Line data Source code
1 : /* Copyright (C) 2003 The PARI group.
2 :
3 : This file is part of the PARI/GP package.
4 :
5 : PARI/GP is free software; you can redistribute it and/or modify it under the
6 : terms of the GNU General Public License as published by the Free Software
7 : Foundation; either version 2 of the License, or (at your option) any later
8 : version. It is distributed in the hope that it will be useful, but WITHOUT
9 : ANY WARRANTY WHATSOEVER.
10 :
11 : Check the License for details. You should have received a copy of it, along
12 : with the package; see the file 'COPYING'. If not, write to the Free Software
13 : Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA. */
14 :
15 : #include "pari.h"
16 : #include "paripriv.h"
17 :
18 : static long
19 2387 : groupelts_sumorders(GEN S)
20 : {
21 2387 : long i, s = 0;
22 47313 : for(i=1; i < lg(S); i++) s += perm_orderu(gel(S,i));
23 2387 : return s;
24 : }
25 :
26 : static long
27 700 : vecgroup_sumorders(GEN L)
28 : {
29 700 : long i, s = 0;
30 32501 : for (i=1; i<lg(L); i++)
31 : {
32 31801 : GEN G = gel(L,i);
33 31801 : s += (lg(G)==3 && typ(gel(G,1))==t_VEC) ? group_order(G): lg(G)-1;
34 : }
35 700 : return s;
36 : }
37 :
38 : static int
39 14 : indexgroupsubgroup(GEN L, long order, const long *good, const long *bad)
40 : {
41 : long i;
42 826 : for(i=1; i<lg(L); i++)
43 : {
44 812 : GEN G=gel(L,i);
45 : long idx;
46 : const long *p;
47 812 : if (group_order(G)!=order) continue;
48 210 : idx = group_ident(G,NULL);
49 420 : for(p=good; *p; p++)
50 210 : if (*p==idx) return 1;
51 210 : for(p=bad; *p; p++)
52 0 : if (*p==idx) return 0;
53 : }
54 14 : return 0;
55 : }
56 :
57 : static int
58 133 : indexgroupcentre(GEN G, GEN Z, const long *good, const long *bad)
59 : {
60 : long i;
61 357 : for(i=1;i<lg(Z);i++)
62 : {
63 357 : GEN z=gel(Z,i);
64 357 : if (perm_orderu(z)==2)
65 : {
66 182 : pari_sp btop=avma;
67 182 : GEN H = cyclicgroup(z,2);
68 182 : GEN C = group_quotient(G,H);
69 182 : GEN Q = quotient_group(C,G);
70 : const long *p;
71 182 : long idx=group_ident(Q,NULL);
72 182 : set_avma(btop);
73 413 : for(p=good;*p;p++)
74 252 : if (*p==idx) return 1;
75 259 : for(p=bad;*p;p++)
76 210 : if (*p==idx) return 0;
77 : }
78 : }
79 0 : return 0;
80 : }
81 :
82 : static GEN
83 91 : vecgroup_idxlist(GEN L, long order)
84 : {
85 91 : pari_sp av = avma;
86 91 : long i, j, l = lg(L);
87 91 : GEN V = cgetg(l, t_VECSMALL);
88 8001 : for (i = j = 1; i < l; i++)
89 7910 : if (group_order(gel(L,i)) == order) V[j++] = group_ident(gel(L,i),NULL);
90 91 : setlg(V, j); return gc_leaf(av, vecsmall_uniq(V));
91 : }
92 :
93 : /* Group identification code.
94 : * The group data are taken from GAP 4 and the SMALL GROUPS LIBRARY by Hans
95 : * Ulrich Besche, Bettina Eick and Eamonn O'Brien.
96 : */
97 :
98 : static long
99 1694 : group_ident_i(GEN G, GEN S)
100 : {
101 1694 : long n = S? lg(S)-1: group_order(G);
102 : long s;
103 : GEN F,p,e;
104 1694 : if (n==1) return 1;
105 1687 : if (!S) S = group_elts(G,group_domain(G));
106 1687 : s = groupelts_sumorders(S);/*This is used as a hash value*/
107 1687 : F = factoru(n);
108 1687 : p = gel(F,1);
109 1687 : e = gel(F,2);
110 1687 : switch(lg(p)-1)
111 : {
112 1232 : case 1:/*prime power*/
113 1232 : switch (e[1])
114 : {
115 315 : case 1: /* p */
116 315 : return 1;
117 70 : case 2: /* p^2 */
118 70 : return (s == 1 - p[1] + n*p[1])? 2: 1; /* pxp || p^2 */
119 231 : case 3: /* p^3 */
120 : {
121 231 : GEN H = group_abelianSNF(G, S);
122 231 : if (H) /*G is abelian*/
123 : {
124 161 : long l = lg(H)-1;
125 161 : return (l==3)?5: l; /*pxpxp || p^3 or p^2xp*/
126 : } /*G is not abelian*/
127 70 : if (p[1] == 2)
128 63 : return (s == 19)? 3: 4; /*D8 || Q8*/
129 : else
130 : {
131 7 : long q = p[1]*p[1];
132 7 : q *= q;
133 7 : return (s == q - p[1] + 1)?3 :4; /* pxp:p || p^2:p */
134 : }
135 : }
136 : }
137 616 : break;
138 420 : case 2:
139 420 : switch(e[1]+e[2])
140 : {
141 161 : case 2: /*pq*/
142 161 : return (p[2]%p[1]!=1)?1:1+group_isabelian(G); /*pq || pq or p:q*/
143 112 : case 3:
144 112 : if (p[1]==2 && e[1]==2) /* 4p */
145 : {
146 98 : long q = p[2], q2 = q*q, pmq2 = (q%4 == 1 || q==3);
147 98 : if (s==3+5*q+3*q2) return 1; /* 2p.2 */
148 98 : if (s==11-11*q+11*q2) return 2; /* 4p */
149 98 : if (s==3+q+3*q2) return 3+pmq2; /* D4p */
150 98 : if (s==7-7*q+7*q2) return 4+pmq2; /* 2px2 */
151 98 : return 3; /*A4 or p:4 */
152 : }
153 14 : else if (p[1]==2 && e[1]==1) /*2p^2*/
154 : {
155 7 : long q = p[2], q2 = q*q, q3 = q*q2, q4 = q*q3;
156 7 : if (s==1-q+3*q2-q3+q4) return 1; /* p^2:2 */
157 7 : if (s==3-3*q+3*q2-3*q3+3*q4) return 2; /* 2p^2 */
158 7 : if (s==1+q-2*q2+3*q3) return 3; /* D2pxp */
159 7 : if (s==1-q+2*q2+q3) return 4; /* p:2+p:2 */
160 7 : return 5; /* 2pxp */
161 : }
162 7 : else if (p[1]==3 && e[1]==2) /*9p, p>3*/
163 : {
164 7 : long q= p[2], q2 = q*q, p3 = (q%3 == 1), p9 = (q%9 == 1);
165 7 : if (s==7+47*q+7*q2) return 1; /* 3p.3 */
166 7 : if (s==61-61*q+61*q2) return 1+p3; /* 9p */
167 7 : if (s==1+59*q+q2) return 3; /* p:9 */
168 7 : if (s==7+11*q+7*q2) return 3+p9; /* p:3x3 */
169 7 : return 2+2*p3+p9; /* 3^2xp */
170 : }
171 0 : break;
172 : }
173 : case 3:
174 182 : switch(e[1]+e[2]+e[3])
175 : {
176 14 : case 3: /*pqr*/
177 14 : if (p[1]==2) /*2qr*/
178 : {
179 14 : long q = p[2],q2 = q*q, qc = 1-q+q2, qd = 1+q+q2;
180 14 : long r = p[3],r2 = r*r, rc = 1-r+r2, rd = 1+r+r2;
181 14 : long pmq = (r%q==1)? 2: 0;
182 14 : if (pmq && s==3*r*(q2-q)+rd) return 1; /* r:2q */
183 14 : if (pmq && s==3*(r2+(q2-q-1)*r+1)) return 2; /* r:qx2 */
184 7 : if (s==qd*rc) return 1+pmq; /* D2qxr */
185 7 : if (s==rd*qc) return 2+pmq; /* D2rxq */
186 7 : if (s==3*qc*rc) return 4+pmq; /* 2qr */
187 0 : return 3+pmq; /* q:2+r:2 */
188 : }
189 0 : break;
190 : }
191 : }
192 : {
193 784 : const long tab[]={
194 : 24, 173, 301, 99, 125, 113, 101, 97, 85, 161, 133, 189, 67, 87, 73, 105, -1,
195 : 36, 255, 671, 265, 219, 427, 243, 147, 275, 115, 127, 121, 159, 111, 175,
196 : -1,
197 : 40, 391, 903, 263, 311, 291, 271, 227, 207, 483, 399, 567, 163, 187, 315,
198 : -1,
199 : 56, 697, 1849, 585, 557, 529, 413, 385, 989, 817, 1161, 351, 357, 645, -1,
200 : 60, 945, 721, 561, 1617, 211, 497, 337, 373, 651, 581, 693, 501, 1029, -1,
201 : 75, 3647, 271, 847, -1,
202 : 84, 647, 935, 1935, 1295, 1071, 3311, 451, 699, 595, 1333, 469, 1099, 1419,
203 : 987, 2107, -1,
204 : 88, 1573, 4773, 1397, 1353, 1309, 953, 909, 2553, 2109, 2997, 865, 1665, -1,
205 : 90, 1659, 1891, 1371, 3843, 775, 1407, 735, 903, 615, 1575, -1,
206 : 104, 2143, 6751, 991, 1935, 1883, 1831, 1307, 1255, 3611, 2983, 4239, 731,
207 : 1203, 2355, -1,
208 : 105, 1785, 6321, -1,
209 : 126, 1533, 2037, 3397, 3477, 2749, 7869, 777, 937, 721, 1281, 1425, 2881,
210 : 1369, 1849, 1201, 3225, -1,
211 : 132, 4995, 2947, 2595, 8547, 1663, 3441, 2639, 3663, 2463, 5439, -1,
212 : 136, 3547, 11739, 1499, 3275, 3207, 3139, 2183, 2115, 6279, 5187, 7371,
213 : 987, 1159, 2047, 4095, -1,
214 : 140, 4429, 3885, 2989, 9933, 3053, 1613, 1697, 3297, 3569, 2849, 6321, -1,
215 : -1};
216 : long i;
217 : const long *t;
218 11382 : for(t=tab;*t!=-1;t++)
219 : {
220 10682 : if (t[0]==n)
221 : {
222 791 : for(i=1; t[i] != -1; i++)
223 791 : if (t[i]==s) return i;
224 0 : return -1;
225 : }
226 146482 : while (*t>=0) t++;
227 : }
228 : }
229 : {
230 700 : const long tab[]={
231 : 16, 1710031, 550075, 70099, 70075, 870059, 110059, 30079, 30071, 30063,
232 : 470131, 70155, 70107, 110115, 310307, -1,
233 : 32, 6830063, 150323, 1830171, /*230171*/0, 230227, 30283, 30251, 30203,
234 : /*70267*/0, 70219, 110227, /*230171*/0, /*70187*/0, /*70187*/0, 110155,
235 : 3430123, 430123, 30191, 30175, 30159, 1110387, 150563, 150387, 230323, 230411,
236 : 230299, 70619, 70467, 70355, /*70379*/0, /*70379*/0, /*70267*/0, 70291, 70555,
237 : 70331, 1750291, 230291, 430275, 70411, 70363, 70315, 110331, 30371, 30323,
238 : 950819, 150995, 150643, 230691, 30747, 30635, 632451, -1,
239 : 48, 430156, 11970124, 10219, 430324, 110324, 30396, 30444, 30348, 230300,
240 : 110300, 230396, /*70396*/0, /*70396*/0, 70540, 30412, 30364, 30380, 30332,
241 : 70492, 3850300, 490396, 490300, 6090236, 770236, 210316, 210284, 210252, 30299,
242 : 30371, 30363, 110299, 70311, 110271, 70588, 230732, 70876, 110636, 30868,
243 : 30628, 30596, 30644, 150684, 70828, 3290524, 490620, 490428, 770460, 30627,
244 : 70571, 10643, 151740, 2171228, -1,
245 : 54, 10256, 16410120, 70292, 610232, 10373, 10292, 10616, 70517, 5610228,
246 : 210309, 210228, 250448, 70616, 11696, 2370552, -1,
247 : /*64*/
248 : 72, 110307, 26230195, 210272, 30523, 110631, 30739, 70575, 30683,
249 : 14030351, 1830403, 1830299, 770346, 110586, 10750330, 10620, 210420, 71223,
250 : 9150663, 30426, 30858, 30978, 30954, 31074, 30762, 210452, 210538, 770634,
251 : 210730, 490626, 210722, 31018, 111234, 31450, 71106, 31322, 5750594, 750682,
252 : 750506, 10346, 10826, 10490, 70620, 11124, 10716, 30786, 31746, 210636, 491202,
253 : 72402, 3751122, -1,
254 : 80, 430250, 35910186, 110282, 430530, 110530, 30650, 30730, 30570,
255 : 230482, 110482, 230642, /*70642*/0, /*70642*/0, 70882, 30666, 30586, 30618,
256 : 30538, 70786, 11550450, 1470594, 1470450, 18270354, 2310354, 630474, 630426,
257 : 630378, 110562, 30562, 110722, 30722, 70546, 30546, 30946, 70962, 231202,
258 : 71442, 111042, 31426, 31026, 30978, 31058, 151106, 71346, 9870786, 1470930,
259 : 1470642, 2310690, 10467, 71266, 152866, 6511842, -1,
260 : 81,49210121, 6730319, 250427, 250319, 16450238, 610238, 70454, 70346,
261 : 70400, 70319, 5650670, 250994, 250670, 610589, 2412452, -1,
262 : /*96*/
263 : 100, 30393, 57310217, 10481, 30693, 36470341, 630408, 30968, 13310392,
264 : 210416, 10576, 11256, 10856, 11096, 630648, 31768, 8470616, -1,
265 : 108, 30552, 60170280, 610359, 30984, 38290440, 210660, 1830540, 30849,
266 : 30660, 31308, 211137, 20570532, 770721, 770532, 70769, 11636, 11813, 610647,
267 : 70647, 250674, 70674, 70890, 211092, 1830852, 31389, 31092, 32388, 211965,
268 : 13090836, 491133, 490836, 751080, 211416, 33576, 8691288, 70904, 11048, 71720,
269 : 13688, 12344, 251538, 751608, 212280, 36600, 5532024,-1,
270 : 112, 430344, 73530248, 430736, 110736, 30904, 31016, 30792, 230664,
271 : 110664, 230888, 0/*70888*/, 0/*70888*/, 71224, 30920, 30808, 30856, 30744,
272 : 71080, 23650600, 3010792, 3010600, 37410472, 4730472, 1290632, 1290568,
273 : 1290504, 71336, 231672, 72008, 111448, 31984, 31424, 31360, 31472, 151528,
274 : 71864, 20211048, 3011240, 3010856, 4730920, 30643, 153992, 13332456,-1,
275 : 120, 2310456, 770488, 110648, 63210360, 30763, 210552, 30712, 31256,
276 : 31240, 31336, 31400, 31496, 31480, 31096, 630498, 210808, 770968, 211128,
277 : 490904, 211064, 630744, 2310888, 631032, 1470840, 630984, 31128, 111368, 31608,
278 : 71224, 31464, 33810648, 4410744, 4410552, 11211, 31263, 11416, 210858, 11290,
279 : 11090, 211032, 31352, 32600, 630738, 491864, 1471704, 72664, 22051224, -1,
280 : 135, 114870240, 39270456, 1470618, 1470456, 16591104, -1,
281 : -1};
282 : long i;
283 : const long *t;
284 700 : GEN Z = groupelts_center(S), L = galoissubgroups(G);
285 700 : long scenter = groupelts_sumorders(Z), svecgroup = vecgroup_sumorders(L);
286 700 : long u = svecgroup+10000*scenter; /*This is used as a hash value*/
287 :
288 2268 : for(t=tab; *t!=-1; t++)
289 : {
290 2191 : if (t[0]==n)
291 : {
292 12894 : for(i=1; t[i] != -1; i++)
293 12971 : if (t[i]==u) return i;
294 105 : switch(n)
295 : {
296 98 : case 32:
297 98 : switch(u)
298 : {
299 42 : case 230171:
300 : {
301 42 : const long good[]={2,0}, bad[]={4,5,0};
302 42 : return indexgroupcentre(G,Z,good,bad)? 4: 12;
303 : }
304 7 : case 70267:
305 7 : if (s==135) return 9;
306 7 : return 32;
307 35 : case 70187:
308 : {
309 35 : const long good[]={8,0}, bad[]={7,9,0};
310 35 : return indexgroupcentre(G,Z,good,bad)? 13: 14;
311 : }
312 14 : case 70379:
313 : {
314 14 : const long good[]={4,0},bad[]={0};
315 14 : return indexgroupsubgroup(L,8,good,bad)? 31: 30;
316 : }
317 : }
318 0 : break;
319 7 : case 48: case 80:
320 : {
321 7 : const long good[]={5,8,0},bad[]={6,7,0};
322 7 : return indexgroupcentre(G,Z,good,bad)? 12: 13;
323 : }
324 0 : case 112:
325 : {
326 0 : const long good[]={7,4,0},bad[]={5,6,0};
327 0 : return indexgroupcentre(G,Z,good,bad)? 11: 12;
328 : }
329 : }
330 0 : return -1;
331 : }
332 47530 : while (*t!=-1) t++;
333 : }
334 : {
335 77 : const long tab[]={ 64, 1270001, /*4270003*/0, /*4270003*/0, 8190072,
336 : 6430073, 6670445, 5550446, 8190278, 7070279, 6350071, 5230072, 8110154,
337 : /*5870155*/0, /*5870155*/0, /*4270042*/0, /*4270042*/0, 7710246, 7390277,
338 : 6750037, 8032377, 8670266, 6750397, 11390022, 7710267, 7070277, /*3630046*/0,
339 : /*3630046*/0, 3630057, 4830196, 4830207, 4671808, 9070697, 6670700, 8750094,
340 : 6990091, 6350111, 5870115, 6671599, 5711601, 5551702, 5871512, 6351709,
341 : 5391711, /*3630046*/0, 3630047, 4111467, /*4430156*/0, /*4430156*/0, 3790166,
342 : /*2510026*/0, /*2510026*/0, 4470028, 4150300, 3830030, 13470021, 20350065,
343 : 10910041, 16514365, /*12190433*/0, 34110271, /*16514475*/0, 15230465,
344 : /*10910433*/0, 9630041, 13470233, /*16514475*/0, 20834696, /*10910433*/0,
345 : 13954343, /*12190433*/0, 19553542, 13474377, 25790466, 15870467, 18914476,
346 : 14110477, /*14590443*/0, 13310443, 11550043, /*14590443*/0, 10270043, 8990002,
347 : 8990546, 8990646, 8993647, 8356896, 13310905, 13310915, 12039018, 16990866,
348 : 12670888, 15071116, 11551217, 12038218, 16031739, 12512740, 12353138, 12993048,
349 : 15391849, 11872850, 12993551, 12353851, 8991446, 8991447, 8354830, 9951566,
350 : 9951666, 8674709, 9317039, 8031897, 8030187, 7713641, 7714641, 7074743,
351 : 9236585, 9236415, 9236586, 10990821, 9879066, 8751833, 9873399, 8751766,
352 : 10990754, 8593054, 8593087, 6830446, 6833546, 17472434, 13953445, 14432313,
353 : 16352544, 12833555, 13313423, 15635143, 13234877, 13874853, 12755287, 17870919,
354 : 14190949, 13075209, 11955310, 10835253, 9715354, 11312124, 10193135, 11074927,
355 : 12197529, 9957664, 11074970, 12196539, 9956674, 9958907, 10439497, 9479551,
356 : 9554015, 8433958, 9553915, 8434058, 8918081, 7798421, 10110856, 10110756,
357 : 9476648, 8991757, 8991857, 8356682, 10994275, 8750435, 8590474, 9230510,
358 : 10355254, 8115355, 13556790, 15790679, 11310691, 12275539, 14035061, 11795172,
359 : 8750465, 7474472, 8750475, 8114920, 6110196, 6111806, 5951808, 10191819,
360 : 9238364, 8271841, 8590736, 9390959, 8432079, 25470255, 41792701, 25470275,
361 : 20355344, 27233751, 18593673, 19717567, 23394762, 17312707, 19717633, 46115277,
362 : 31557088, 22917189, 24677288, 24039835, 24676366, 16032362, 17793529, 17153269,
363 : 38432486, 21153763, 23393635, 16037076, 27710971, 27074338, 20995174, 23396204,
364 : 20193482, 17157790, 19550231, 14751475, 17153832, 19070249, 16038080, 33391110,
365 : 25875097, 22197835, 22195018, 21070221, 24590112, 18999456, 15952565, 18356361,
366 : 17237769, 18359003, 15951169, 14832955, 16110295, 18350268, 21392354, 22030301,
367 : 18353365, 15955257, 13550032, 18430405, 18434015, 17150260, 17154128, 27234036,
368 : 23710639, 20194057, 21157900, 24198470, 20679613, 21158141, 22435065, 21318520,
369 : 20197076, 67390501, 83715011, 51070497, 54590283, 58915129, 50275230, 52035340,
370 : 263870051, -1,
371 : -1};
372 : long i;
373 : const long *t;
374 77 : GEN V=vecgroup_idxlist(L,32);
375 77 : long idxlist=vecsmall_pack(V,10,9967);
376 77 : long w=10000*svecgroup+idxlist; /*This is used as a hash value*/
377 84 : for(t=tab; *t!=-1; t++)
378 : {
379 77 : if (t[0]==n)
380 : {
381 18760 : for(i=1; t[i] != -1; i++)
382 18760 : if (t[i]==w) return i;
383 70 : switch(n)
384 : {
385 70 : case 64:
386 70 : switch(w)
387 : {
388 7 : case 4270003:
389 7 : return (scenter==439)? 2: 3;
390 7 : case 5870155:
391 : {
392 7 : const long good[]={8,9,0},bad[]={7,0};
393 7 : return indexgroupcentre(G,Z,good,bad)? 13: 14;
394 : }
395 7 : case 4270042:
396 : {
397 7 : const long good[]={13,0},bad[]={14,0};
398 7 : return indexgroupcentre(G,Z,good,bad)? 15: 16;
399 : }
400 7 : case 4430156:
401 : {
402 7 : const long good[]={18,20,0},bad[]={19,0};
403 7 : return indexgroupcentre(G,Z,good,bad)? 47: 48;
404 : }
405 7 : case 2510026:
406 7 : return scenter==1367? 50: 51;
407 7 : case 12190433:
408 7 : return scenter==47? 59: 70;
409 7 : case 16514475:
410 : {
411 7 : const long good[]={22,24,28,0},bad[]={23,25,27,30,0};
412 7 : return indexgroupcentre(G,Z,good,bad)? 61: 66;
413 : }
414 7 : case 10910433:
415 : {
416 7 : const long good[]={23,31,0},bad[]={25,26,29,30,33,0};
417 7 : return indexgroupcentre(G,Z,good,bad)? 63: 68;
418 : }
419 7 : case 14590443:
420 : {
421 7 : const long good[]={28,33,0},bad[]={30,34,0};
422 7 : return indexgroupcentre(G,Z,good,bad)? 77: 80;
423 : }
424 7 : case 3630046:
425 : {
426 7 : const long good[]={3,0},bad[]={12,16,0};
427 7 : if (scenter==695) return 26;
428 7 : return indexgroupcentre(G,Z,good,bad)? 27: 44;
429 : }
430 : }
431 0 : break;
432 : }
433 0 : return -1;
434 : }
435 1883 : while (*t!=-1) t++;
436 : }
437 : }
438 : {
439 7 : const long tab[]={ 96, 316010002, 252010002, 707020000, 676160124,
440 : 676170124, 87180027, 988190278, 892200028, 876030110, 876040110, 876120110,
441 : 215111237, 503062153, 972141052, 972131052, 455091156, 167101154, 620160033,
442 : 620170033, 908031033, 908121033, 908041033, 199101564, 7130153, 7140153,
443 : 812150123, 247051165, 487091566, 812151024, 391071276, 103081274, 247111377,
444 : 988180195, 892190205, 924190197, 828200207, 103050134, 679020464, 295091075,
445 : 199070145, 391060235, 103101076, 7080146, 135111157, 295020044, 684030223,
446 : 684040223, 908050274, 135060255, 7070285, 812080286, 71092475, 876102476,
447 : 908112287, 684120223, 748130243, 748140243, 620150254, 492160043, 492170043,
448 : 764180045, 700190477, 636200047, 963110003, 779050031, 935100032, 799110033,
449 : 819210003, 791260032, 246270050, 723330003, 987340003, 651360031, 623380033,
450 : 647263930, 839351534, 455321350, 178211335, 791244031, 322256848, 189340236,
451 : 130316409, 599331360, 743244548, 935295937, 551333907, 189222029, 274255883,
452 : 525275609, 82306043, 610289391, 82315641, 82307025, 647262487, 839353950,
453 : 0/*455322385*/, 0/*455322385*/, 178233588, 791245051, 322256982, 130307015,
454 : 658286619, 983297004, 983297037, 599333858, 631365165, 631376165, 535386399,
455 : 66408676, 354390966, 871428265, 775411064, 631376407, 535386309, 114430028,
456 : 823441008, 314398920, 74437993, 831420054, 42405827, 90439425, 799440830,
457 : 847426805, 767410275, 815440314, 863429143, 487360134, 487371044, 66211564,
458 : 66231664, 871295713, 66231764, 679242567, 125228724, 210253894, 18306803,
459 : 546288536, 162390938, 919437378, 871401018, 162255761, 967304398, 967313318,
460 : 413274329, 498283470, 498288163, 29345108, 967401139, 727449579, 679411219,
461 : 775352619, 583261276, 919295225, 66312839, 423381047, 2437470, 759424560,
462 : 711448550, 770222372, 109272382, 551210244, 258222592, 551230264, 295242430,
463 : 647254411, 199262266, 482272602, 871283751, 423293752, 519303751, 519312662,
464 : 71320222, 167332232, 226340245, 327352266, 167360274, 167372584, 103382587,
465 : 647392595, 455406162, 263412616, 327428742, 487438955, 295440098, 358290331,
466 : 622253358, 886280358, 322410312, 754400322, 394443122, 282440313, 354423123,
467 : 522430323, 726220349, 990273529, 470450359, 742460359, 522470032, 198470031,
468 : 282480353, 290490033, 274500353, 414470000, 614490000, 605473864, 664459790,
469 : 723464091, 893482714, 675465704, 845486215, 184493728, 653478045, 941489155,
470 : 605501588, 925482982, 264492577, 589502601, 312450472, 371466994, 285450492,
471 : 989464902, 578470486, 770489139, 994490497, 546500507, 604460529, 65270050,
472 : 684510049, 468510050, 134510562, 831510052, -1
473 : -1};
474 : long i;
475 : const long *t;
476 7 : GEN V=vecgroup_idxlist(L,48);
477 7 : long idx48=vecsmall_pack(V,10,9967);
478 7 : long idx32=vecgroup_idxlist(L,32)[1];
479 7 : long w=1000000*(svecgroup%997)+10000*idx32+idx48;
480 : /*This is used as a hash value*/
481 7 : for(t=tab; *t!=-1; t++)
482 : {
483 7 : if (t[0]==n)
484 : {
485 1127 : for(i=1; t[i] != -1; i++)
486 1127 : if (t[i]==w) return i;
487 0 : switch(n)
488 : {
489 0 : case 96:
490 0 : switch(w)
491 : {
492 0 : case 455322385:
493 : {
494 0 : const long good[]={37,40,0},bad[]={34,41,0};
495 0 : return indexgroupcentre(G,Z,good,bad)? 96: 97;
496 : }
497 : }
498 0 : break;
499 : }
500 0 : return -1;
501 : }
502 0 : while (*t!=-1) t++;
503 : }
504 : }
505 : }
506 0 : return 0;
507 : }
508 :
509 : long
510 1694 : group_ident(GEN G, GEN S)
511 : {
512 1694 : pari_sp av = avma;
513 1694 : long idx = group_ident_i(G, S);
514 1694 : if (idx < 0) pari_err_TYPE("group_ident [not a group]", G);
515 1694 : if (!idx) pari_err_IMPL("galoisidentify for groups of order > 127");
516 1694 : return gc_long(av, idx);
517 : }
518 :
519 : long
520 0 : group_ident_trans(GEN G, GEN S)
521 : {
522 0 : const long tab[]={
523 : 4, 1, 2, -1,
524 : 6, 2, 1, -1,
525 : 8, 1, 2, 4, 5, 3, -1,
526 : 9, 1, 2, -1,
527 : 10, 2, 1, -1,
528 : 12, 5, 1, 4, 3, 2, -1,
529 : 14, 2, 1, -1,
530 : 15, 1, -1,
531 : 16, 1, 4, 10, 8, 5, 6, 13, 12, 14, 2, 9, 7, 11, 3, -1,
532 : 18, 5, 1, 3, 4, 2, -1,
533 : 20, 2, 1, 5, 4, 3, -1,
534 : 21, 2, 1, -1,
535 : 22, 2, 1, -1,
536 : 24, 8, 1, 7, 5, 12, 13, 6, 14, 2, 15, 4, 10, 9, 11, 3, -1,
537 : 25, 1, 2, -1,
538 : 26, 2, 1, -1,
539 : 27, 1, 2, 3, 5, 4, -1,
540 : 28, 3, 1, 4, 2, -1,
541 : 30, 2, 4, 3, 1, -1,
542 : -1};
543 0 : long n = group_order(G), s;
544 : const long *t;
545 0 : if (n == 1) return 1;
546 : /* N.B. known up to 32 (Cannon-Holt) */
547 0 : if (n > 30) pari_err_IMPL("group_ident_trans [n > 30]");
548 0 : if (uisprime(n)) return 1;
549 0 : s = group_ident(G,S);
550 0 : for(t=tab;*t>=0;t++)
551 : {
552 0 : if (t[0]==n) return t[s];
553 0 : while (*t>=0) t++;
554 : }
555 : return 0; /*LCOV_EXCL_LINE*/
556 : }
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