134379, 795971, 1, 53, 7, r);
875	specialPlusTerm(p, 145150, 185558, 1, 52, 7, r);
876	specialPlusTerm(p, 155507, 148257, 1, 51, 7, r);
877	specialPlusTerm(p, 165248, 62169, 1, 50, 7, r);
878	specialPlusTerm(p, 174170, 864688, 1, 49, 7, r);
879	specialPlusTerm(p, 182080, 454274, 1, 48, 7, r);
880	specialPlusTerm(p, 188795, 252141, 1, 47, 7, r);
881	specialPlusTerm(p, 194153, 640367, 1, 46, 7, r);
882	specialPlusTerm(p, 198019, 981033, 1, 45, 7, r);
883	specialPlusTerm(p, 200289, 925212, 1, 44, 7, r);
884	specialPlusTerm(p, 200894, 741748, 1, 43, 7, r);
885	specialPlusTerm(p, 199804, 433264, 1, 42, 7, r);
886	specialPlusTerm(p, 197029, 459520, 1, 41, 7, r);
887	specialPlusTerm(p, 192620, 953188, 1, 40, 7, r);
888	specialPlusTerm(p, 186669, 386562, 1, 39, 7, r);
889	specialPlusTerm(p, 179301, 725204, 1, 38, 7, r);
890	specialPlusTerm(p, 170677, 181240, 1, 37, 7, r);
891	specialPlusTerm(p, 160981, 751274, 1, 36, 7, r);
892	specialPlusTerm(p, 150421, 786460, 1, 35, 7, r);
893	specialPlusTerm(p, 139216, 891710, 1, 34, 7, r);
894	specialPlusTerm(p, 127592, 483930, 1, 33, 7, r);
895	specialPlusTerm(p, 115772, 353582, 1, 32, 7, r);
896	specialPlusTerm(p, 103971, 568098, 1, 31, 7, r);
897	specialPlusTerm(p, 92390, 30732, 1, 30, 7, r);
898	specialPlusTerm(p, 81206, 964790, 1, 29, 7, r);
899	specialPlusTerm(p, 70576, 534794, 1, 28, 7, r);
900	specialPlusTerm(p, 60624, 746714, 1, 27, 7, r);
901	specialPlusTerm(p, 51447, 694586, 1, 26, 7, r);
902	specialPlusTerm(p, 43111, 145244, 1, 25, 7, r);
903	specialPlusTerm(p, 35651, 383472, 1, 24, 7, r);
904	specialPlusTerm(p, 29077, 179220, 1, 23, 7, r);
905	specialPlusTerm(p, 23372, 689230, 1, 22, 7, r);
906	specialPlusTerm(p, 18501, 69995, 1, 21, 7, r);
907	specialPlusTerm(p, 14408, 558395, 1, 20, 7, r);
908	specialPlusTerm(p, 11028, 771237, 1, 19, 7, r);
909	specialPlusTerm(p, 8286, 985223, 1, 18, 7, r);
910	specialPlusTerm(p, 6104, 182964, 1, 17, 7, r);
911	specialPlusTerm(p, 4400, 686554, 1, 16, 7, r);
912	specialPlusTerm(p, 3099, 245270, 1, 15, 7, r);
913	specialPlusTerm(p, 2127, 493720, 1, 14, 7, r);
914	specialPlusTerm(p, 1419, 747120, 1, 13, 7, r);
915	specialPlusTerm(p, 918, 147362, 1, 12, 7, r);
916	specialPlusTerm(p, 573, 212794, 1, 11, 7, r);
917	specialPlusTerm(p, 343, 872738, 1, 10, 7, r);
918	specialPlusTerm(p, 197, 84030, 1, 9, 7, r);
919	specialPlusTerm(p, 107, 132168, 1, 8, 7, r);
920	specialPlusTerm(p, 54, 719808, 1, 7, 7, r);
921	specialPlusTerm(p, 25, 940200, 1, 6, 7, r);
922	specialPlusTerm(p, 11, 223212, 1, 5, 7, r);
923	specialPlusTerm(p, 4, 327323, 1, 4, 7, r);
924	specialPlusTerm(p, 1, 434433, 1, 3, 7, r);
925	specialPlusTerm(p, 0, 385385, 1, 2, 7, r);
926	specialPlusTerm(p, 0, 75075, 1, 1, 7, r);
927	specialPlusTerm(p, 0, 8008, 1, 0, 7, r);
928	specialPlusTerm(p, 0, 1, -1, 110, 6, r);
929	specialPlusTerm(p, 0, 12, -1, 109, 6, r);
930	specialPlusTerm(p, 0, 79, -1, 108, 6, r);
931	specialPlusTerm(p, 0, 377, -1, 107, 6, r);
932	specialPlusTerm(p, 0, 1457, -1, 106, 6, r);
933	specialPlusTerm(p, 0, 4836, -1, 105, 6, r);
934	specialPlusTerm(p, 0, 14282, -1, 104, 6, r);
935	specialPlusTerm(p, 0, 38408, -1, 103, 6, r);
936	specialPlusTerm(p, 0, 95585, -1, 102, 6, r);
937	specialPlusTerm(p, 0, 222755, -1, 101, 6, r);
938	specialPlusTerm(p, 0, 490512, -1, 100, 6, r);
939	specialPlusTerm(p, 1, 27858, -1, 99, 6, r);
940	specialPlusTerm(p, 2, 61348, -1, 98, 6, r);
941	specialPlusTerm(p, 3, 974921, -1, 97, 6, r);
942	specialPlusTerm(p, 7, 398548, -1, 96, 6, r);
943	specialPlusTerm(p, 13, 335851, -1, 95, 6, r);
944	specialPlusTerm(p, 23, 342939, -1, 94, 6, r);
945	specialPlusTerm(p, 39, 772696, -1, 93, 6, r);
946	specialPlusTerm(p, 66, 100395, -1, 92, 6, r);
947	specialPlusTerm(p, 107, 347509, -1, 91, 6, r);
948	specialPlusTerm(p, 170, 620609, -1, 90, 6, r);
949	specialPlusTerm(p, 265, 780891, -1, 89, 6, r);
950	specialPlusTerm(p, 406, 256761, -1, 88, 6, r);
951	specialPlusTerm(p, 610, 6662, -1, 87, 6, r);
952	specialPlusTerm(p, 900, 631638, -1, 86, 6, r);
953	specialPlusTerm(p, 1308, 626820, -1, 85, 6, r);
954	specialPlusTerm(p, 1872, 748088, -1, 84, 6, r);
955	specialPlusTerm(p, 2641, 454830, -1, 83, 6, r);
956	specialPlusTerm(p, 3674, 372459, -1, 82, 6, r);
957	specialPlusTerm(p, 5043, 699859, -1, 81, 6, r);
958	specialPlusTerm(p, 6835, 468267, -1, 80, 6, r);
959	specialPlusTerm(p, 9150, 540598, -1, 79, 6, r);
960	specialPlusTerm(p, 12105, 225506, -1, 78, 6, r);
961	specialPlusTerm(p, 15831, 370284, -1, 77, 6, r);
962	specialPlusTerm(p, 20475, 792894, -1, 76, 6, r);
963	specialPlusTerm(p, 26198, 917672, -1, 75, 6, r);
964	specialPlusTerm(p, 33172, 493074, -1, 74, 6, r);
965	specialPlusTerm(p, 41576, 294268, -1, 73, 6, r);
966	specialPlusTerm(p, 51593, 749027, -1, 72, 6, r);
967	specialPlusTerm(p, 63406, 472134, -1, 71, 6, r);
968	specialPlusTerm(p, 77187, 750422, -1, 70, 6, r);
969	specialPlusTerm(p, 93095, 85649, -1, 69, 6, r);
970	specialPlusTerm(p, 111261, 972846, -1, 68, 6, r);
971	specialPlusTerm(p, 131789, 163843, -1, 67, 6, r);
972	specialPlusTerm(p, 154735, 735031, -1, 66, 6, r);
973	specialPlusTerm(p, 180110, 340164, -1, 65, 6, r);
974	specialPlusTerm(p, 207863, 78032, -1, 64, 6, r);
975	specialPlusTerm(p, 237878, 436148, -1, 63, 6, r);
976	specialPlusTerm(p, 269969, 780853, -1, 62, 6, r);
977	specialPlusTerm(p, 303875, 847919, -1, 61, 6, r);
978	specialPlusTerm(p, 339259, 643405, -1, 60, 6, r);
979	specialPlusTerm(p, 375710, 91709, -1, 59, 6, r);
980	specialPlusTerm(p, 412746, 667621, -1, 58, 6, r);
981	specialPlusTerm(p, 449827, 124838, -1, 57, 6, r);
982	specialPlusTerm(p, 486358, 289884, -1, 56, 6, r);
983	specialPlusTerm(p, 521709, 734617, -1, 55, 6, r);
984	specialPlusTerm(p, 555229, 980825, -1, 54, 6, r);
985	specialPlusTerm(p, 586264, 736452, -1, 53, 6, r);
986	specialPlusTerm(p, 614176, 524327, -1, 52, 6, r);
987	specialPlusTerm(p, 638364, 950461, -1, 51, 6, r);
988	specialPlusTerm(p, 658286, 778382, -1, 50, 6, r);
989	specialPlusTerm(p, 673474, 935703, -1, 49, 6, r);
990	specialPlusTerm(p, 683555, 584035, -1, 48, 6, r);
991	specialPlusTerm(p, 688262, 435939, -1, 47, 6, r);
992	specialPlusTerm(p, 687447, 601958, -1, 46, 6, r);
993	specialPlusTerm(p, 681088, 393321, -1, 45, 6, r);
994	specialPlusTerm(p, 669289, 685002, -1, 44, 6, r);
995	specialPlusTerm(p, 652281, 650056, -1, 43, 6, r);
996	specialPlusTerm(p, 630412, 897910, -1, 42, 6, r);
997	specialPlusTerm(p, 604139, 273828, -1, 41, 6, r);
998	specialPlusTerm(p, 574008, 790372, -1, 40, 6, r);
999	specialPlusTerm(p, 540643, 351434, -1, 39, 6, r);
1000	specialPlusTerm(p, 504718, 83850, -1, 38, 6, r);
1001	specialPlusTerm(p, 466939, 201686, -1, 37, 6, r);
1002	specialPlusTerm(p, 428021, 387818, -1, 36, 6, r);
1003	specialPlusTerm(p, 388665, 682772, -1, 35, 6, r);
1004	specialPlusTerm(p, 349538, 822179, -1, 34, 6, r);
1005	specialPlusTerm(p, 311254, 865006, -1, 33, 6, r);
1006	specialPlusTerm(p, 274359, 811613, -1, 32, 6, r);
1007	specialPlusTerm(p, 239319, 732987, -1, 31, 6, r);
1008	specialPlusTerm(p, 206512, 732148, -1, 30, 6, r);
1009	specialPlusTerm(p, 176224, 848533, -1, 29, 6, r);
1010	specialPlusTerm(p, 148649, 810169, -1, 28, 6, r);
1011	specialPlusTerm(p, 123892, 349306, -1, 27, 6, r);
1012	specialPlusTerm(p, 101974, 636229, -1, 26, 6, r);
1013	specialPlusTerm(p, 82845, 261439, -1, 25, 6, r);
1014	specialPlusTerm(p, 66390, 113996, -1, 24, 6, r);
1015	specialPlusTerm(p, 52444, 464455, -1, 23, 6, r);
1016	specialPlusTerm(p, 40805, 563557, -1, 22, 6, r);
1017	specialPlusTerm(p, 31245, 109466, -1, 21, 6, r);
1018	specialPlusTerm(p, 23521, 11382, -1, 20, 6, r);
1019	specialPlusTerm(p, 17387, 978784, -1, 19, 6, r);
1020	specialPlusTerm(p, 12606, 585145, -1, 18, 6, r);
1021	specialPlusTerm(p, 8950, 583389, -1, 17, 6, r);
1022	specialPlusTerm(p, 6212, 378502, -1, 16, 6, r);
1023	specialPlusTerm(p, 4206, 681655, -1, 15, 6, r);
1024	specialPlusTerm(p, 2772, 472065, -1, 14, 6, r);
1025	specialPlusTerm(p, 1773, 471986, -1, 13, 6, r);
1026	specialPlusTerm(p, 1097, 393517, -1, 12, 6, r);
1027	specialPlusTerm(p, 654, 242447, -1, 11, 6, r);
1028	specialPlusTerm(p, 373, 966384, -1, 10, 6, r);
1029	specialPlusTerm(p, 203, 716799, -1, 9, 6, r);
1030	specialPlusTerm(p, 104, 963287, -1, 8, 6, r);
1031	specialPlusTerm(p, 50, 659180, -1, 7, 6, r);
1032	specialPlusTerm(p, 22, 613305, -1, 6, 6, r);
1033	specialPlusTerm(p, 9, 176167, -1, 5, 6, r);
1034	specialPlusTerm(p, 3, 303300, -1, 4, 6, r);
1035	specialPlusTerm(p, 1, 17016, -1, 3, 6, r);
1036	specialPlusTerm(p, 0, 252252, -1, 2, 6, r);
1037	specialPlusTerm(p, 0, 45045, -1, 1, 6, r);
1038	specialPlusTerm(p, 0, 4368, -1, 0, 6, r);
1039	specialPlusTerm(p, 0, 1, 1, 114, 5, r);
1040	specialPlusTerm(p, 0, 13, 1, 113, 5, r);
1041	specialPlusTerm(p, 0, 92, 1, 112, 5, r);
1042	specialPlusTerm(p, 0, 469, 1, 111, 5, r);
1043	specialPlusTerm(p, 0, 1926, 1, 110, 5, r);
1044	specialPlusTerm(p, 0, 6756, 1, 109, 5, r);
1045	specialPlusTerm(p, 0, 20972, 1, 108, 5, r);
1046	specialPlusTerm(p, 0, 58978, 1, 107, 5, r);
1047	specialPlusTerm(p, 0, 152775, 1, 106, 5, r);
1048	specialPlusTerm(p, 0, 369050, 1, 105, 5, r);
1049	specialPlusTerm(p, 0, 839288, 1, 104, 5, r);
1050	specialPlusTerm(p, 1, 810449, 1, 103, 5, r);
1051	specialPlusTerm(p, 3, 726832, 1, 102, 5, r);
1052	specialPlusTerm(p, 7, 357527, 1, 101, 5, r);
1053	specialPlusTerm(p, 13, 988283, 1, 100, 5, r);
1054	specialPlusTerm(p, 25, 701547, 1, 99, 5, r);
1055	specialPlusTerm(p, 45, 773588, 1, 98, 5, r);
1056	specialPlusTerm(p, 79, 222619, 1, 97, 5, r);
1057	specialPlusTerm(p, 133, 546121, 1, 96, 5, r);
1058	specialPlusTerm(p, 219, 688458, 1, 95, 5, r);
1059	specialPlusTerm(p, 353, 280515, 1, 94, 5, r);
1060	specialPlusTerm(p, 556, 190572, 1, 93, 5, r);
1061	specialPlusTerm(p, 858, 418990, 1, 92, 5, r);
1062	specialPlusTerm(p, 1300, 357646, 1, 91, 5, r);
1063	specialPlusTerm(p, 1935, 417677, 1, 90, 5, r);
1064	specialPlusTerm(p, 2833, 5498, 1, 89, 5, r);
1065	specialPlusTerm(p, 4081, 797160, 1, 88, 5, r);
1066	specialPlusTerm(p, 5793, 225338, 1, 87, 5, r);
1067	specialPlusTerm(p, 8105, 52608, 1, 86, 5, r);
1068	specialPlusTerm(p, 11184, 860904, 1, 85, 5, r);
1069	specialPlusTerm(p, 15233, 242543, 1, 84, 5, r);
1070	specialPlusTerm(p, 20486, 436025, 1, 83, 5, r);
1071	specialPlusTerm(p, 27218, 113560, 1, 82, 5, r);
1072	specialPlusTerm(p, 35740, 941, 1, 81, 5, r);
1073	specialPlusTerm(p, 46400, 998184, 1, 80, 5, r);
1074	specialPlusTerm(p, 59584, 475380, 1, 79, 5, r);
1075	specialPlusTerm(p, 75703, 446044, 1, 78, 5, r);
1076	specialPlusTerm(p, 95193, 372588, 1, 77, 5, r);
1077	specialPlusTerm(p, 118502, 436837, 1, 76, 5, r);
1078	specialPlusTerm(p, 146079, 212557, 1, 75, 5, r);
1079	specialPlusTerm(p, 178357, 804753, 1, 74, 5, r);
1080	specialPlusTerm(p, 215740, 667987, 1, 73, 5, r);
1081	specialPlusTerm(p, 258579, 477117, 1, 72, 5, r);
1082	specialPlusTerm(p, 307154, 590636, 1, 71, 5, r);
1083	specialPlusTerm(p, 361653, 809467, 1, 70, 5, r);
1084	specialPlusTerm(p, 422151, 281668, 1, 69, 5, r);
1085	specialPlusTerm(p, 488587, 524562, 1, 68, 5, r);
1086	specialPlusTerm(p, 560751, 619043, 1, 67, 5, r);
1087	specialPlusTerm(p, 638266, 666013, 1, 66, 5, r);
1088	specialPlusTerm(p, 720579, 573693, 1, 65, 5, r);
1089	specialPlusTerm(p, 806956, 161270, 1, 64, 5, r);
1090	specialPlusTerm(p, 896482, 416756, 1, 63, 5, r);
1091	specialPlusTerm(p, 988072, 536828, 1, 62, 5, r);
1092	specialPlusTerm(p, 1080484, 109735, 1, 61, 5, r);
1093	specialPlusTerm(p, 1172340, 489345, 1, 60, 5, r);
1094	specialPlusTerm(p, 1262160, 63390, 1, 59, 5, r);
1095	specialPlusTerm(p, 1348391, 759522, 1, 58, 5, r);
1096	specialPlusTerm(p, 1429455, 778912, 1, 57, 5, r);
1097	specialPlusTerm(p, 1503788, 220123, 1, 56, 5, r);
1098	specialPlusTerm(p, 1569887, 977111, 1, 55, 5, r);
1099	specialPlusTerm(p, 1626364, 84113, 1, 54, 5, r);
1100	specialPlusTerm(p, 1671981, 553512, 1, 53, 5, r);
1101	specialPlusTerm(p, 1705703, 722632, 1, 52, 5, r);
1102	specialPlusTerm(p, 1726729, 198623, 1, 51, 5, r);
1103	specialPlusTerm(p, 1734521, 667786, 1, 50, 5, r);
1104	specialPlusTerm(p, 1728831, 111168, 1, 49, 5, r);
1105	specialPlusTerm(p, 1709705, 329909, 1, 48, 5, r);
1106	specialPlusTerm(p, 1677491, 113716, 1, 47, 5, r);
1107	specialPlusTerm(p, 1632824, 861010, 1, 46, 5, r);
1108	specialPlusTerm(p, 1576612, 953462, 1, 45, 5, r);
1109	specialPlusTerm(p, 1510002, 672602, 1, 44, 5, r);
1110	specialPlusTerm(p, 1434344, 893769, 1, 43, 5, r);
1111	specialPlusTerm(p, 1351150, 176624, 1, 42, 5, r);
1112	specialPlusTerm(p, 1262040, 169393, 1, 41, 5, r);
1113	specialPlusTerm(p, 1168696, 438727, 1, 40, 5, r);
1114	specialPlusTerm(p, 1072808, 918138, 1, 39, 5, r);
1115	specialPlusTerm(p, 976026, 132162, 1, 38, 5, r);
1116	specialPlusTerm(p, 879909, 204828, 1, 37, 5, r);
1117	specialPlusTerm(p, 785891, 410576, 1, 36, 5, r);
1118	specialPlusTerm(p, 695244, 690346, 1, 35, 5, r);
1119	specialPlusTerm(p, 609054, 157073, 1, 34, 5, r);
1120	specialPlusTerm(p, 528201, 178547, 1, 33, 5, r);
1121	specialPlusTerm(p, 453355, 178523, 1, 32, 5, r);
1122	specialPlusTerm(p, 384973, 865967, 1, 31, 5, r);
1123	specialPlusTerm(p, 323311, 212357, 1, 30, 5, r);
1124	specialPlusTerm(p, 268432, 169189, 1, 29, 5, r);
1125	specialPlusTerm(p, 220232, 868421, 1, 28, 5, r);
1126	specialPlusTerm(p, 178464, 887323, 1, 27, 5, r);
1127	specialPlusTerm(p, 142762, 89447, 1, 26, 5, r);
1128	specialPlusTerm(p, 112668, 572043, 1, 25, 5, r);
1129	specialPlusTerm(p, 87666, 348585, 1, 24, 5, r);
1130	specialPlusTerm(p, 67201, 559745, 1, 23, 5, r);
1131	specialPlusTerm(p, 50708, 221257, 1, 22, 5, r);
1132	specialPlusTerm(p, 37628, 764983, 1, 21, 5, r);
1133	specialPlusTerm(p, 27430, 891847, 1, 20, 5, r);
1134	specialPlusTerm(p, 19620, 514504, 1, 19, 5, r);
1135	specialPlusTerm(p, 13750, 807706, 1, 18, 5, r);
1136	specialPlusTerm(p, 9427, 591898, 1, 17, 5, r);
1137	specialPlusTerm(p, 6311, 440762, 1, 16, 5, r);
1138	specialPlusTerm(p, 4117, 20228, 1, 15, 5, r);
1139	specialPlusTerm(p, 2610, 233212, 1, 14, 5, r);
1140	specialPlusTerm(p, 1603, 763552, 1, 13, 5, r);
1141	specialPlusTerm(p, 951, 590329, 1, 12, 5, r);
1142	specialPlusTerm(p, 542, 988511, 1, 11, 5, r);
1143	specialPlusTerm(p, 296, 453834, 1, 10, 5, r);
1144	specialPlusTerm(p, 153, 899291, 1, 9, 5, r);
1145	specialPlusTerm(p, 75, 376496, 1, 8, 5, r);
1146	specialPlusTerm(p, 34, 484437, 1, 7, 5, r);
1147	specialPlusTerm(p, 14, 545453, 1, 6, 5, r);
1148	specialPlusTerm(p, 5, 557552, 1, 5, 5, r);
1149	specialPlusTerm(p, 1, 876238, 1, 4, 5, r);
1150	specialPlusTerm(p, 0, 539266, 1, 3, 5, r);
1151	specialPlusTerm(p, 0, 124215, 1, 2, 5, r);
1152	specialPlusTerm(p, 0, 20475, 1, 1, 5, r);
1153	specialPlusTerm(p, 0, 1820, 1, 0, 5, r);
1154	specialPlusTerm(p, 0, 1, -1, 117, 4, r);
1155	specialPlusTerm(p, 0, 14, -1, 116, 4, r);
1156	specialPlusTerm(p, 0, 106, -1, 115, 4, r);
1157	specialPlusTerm(p, 0, 575, -1, 114, 4, r);
1158	specialPlusTerm(p, 0, 2496, -1, 113, 4, r);
1159	specialPlusTerm(p, 0, 9192, -1, 112, 4, r);
1160	specialPlusTerm(p, 0, 29769, -1, 111, 4, r);
1161	specialPlusTerm(p, 0, 86862, -1, 110, 4, r);
1162	specialPlusTerm(p, 0, 232352, -1, 109, 4, r);
1163	specialPlusTerm(p, 0, 577237, -1, 108, 4, r);
1164	specialPlusTerm(p, 1, 345280, -1, 107, 4, r);
1165	specialPlusTerm(p, 2, 964694, -1, 106, 4, r);
1166	specialPlusTerm(p, 6, 218071, -1, 105, 4, r);
1167	specialPlusTerm(p, 12, 478024, -1, 104, 4, r);
1168	specialPlusTerm(p, 24, 64445, -1, 103, 4, r);
1169	specialPlusTerm(p, 44, 768554, -1, 102, 4, r);
1170	specialPlusTerm(p, 80, 598456, -1, 101, 4, r);
1171	specialPlusTerm(p, 140, 809905, -1, 100, 4, r);
1172	specialPlusTerm(p, 239, 293294, -1, 99, 4, r);
1173	specialPlusTerm(p, 396, 392192, -1, 98, 4, r);
1174	specialPlusTerm(p, 641, 228471, -1, 97, 4, r);
1175	specialPlusTerm(p, 1014, 602512, -1, 96, 4, r);
1176	specialPlusTerm(p, 1572, 522451, -1, 95, 4, r);
1177	specialPlusTerm(p, 2390, 392393, -1, 94, 4, r);
1178	specialPlusTerm(p, 3567, 854826, -1, 93, 4, r);
1179	specialPlusTerm(p, 5234, 236531, -1, 92, 4, r);
1180	specialPlusTerm(p, 7554, 490334, -1, 91, 4, r);
1181	specialPlusTerm(p, 10735, 458285, -1, 90, 4, r);
1182	specialPlusTerm(p, 15032, 207608, -1, 89, 4, r);
1183	specialPlusTerm(p, 20754, 112592, -1, 88, 4, r);
1184	specialPlusTerm(p, 28270, 278236, -1, 87, 4, r);
1185	specialPlusTerm(p, 38013, 830749, -1, 86, 4, r);
1186	specialPlusTerm(p, 50484, 542623, -1, 85, 4, r);
1187	specialPlusTerm(p, 66249, 223101, -1, 84, 4, r);
1188	specialPlusTerm(p, 85939, 295631, -1, 83, 4, r);
1189	specialPlusTerm(p, 110245, 8968, -1, 82, 4, r);
1190	specialPlusTerm(p, 139905, 793448, -1, 81, 4, r);
1191	specialPlusTerm(p, 175696, 382307, -1, 80, 4, r);
1192	specialPlusTerm(p, 218408, 471011, -1, 79, 4, r);
1193	specialPlusTerm(p, 268827, 883672, -1, 78, 4, r);
1194	specialPlusTerm(p, 327707, 449671, -1, 77, 4, r);
1195	specialPlusTerm(p, 395736, 57018, -1, 76, 4, r);
1196	specialPlusTerm(p, 473504, 629765, -1, 75, 4, r);
1197	specialPlusTerm(p, 561470, 59952, -1, 74, 4, r);
1198	specialPlusTerm(p, 659918, 392736, -1, 73, 4, r);
1199	specialPlusTerm(p, 768928, 797683, -1, 72, 4, r);
1200	specialPlusTerm(p, 888340, 40490, -1, 71, 4, r);
1201	specialPlusTerm(p, 1017721, 279436, -1, 70, 4, r);
1202	specialPlusTerm(p, 1156349, 33848, -1, 69, 4, r);
1203	specialPlusTerm(p, 1303192, 95883, -1, 68, 4, r);
1204	specialPlusTerm(p, 1456905, 975122, -1, 67, 4, r);
1205	specialPlusTerm(p, 1615838, 177110, -1, 66, 4, r);
1206	specialPlusTerm(p, 1778045, 228075, -1, 65, 4, r);
1207	specialPlusTerm(p, 1941321, 881690, -1, 64, 4, r);
1208	specialPlusTerm(p, 2103242, 399767, -1, 63, 4, r);
1209	specialPlusTerm(p, 2261213, 213104, -1, 62, 4, r);
1210	specialPlusTerm(p, 2412535, 672007, -1, 61, 4, r);
1211	specialPlusTerm(p, 2554477, 22053, -1, 60, 4, r);
1212	specialPlusTerm(p, 2684347, 224260, -1, 59, 4, r);
1213	specialPlusTerm(p, 2799578, 813532, -1, 58, 4, r);
1214	specialPlusTerm(p, 2897806, 685056, -1, 57, 4, r);
1215	specialPlusTerm(p, 2976944, 539523, -1, 56, 4, r);
1216	specialPlusTerm(p, 3035254, 721183, -1, 55, 4, r);
1217	specialPlusTerm(p, 3071408, 355156, -1, 54, 4, r);
1218	specialPlusTerm(p, 3084533, 29299, -1, 53, 4, r);
1219	specialPlusTerm(p, 3074245, 758101, -1, 52, 4, r);
1220	specialPlusTerm(p, 3040669, 588583, -1, 51, 4, r);
1221	specialPlusTerm(p, 2984432, 929416, -1, 50, 4, r);
1222	specialPlusTerm(p, 2906651, 466023, -1, 49, 4, r);
1223	specialPlusTerm(p, 2808893, 323361, -1, 48, 4, r);
1224	specialPlusTerm(p, 2693128, 909640, -1, 47, 4, r);
1225	specialPlusTerm(p, 2561667, 574760, -1, 46, 4, r);
1226	specialPlusTerm(p, 2417083, 807115, -1, 45, 4, r);
1227	specialPlusTerm(p, 2262136, 138608, -1, 44, 4, r);
1228	specialPlusTerm(p, 2099682, 206060, -1, 43, 4, r);
1229	specialPlusTerm(p, 1932593, 513922, -1, 42, 4, r);
1230	specialPlusTerm(p, 1763673, 355846, -1, 41, 4, r);
1231	specialPlusTerm(p, 1595581, 90061, -1, 40, 4, r);
1232	specialPlusTerm(p, 1430765, 545095, -1, 39, 4, r);
1233	specialPlusTerm(p, 1271409, 786637, -1, 38, 4, r);
1234	specialPlusTerm(p, 1119388, 838595, -1, 37, 4, r);
1235	specialPlusTerm(p, 976241, 261398, -1, 36, 4, r);
1236	specialPlusTerm(p, 843154, 789753, -1, 35, 4, r);
1237	specialPlusTerm(p, 720965, 560845, -1, 34, 4, r);
1238	specialPlusTerm(p, 610169, 859179, -1, 33, 4, r);
1239	specialPlusTerm(p, 510946, 796821, -1, 32, 4, r);
1240	specialPlusTerm(p, 423189, 960892, -1, 31, 4, r);
1241	specialPlusTerm(p, 346545, 808032, -1, 30, 4, r);
1242	specialPlusTerm(p, 280456, 472902, -1, 29, 4, r);
1243	specialPlusTerm(p, 224204, 680080, -1, 28, 4, r);
1244	specialPlusTerm(p, 176958, 593014, -1, 27, 4, r);
1245	specialPlusTerm(p, 137814, 680334, -1, 26, 4, r);
1246	specialPlusTerm(p, 105837, 4252, -1, 25, 4, r);
1247	specialPlusTerm(p, 80091, 710806, -1, 24, 4, r);
1248	specialPlusTerm(p, 59675, 899582, -1, 23, 4, r);
1249	specialPlusTerm(p, 43740, 445029, -1, 22, 4, r);
1250	specialPlusTerm(p, 31506, 709211, -1, 21, 4, r);
1251	specialPlusTerm(p, 22277, 407599, -1, 20, 4, r);
1252	specialPlusTerm(p, 15442, 151129, -1, 19, 4, r);
1253	specialPlusTerm(p, 10478, 380611, -1, 18, 4, r);
1254	specialPlusTerm(p, 6948, 530664, -1, 17, 4, r);
1255	specialPlusTerm(p, 4494, 312038, -1, 16, 4, r);
1256	specialPlusTerm(p, 2828, 990461, -1, 15, 4, r);
1257	specialPlusTerm(p, 1728, 477668, -1, 14, 4, r);
1258	specialPlusTerm(p, 1021, 949004, -1, 13, 4, r);
1259	specialPlusTerm(p, 582, 575810, -1, 12, 4, r);
1260	specialPlusTerm(p, 318, 823114, -1, 11, 4, r);
1261	specialPlusTerm(p, 166, 625848, -1, 10, 4, r);
1262	specialPlusTerm(p, 82, 629352, -1, 9, 4, r);
1263	specialPlusTerm(p, 38, 568972, -1, 8, 4, r);
1264	specialPlusTerm(p, 16, 773120, -1, 7, 4, r);
1265	specialPlusTerm(p, 6, 706050, -1, 6, 4, r);
1266	specialPlusTerm(p, 2, 420964, -1, 5, 4, r);
1267	specialPlusTerm(p, 0, 769496, -1, 4, 4, r);
1268	specialPlusTerm(p, 0, 207389, -1, 3, 4, r);
1269	specialPlusTerm(p, 0, 44590, -1, 2, 4, r);
1270	specialPlusTerm(p, 0, 6825, -1, 1, 4, r);
1271	specialPlusTerm(p, 0, 560, -1, 0, 4, r);
1272	specialPlusTerm(p, 0, 1, 1, 119, 3, r);
1273	specialPlusTerm(p, 0, 15, 1, 118, 3, r);
1274	specialPlusTerm(p, 0, 121, 1, 117, 3, r);
1275	specialPlusTerm(p, 0, 692, 1, 116, 3, r);
1276	specialPlusTerm(p, 0, 3136, 1, 115, 3, r);
1277	specialPlusTerm(p, 0, 11960, 1, 114, 3, r);
1278	specialPlusTerm(p, 0, 39853, 1, 113, 3, r);
1279	specialPlusTerm(p, 0, 119021, 1, 112, 3, r);
1280	specialPlusTerm(p, 0, 324469, 1, 111, 3, r);
1281	specialPlusTerm(p, 0, 818608, 1, 110, 3, r);
1282	specialPlusTerm(p, 1, 931746, 1, 109, 3, r);
1283	specialPlusTerm(p, 4, 299910, 1, 108, 3, r);
1284	specialPlusTerm(p, 9, 90121, 1, 107, 3, r);
1285	specialPlusTerm(p, 18, 353593, 1, 106, 3, r);
1286	specialPlusTerm(p, 35, 558983, 1, 105, 3, r);
1287	specialPlusTerm(p, 66, 370113, 1, 104, 3, r);
1288	specialPlusTerm(p, 119, 744513, 1, 103, 3, r);
1289	specialPlusTerm(p, 209, 439344, 1, 102, 3, r);
1290	specialPlusTerm(p, 356, 18067, 1, 101, 3, r);
1291	specialPlusTerm(p, 589, 452669, 1, 100, 3, r);
1292	specialPlusTerm(p, 952, 410212, 1, 99, 3, r);
1293	specialPlusTerm(p, 1504, 296795, 1, 98, 3, r);
1294	specialPlusTerm(p, 2326, 104760, 1, 97, 3, r);
1295	specialPlusTerm(p, 3526, 68612, 1, 96, 3, r);
1296	specialPlusTerm(p, 5246, 80850, 1, 95, 3, r);
1297	specialPlusTerm(p, 7668, 750896, 1, 94, 3, r);
1298	specialPlusTerm(p, 11024, 909967, 1, 93, 3, r);
1299	specialPlusTerm(p, 15601, 274876, 1, 92, 3, r);
1300	specialPlusTerm(p, 21747, 888690, 1, 91, 3, r);
1301	specialPlusTerm(p, 29884, 861708, 1, 90, 3, r);
1302	specialPlusTerm(p, 40507, 849459, 1, 89, 3, r);
1303	specialPlusTerm(p, 54191, 633482, 1, 88, 3, r);
1304	specialPlusTerm(p, 71591, 124221, 1, 87, 3, r);
1305	specialPlusTerm(p, 93439, 92109, 1, 86, 3, r);
1306	specialPlusTerm(p, 120539, 960778, 1, 85, 3, r);
1307	specialPlusTerm(p, 153759, 71799, 1, 84, 3, r);
1308	specialPlusTerm(p, 194006, 957680, 1, 83, 3, r);
1309	specialPlusTerm(p, 242218, 340335, 1, 82, 3, r);
1310	specialPlusTerm(p, 299325, 803637, 1, 81, 3, r);
1311	specialPlusTerm(p, 366228, 364763, 1, 80, 3, r);
1312	specialPlusTerm(p, 443755, 479465, 1, 79, 3, r);
1313	specialPlusTerm(p, 532627, 346793, 1, 78, 3, r);
1314	specialPlusTerm(p, 633412, 711280, 1, 77, 3, r);
1315	specialPlusTerm(p, 746485, 674616, 1, 76, 3, r);
1316	specialPlusTerm(p, 871983, 302274, 1, 75, 3, r);
1317	specialPlusTerm(p, 1009766, 21123, 1, 74, 3, r);
1318	specialPlusTerm(p, 1159382, 930867, 1, 73, 3, r);
1319	specialPlusTerm(p, 1320044, 177277, 1, 72, 3, r);
1320	specialPlusTerm(p, 1490602, 445312, 1, 71, 3, r);
1321	specialPlusTerm(p, 1669545, 418046, 1, 70, 3, r);
1322	specialPlusTerm(p, 1855000, 712658, 1, 69, 3, r);
1323	specialPlusTerm(p, 2044754, 355265, 1, 68, 3, r);
1324	specialPlusTerm(p, 2236283, 307760, 1, 67, 3, r);
1325	specialPlusTerm(p, 2426801, 935374, 1, 66, 3, r);
1326	specialPlusTerm(p, 2613321, 633418, 1, 65, 3, r);
1327	specialPlusTerm(p, 2792722, 150781, 1, 64, 3, r);
1328	specialPlusTerm(p, 2961832, 494671, 1, 63, 3, r);
1329	specialPlusTerm(p, 3117518, 715055, 1, 62, 3, r);
1330	specialPlusTerm(p, 3256775, 385842, 1, 61, 3, r);
1331	specialPlusTerm(p, 3376817, 256340, 1, 60, 3, r);
1332	specialPlusTerm(p, 3475167, 367466, 1, 59, 3, r);
1333	specialPlusTerm(p, 3549737, 930366, 1, 58, 3, r);
1334	specialPlusTerm(p, 3598900, 457938, 1, 57, 3, r);
1335	specialPlusTerm(p, 3621542, 18424, 1, 56, 3, r);
1336	specialPlusTerm(p, 3617105, 29495, 1, 55, 3, r);
1337	specialPlusTerm(p, 3585608, 705050, 1, 54, 3, r);
1338	specialPlusTerm(p, 3527651, 69853, 1, 53, 3, r);
1339	specialPlusTerm(p, 3444391, 326416, 1, 52, 3, r);
1340	specialPlusTerm(p, 3337513, 246817, 1, 51, 3, r);
1341	specialPlusTerm(p, 3209171, 120352, 1, 50, 3, r);
1342	specialPlusTerm(p, 3061920, 568442, 1, 49, 3, r);
1343	specialPlusTerm(p, 2898637, 197953, 1, 48, 3, r);
1344	specialPlusTerm(p, 2722426, 567254, 1, 47, 3, r);
1345	specialPlusTerm(p, 2536529, 259766, 1, 46, 3, r);
1346	specialPlusTerm(p, 2344224, 982535, 1, 45, 3, r);
1347	specialPlusTerm(p, 2148739, 529673, 1, 44, 3, r);
1348	specialPlusTerm(p, 1953158, 181630, 1, 43, 3, r);
1349	specialPlusTerm(p, 1760348, 671733, 1, 42, 3, r);
1350	specialPlusTerm(p, 1572896, 271477, 1, 41, 3, r);
1351	specialPlusTerm(p, 1393052, 863345, 1, 40, 3, r);
1352	specialPlusTerm(p, 1222701, 126910, 1, 39, 3, r);
1353	specialPlusTerm(p, 1063334, 204889, 1, 38, 3, r);
1354	specialPlusTerm(p, 916050, 483828, 1, 37, 3, r);
1355	specialPlusTerm(p, 781562, 458519, 1, 36, 3, r);
1356	specialPlusTerm(p, 660218, 83241, 1, 35, 3, r);
1357	specialPlusTerm(p, 552032, 571637, 1, 34, 3, r);
1358	specialPlusTerm(p, 456728, 306449, 1, 33, 3, r);
1359	specialPlusTerm(p, 373780, 366678, 1, 32, 3, r);
1360	specialPlusTerm(p, 302465, 169735, 1, 31, 3, r);
1361	specialPlusTerm(p, 241909, 847846, 1, 30, 3, r);
1362	specialPlusTerm(p, 191140, 212177, 1, 29, 3, r);
1363	specialPlusTerm(p, 149125, 480301, 1, 28, 3, r);
1364	specialPlusTerm(p, 114818, 324960, 1, 27, 3, r);
1365	specialPlusTerm(p, 87189, 215772, 1, 26, 3, r);
1366	specialPlusTerm(p, 65254, 442815, 1, 25, 3, r);
1367	specialPlusTerm(p, 48097, 606920, 1, 24, 3, r);
1368	specialPlusTerm(p, 34884, 715247, 1, 23, 3, r);
1369	specialPlusTerm(p, 24873, 316659, 1, 22, 3, r);
1370	specialPlusTerm(p, 17416, 339482, 1, 21, 3, r);
1371	specialPlusTerm(p, 11961, 450014, 1, 20, 3, r);
1372	specialPlusTerm(p, 8046, 834503, 1, 19, 3, r);
1373	specialPlusTerm(p, 5294, 325768, 1, 18, 3, r);
1374	specialPlusTerm(p, 3400, 757398, 1, 17, 3, r);
1375	specialPlusTerm(p, 2128, 345318, 1, 16, 3, r);
1376	specialPlusTerm(p, 1294, 781596, 1, 15, 3, r);
1377	specialPlusTerm(p, 763, 591975, 1, 14, 3, r);
1378	specialPlusTerm(p, 435, 169111, 1, 13, 3, r);
1379	specialPlusTerm(p, 238, 758463, 1, 12, 3, r);
1380	specialPlusTerm(p, 125, 551459, 1, 11, 3, r);
1381	specialPlusTerm(p, 62, 936621, 1, 10, 3, r);
1382	specialPlusTerm(p, 29, 876893, 1, 9, 3, r);
1383	specialPlusTerm(p, 13, 321355, 1, 8, 3, r);
1384	specialPlusTerm(p, 5, 520901, 1, 7, 3, r);
1385	specialPlusTerm(p, 2, 98067, 1, 6, 3, r);
1386	specialPlusTerm(p, 0, 717871, 1, 5, 3, r);
1387	specialPlusTerm(p, 0, 215565, 1, 4, 3, r);
1388	specialPlusTerm(p, 0, 54691, 1, 3, 3, r);
1389	specialPlusTerm(p, 0, 11025, 1, 2, 3, r);
1390	specialPlusTerm(p, 0, 1575, 1, 1, 3, r);
1391	specialPlusTerm(p, 0, 120, 1, 0, 3, r);
1392	specialPlusTerm(p, 0, 1, -1, 120, 2, r);
1393	specialPlusTerm(p, 0, 16, -1, 119, 2, r);
1394	specialPlusTerm(p, 0, 134, -1, 118, 2, r);
1395	specialPlusTerm(p, 0, 784, -1, 117, 2, r);
1396	specialPlusTerm(p, 0, 3602, -1, 116, 2, r);
1397	specialPlusTerm(p, 0, 13843, -1, 115, 2, r);
1398	specialPlusTerm(p, 0, 46286, -1, 114, 2, r);
1399	specialPlusTerm(p, 0, 138283, -1, 113, 2, r);
1400	specialPlusTerm(p, 0, 376259, -1, 112, 2, r);
1401	specialPlusTerm(p, 0, 945827, -1, 111, 2, r);
1402	specialPlusTerm(p, 2, 220933, -1, 110, 2, r);
1403	specialPlusTerm(p, 4, 914174, -1, 109, 2, r);
1404	specialPlusTerm(p, 10, 318553, -1, 108, 2, r);
1405	specialPlusTerm(p, 20, 680144, -1, 107, 2, r);
1406	specialPlusTerm(p, 39, 750869, -1, 106, 2, r);
1407	specialPlusTerm(p, 73, 579984, -1, 105, 2, r);
1408	specialPlusTerm(p, 131, 610793, -1, 104, 2, r);
1409	specialPlusTerm(p, 228, 154162, -1, 103, 2, r);
1410	specialPlusTerm(p, 384, 310996, -1, 102, 2, r);
1411	specialPlusTerm(p, 630, 410278, -1, 101, 2, r);
1412	specialPlusTerm(p, 1009, 15895, -1, 100, 2, r);
1413	specialPlusTerm(p, 1578, 532849, -1, 99, 2, r);
1414	specialPlusTerm(p, 2417, 410542, -1, 98, 2, r);
1415	specialPlusTerm(p, 3628, 897233, -1, 97, 2, r);
1416	specialPlusTerm(p, 5346, 245930, -1, 96, 2, r);
1417	specialPlusTerm(p, 7738, 209354, -1, 95, 2, r);
1418	specialPlusTerm(p, 11014, 592780, -1, 94, 2, r);
1419	specialPlusTerm(p, 15431, 562271, -1, 93, 2, r);
1420	specialPlusTerm(p, 21296, 336917, -1, 92, 2, r);
1421	specialPlusTerm(p, 28970, 832923, -1, 91, 2, r);
1422	specialPlusTerm(p, 38873, 781118, -1, 90, 2, r);
1423	specialPlusTerm(p, 51480, 814244, -1, 89, 2, r);
1424	specialPlusTerm(p, 67322, 22502, -1, 88, 2, r);
1425	specialPlusTerm(p, 86976, 510707, -1, 87, 2, r);
1426	specialPlusTerm(p, 111063, 562039, -1, 86, 2, r);
1427	specialPlusTerm(p, 140230, 123797, -1, 85, 2, r);
1428	specialPlusTerm(p, 175134, 479331, -1, 84, 2, r);
1429	specialPlusTerm(p, 216426, 154185, -1, 83, 2, r);
1430	specialPlusTerm(p, 264722, 317163, -1, 82, 2, r);
1431	specialPlusTerm(p, 320581, 169273, -1, 81, 2, r);
1432	specialPlusTerm(p, 384473, 53329, -1, 80, 2, r);
1433	specialPlusTerm(p, 456750, 250207, -1, 79, 2, r);
1434	specialPlusTerm(p, 537616, 638714, -1, 78, 2, r);
1435	specialPlusTerm(p, 627098, 568602, -1, 77, 2, r);
1436	specialPlusTerm(p, 725018, 414915, -1, 76, 2, r);
1437	specialPlusTerm(p, 830972, 332853, -1, 75, 2, r);
1438	specialPlusTerm(p, 944313, 704873, -1, 74, 2, r);
1439	specialPlusTerm(p, 1064143, 659019, -1, 73, 2, r);
1440	specialPlusTerm(p, 1189309, 837532, -1, 72, 2, r);
1441	specialPlusTerm(p, 1318414, 311129, -1, 71, 2, r);
1442	specialPlusTerm(p, 1449831, 176128, -1, 70, 2, r);
1443	specialPlusTerm(p, 1581733, 953526, -1, 69, 2, r);
1444	specialPlusTerm(p, 1712132, 450851, -1, 68, 2, r);
1445	specialPlusTerm(p, 1838918, 272730, -1, 67, 2, r);
1446	specialPlusTerm(p, 1959917, 700931, -1, 66, 2, r);
1447	specialPlusTerm(p, 2072950, 236513, -1, 65, 2, r);
1448	specialPlusTerm(p, 2175890, 732337, -1, 64, 2, r);
1449	specialPlusTerm(p, 2266732, 767744, -1, 63, 2, r);
1450	specialPlusTerm(p, 2343650, 748669, -1, 62, 2, r);
1451	specialPlusTerm(p, 2405058, 170088, -1, 61, 2, r);
1452	specialPlusTerm(p, 2449659, 560856, -1, 60, 2, r);
1453	specialPlusTerm(p, 2476493, 843437, -1, 59, 2, r);
1454	specialPlusTerm(p, 2484967, 174656, -1, 58, 2, r);
1455	specialPlusTerm(p, 2474873, 772785, -1, 57, 2, r);
1456	specialPlusTerm(p, 2446403, 758673, -1, 56, 2, r);
1457	specialPlusTerm(p, 2400137, 616515, -1, 55, 2, r);
1458	specialPlusTerm(p, 2337027, 481818, -1, 54, 2, r);
1459	specialPlusTerm(p, 2258366, 57059, -1, 53, 2, r);
1460	specialPlusTerm(p, 2165744, 506758, -1, 52, 2, r);
1461	specialPlusTerm(p, 2061001, 163040, -1, 51, 2, r);
1462	specialPlusTerm(p, 1946163, 254505, -1, 50, 2, r);
1463	specialPlusTerm(p, 1823384, 135692, -1, 49, 2, r);
1464	specialPlusTerm(p, 1694878, 629195, -1, 48, 2, r);
1465	specialPlusTerm(p, 1562859, 93097, -1, 47, 2, r);
1466	specialPlusTerm(p, 1429474, 696453, -1, 46, 2, r);
1467	specialPlusTerm(p, 1296756, 136371, -1, 45, 2, r);
1468	specialPlusTerm(p, 1166567, 679850, -1, 44, 2, r);
1469	specialPlusTerm(p, 1040567, 985354, -1, 43, 2, r);
1470	specialPlusTerm(p, 920180, 680239, -1, 42, 2, r);
1471	specialPlusTerm(p, 806575, 169521, -1, 41, 2, r);
1472	specialPlusTerm(p, 700657, 657865, -1, 40, 2, r);
1473	specialPlusTerm(p, 603071, 906907, -1, 39, 2, r);
1474	specialPlusTerm(p, 514208, 847321, -1, 38, 2, r);
1475	specialPlusTerm(p, 434223, 837763, -1, 37, 2, r);
1476	specialPlusTerm(p, 363060, 123557, -1, 36, 2, r);
1477	specialPlusTerm(p, 300476, 903127, -1, 35, 2, r);
1478	specialPlusTerm(p, 246080, 359923, -1, 34, 2, r);
1479	specialPlusTerm(p, 199356, 56374, -1, 33, 2, r);
1480	specialPlusTerm(p, 159701, 203700, -1, 32, 2, r);
1481	specialPlusTerm(p, 126455, 502830, -1, 31, 2, r);
1482	specialPlusTerm(p, 98929, 480219, -1, 30, 2, r);
1483	specialPlusTerm(p, 76429, 499829, -1, 29, 2, r);
1484	specialPlusTerm(p, 58278, 900847, -1, 28, 2, r);
1485	specialPlusTerm(p, 43834, 973084, -1, 27, 2, r);
1486	specialPlusTerm(p, 32501, 723962, -1, 26, 2, r);
1487	specialPlusTerm(p, 23738, 601098, -1, 25, 2, r);
1488	specialPlusTerm(p, 17065, 504721, -1, 24, 2, r);
1489	specialPlusTerm(p, 12064, 550062, -1, 23, 2, r);
1490	specialPlusTerm(p, 8379, 120417, -1, 22, 2, r);
1491	specialPlusTerm(p, 5710, 788839, -1, 21, 2, r);
1492	specialPlusTerm(p, 3814, 684934, -1, 20, 2, r);
1493	specialPlusTerm(p, 2493, 849460, -1, 19, 2, r);
1494	specialPlusTerm(p, 1593, 60962, -1, 18, 2, r);
1495	specialPlusTerm(p, 992, 543577, -1, 17, 2, r);
1496	specialPlusTerm(p, 601, 881264, -1, 16, 2, r);
1497	specialPlusTerm(p, 354, 378149, -1, 15, 2, r);
1498	specialPlusTerm(p, 202, 23344, -1, 14, 2, r);
1499	specialPlusTerm(p, 111, 145993, -1, 13, 2, r);
1500	specialPlusTerm(p, 58, 785390, -1, 12, 2, r);
1501	specialPlusTerm(p, 29, 753317, -1, 11, 2, r);
1502	specialPlusTerm(p, 14, 331491, -1, 10, 2, r);
1503	specialPlusTerm(p, 6, 525379, -1, 9, 2, r);
1504	specialPlusTerm(p, 2, 785083, -1, 8, 2, r);
1505	specialPlusTerm(p, 1, 102494, -1, 7, 2, r);
1506	specialPlusTerm(p, 0, 399235, -1, 6, 2, r);
1507	specialPlusTerm(p, 0, 129826, -1, 5, 2, r);
1508	specialPlusTerm(p, 0, 36944, -1, 4, 2, r);
1509	specialPlusTerm(p, 0, 8854, -1, 3, 2, r);
1510	specialPlusTerm(p, 0, 1680, -1, 2, 2, r);
1511	specialPlusTerm(p, 0, 225, -1, 1, 2, r);
1512	specialPlusTerm(p, 0, 16, -1, 0, 2, r);
1513	specialPlusTerm(p, 0, 1, 1, 120, 1, r);
1514	specialPlusTerm(p, 0, 15, 1, 119, 1, r);
1515	specialPlusTerm(p, 0, 119, 1, 118, 1, r);
1516	specialPlusTerm(p, 0, 664, 1, 117, 1, r);
1517	specialPlusTerm(p, 0, 2924, 1, 116, 1, r);
1518	specialPlusTerm(p, 0, 10813, 1, 115, 1, r);
1519	specialPlusTerm(p, 0, 34900, 1, 114, 1, r);
1520	specialPlusTerm(p, 0, 100913, 1, 113, 1, r);
1521	specialPlusTerm(p, 0, 266338, 1, 112, 1, r);
1522	specialPlusTerm(p, 0, 650658, 1, 111, 1, r);
1523	specialPlusTerm(p, 1, 487262, 1, 110, 1, r);
1524	specialPlusTerm(p, 3, 208036, 1, 109, 1, r);
1525	specialPlusTerm(p, 6, 574987, 1, 108, 1, r);
1526	specialPlusTerm(p, 12, 876702, 1, 107, 1, r);
1527	specialPlusTerm(p, 24, 210652, 1, 106, 1, r);
1528	specialPlusTerm(p, 43, 874857, 1, 105, 1, r);
1529	specialPlusTerm(p, 76, 893687, 1, 104, 1, r);
1530	specialPlusTerm(p, 130, 701986, 1, 103, 1, r);
1531	specialPlusTerm(p, 216, 8661, 1, 102, 1, r);
1532	specialPlusTerm(p, 347, 854815, 1, 101, 1, r);
1533	specialPlusTerm(p, 546, 871981, 1, 100, 1, r);
1534	specialPlusTerm(p, 840, 732790, 1, 99, 1, r);
1535	specialPlusTerm(p, 1265, 769513, 1, 98, 1, r);
1536	specialPlusTerm(p, 1868, 715733, 1, 97, 1, r);
1537	specialPlusTerm(p, 2708, 503701, 1, 96, 1, r);
1538	specialPlusTerm(p, 3858, 25899, 1, 95, 1, r);
1539	specialPlusTerm(p, 5405, 745562, 1, 94, 1, r);
1540	specialPlusTerm(p, 7457, 19331, 1, 93, 1, r);
1541	specialPlusTerm(p, 10134, 977992, 1, 92, 1, r);
1542	specialPlusTerm(p, 13580, 800674, 1, 91, 1, r);
1543	specialPlusTerm(p, 17953, 216130, 1, 90, 1, r);
1544	specialPlusTerm(p, 23427, 73737, 1, 89, 1, r);
1545	specialPlusTerm(p, 30190, 848078, 1, 88, 1, r);
1546	specialPlusTerm(p, 38442, 975195, 1, 87, 1, r);
1547	specialPlusTerm(p, 48386, 965771, 1, 86, 1, r);
1548	specialPlusTerm(p, 60225, 299589, 1, 85, 1, r);
1549	specialPlusTerm(p, 74152, 174574, 1, 84, 1, r);
1550	specialPlusTerm(p, 90345, 259476, 1, 83, 1, r);
1551	specialPlusTerm(p, 108956, 677797, 1, 82, 1, r);
1552	specialPlusTerm(p, 130103, 527156, 1, 81, 1, r);
1553	specialPlusTerm(p, 153858, 307693, 1, 80, 1, r);
1554	specialPlusTerm(p, 180239, 689955, 1, 79, 1, r);
1555	specialPlusTerm(p, 209204, 91832, 1, 78, 1, r);
1556	specialPlusTerm(p, 240638, 550997, 1, 77, 1, r);
1557	specialPlusTerm(p, 274355, 370450, 1, 76, 1, r);
1558	specialPlusTerm(p, 310088, 978041, 1, 75, 1, r);
1559	specialPlusTerm(p, 347495, 375766, 1, 74, 1, r);
1560	specialPlusTerm(p, 386154, 462530, 1, 73, 1, r);
1561	specialPlusTerm(p, 425575, 398166, 1, 72, 1, r);
1562	specialPlusTerm(p, 465205, 41801, 1, 71, 1, r);
1563	specialPlusTerm(p, 504439, 350762, 1, 70, 1, r);
1564	specialPlusTerm(p, 542637, 474944, 1, 69, 1, r);
1565	specialPlusTerm(p, 579138, 134521, 1, 68, 1, r);
1566	specialPlusTerm(p, 613277, 734909, 1, 67, 1, r);
1567	specialPlusTerm(p, 644409, 560477, 1, 66, 1, r);
1568	specialPlusTerm(p, 671923, 305201, 1, 65, 1, r);
1569	specialPlusTerm(p, 695264, 150336, 1, 64, 1, r);
1570	specialPlusTerm(p, 713950, 590364, 1, 63, 1, r);
1571	specialPlusTerm(p, 727590, 240796, 1, 62, 1, r);
1572	specialPlusTerm(p, 735892, 934219, 1, 61, 1, r);
1573	specialPlusTerm(p, 738680, 521142, 1, 60, 1, r);
1574	specialPlusTerm(p, 735892, 934219, 1, 59, 1, r);
1575	specialPlusTerm(p, 727590, 240796, 1, 58, 1, r);
1576	specialPlusTerm(p, 713950, 590364, 1, 57, 1, r);
1577	specialPlusTerm(p, 695264, 150336, 1, 56, 1, r);
1578	specialPlusTerm(p, 671923, 305201, 1, 55, 1, r);
1579	specialPlusTerm(p, 644409, 560477, 1, 54, 1, r);
1580	specialPlusTerm(p, 613277, 734909, 1, 53, 1, r);
1581	specialPlusTerm(p, 579138, 134521, 1, 52, 1, r);
1582	specialPlusTerm(p, 542637, 474944, 1, 51, 1, r);
1583	specialPlusTerm(p, 504439, 350762, 1, 50, 1, r);
1584	specialPlusTerm(p, 465205, 41801, 1, 49, 1, r);
1585	specialPlusTerm(p, 425575, 398166, 1, 48, 1, r);
1586	specialPlusTerm(p, 386154, 462530, 1, 47, 1, r);
1587	specialPlusTerm(p, 347495, 375766, 1, 46, 1, r);
1588	specialPlusTerm(p, 310088, 978041, 1, 45, 1, r);
1589	specialPlusTerm(p, 274355, 370450, 1, 44, 1, r);
1590	specialPlusTerm(p, 240638, 550997, 1, 43, 1, r);
1591	specialPlusTerm(p, 209204, 91832, 1, 42, 1, r);
1592	specialPlusTerm(p, 180239, 689955, 1, 41, 1, r);
1593	specialPlusTerm(p, 153858, 307693, 1, 40, 1, r);
1594	specialPlusTerm(p, 130103, 527156, 1, 39, 1, r);
1595	specialPlusTerm(p, 108956, 677797, 1, 38, 1, r);
1596	specialPlusTerm(p, 90345, 259476, 1, 37, 1, r);
1597	specialPlusTerm(p, 74152, 174574, 1, 36, 1, r);
1598	specialPlusTerm(p, 60225, 299589, 1, 35, 1, r);
1599	specialPlusTerm(p, 48386, 965771, 1, 34, 1, r);
1600	specialPlusTerm(p, 38442, 975195, 1, 33, 1, r);
1601	specialPlusTerm(p, 30190, 848078, 1, 32, 1, r);
1602	specialPlusTerm(p, 23427, 73737, 1, 31, 1, r);
1603	specialPlusTerm(p, 17953, 216130, 1, 30, 1, r);
1604	specialPlusTerm(p, 13580, 800674, 1, 29, 1, r);
1605	specialPlusTerm(p, 10134, 977992, 1, 28, 1, r);
1606	specialPlusTerm(p, 7457, 19331, 1, 27, 1, r);
1607	specialPlusTerm(p, 5405, 745562, 1, 26, 1, r);
1608	specialPlusTerm(p, 3858, 25899, 1, 25, 1, r);
1609	specialPlusTerm(p, 2708, 503701, 1, 24, 1, r);
1610	specialPlusTerm(p, 1868, 715733, 1, 23, 1, r);
1611	specialPlusTerm(p, 1265, 769513, 1, 22, 1, r);
1612	specialPlusTerm(p, 840, 732790, 1, 21, 1, r);
1613	specialPlusTerm(p, 546, 871981, 1, 20, 1, r);
1614	specialPlusTerm(p, 347, 854815, 1, 19, 1, r);
1615	specialPlusTerm(p, 216, 8661, 1, 18, 1, r);
1616	specialPlusTerm(p, 130, 701986, 1, 17, 1, r);
1617	specialPlusTerm(p, 76, 893687, 1, 16, 1, r);
1618	specialPlusTerm(p, 43, 874857, 1, 15, 1, r);
1619	specialPlusTerm(p, 24, 210652, 1, 14, 1, r);
1620	specialPlusTerm(p, 12, 876702, 1, 13, 1, r);
1621	specialPlusTerm(p, 6, 574987, 1, 12, 1, r);
1622	specialPlusTerm(p, 3, 208036, 1, 11, 1, r);
1623	specialPlusTerm(p, 1, 487262, 1, 10, 1, r);
1624	specialPlusTerm(p, 0, 650658, 1, 9, 1, r);
1625	specialPlusTerm(p, 0, 266338, 1, 8, 1, r);
1626	specialPlusTerm(p, 0, 100913, 1, 7, 1, r);
1627	specialPlusTerm(p, 0, 34900, 1, 6, 1, r);
1628	specialPlusTerm(p, 0, 10813, 1, 5, 1, r);
1629	specialPlusTerm(p, 0, 2924, 1, 4, 1, r);
1630	specialPlusTerm(p, 0, 664, 1, 3, 1, r);
1631	specialPlusTerm(p, 0, 119, 1, 2, 1, r);
1632	specialPlusTerm(p, 0, 15, 1, 1, 1, r);
1633	specialPlusTerm(p, 0, 1, 1, 0, 1, r);
1634	}
1635	void checkInverse(number n, const coeffs cf)
1636	{
1637	clog << "n = "; p_Write((poly)n, cf->extRing);
1638	number n1 = n_Invers(n, cf);
1639	clog << "==> n^(-1) = "; p_Write((poly)n1, cf->extRing);
1640	number n2 = n_Mult(n, n1, cf);
1641	clog << "check: n * n^(-1) = "; p_Write((poly)n2, cf->extRing);
1642	TS_ASSERT( n_IsOne(n2, cf) );
1643	n_Delete(&n1, cf); n_Delete(&n2, cf);
1644	}
1645	/* to be used over a rational function field, only!
1646	assumes that cf represents a rational function field;
1647	uses p inside the resulting number (and not a copy of it!) */
1648	number toFractionNumber(poly p, const coeffs cf)
1649	{
1650	number n = n_Init(1, cf);
1651	fraction f = (fraction)n;
1652	p_Delete(&(f->numerator), cf->extRing);
1653	f->numerator = p;
1654	return n;
1655	}
1656	void TestArithCf(const coeffs r)
1657	{
1658	clog << ("TEST: Simple Arithmetics: ");
1659	clog << endl;
1660
1661	number two = n_Init(2, r);
1662
1663	number t = n_Init(1, r);
1664	ndInpAdd(t, t, r);
1665	TS_ASSERT( n_Equal(two, t, r) );
1666	n_Delete(&t, r);
1667
1668	if( getCoeffType(r) == n_Q )
1669	{
1670	number t = n_Init(1, r);
1671	nlInpAdd(t, t, r);
1672	TS_ASSERT( n_Equal(two, t, r) );
1673	n_Delete(&t, r);
1674	}
1675
1676	const int N = 66666;
1677
1678	number a = n_Init(N, r);
1679
1680	clog<< "a: "; PrintSized(a, r);
1681
1682	clog<< "two: "; PrintSized(two, r);
1683
1684	number aa0 = n_Init(N*2, r);
1685
1686	number aa = n_Add(a, a, r);
1687
1688	clog<< "aa = a + a: "; PrintSized(aa, r);
1689
1690	number aa2 = n_Mult(a, two, r);
1691
1692	clog<< "aa2 = a * 2: "; PrintSized(aa2, r);
1693
1694	number aa1 = n_Mult(two, a, r);
1695
1696	clog<< "aa1 = 2 * a: "; PrintSized(aa1, r);
1697
1698	n_Delete(&a, r);
1699	n_Delete(&two, r);
1700
1701	a = n_Sub( aa, aa1, r );
1702
1703	clog<< "a = aa - aa1: "; PrintSized(a, r);
1704
1705	TS_ASSERT( n_IsZero(a, r) );
1706
1707	n_Delete(&a, r);
1708
1709	a = n_Sub( aa, aa2, r );
1710
1711	clog<< "a = aa - aa2: "; PrintSized(a, r);
1712
1713	TS_ASSERT( n_IsZero(a, r) );
1714
1715	n_Delete(&a, r);
1716
1717	a = n_Sub( aa1, aa2, r );
1718
1719	clog<< "a = aa1 - aa2: "; PrintSized(a, r);
1720
1721	TS_ASSERT( n_IsZero(a, r) );
1722
1723	n_Delete(&a, r);
1724
1725	TS_ASSERT( n_Equal(aa, aa1, r) );
1726	TS_ASSERT( n_Equal(aa, aa2, r) );
1727	TS_ASSERT( n_Equal(aa1, aa2, r) );
1728
1729	TS_ASSERT( n_Equal(aa0, aa, r) );
1730	TS_ASSERT( n_Equal(aa0, aa1, r) );
1731	TS_ASSERT( n_Equal(aa0, aa2, r) );
1732
1733	n_Delete(&aa, r);
1734	n_Delete(&aa1, r);
1735	n_Delete(&aa2, r);
1736
1737	n_Delete(&aa0, r);
1738
1739	clog << ( " >>> TEST DONE!" );
1740	clog << endl;
1741	}
1742	void TestSumCf(const coeffs r, const unsigned long N)
1743	{
1744	clog << ( _2S("TEST: sum[0..") + _2S(N) + "]: ");
1745	clog << endl;
1746
1747	assume( N > 0 ); // just for now...
1748
1749	const unsigned long ssss = (N * (N+1)) / 2;
1750
1751	number sum1 = n_Init(ssss, r);
1752	clog<< "N*(N+1)/2 (int: " << ssss << "): "; PrintSized(sum1, r);
1753
1754	number s, ss, i, res;
1755
1756	s = n_Init(N , r);
1757	i = n_Init(N+1, r);
1758	ndInpMult(s, i, r);
1759	n_Delete(&i, r);
1760
1761	clog<< "N(N+1): ("<< N(N+1) << ")"; PrintSized(s, r);
1762
1763	i = n_Init(2, r);
1764	clog<< "2: "; PrintSized(i, r);
1765
1766	if( !n_IsZero( i, r) )
1767	{
1768	#ifdef HAVE_RINGS
1769	TS_ASSERT( n_DivBy(s, i, r) );
1770	#endif
1771
1772	res = n_Div(s, i, r);
1773
1774	clog<< "N*(N+1)/2: "; PrintSized(res, r);
1775
1776
1777	number d = n_Sub(res, sum1, r);
1778	TS_ASSERT( n_IsZeroDivisor(d, r) );
1779	n_Delete(&d, r);
1780
1781	if( n_GetChar(r) == 0 )
1782	{
1783	TS_ASSERT( n_Equal(sum1, res, r) );
1784	TS_ASSERT( n_Equal(res, sum1, r) );
1785	}
1786	} else
1787	TS_ASSERT_EQUALS( n_GetChar(r), 2);
1788
1789
1790	n_Delete(&s, r); n_Delete(&i, r);
1791
1792	n_Delete(&sum1, r); n_Delete(&res, r);
1793
1794
1795	s = n_Init(0 , r);
1796	ss = n_Init(0 , r);
1797	for( int k = N; k >= 0; k-- )
1798	{
1799	i = n_Init(k, r);
1800	ndInpAdd(s, i, r); // s += i
1801
1802	i = n_Neg(i, r);
1803	ndInpAdd(ss, i, r); // ss -= i
1804
1805	n_Delete(&i, r);
1806	}
1807	clog<< "ss: "; PrintSized(ss, r);
1808
1809	ss = n_Neg(ss, r); // ss = -ss
1810
1811	clog<< "real sum : "; PrintSized(s, r);
1812	clog<< "real sum(--): "; PrintSized(ss, r);
1813
1814	TS_ASSERT( n_Equal(s, ss, r) );
1815	TS_ASSERT( n_Equal(ss, s, r) );
1816
1817	n_Delete(&s, r);
1818	n_Delete(&ss, r);
1819
1820	clog << ( " >>> TEST DONE!" );
1821	clog << endl;
1822
1823	}
1824	public:
1825	void test_Z13_t()
1826	{
1827	clog << "Creating Z/13[t]: " << endl;
1828
1829	char* n[] = {"t"};
1830	ring r = rDefault( 13, 1, n);
1831	TS_ASSERT_DIFFERS( r, NULLp );
1832
1833	PrintRing(r);
1834
1835	TS_ASSERT( rField_is_Domain(r) );
1836	TS_ASSERT( !rField_is_Q(r) );
1837
1838	TS_ASSERT( rField_is_Zp(r) );
1839	TS_ASSERT( !rField_is_Zp(r, 11) );
1840	TS_ASSERT( rField_is_Zp(r, 13) );
1841
1842	TS_ASSERT_EQUALS( rVar(r), 1);
1843
1844	Test(r);
1845
1846	rDelete(r);
1847	}
1848
1849	void test_QQ_t()
1850	{
1851	clog << "Creating Q[s]: " << endl;
1852
1853	char* n[] = {"s"};
1854	ring r = rDefault( 0, 1, n);
1855	TS_ASSERT_DIFFERS( r, NULLp );
1856
1857	PrintRing(r);
1858
1859	TS_ASSERT( rField_is_Domain(r) );
1860	TS_ASSERT( rField_is_Q(r) );
1861
1862	TS_ASSERT( !rField_is_Zp(r) );
1863	TS_ASSERT( !rField_is_Zp(r, 11) );
1864
1865	TS_ASSERT_EQUALS( rVar(r), 1);
1866
1867	Test(r);
1868
1869	rDelete(r);
1870	}
1871
1872	void test_Z11_x_y_z()
1873	{
1874	clog << "Creating Z/11[x, y, z]: " << endl;
1875
1876	char* n[] = {"x", "y", "z"};
1877	ring r = rDefault( 11, 3, n);
1878	TS_ASSERT_DIFFERS( r, NULLp );
1879
1880	PrintRing(r);
1881
1882	TS_ASSERT( rField_is_Domain(r) );
1883	TS_ASSERT( !rField_is_Q(r) );
1884
1885	TS_ASSERT( rField_is_Zp(r) );
1886	TS_ASSERT( rField_is_Zp(r, 11) );
1887	TS_ASSERT( !rField_is_Zp(r, 13) );
1888
1889	TS_ASSERT_EQUALS( rVar(r), 3);
1890
1891	Test(r);
1892
1893	rDelete(r);
1894	}
1895	void test_QQ_x_y_z()
1896	{
1897	clog << "Creating QQ[x, y, z, u]: " << endl;
1898
1899	char* n[] = {"x", "y", "z", "u"};
1900	ring r = rDefault( 0, 4, n);
1901	TS_ASSERT_DIFFERS( r, NULLp );
1902
1903	PrintRing(r);
1904
1905	TS_ASSERT( rField_is_Domain(r) );
1906	TS_ASSERT( rField_is_Q(r) );
1907
1908	TS_ASSERT( !rField_is_Zp(r) );
1909	TS_ASSERT( !rField_is_Zp(r, 11) );
1910
1911	TS_ASSERT_EQUALS( rVar(r), 4);
1912
1913	Test(r);
1914
1915	rDelete(r);
1916	}
1917
1918
1919	void test_Z13_t_GF()
1920	{
1921	clog << "Creating GF[t]: " << endl;
1922
1923	char* n[] = {"t"};
1924
1925	GFInfo param;
1926
1927	param.GFChar= 5;
1928	param.GFDegree= 2;
1929	param.GFPar_name= (const char*)"Q";
1930
1931	const coeffs cf = nInitChar( n_GF, &param );
1932
1933	if( cf == NULL )
1934	TS_FAIL("Could not get needed coeff. domain");
1935
1936	TS_ASSERT_DIFFERS( cf, NULLp );
1937
1938	ring r = rDefault( cf, 1, n); // now cf belongs to r!
1939	TS_ASSERT_DIFFERS( r, NULLp );
1940
1941	PrintRing(r);
1942
1943	TS_ASSERT( rField_is_Domain(r) );
1944	TS_ASSERT( !rField_is_Q(r) );
1945
1946	TS_ASSERT( !rField_is_Zp(r) );
1947	TS_ASSERT( !rField_is_Zp(r, 11) );
1948	TS_ASSERT( !rField_is_Zp(r, 13) );
1949	TS_ASSERT( rField_is_GF(r) );
1950
1951	TS_ASSERT( rField_is_GF(r, 5) );
1952	TS_ASSERT( !rField_is_GF(r, 25) );
1953
1954	TS_ASSERT_EQUALS( rVar(r), 1);
1955
1956	Test(r);
1957
1958	rDelete(r); // kills 'cf' as well!
1959	}
1960
1961	void test_Q_Ext_a()
1962	{
1963	clog << "Start by creating Q[a]..." << endl;
1964
1965	char* n[] = {"a"};
1966	ring r = rDefault( 0, 1, n); // Q[a]
1967	TS_ASSERT_DIFFERS( r, NULLp );
1968
1969	PrintRing(r);
1970
1971	TS_ASSERT( rField_is_Domain(r) );
1972	TS_ASSERT( rField_is_Q(r) );
1973
1974	TS_ASSERT( !rField_is_Zp(r) );
1975	TS_ASSERT( !rField_is_Zp(r, 11) );
1976
1977	TS_ASSERT_EQUALS( rVar(r), 1);
1978
1979	poly minPoly = p_ISet(1, r); // minPoly = 1
1980	p_SetExp(minPoly, 1, 2, r); p_Setm(minPoly, r); // minPoly = a^2
1981	minPoly = p_Add_q(minPoly, p_ISet(1, r), r); // minPoly = a^2 + 1
1982	ideal minIdeal = idInit(1); // minIdeal = < 0 >
1983	minIdeal->m[0] = minPoly; // minIdeal = < a^2 + 1 >
1984
1985	n_coeffType type = nRegister(n_algExt, naInitChar);
1986	TS_ASSERT(type == n_algExt);
1987
1988	AlgExtInfo extParam;
1989	extParam.r = r;
1990	extParam.i = minIdeal;
1991
1992	clog << "Next create the extension field Q[a]/<a2+1>..." << endl;
1993
1994	const coeffs cf = nInitChar(type, &extParam); // Q[a]/<a2+1>
1995
1996	if( cf == NULL )
1997	TS_FAIL("Could not get needed coeff. domain");
1998
1999	TS_ASSERT_DIFFERS( cf->cfCoeffWrite, NULLp );
2000
2001	if( cf->cfCoeffWrite != NULL )
2002	{
2003	clog << "Coeff-domain: " << endl;
2004	n_CoeffWrite(cf); PrintLn();
2005	}
2006
2007	TS_ASSERT( nCoeff_is_algExt(cf) );
2008	TS_ASSERT( !nCoeff_is_transExt(cf) );
2009
2010	// some tests for the coefficient field represented by cf:
2011	TestArithCf(cf);
2012	TestSumCf(cf, 10);
2013	TestSumCf(cf, 100);
2014	TestSumCf(cf, 101);
2015	TestSumCf(cf, 1001);
2016	TestSumCf(cf, 2000);
2017
2018	clog << "Finally create the polynomial ring (Q[a]/<a2+1>)[x, y]..."
2019	<< endl;
2020
2021	char* m[] = {"x", "y"};
2022	ring s = rDefault(cf, 2, m); // (Q[a]/<a2+1>)[x, y]
2023	TS_ASSERT_DIFFERS(s, NULLp);
2024
2025	PrintRing(s);
2026
2027	TS_ASSERT( rField_is_Domain(s) );
2028	TS_ASSERT( !rField_is_Q(s) );
2029	TS_ASSERT( !rField_is_Zp(s) );
2030	TS_ASSERT( !rField_is_Zp(s, 11) );
2031	TS_ASSERT( !rField_is_Zp(s, 13) );
2032	TS_ASSERT( !rField_is_GF(s) );
2033	TS_ASSERT( rField_is_Extension(s) );
2034	TS_ASSERT( !rField_is_GF(s, 25) );
2035	TS_ASSERT_EQUALS(rVar(s), 2);
2036
2037	Test(s);
2038
2039	clog << endl
2040	<< "Now let's compute some inverses in Q[a]/<a^2+1>..."
2041	<< endl;
2042
2043	poly u;
2044	u = NULL; plusTerm(u, 1, 1, 1, cf->extRing);
2045	plusTerm(u, 1, 1, 0, cf->extRing); // a + 1
2046	checkInverse((number)u, cf); p_Delete(&u, cf->extRing);
2047	u = NULL; plusTerm(u, 1, 1, 1, cf->extRing);
2048	plusTerm(u, -1, 1, 0, cf->extRing); // a - 1
2049	checkInverse((number)u, cf); p_Delete(&u, cf->extRing);
2050	u = NULL; plusTerm(u, 1, 1, 1, cf->extRing);
2051	plusTerm(u, 5, 1, 0, cf->extRing); // a + 5
2052	checkInverse((number)u, cf); p_Delete(&u, cf->extRing);
2053	u = NULL; plusTerm(u, 1, 1, 1, cf->extRing);
2054	plusTerm(u, -5, 1, 0, cf->extRing); // a - 5
2055	checkInverse((number)u, cf); p_Delete(&u, cf->extRing);
2056	u = NULL; plusTerm(u, 17, 1, 1, cf->extRing);
2057	plusTerm(u, 5, 1, 0, cf->extRing); // 17a + 5
2058	checkInverse((number)u, cf); p_Delete(&u, cf->extRing);
2059
2060	rDelete(s); // kills 'cf' and 'r' as well
2061	}
2062	void test_Q_Ext_b()
2063	{
2064	clog << "Start by creating Q[b]..." << endl;
2065
2066	char* n[] = {"b"};
2067	ring r = rDefault( 0, 1, n); // Q[b]
2068	TS_ASSERT_DIFFERS( r, NULLp );
2069
2070	PrintRing(r);
2071
2072	TS_ASSERT( rField_is_Domain(r) );
2073	TS_ASSERT( rField_is_Q(r) );
2074
2075	TS_ASSERT( !rField_is_Zp(r) );
2076	TS_ASSERT( !rField_is_Zp(r, 11) );
2077
2078	TS_ASSERT_EQUALS( rVar(r), 1);
2079
2080	poly minPoly = p_ISet(1, r); // minPoly = 1
2081	p_SetExp(minPoly, 1, 7, r); p_Setm(minPoly, r); // minPoly = b^7
2082	minPoly = p_Add_q(minPoly, p_ISet(17, r), r); // minPoly = b^7 + 17
2083	ideal minIdeal = idInit(1); // minIdeal = < 0 >
2084	minIdeal->m[0] = minPoly; // minIdeal = < b^7 + 17 >
2085
2086	n_coeffType type = nRegister(n_algExt, naInitChar);
2087	TS_ASSERT(type == n_algExt);
2088
2089	AlgExtInfo extParam;
2090	extParam.r = r;
2091	extParam.i = minIdeal;
2092
2093	clog << "Next create the extension field Q[b]/<b^7+17>..." << endl;
2094
2095	const coeffs cf = nInitChar(type, &extParam); // Q[b]/<b^7+17>
2096
2097	if( cf == NULL )
2098	TS_FAIL("Could not get needed coeff. domain");
2099
2100	TS_ASSERT_DIFFERS( cf->cfCoeffWrite, NULLp );
2101
2102	if( cf->cfCoeffWrite != NULL )
2103	{
2104	clog << "Coeff-domain: " << endl;
2105	n_CoeffWrite(cf); PrintLn();
2106	}
2107
2108	TS_ASSERT( nCoeff_is_algExt(cf) );
2109	TS_ASSERT( !nCoeff_is_transExt(cf) );
2110
2111	// some tests for the coefficient field represented by cf:
2112	TestArithCf(cf);
2113	TestSumCf(cf, 10);
2114	TestSumCf(cf, 100);
2115	TestSumCf(cf, 101);
2116	TestSumCf(cf, 1001);
2117	TestSumCf(cf, 9000);
2118
2119	clog << "Finally create the polynomial ring (Q[b]/<b^7+17>)[u, v, w]..."
2120	<< endl;
2121
2122	char* m[] = {"u", "v", "w"};
2123	ring s = rDefault(cf, 3, m); // (Q[b]/<b^7+17>)[u, v, w]
2124	TS_ASSERT_DIFFERS(s, NULLp);
2125
2126	PrintRing(s);
2127
2128	TS_ASSERT( rField_is_Domain(s) );
2129	TS_ASSERT( !rField_is_Q(s) );
2130	TS_ASSERT( !rField_is_Zp(s) );
2131	TS_ASSERT( !rField_is_Zp(s, 11) );
2132	TS_ASSERT( !rField_is_Zp(s, 13) );
2133	TS_ASSERT( !rField_is_GF(s) );
2134	TS_ASSERT( rField_is_Extension(s) );
2135	TS_ASSERT( !rField_is_GF(s, 25) );
2136	TS_ASSERT_EQUALS(rVar(s), 3);
2137
2138	Test(s);
2139
2140	clog << endl
2141	<< "Now let's compute some inverses in Q[b]/<b^7+17>..."
2142	<< endl;
2143
2144	poly u;
2145	u = NULL; plusTerm(u, 1, 1, 2, cf->extRing);
2146	plusTerm(u, 33, 1, 0, cf->extRing); // b^2 + 33
2147	checkInverse((number)u, cf); p_Delete(&u, cf->extRing);
2148	u = NULL; plusTerm(u, 1, 1, 5, cf->extRing);
2149	plusTerm(u, -137, 1, 0, cf->extRing); // b^5 - 137
2150	checkInverse((number)u, cf); p_Delete(&u, cf->extRing);
2151
2152	clog << endl
2153	<< "Now let's check a gcd computation in Q[b]..."
2154	<< endl;
2155
2156	poly v;
2157	v = NULL; plusTerm(v, 1, 1, 2, cf->extRing);
2158	plusTerm(v, 7, 1, 1, cf->extRing);
2159	plusTerm(v, 1, 1, 0, cf->extRing); // b^2 + 7b + 1
2160	number w = n_Mult((number)v, (number)v, cf); // (b^2 + 7b + 1)^2
2161	number y = n_Mult((number)v, (number)w, cf); // (b^2 + 7b + 1)^3
2162	p_Delete(&v, cf->extRing);
2163	v = NULL; plusTerm(v, 2, 1, 2, cf->extRing);
2164	plusTerm(v, -61, 1, 1, cf->extRing); // 2b^2 - 61b
2165	number z = n_Mult((number)w,
2166	(number)v, cf); // (b^2 + 7b + 1)^2 * (2b^2 - 61b)
2167	p_Delete(&v, cf->extRing);
2168
2169	clog << "z = "; p_Write((poly)z, cf->extRing);
2170	clog << "y = "; p_Write((poly)y, cf->extRing);
2171	number theGcd = n_Gcd(z, y, cf); // should yield w = (b^2 + 7b + 1)^2
2172	clog << "gcd(z, y) = "; p_Write((poly)theGcd, cf->extRing);
2173
2174	v = (poly)n_Sub(theGcd, w, cf);
2175	TS_ASSERT( v == NULL );
2176	p_Delete(&v, cf->extRing);
2177
2178	clog << endl
2179	<< "Now let's check an ext_gcd computation in Q[b]..."
2180	<< endl;
2181
2182	poly zFactor; poly yFactor;
2183	poly ppp = p_ExtGcd((poly)z, zFactor, (poly)y, yFactor, cf->extRing);
2184	v = (poly)n_Sub(theGcd, (number)ppp, cf);
2185	TS_ASSERT( v == NULL );
2186	clog << "z = "; p_Write((poly)z, cf->extRing);
2187	clog << "zFactor = "; p_Write(zFactor, cf->extRing);
2188	clog << "y = "; p_Write((poly)y, cf->extRing);
2189	clog << "yFactor = "; p_Write((poly)yFactor, cf->extRing);
2190	number v1 = n_Mult(z, (number)zFactor, cf);
2191	number v2 = n_Mult(y, (number)yFactor, cf);
2192	number v3 = n_Add(v1, v2, cf);
2193	clog << "z * zFactor + y * yFactor = "; p_Write((poly)v3, cf->extRing);
2194	clog << "gcd(z, y) = "; p_Write(ppp, cf->extRing);
2195	number v4 = n_Sub(v3, w, cf);
2196	TS_ASSERT( v4 == NULL );
2197
2198	p_Delete(&ppp, cf->extRing); p_Delete(&zFactor, cf->extRing);
2199	p_Delete(&yFactor, cf->extRing);
2200	n_Delete(&z, cf); n_Delete(&y, cf); n_Delete(&w, cf);
2201	n_Delete(&theGcd, cf); p_Delete(&v, cf->extRing); n_Delete(&v1, cf);
2202	n_Delete(&v2, cf); n_Delete(&v3, cf); n_Delete(&v4, cf);
2203
2204	rDelete(s); // kills 'cf' and 'r' as well
2205	}
2206	void test_Z_17_Ext_a()
2207	{
2208	clog << "Start by creating Z_17[a]..." << endl;
2209
2210	char* n[] = {"a"};
2211	ring r = rDefault( 17, 1, n); // Z/17Z[a]
2212	TS_ASSERT_DIFFERS( r, NULLp );
2213
2214	PrintRing(r);
2215
2216	TS_ASSERT( rField_is_Domain(r) );
2217	TS_ASSERT( !rField_is_Q(r) );
2218
2219	TS_ASSERT( rField_is_Zp(r) );
2220	TS_ASSERT( rField_is_Zp(r, 17) );
2221
2222	TS_ASSERT_EQUALS( rVar(r), 1);
2223
2224	poly minPoly = p_ISet(1, r); // minPoly = 1
2225	p_SetExp(minPoly, 1, 2, r); p_Setm(minPoly, r); // minPoly = a^2
2226	minPoly = p_Add_q(minPoly, p_ISet(3, r), r); // minPoly = a^2 + 3
2227	ideal minIdeal = idInit(1); // minIdeal = < 0 >
2228	minIdeal->m[0] = minPoly; // minIdeal = < a^2 + 3 >
2229
2230	n_coeffType type = nRegister(n_algExt, naInitChar);
2231	TS_ASSERT(type == n_algExt);
2232
2233	AlgExtInfo extParam;
2234	extParam.r = r;
2235	extParam.i = minIdeal;
2236
2237	clog << "Next create the extension field Z_17[a]/<a^2+3>..." << endl;
2238
2239	const coeffs cf = nInitChar(type, &extParam); // Z_17[a]/<a^2+3>
2240
2241	if( cf == NULL )
2242	TS_FAIL("Could not get needed coeff. domain");
2243
2244	TS_ASSERT_DIFFERS( cf->cfCoeffWrite, NULLp );
2245
2246	if( cf->cfCoeffWrite != NULL )
2247	{
2248	clog << "Coeff-domain: " << endl;
2249	n_CoeffWrite(cf); PrintLn();
2250	}
2251
2252	TS_ASSERT( nCoeff_is_algExt(cf) );
2253	TS_ASSERT( !nCoeff_is_transExt(cf) );
2254
2255	// some tests for the coefficient field represented by cf:
2256	TestArithCf(cf);
2257	TestSumCf(cf, 10);
2258	TestSumCf(cf, 100);
2259	TestSumCf(cf, 101);
2260	TestSumCf(cf, 1001);
2261	TestSumCf(cf, 9000);
2262
2263	clog << "Finally create the polynomial ring (Z_17[a]/<a^2+3>)[u, v, w]..."
2264	<< endl;
2265
2266	char* m[] = {"u", "v", "w"};
2267	ring s = rDefault(cf, 3, m); // (Z_17[a]/<a^2+3>)[u, v, w]
2268	TS_ASSERT_DIFFERS(s, NULLp);
2269
2270	PrintRing(s);
2271
2272	TS_ASSERT( rField_is_Domain(s) );
2273	TS_ASSERT( !rField_is_Q(s) );
2274	TS_ASSERT( !rField_is_Zp(s) );
2275	TS_ASSERT( !rField_is_Zp(s, 11) );
2276	TS_ASSERT( !rField_is_Zp(s, 17) );
2277	TS_ASSERT( !rField_is_GF(s) );
2278	TS_ASSERT( rField_is_Extension(s) );
2279	TS_ASSERT( !rField_is_GF(s, 25) );
2280	TS_ASSERT_EQUALS(rVar(s), 3);
2281
2282	Test(s);
2283
2284	rDelete(s); // kills 'cf' and 'r' as well
2285	}
2286	void test_Q_Ext_s_t()
2287	{
2288	clog << "Start by creating Q[s, t]..." << endl;
2289
2290	char* n[] = {"s", "t"};
2291	ring r = rDefault( 0, 2, n); // Q[s, t]
2292	TS_ASSERT_DIFFERS( r, NULLp );
2293
2294	PrintRing(r);
2295
2296	TS_ASSERT( rField_is_Domain(r) );
2297	TS_ASSERT( rField_is_Q(r) );
2298
2299	TS_ASSERT( !rField_is_Zp(r) );
2300	TS_ASSERT( !rField_is_Zp(r, 17) );
2301
2302	TS_ASSERT_EQUALS( rVar(r), 2);
2303
2304	n_coeffType type = nRegister(n_transExt, ntInitChar);
2305	TS_ASSERT(type == n_transExt);
2306
2307	TransExtInfo extParam;
2308	extParam.r = r;
2309
2310	clog << "Next create the rational function field Q(s, t)..." << endl;
2311
2312	const coeffs cf = nInitChar(type, &extParam); // Q(s, t)
2313
2314	if( cf == NULL )
2315	TS_FAIL("Could not get needed coeff. domain");
2316
2317	TS_ASSERT_DIFFERS( cf->cfCoeffWrite, NULLp );
2318
2319	if( cf->cfCoeffWrite != NULL )
2320	{
2321	clog << "Coeff-domain: " << endl;
2322	n_CoeffWrite(cf); PrintLn();
2323	}
2324
2325	TS_ASSERT( !nCoeff_is_algExt(cf) );
2326	TS_ASSERT( nCoeff_is_transExt(cf) );
2327
2328	// some tests for the coefficient field represented by cf:
2329	TestArithCf(cf);
2330	TestSumCf(cf, 10);
2331	TestSumCf(cf, 100);
2332	TestSumCf(cf, 101);
2333	TestSumCf(cf, 1001);
2334	TestSumCf(cf, 9000);
2335
2336	clog << "Finally create the polynomial ring Q(s, t)[x, y, z]..."
2337	<< endl;
2338
2339	char* m[] = {"x", "y", "z"};
2340	ring s = rDefault(cf, 3, m); // Q(s, t)[x, y, z]
2341	TS_ASSERT_DIFFERS(s, NULLp);
2342
2343	PrintRing(s);
2344
2345	TS_ASSERT( rField_is_Domain(s) );
2346	TS_ASSERT( !rField_is_Q(s) );
2347	TS_ASSERT( !rField_is_Zp(s) );
2348	TS_ASSERT( !rField_is_Zp(s, 11) );
2349	TS_ASSERT( !rField_is_Zp(s, 17) );
2350	TS_ASSERT( !rField_is_GF(s) );
2351	TS_ASSERT( rField_is_Extension(s) );
2352	TS_ASSERT( !rField_is_GF(s, 25) );
2353	TS_ASSERT_EQUALS(rVar(s), 3);
2354
2355	Test(s);
2356
2357	/* some special tests: */
2358	poly v1 = NULL;
2359	plusTerm(v1, 1, 1, 1, cf->extRing); // s
2360	plusTerm(v1, 1, 1, 0, cf->extRing); // s + 1
2361	poly v2 = NULL;
2362	plusTerm(v2, 1, 1, 1, cf->extRing); // s
2363	plusTerm(v2, 2, 2, 1, cf->extRing); // s + 2t
2364	poly v = p_Mult_q(v1, v2, cf->extRing); // (s + 1) * (s + 2t)
2365	number v_n = toFractionNumber(v, cf);
2366	PrintSized(v_n, cf);
2367	poly w1 = NULL;
2368	plusTerm(w1, 1, 1, 1, cf->extRing); // s
2369	plusTerm(w1, 1, 1, 0, cf->extRing); // s + 1
2370	poly w2 = NULL;
2371	plusTerm(w2, 3, 1, 1, cf->extRing); // 3s
2372	plusTerm(w2, -7, 2, 1, cf->extRing); // 3s - 7t
2373	poly w = p_Mult_q(w1, w2, cf->extRing); // (s + 1) * (3s - 7t)
2374	number w_n = toFractionNumber(w, cf);
2375	PrintSized(w_n, cf);
2376	number vOverW_n = n_Div(v_n, w_n, cf);
2377	PrintSized(vOverW_n, cf);
2378	number wOverV_n = n_Invers(vOverW_n, cf);
2379	PrintSized(wOverV_n, cf);
2380	number prod = n_Mult(vOverW_n, wOverV_n, cf);
2381	PrintSized(prod, cf);
2382	number tmp; number nn = n_Copy(vOverW_n, cf);
2383	for (int i = 1; i <= 6; i++)
2384	{
2385	tmp = n_Div(nn, v_n, cf);
2386	n_Delete(&nn, cf);
2387	nn = tmp;
2388	clog << i << ". "; PrintSized(nn, cf);
2389	}
2390
2391	n_Delete(&prod, cf); n_Delete(&nn, cf);
2392	n_Delete(&v_n, cf); n_Delete(&w_n, cf);
2393	n_Delete(&vOverW_n, cf); n_Delete(&wOverV_n, cf);
2394
2395	rDelete(s); // kills 'cf' and 'r' as well
2396	}
2397	void test_Q_Ext_Performance()
2398	{
2399	clog << "Start by creating Q[q]..." << endl;
2400
2401	char* n[] = {"q"};
2402	ring r = rDefault( 0, 1, n); // Q[q]
2403	r->order[0] = ringorder_dp;
2404	TS_ASSERT_DIFFERS( r, NULLp );
2405
2406	PrintRing(r);
2407
2408	TS_ASSERT( rField_is_Domain(r) );
2409	TS_ASSERT( rField_is_Q(r) );
2410
2411	TS_ASSERT( !rField_is_Zp(r) );
2412	TS_ASSERT( !rField_is_Zp(r, 17) );
2413
2414	TS_ASSERT_EQUALS( rVar(r), 1);
2415
2416	n_coeffType type = nRegister(n_transExt, ntInitChar);
2417	TS_ASSERT(type == n_transExt);
2418
2419	TransExtInfo extParam;
2420	extParam.r = r;
2421
2422	clog << "Next create the rational function field Q(q)..." << endl;
2423
2424	const coeffs cf = nInitChar(type, &extParam); // Q(q)
2425
2426	if( cf == NULL )
2427	TS_FAIL("Could not get needed coeff. domain");
2428
2429	TS_ASSERT_DIFFERS( cf->cfCoeffWrite, NULLp );
2430
2431	if( cf->cfCoeffWrite != NULL )
2432	{
2433	clog << "Coeff-domain: " << endl;
2434	n_CoeffWrite(cf); PrintLn();
2435	}
2436
2437	TS_ASSERT( !nCoeff_is_algExt(cf) );
2438	TS_ASSERT( nCoeff_is_transExt(cf) );
2439
2440	// some tests for the coefficient field represented by cf:
2441	TestArithCf(cf);
2442	TestSumCf(cf, 10);
2443	TestSumCf(cf, 100);
2444	TestSumCf(cf, 101);
2445	TestSumCf(cf, 1001);
2446	TestSumCf(cf, 9000);
2447
2448	clog << "Finally create the polynomial ring Q(q)[t]..."
2449	<< endl;
2450
2451	char* m[] = {"t"};
2452	ring s = rDefault(cf, 1, m); // Q(q)[t]
2453	s->order[0] = ringorder_dp;
2454	TS_ASSERT_DIFFERS(s, NULLp);
2455
2456	PrintRing(s);
2457
2458	TS_ASSERT( rField_is_Domain(s) );
2459	TS_ASSERT( !rField_is_Q(s) );
2460	TS_ASSERT( !rField_is_Zp(s) );
2461	TS_ASSERT( !rField_is_Zp(s, 11) );
2462	TS_ASSERT( !rField_is_Zp(s, 17) );
2463	TS_ASSERT( !rField_is_GF(s) );
2464	TS_ASSERT( rField_is_Extension(s) );
2465	TS_ASSERT( !rField_is_GF(s, 25) );
2466	TS_ASSERT_EQUALS(rVar(s), 1);
2467
2468	Test(s);
2469
2470	/* a special performance test: */
2471	poly entry = NULL;
2472	for (int ti = 0; ti <= 20; ti++)
2473	{
2474	for (int qi = 0; qi <= 100; qi++)
2475	{
2476	int c = rand() % 1000000;
2477	poly qterm = p_ISet(c, r); p_SetExp(qterm, 1, qi, r);
2478	p_Setm(qterm, r);
2479	number qtermAsN = toFractionNumber(qterm, cf);
2480	poly tterm = p_ISet(1, s); p_SetExp(tterm, 1, ti, s);
2481	p_Setm(tterm, r); p_SetCoeff(tterm, qtermAsN, s);
2482	entry = p_Add_q(entry, tterm, s);
2483	}
2484	}
2485	p_Write(entry, s);
2486	poly qfactor = p_ISet(1, r); p_SetExp(qfactor, 1, 66, r);
2487	p_Setm(qfactor, r); /* q^66 */
2488	number qfactorAsN = toFractionNumber(qfactor, cf);
2489	number uuu = n_Invers(qfactorAsN, cf); /* 1 / q^66 */
2490	poly factor = p_ISet(1, s); p_SetCoeff(factor, uuu, s); /* 1 / q^66 */
2491	p_Write(factor, s);
2492	clog << "starting multiplication..." << endl;
2493	poly theProduct = p_Mult_q(entry, factor, s);
2494	p_Write(theProduct, s);
2495	clog << "ending multiplication..." << endl;
2496	n_Delete(&qfactorAsN, cf); p_Delete(&theProduct, s);
2497
2498	/* a very special performance test: */
2499	specialPoly(entry, s);
2500	p_Write(entry, s);
2501	qfactor = p_ISet(1, r); p_SetExp(qfactor, 1, 66, r);
2502	p_Setm(qfactor, r); /* q^66 */
2503	qfactorAsN = toFractionNumber(qfactor, cf);
2504	uuu = n_Invers(qfactorAsN, cf); /* 1 / q^66 */
2505	factor = p_ISet(1, s); p_SetCoeff(factor, uuu, s); /* 1 / q^66 */
2506	p_Write(factor, s);
2507	clog << "starting very special multiplication..." << endl;
2508	/* The following multiplication + output of the product is very slow
2509	in the svn/trunk SINGULAR version; see trac ticket #308.
2510	Here, in the Spielwiese, the result is instantaneous! */
2511	theProduct = p_Mult_q(entry, factor, s);
2512	p_Write(theProduct, s);
2513	clog << "ending very special multiplication..." << endl;
2514	n_Delete(&qfactorAsN, cf); p_Delete(&theProduct, s);
2515
2516	rDelete(s); // kills 'cf' and 'r' as well
2517	}
2518	};
2519

Note: See TracBrowser for help on using the repository browser.

Download in other formats: