Line data Source code
1 : /* Copyright (C) 2019 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 : /***********************************************************************/
19 : /** **/
20 : /** FlxX **/
21 : /** **/
22 : /***********************************************************************/
23 :
24 : /* FlxX are t_POL with Flx coefficients.
25 : * Normally the variable ordering should be respected.*/
26 :
27 : /*Similar to normalizepol, in place*/
28 : /*FlxX_renormalize=zxX_renormalize */
29 : GEN
30 15238377 : FlxX_renormalize(GEN /*in place*/ x, long lx)
31 : {
32 : long i;
33 20068686 : for (i = lx-1; i>1; i--)
34 19289839 : if (lgpol(gel(x,i))) break;
35 15238364 : stackdummy((pari_sp)(x + lg(x)), (pari_sp)(x + i+1));
36 15238846 : setlg(x, i+1); setsigne(x, i!=1); return x;
37 : }
38 :
39 : GEN
40 758609 : pol1_FlxX(long v, long sv)
41 : {
42 758609 : GEN z = cgetg(3, t_POL);
43 758609 : z[1] = evalsigne(1) | evalvarn(v);
44 758609 : gel(z,2) = pol1_Flx(sv); return z;
45 : }
46 :
47 : GEN
48 690500 : polx_FlxX(long v, long sv)
49 : {
50 690500 : GEN z = cgetg(4, t_POL);
51 690500 : z[1] = evalsigne(1) | evalvarn(v);
52 690500 : gel(z,2) = pol0_Flx(sv);
53 690500 : gel(z,3) = pol1_Flx(sv); return z;
54 : }
55 :
56 : long
57 2869415 : FlxY_degreex(GEN b)
58 : {
59 2869415 : long deg = 0, i;
60 2869415 : if (!signe(b)) return -1;
61 10342270 : for (i = 2; i < lg(b); ++i)
62 7472707 : deg = maxss(deg, degpol(gel(b, i)));
63 2869563 : return deg;
64 : }
65 :
66 : /*Lift coefficient of B to constant Flx, to give a FlxY*/
67 : GEN
68 2498 : Fly_to_FlxY(GEN B, long sv)
69 : {
70 2498 : long lb=lg(B);
71 : long i;
72 2498 : GEN b=cgetg(lb,t_POL);
73 2497 : b[1]=evalsigne(1)|(((ulong)B[1])&VARNBITS);
74 64850 : for (i=2; i<lb; i++)
75 62361 : gel(b,i) = Fl_to_Flx(B[i], sv);
76 2489 : return FlxX_renormalize(b, lb);
77 : }
78 :
79 : GEN
80 2665351 : zxX_to_FlxX(GEN B, ulong p)
81 : {
82 2665351 : long i, lb = lg(B);
83 2665351 : GEN b = cgetg(lb,t_POL);
84 8688960 : for (i=2; i<lb; i++)
85 6029077 : gel(b,i) = zx_to_Flx(gel(B,i), p);
86 2659883 : b[1] = B[1]; return FlxX_renormalize(b, lb);
87 : }
88 :
89 : GEN
90 2770931 : FlxX_to_ZXX(GEN B)
91 : {
92 2770931 : long i, lb = lg(B);
93 2770931 : GEN b = cgetg(lb,t_POL);
94 8886123 : for (i=2; i<lb; i++)
95 : {
96 6116625 : GEN c = gel(B,i);
97 6116625 : switch(lgpol(c))
98 : {
99 267438 : case 0: c = gen_0; break;
100 795225 : case 1: c = utoi(c[2]); break;
101 5053924 : default: c = Flx_to_ZX(c); break;
102 : }
103 6114856 : gel(b,i) = c;
104 : }
105 2769498 : b[1] = B[1]; return b;
106 : }
107 :
108 : /* Note: v is used _only_ for the t_INT. It must match
109 : * the variable of any t_POL coefficients. */
110 : GEN
111 2818163 : ZXX_to_FlxX(GEN B, ulong p, long v)
112 : {
113 2818163 : long lb=lg(B);
114 : long i;
115 2818163 : GEN b=cgetg(lb,t_POL);
116 2818263 : b[1]=evalsigne(1)|(((ulong)B[1])&VARNBITS);
117 13781484 : for (i=2; i<lb; i++)
118 10964872 : switch (typ(gel(B,i)))
119 : {
120 2143720 : case t_INT:
121 2143720 : gel(b,i) = Z_to_Flx(gel(B,i), p, evalvarn(v));
122 2143608 : break;
123 8823126 : case t_POL:
124 8823126 : gel(b,i) = ZX_to_Flx(gel(B,i), p);
125 8821587 : break;
126 : }
127 2816612 : return FlxX_renormalize(b, lb);
128 : }
129 :
130 : GEN
131 0 : ZXXV_to_FlxXV(GEN x, ulong p, long v)
132 0 : { pari_APPLY_type(t_VEC, ZXX_to_FlxX(gel(x,i), p, v)) }
133 :
134 : GEN
135 512 : ZXXT_to_FlxXT(GEN x, ulong p, long v)
136 : {
137 512 : if (typ(x) == t_POL)
138 491 : return ZXX_to_FlxX(x, p, v);
139 : else
140 63 : pari_APPLY_type(t_VEC, ZXXT_to_FlxXT(gel(x,i), p, v))
141 : }
142 :
143 : GEN
144 319858 : FlxX_to_FlxC(GEN x, long N, long sv)
145 : {
146 : long i, l;
147 : GEN z;
148 319858 : l = lg(x)-1; x++;
149 319858 : if (l > N+1) l = N+1; /* truncate higher degree terms */
150 319858 : z = cgetg(N+1,t_COL);
151 2417645 : for (i=1; i<l ; i++) gel(z,i) = gel(x,i);
152 3486844 : for ( ; i<=N; i++) gel(z,i) = pol0_Flx(sv);
153 319858 : return z;
154 : }
155 :
156 : /* matrix whose entries are given by the coeffs of the polynomial v in
157 : * two variables (considered as degree n polynomials) */
158 : GEN
159 57220 : FlxX_to_Flm(GEN v, long n)
160 : {
161 57220 : long j, N = lg(v)-1;
162 57220 : GEN y = cgetg(N, t_MAT);
163 57221 : v++;
164 196015 : for (j=1; j<N; j++) gel(y,j) = Flx_to_Flv(gel(v,j), n);
165 57217 : return y;
166 : }
167 :
168 : GEN
169 364633 : FlxX_to_Flx(GEN f)
170 : {
171 364633 : long i, l = lg(f);
172 364633 : GEN V = cgetg(l, t_VECSMALL);
173 364634 : V[1] = ((ulong)f[1])&VARNBITS;
174 3496703 : for(i=2; i<l; i++)
175 3132069 : V[i] = lgpol(gel(f,i)) ? mael(f,i,2): 0L;
176 364634 : return V;
177 : }
178 :
179 : GEN
180 221456 : Flm_to_FlxX(GEN x, long v,long w)
181 : {
182 221456 : long j, lx = lg(x);
183 221456 : GEN y = cgetg(lx+1, t_POL);
184 221456 : y[1]=evalsigne(1) | v;
185 221456 : y++;
186 814219 : for (j=1; j<lx; j++) gel(y,j) = Flv_to_Flx(gel(x,j), w);
187 221437 : return FlxX_renormalize(--y, lx+1);
188 : }
189 :
190 : /* P(X,Y) --> P(Y,X), n is the degree in Y */
191 : GEN
192 181750 : FlxX_swap(GEN x, long n, long ws)
193 : {
194 181750 : long j, lx = lg(x), ly = n+3;
195 181750 : GEN y = cgetg(ly, t_POL);
196 181756 : y[1] = x[1];
197 1168622 : for (j=2; j<ly; j++)
198 : {
199 : long k;
200 986867 : GEN p1 = cgetg(lx, t_VECSMALL);
201 986866 : p1[1] = ws;
202 11225263 : for (k=2; k<lx; k++)
203 10238397 : if (j<lg(gel(x,k)))
204 7199276 : p1[k] = mael(x,k,j);
205 : else
206 3039121 : p1[k] = 0;
207 986866 : gel(y,j) = Flx_renormalize(p1,lx);
208 : }
209 181755 : return FlxX_renormalize(y,ly);
210 : }
211 :
212 : static GEN
213 4359701 : zxX_to_Kronecker_spec(GEN P, long lp, long n)
214 : { /* P(X) = sum Pi(Y) * X^i, return P( Y^(2n-1) ) */
215 4359701 : long i, j, k, l, N = (n<<1) + 1;
216 4359701 : GEN y = cgetg((N-2)*lp + 2, t_VECSMALL) + 2;
217 28820270 : for (k=i=0; i<lp; i++)
218 : {
219 28783883 : GEN c = gel(P,i);
220 28783883 : l = lg(c);
221 28783883 : if (l-3 >= n)
222 0 : pari_err_BUG("zxX_to_Kronecker, P is not reduced mod Q");
223 168688772 : for (j=2; j < l; j++) y[k++] = c[j];
224 28783847 : if (i == lp-1) break;
225 219122349 : for ( ; j < N; j++) y[k++] = 0;
226 : }
227 4359634 : y -= 2;
228 4359634 : y[1] = 0; setlg(y, k+2); return y;
229 : }
230 :
231 : GEN
232 3773434 : zxX_to_Kronecker(GEN P, GEN Q)
233 : {
234 3773434 : GEN z = zxX_to_Kronecker_spec(P+2, lg(P)-2, degpol(Q));
235 3773445 : z[1] = P[1]; return z;
236 : }
237 :
238 : GEN
239 348540 : FlxX_add(GEN x, GEN y, ulong p)
240 : {
241 : long i,lz;
242 : GEN z;
243 348540 : long lx=lg(x);
244 348540 : long ly=lg(y);
245 348540 : if (ly>lx) swapspec(x,y, lx,ly);
246 348540 : lz = lx; z = cgetg(lz, t_POL); z[1]=x[1];
247 3922222 : for (i=2; i<ly; i++) gel(z,i) = Flx_add(gel(x,i), gel(y,i), p);
248 2148291 : for ( ; i<lx; i++) gel(z,i) = Flx_copy(gel(x,i));
249 348525 : return FlxX_renormalize(z, lz);
250 : }
251 :
252 : GEN
253 245 : FlxX_Flx_add(GEN y, GEN x, ulong p)
254 : {
255 245 : long i, lz = lg(y);
256 : GEN z;
257 245 : if (signe(y) == 0) return scalarpol(x, varn(y));
258 245 : z = cgetg(lz,t_POL); z[1] = y[1];
259 245 : gel(z,2) = Flx_add(gel(y,2), x, p);
260 245 : if (lz == 3) z = FlxX_renormalize(z,lz);
261 : else
262 1071 : for(i=3;i<lz;i++) gel(z,i) = Flx_copy(gel(y,i));
263 245 : return z;
264 : }
265 :
266 : GEN
267 11662 : FlxX_Flx_sub(GEN y, GEN x, ulong p)
268 : {
269 11662 : long i, lz = lg(y);
270 : GEN z;
271 11662 : if (signe(y) == 0) return scalarpol(x, varn(y));
272 11662 : z = cgetg(lz,t_POL); z[1] = y[1];
273 11662 : gel(z,2) = Flx_sub(gel(y,2), x, p);
274 11662 : if (lz == 3) z = FlxX_renormalize(z,lz);
275 : else
276 84532 : for(i=3;i<lz;i++) gel(z,i) = Flx_copy(gel(y,i));
277 11662 : return z;
278 : }
279 :
280 : GEN
281 2657 : FlxX_neg(GEN x, ulong p)
282 : {
283 2657 : long i, lx=lg(x);
284 2657 : GEN z = cgetg(lx, t_POL);
285 2657 : z[1]=x[1];
286 45554 : for (i=2; i<lx; i++) gel(z,i) = Flx_neg(gel(x,i), p);
287 2657 : return z;
288 : }
289 :
290 : GEN
291 761 : FlxX_Fl_mul(GEN x, ulong y, ulong p)
292 : {
293 761 : long i, lx=lg(x);
294 761 : GEN z = cgetg(lx, t_POL);
295 761 : z[1]=x[1];
296 3667 : for (i=2; i<lx; i++) gel(z,i) = Flx_Fl_mul(gel(x,i), y, p);
297 761 : return FlxX_renormalize(z, lx);
298 : }
299 :
300 : GEN
301 0 : FlxX_triple(GEN x, ulong p)
302 : {
303 0 : long i, lx=lg(x);
304 0 : GEN z = cgetg(lx, t_POL);
305 0 : z[1]=x[1];
306 0 : for (i=2; i<lx; i++) gel(z,i) = Flx_triple(gel(x,i), p);
307 0 : return FlxX_renormalize(z, lx);
308 : }
309 :
310 : GEN
311 761 : FlxX_double(GEN x, ulong p)
312 : {
313 761 : long i, lx=lg(x);
314 761 : GEN z = cgetg(lx, t_POL);
315 761 : z[1]=x[1];
316 6088 : for (i=2; i<lx; i++) gel(z,i) = Flx_double(gel(x,i), p);
317 761 : return FlxX_renormalize(z, lx);
318 : }
319 :
320 : GEN
321 84241 : FlxX_deriv(GEN z, ulong p)
322 : {
323 84241 : long i,l = lg(z)-1;
324 : GEN x;
325 84241 : if (l < 2) l = 2;
326 84241 : x = cgetg(l, t_POL); x[1] = z[1];
327 903912 : for (i=2; i<l; i++) gel(x,i) = Flx_mulu(gel(z,i+1), (ulong) i-1, p);
328 84242 : return FlxX_renormalize(x,l);
329 : }
330 :
331 : GEN
332 0 : FlxX_translate1(GEN P, long p, long n)
333 : {
334 : GEN Q;
335 0 : long i, l, ws, lP = lgpol(P);
336 0 : if (!lP) return gcopy(P);
337 0 : ws = mael(P,2,1);
338 0 : Q = FlxX_swap(P, n, ws);
339 0 : l = lg(Q);
340 0 : for (i=2; i<l; i++) gel(Q, i) = Flx_translate1(gel(Q, i), p);
341 0 : return FlxX_swap(Q, lP, ws);
342 : }
343 :
344 : GEN
345 0 : zlxX_translate1(GEN P, long p, long e, long n)
346 : {
347 : GEN Q;
348 0 : long i, l, ws, lP = lgpol(P);
349 0 : if (!lP) return gcopy(P);
350 0 : ws = mael(P,2,1);
351 0 : Q = FlxX_swap(P, n, ws);
352 0 : l = lg(Q);
353 0 : for (i=2; i<l; i++) gel(Q, i) = zlx_translate1(gel(Q, i), p, e);
354 0 : return FlxX_swap(Q, lP, ws);
355 : }
356 :
357 : static GEN
358 110317 : FlxX_subspec(GEN x, GEN y, ulong p, long lx, long ly)
359 : {
360 : long i,lz;
361 : GEN z;
362 :
363 110317 : if (ly <= lx)
364 : {
365 110317 : lz = lx+2; z = cgetg(lz, t_POL);
366 3346614 : for (i=0; i<ly; i++) gel(z,i+2) = Flx_sub(gel(x,i),gel(y,i),p);
367 112124 : for ( ; i<lx; i++) gel(z,i+2) = Flx_copy(gel(x,i));
368 : }
369 : else
370 : {
371 0 : lz = ly+2; z = cgetg(lz, t_POL);
372 0 : for (i=0; i<lx; i++) gel(z,i+2) = Flx_sub(gel(x,i),gel(y,i),p);
373 0 : for ( ; i<ly; i++) gel(z,i+2) = Flx_neg(gel(y,i),p);
374 : }
375 110317 : z[1] = 0; return FlxX_renormalize(z, lz);
376 : }
377 :
378 : GEN
379 623866 : FlxX_sub(GEN x, GEN y, ulong p)
380 : {
381 : long lx,ly,i,lz;
382 : GEN z;
383 623866 : lx = lg(x); ly = lg(y);
384 623866 : lz=maxss(lx,ly);
385 623866 : z = cgetg(lz,t_POL);
386 623864 : if (lx >= ly)
387 : {
388 109985 : z[1] = x[1];
389 635507 : for (i=2; i<ly; i++) gel(z,i) = Flx_sub(gel(x,i),gel(y,i),p);
390 388611 : for ( ; i<lx; i++) gel(z,i) = Flx_copy(gel(x,i));
391 109985 : if (lx==ly) z = FlxX_renormalize(z, lz);
392 : }
393 : else
394 : {
395 513879 : z[1] = y[1];
396 1294806 : for (i=2; i<lx; i++) gel(z,i) = Flx_sub(gel(x,i),gel(y,i),p);
397 1381470 : for ( ; i<ly; i++) gel(z,i) = Flx_neg(gel(y,i),p);
398 : }
399 623807 : if (!lgpol(z)) { set_avma((pari_sp)(z + lz)); z = pol_0(varn(x)); }
400 623843 : return z;
401 : }
402 :
403 : GEN
404 0 : FlxX_Flx_mul(GEN P, GEN U, ulong p)
405 : {
406 0 : long i, lP = lg(P);
407 0 : GEN res = cgetg(lP,t_POL);
408 0 : ulong pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
409 0 : res[1] = P[1];
410 0 : for(i=2; i<lP; i++) gel(res,i) = Flx_mul_pre(U,gel(P,i), p, pi);
411 0 : return FlxX_renormalize(res, lP);
412 : }
413 :
414 : GEN
415 5577869 : FlxY_evalx_pre(GEN Q, ulong x, ulong p, ulong pi)
416 : {
417 5577869 : long i, lb = lg(Q);
418 : GEN z;
419 5577869 : z = cgetg(lb,t_VECSMALL); z[1] = evalvarn(varn(Q));
420 75833005 : for (i=2; i<lb; i++) z[i] = Flx_eval_pre(gel(Q,i), x, p, pi);
421 5579678 : return Flx_renormalize(z, lb);
422 : }
423 : GEN
424 231 : FlxY_evalx(GEN Q, ulong x, ulong p)
425 231 : { return FlxY_evalx_pre(Q, x, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
426 :
427 : GEN
428 0 : FlxY_Flx_translate(GEN P, GEN c, ulong p)
429 : {
430 0 : pari_sp av = avma;
431 0 : ulong pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
432 : GEN Q;
433 : long i, k, n;
434 :
435 0 : if (!signe(P) || gequal0(c)) return RgX_copy(P);
436 0 : Q = leafcopy(P); n = degpol(P);
437 0 : for (i=1; i<=n; i++)
438 : {
439 0 : for (k=n-i; k<n; k++)
440 0 : gel(Q,2+k) = Flx_add(gel(Q,2+k), Flx_mul_pre(gel(Q,2+k+1), c, p, pi), p);
441 0 : if (gc_needed(av,2))
442 : {
443 0 : if(DEBUGMEM>1)
444 0 : pari_warn(warnmem,"FlxY_Flx_translate, i = %ld/%ld", i,n);
445 0 : Q = gc_GEN(av, Q);
446 : }
447 : }
448 0 : return gc_GEN(av, Q);
449 : }
450 :
451 : /* allow pi = 0 */
452 : GEN
453 10084850 : FlxY_evalx_powers_pre(GEN pol, GEN ypowers, ulong p, ulong pi)
454 : {
455 10084850 : long i, len = lg(pol);
456 10084850 : GEN res = cgetg(len, t_VECSMALL);
457 10083013 : res[1] = pol[1] & VARNBITS;
458 34199906 : for (i = 2; i < len; ++i)
459 24100706 : res[i] = Flx_eval_powers_pre(gel(pol, i), ypowers, p, pi);
460 10099200 : return Flx_renormalize(res, len);
461 : }
462 :
463 : /* allow pi = 0 */
464 : ulong
465 6761603 : FlxY_eval_powers_pre(GEN pol, GEN ypowers, GEN xpowers, ulong p, ulong pi)
466 : {
467 6761603 : pari_sp av = avma;
468 6761603 : GEN t = FlxY_evalx_powers_pre(pol, ypowers, p, pi);
469 6760517 : return gc_ulong(av, Flx_eval_powers_pre(t, xpowers, p, pi));
470 : }
471 :
472 : GEN
473 136362 : FlxY_FlxqV_evalx_pre(GEN P, GEN x, GEN T, ulong p, ulong pi)
474 : {
475 136362 : long i, lP = lg(P);
476 136362 : GEN res = cgetg(lP,t_POL);
477 136362 : res[1] = P[1];
478 930268 : for(i=2; i<lP; i++)
479 793906 : gel(res,i) = Flx_FlxqV_eval_pre(gel(P,i), x, T, p, pi);
480 136362 : return FlxX_renormalize(res, lP);
481 : }
482 : GEN
483 0 : FlxY_FlxqV_evalx(GEN P, GEN x, GEN T, ulong p)
484 0 : { return FlxY_FlxqV_evalx_pre(P, x, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
485 :
486 : GEN
487 0 : FlxY_Flxq_evalx_pre(GEN P, GEN x, GEN T, ulong p, ulong pi)
488 : {
489 0 : pari_sp av = avma;
490 0 : long n = brent_kung_optpow(get_Flx_degree(T)-1,lgpol(P),1);
491 0 : GEN xp = Flxq_powers_pre(x, n, T, p, pi);
492 0 : return gerepileupto(av, FlxY_FlxqV_evalx_pre(P, xp, T, p, pi));
493 : }
494 : GEN
495 0 : FlxY_Flxq_evalx(GEN P, GEN x, GEN T, ulong p)
496 0 : { return FlxY_Flxq_evalx_pre(P, x, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
497 :
498 : GEN
499 7467 : FlxY_Flx_div(GEN x, GEN y, ulong p)
500 : {
501 : long i, l;
502 : GEN z;
503 7467 : if (degpol(y) == 0)
504 : {
505 5530 : ulong t = uel(y,2);
506 5530 : if (t == 1) return x;
507 0 : t = Fl_inv(t, p);
508 0 : z = cgetg_copy(x, &l); z[1] = x[1];
509 0 : for (i=2; i<l; i++) gel(z,i) = Flx_Fl_mul(gel(x,i),t,p);
510 : }
511 : else
512 : {
513 1936 : ulong pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
514 1936 : z = cgetg_copy(x, &l); z[1] = x[1];
515 3874 : for (i=2; i<l; i++) gel(z,i) = Flx_div_pre(gel(x,i),y,p,pi);
516 : }
517 1937 : return z;
518 : }
519 :
520 : GEN
521 71625 : FlxX_shift(GEN a, long n, long vs)
522 : {
523 71625 : long i, l = lg(a);
524 : GEN b;
525 71625 : if (l == 2 || !n) return a;
526 64631 : l += n;
527 64631 : if (n < 0)
528 : {
529 35774 : if (l <= 2) return pol_0(varn(a));
530 29404 : b = cgetg(l, t_POL); b[1] = a[1];
531 29404 : a -= n;
532 612668 : for (i=2; i<l; i++) gel(b,i) = gel(a,i);
533 : } else {
534 28857 : b = cgetg(l, t_POL); b[1] = a[1];
535 28857 : a -= n; n += 2;
536 507050 : for (i=2; i<n; i++) gel(b,i) = pol0_Flx(vs);
537 365801 : for ( ; i<l; i++) gel(b,i) = gel(a,i);
538 : }
539 58261 : return b;
540 : }
541 :
542 : GEN
543 13194 : FlxX_blocks(GEN P, long n, long m, long vs)
544 : {
545 13194 : GEN z = cgetg(m+1,t_VEC);
546 13194 : long i,j, k=2, l = lg(P);
547 39585 : for(i=1; i<=m; i++)
548 : {
549 26389 : GEN zi = cgetg(n+2,t_POL);
550 26387 : zi[1] = P[1];
551 26387 : gel(z,i) = zi;
552 160472 : for(j=2; j<n+2; j++)
553 134172 : gel(zi, j) = k==l ? pol0_Flx(vs) : gel(P,k++);
554 26300 : zi = FlxX_renormalize(zi, n+2);
555 : }
556 13196 : return z;
557 : }
558 :
559 : static GEN
560 235489 : FlxX_recipspec(GEN x, long l, long n, long vs)
561 : {
562 : long i;
563 235489 : GEN z = cgetg(n+2,t_POL);
564 235489 : z[1] = 0; z += 2;
565 5279930 : for(i=0; i<l; i++)
566 5044441 : gel(z,n-i-1) = Flx_copy(gel(x,i));
567 242331 : for( ; i<n; i++)
568 6842 : gel(z,n-i-1) = pol0_Flx(vs);
569 235489 : return FlxX_renormalize(z-2,n+2);
570 : }
571 :
572 : GEN
573 2432 : FlxX_invLaplace(GEN x, ulong p)
574 : {
575 2432 : long i, d = degpol(x);
576 : GEN y;
577 : ulong t;
578 2432 : if (d <= 1) return gcopy(x);
579 2425 : t = Fl_inv(factorial_Fl(d, p), p);
580 2425 : y = cgetg(d+3, t_POL);
581 2425 : y[1] = x[1];
582 47642 : for (i=d; i>=2; i--)
583 : {
584 45217 : gel(y,i+2) = Flx_Fl_mul(gel(x,i+2), t, p);
585 45219 : t = Fl_mul(t, i, p);
586 : }
587 2425 : gel(y,3) = Flx_copy(gel(x,3));
588 2425 : gel(y,2) = Flx_copy(gel(x,2));
589 2425 : return FlxX_renormalize(y, d+3);
590 : }
591 :
592 : GEN
593 1216 : FlxX_Laplace(GEN x, ulong p)
594 : {
595 1216 : long i, d = degpol(x);
596 1216 : ulong t = 1;
597 : GEN y;
598 1216 : if (d <= 1) return gcopy(x);
599 1216 : y = cgetg(d+3, t_POL);
600 1216 : y[1] = x[1];
601 1216 : gel(y,2) = Flx_copy(gel(x,2));
602 1216 : gel(y,3) = Flx_copy(gel(x,3));
603 23850 : for (i=2; i<=d; i++)
604 : {
605 22634 : t = Fl_mul(t, i%p, p);
606 22634 : gel(y,i+2) = Flx_Fl_mul(gel(x,i+2), t, p);
607 : }
608 1216 : return FlxX_renormalize(y, d+3);
609 : }
610 :
611 : /***********************************************************************/
612 : /** **/
613 : /** FlxXV **/
614 : /** **/
615 : /***********************************************************************/
616 :
617 : GEN
618 0 : FlxXC_sub(GEN x, GEN y, ulong p)
619 0 : { pari_APPLY_same(FlxX_sub(gel(x, i), gel(y,i), p)) }
620 :
621 : static GEN
622 138362 : FlxXV_to_FlxM_lg(GEN x, long m, long n, long sv)
623 : {
624 : long i;
625 138362 : GEN y = cgetg(n+1, t_MAT);
626 458220 : for (i=1; i<=n; i++) gel(y,i) = FlxX_to_FlxC(gel(x,i), m, sv);
627 138362 : return y;
628 : }
629 :
630 : GEN
631 0 : FlxXV_to_FlxM(GEN v, long n, long sv)
632 0 : { return FlxXV_to_FlxM_lg(v, n, lg(v)-1, sv); }
633 :
634 : GEN
635 12460 : FlxXC_to_ZXXC(GEN x)
636 62416 : { pari_APPLY_type(t_COL, FlxX_to_ZXX(gel(x,i))) }
637 :
638 : GEN
639 0 : FlxXM_to_ZXXM(GEN x)
640 0 : { pari_APPLY_same(FlxXC_to_ZXXC(gel(x,i))) }
641 :
642 : /***********************************************************************/
643 : /** **/
644 : /** FlxqX **/
645 : /** **/
646 : /***********************************************************************/
647 :
648 : static GEN
649 3602700 : get_FlxqX_red(GEN T, GEN *B)
650 : {
651 3602700 : if (typ(T)!=t_VEC) { *B=NULL; return T; }
652 141825 : *B = gel(T,1); return gel(T,2);
653 : }
654 :
655 : GEN
656 151976 : RgX_to_FlxqX(GEN x, GEN T, ulong p)
657 : {
658 151976 : long i, l = lg(x);
659 151976 : GEN z = cgetg(l, t_POL); z[1] = x[1];
660 2326256 : for (i = 2; i < l; i++)
661 2174284 : gel(z,i) = Rg_to_Flxq(gel(x,i), T, p);
662 151972 : return FlxX_renormalize(z, l);
663 : }
664 :
665 : /* FlxqX are t_POL with Flxq coefficients.
666 : * Normally the variable ordering should be respected.*/
667 :
668 : GEN
669 590 : random_FlxqX(long d1, long v, GEN T, ulong p)
670 : {
671 590 : long dT = get_Flx_degree(T), vT = get_Flx_var(T);
672 590 : long i, d = d1+2;
673 590 : GEN y = cgetg(d,t_POL); y[1] = evalsigne(1) | evalvarn(v);
674 3124 : for (i=2; i<d; i++) gel(y,i) = random_Flx(dT, vT, p);
675 590 : return FlxX_renormalize(y,d);
676 : }
677 :
678 : /*Not stack clean*/
679 : GEN
680 2356806 : Kronecker_to_FlxqX_pre(GEN z, GEN T, ulong p, ulong pi)
681 : {
682 2356806 : long i,j,lx,l, N = (get_Flx_degree(T)<<1) + 1;
683 2356807 : GEN x, t = cgetg(N,t_VECSMALL);
684 2356804 : t[1] = get_Flx_var(T);
685 2356804 : l = lg(z); lx = (l-2) / (N-2);
686 2356804 : x = cgetg(lx+3,t_POL);
687 2356807 : x[1] = z[1];
688 28859458 : for (i=2; i<lx+2; i++)
689 : {
690 370677990 : for (j=2; j<N; j++) t[j] = z[j];
691 26502676 : z += (N-2);
692 26502676 : gel(x,i) = Flx_rem_pre(Flx_renormalize(t,N), T,p,pi);
693 : }
694 2356782 : N = (l-2) % (N-2) + 2;
695 7565689 : for (j=2; j<N; j++) t[j] = z[j];
696 2356782 : gel(x,i) = Flx_rem_pre(Flx_renormalize(t,N), T,p,pi);
697 2356745 : return FlxX_renormalize(x, i+1);
698 : }
699 : GEN
700 0 : Kronecker_to_FlxqX(GEN z, GEN T, ulong p)
701 0 : { return Kronecker_to_FlxqX_pre(z, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
702 :
703 : GEN
704 1264699 : FlxqX_red_pre(GEN z, GEN T, ulong p, ulong pi)
705 : {
706 : GEN res;
707 1264699 : long i, l = lg(z);
708 1264699 : res = cgetg(l,t_POL); res[1] = z[1];
709 13067506 : for(i=2;i<l;i++) gel(res,i) = Flx_rem_pre(gel(z,i),T,p,pi);
710 1264660 : return FlxX_renormalize(res,l);
711 : }
712 : GEN
713 0 : FlxqX_red(GEN z, GEN T, ulong p)
714 0 : { return FlxqX_red_pre(z, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
715 :
716 : static GEN
717 293138 : FlxqX_mulspec(GEN x, GEN y, GEN T, ulong p, ulong pi, long lx, long ly)
718 : {
719 293138 : pari_sp av = avma;
720 : GEN z,kx,ky;
721 293138 : long dT = get_Flx_degree(T);
722 293138 : kx= zxX_to_Kronecker_spec(x,lx,dT);
723 293138 : ky= zxX_to_Kronecker_spec(y,ly,dT);
724 293138 : z = Flx_mul_pre(ky, kx, p, pi);
725 293138 : z = Kronecker_to_FlxqX_pre(z,T,p,pi);
726 293138 : return gerepileupto(av, z);
727 : }
728 :
729 : GEN
730 1709735 : FlxqX_mul_pre(GEN x, GEN y, GEN T, ulong p, ulong pi)
731 : {
732 1709735 : pari_sp av = avma;
733 1709735 : GEN z, kx, ky, Tm = get_Flx_mod(T);
734 1709730 : kx= zxX_to_Kronecker(x, Tm);
735 1709743 : ky= zxX_to_Kronecker(y, Tm);
736 1709739 : z = Flx_mul_pre(ky, kx, p, pi);
737 1709696 : z = Kronecker_to_FlxqX_pre(z, T, p, pi);
738 1709649 : return gerepileupto(av, z);
739 : }
740 : GEN
741 63586 : FlxqX_mul(GEN x, GEN y, GEN T, ulong p)
742 63586 : { return FlxqX_mul_pre(x, y, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
743 :
744 : GEN
745 353989 : FlxqX_sqr_pre(GEN x, GEN T, ulong p, ulong pi)
746 : {
747 353989 : pari_sp av = avma;
748 : GEN z,kx;
749 353989 : kx= zxX_to_Kronecker(x,get_Flx_mod(T));
750 353987 : z = Flx_sqr_pre(kx, p, pi);
751 353988 : z = Kronecker_to_FlxqX_pre(z,T,p,pi);
752 353986 : return gerepileupto(av, z);
753 : }
754 : GEN
755 1218 : FlxqX_sqr(GEN x, GEN T, ulong p)
756 1218 : { return FlxqX_sqr_pre(x, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
757 :
758 : GEN
759 155138 : FlxqX_Flxq_mul_pre(GEN P, GEN U, GEN T, ulong p, ulong pi)
760 : {
761 155138 : long i, lP = lg(P);
762 155138 : GEN res = cgetg(lP,t_POL);
763 155139 : res[1] = P[1];
764 554361 : for(i=2; i<lP; i++) gel(res,i) = Flxq_mul_pre(U,gel(P,i), T,p,pi);
765 155112 : return FlxX_renormalize(res, lP);
766 : }
767 : GEN
768 0 : FlxqX_Flxq_mul(GEN P, GEN U, GEN T, ulong p)
769 0 : { return FlxqX_Flxq_mul_pre(P, U, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
770 :
771 : GEN
772 647912 : FlxqX_Flxq_mul_to_monic_pre(GEN P, GEN U, GEN T, ulong p, ulong pi)
773 : {
774 647912 : long i, lP = lg(P);
775 647912 : GEN res = cgetg(lP,t_POL);
776 647903 : res[1] = P[1];
777 3487089 : for(i=2; i<lP-1; i++) gel(res,i) = Flxq_mul_pre(U,gel(P,i), T,p,pi);
778 647519 : gel(res,lP-1) = pol1_Flx(get_Flx_var(T));
779 647914 : return FlxX_renormalize(res, lP);
780 : }
781 : GEN
782 0 : FlxqX_Flxq_mul_to_monic(GEN P, GEN U, GEN T, ulong p)
783 : {
784 0 : ulong pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
785 0 : return FlxqX_Flxq_mul_to_monic_pre(P, U, T, p, pi);
786 : }
787 :
788 : GEN
789 190041 : FlxqX_normalize_pre(GEN z, GEN T, ulong p, ulong pi)
790 : {
791 190041 : GEN p1 = leading_coeff(z);
792 190041 : if (!lgpol(z) || (!degpol(p1) && p1[1] == 1)) return z;
793 190020 : return FlxqX_Flxq_mul_to_monic_pre(z, Flxq_inv_pre(p1,T,p,pi), T,p,pi);
794 : }
795 : GEN
796 133 : FlxqX_normalize(GEN z, GEN T, ulong p)
797 133 : { return FlxqX_normalize_pre(z, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
798 :
799 : struct _FlxqXQ {
800 : GEN T, S;
801 : ulong p, pi;
802 : };
803 :
804 538530 : static GEN _FlxqX_mul(void *data,GEN a,GEN b)
805 : {
806 538530 : struct _FlxqXQ *d=(struct _FlxqXQ*)data;
807 538530 : return FlxqX_mul_pre(a,b,d->T,d->p,d->pi);
808 : }
809 10283 : static GEN _FlxqX_sqr(void *data,GEN a)
810 : {
811 10283 : struct _FlxqXQ *d=(struct _FlxqXQ*)data;
812 10283 : return FlxqX_sqr_pre(a,d->T,d->p,d->pi);
813 : }
814 :
815 : GEN
816 10248 : FlxqX_powu_pre(GEN V, ulong n, GEN T, ulong p, ulong pi)
817 : {
818 10248 : struct _FlxqXQ d; d.p = p; d.pi = pi; d.T = T;
819 10248 : return gen_powu(V, n, (void*)&d, &_FlxqX_sqr, &_FlxqX_mul);
820 : }
821 : GEN
822 0 : FlxqX_powu(GEN V, ulong n, GEN T, ulong p)
823 0 : { return FlxqX_powu_pre(V, n, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
824 :
825 : /* x and y in Z[Y][X]. Assume T irreducible mod p */
826 : static GEN
827 3150584 : FlxqX_divrem_basecase(GEN x, GEN y, GEN T, ulong p, ulong pi, GEN *pr)
828 : {
829 : long vx, dx, dy, dz, i, j, sx, lr;
830 :
831 : pari_sp av0, av, tetpil;
832 : GEN z,p1,rem,lead;
833 :
834 3150584 : if (!signe(y)) pari_err_INV("FlxqX_divrem",y);
835 3150584 : vx=varn(x); dy=degpol(y); dx=degpol(x);
836 3150597 : if (dx < dy)
837 : {
838 21604 : if (pr)
839 : {
840 21352 : av0 = avma; x = FlxqX_red_pre(x, T, p, pi);
841 21352 : if (pr == ONLY_DIVIDES) { set_avma(av0); return signe(x)? NULL: pol_0(vx); }
842 21352 : if (pr == ONLY_REM) return x;
843 21352 : *pr = x;
844 : }
845 21604 : return pol_0(vx);
846 : }
847 3128993 : lead = leading_coeff(y);
848 3129002 : if (!dy) /* y is constant */
849 : {
850 326429 : if (pr && pr != ONLY_DIVIDES)
851 : {
852 321754 : if (pr == ONLY_REM) return pol_0(vx);
853 133819 : *pr = pol_0(vx);
854 : }
855 138494 : if (Flx_equal1(lead)) return gcopy(x);
856 134295 : av0 = avma; x = FlxqX_Flxq_mul_pre(x,Flxq_inv(lead,T,p),T,p,pi);
857 134292 : return gerepileupto(av0,x);
858 : }
859 2802573 : av0 = avma; dz = dx-dy;
860 2802573 : lead = Flx_equal1(lead)? NULL: gclone(Flxq_inv_pre(lead,T,p,pi));
861 2802603 : set_avma(av0);
862 2802592 : z = cgetg(dz+3,t_POL); z[1] = x[1];
863 2802602 : x += 2; y += 2; z += 2;
864 :
865 2802602 : p1 = gel(x,dx); av = avma;
866 2802602 : gel(z,dz) = lead? gerepileupto(av, Flxq_mul_pre(p1,lead, T,p,pi)): gcopy(p1);
867 6460793 : for (i=dx-1; i>=dy; i--)
868 : {
869 3658128 : av=avma; p1=gel(x,i);
870 11904490 : for (j=i-dy+1; j<=i && j<=dz; j++)
871 8246612 : p1 = Flx_sub(p1, Flx_mul_pre(gel(z,j),gel(y,i-j),p,pi),p);
872 3657878 : if (lead) p1 = Flx_mul_pre(p1, lead,p,pi);
873 3657881 : tetpil=avma; gel(z,i-dy) = gerepile(av,tetpil,Flx_rem_pre(p1,T,p,pi));
874 : }
875 2802665 : if (!pr) { guncloneNULL(lead); return z-2; }
876 :
877 2608606 : rem = (GEN)avma; av = (pari_sp)new_chunk(dx+3);
878 2918722 : for (sx=0; ; i--)
879 : {
880 2918722 : p1 = gel(x,i);
881 8630731 : for (j=0; j<=i && j<=dz; j++)
882 5712413 : p1 = Flx_sub(p1, Flx_mul_pre(gel(z,j),gel(y,i-j),p,pi),p);
883 2918318 : tetpil=avma; p1 = Flx_rem_pre(p1, T,p,pi); if (lgpol(p1)) { sx = 1; break; }
884 383994 : if (!i) break;
885 310081 : set_avma(av);
886 : }
887 2608274 : if (pr == ONLY_DIVIDES)
888 : {
889 0 : guncloneNULL(lead);
890 0 : if (sx) return gc_NULL(av0);
891 0 : return gc_const((pari_sp)rem, z-2);
892 : }
893 2608274 : lr=i+3; rem -= lr;
894 2608274 : rem[0] = evaltyp(t_POL) | _evallg(lr);
895 2608274 : rem[1] = z[-1];
896 2608274 : p1 = gerepile((pari_sp)rem,tetpil,p1);
897 2608576 : rem += 2; gel(rem,i) = p1;
898 16310941 : for (i--; i>=0; i--)
899 : {
900 13702352 : av=avma; p1 = gel(x,i);
901 44718662 : for (j=0; j<=i && j<=dz; j++)
902 31024004 : p1 = Flx_sub(p1, Flx_mul_pre(gel(z,j),gel(y,i-j),p,pi), p);
903 13694658 : tetpil=avma; gel(rem,i) = gerepile(av,tetpil, Flx_rem_pre(p1, T,p,pi));
904 : }
905 2608589 : rem -= 2;
906 2608589 : guncloneNULL(lead);
907 2608601 : if (!sx) (void)FlxX_renormalize(rem, lr);
908 2608607 : if (pr == ONLY_REM) return gerepileupto(av0,rem);
909 1221211 : *pr = rem; return z-2;
910 : }
911 :
912 : static GEN
913 1419 : FlxqX_invBarrett_basecase(GEN T, GEN Q, ulong p, ulong pi)
914 : {
915 1419 : long i, l=lg(T)-1, lr = l-1, k;
916 1419 : long sv=Q[1];
917 1419 : GEN r=cgetg(lr,t_POL); r[1]=T[1];
918 1419 : gel(r,2) = pol1_Flx(sv);
919 16396 : for (i=3;i<lr;i++)
920 : {
921 14977 : pari_sp ltop=avma;
922 14977 : GEN u = Flx_neg(gel(T,l-i+2),p);
923 108758 : for (k=3;k<i;k++)
924 93781 : u = Flx_sub(u, Flxq_mul_pre(gel(T,l-i+k), gel(r,k), Q, p, pi), p);
925 14977 : gel(r,i) = gerepileupto(ltop, u);
926 : }
927 1419 : r = FlxX_renormalize(r,lr);
928 1419 : return r;
929 : }
930 :
931 : /* Return new lgpol */
932 : static long
933 328043 : FlxX_lgrenormalizespec(GEN x, long lx)
934 : {
935 : long i;
936 359738 : for (i = lx-1; i>=0; i--)
937 359738 : if (lgpol(gel(x,i))) break;
938 328043 : return i+1;
939 : }
940 :
941 : static GEN
942 6711 : FlxqX_invBarrett_Newton(GEN S, GEN T, ulong p, ulong pi)
943 : {
944 6711 : pari_sp av = avma;
945 6711 : long nold, lx, lz, lq, l = degpol(S), i, lQ;
946 6711 : GEN q, y, z, x = cgetg(l+2, t_POL) + 2;
947 6711 : long dT = get_Flx_degree(T), vT = get_Flx_var(T);
948 6711 : ulong mask = quadratic_prec_mask(l-2); /* assume l > 2 */
949 273213 : for (i=0;i<l;i++) gel(x,i) = pol0_Flx(vT);
950 6711 : q = FlxX_recipspec(S+2,l+1,l+1,dT);
951 6711 : lQ = lgpol(q); q+=2;
952 : /* We work on _spec_ FlxX's, all the l[xzq] below are lgpol's */
953 :
954 : /* initialize */
955 6711 : gel(x,0) = Flxq_inv_pre(gel(q,0),T, p, pi);
956 6711 : if (lQ>1 && degpol(gel(q,1)) >= dT)
957 0 : gel(q,1) = Flx_rem_pre(gel(q,1), T, p, pi);
958 6711 : if (lQ>1 && lgpol(gel(q,1)))
959 5686 : {
960 5686 : GEN u = gel(q, 1);
961 5686 : if (!Flx_equal1(gel(x,0)))
962 7 : u = Flxq_mul_pre(u, Flxq_sqr_pre(gel(x,0), T,p,pi), T,p,pi);
963 5686 : gel(x,1) = Flx_neg(u, p); lx = 2;
964 : }
965 : else
966 1025 : lx = 1;
967 6711 : nold = 1;
968 43278 : for (; mask > 1; )
969 : { /* set x -= x(x*q - 1) + O(t^(nnew + 1)), knowing x*q = 1 + O(t^(nold+1)) */
970 36567 : long i, lnew, nnew = nold << 1;
971 :
972 36567 : if (mask & 1) nnew--;
973 36567 : mask >>= 1;
974 :
975 36567 : lnew = nnew + 1;
976 36567 : lq = FlxX_lgrenormalizespec(q, minss(lQ,lnew));
977 36567 : z = FlxqX_mulspec(x, q, T,p,pi, lx, lq); /* FIXME: high product */
978 36567 : lz = lgpol(z); if (lz > lnew) lz = lnew;
979 36567 : z += 2;
980 : /* subtract 1 [=>first nold words are 0]: renormalize so that z(0) != 0 */
981 74746 : for (i = nold; i < lz; i++) if (lgpol(gel(z,i))) break;
982 36567 : nold = nnew;
983 36567 : if (i >= lz) continue; /* z-1 = 0(t^(nnew + 1)) */
984 :
985 : /* z + i represents (x*q - 1) / t^i */
986 35664 : lz = FlxX_lgrenormalizespec (z+i, lz-i);
987 35664 : z = FlxqX_mulspec(x, z+i, T,p,pi, lx, lz); /* FIXME: low product */
988 35664 : lz = lgpol(z); z += 2;
989 35664 : if (lz > lnew-i) lz = FlxX_lgrenormalizespec(z, lnew-i);
990 :
991 35664 : lx = lz+ i;
992 35664 : y = x + i; /* x -= z * t^i, in place */
993 278801 : for (i = 0; i < lz; i++) gel(y,i) = Flx_neg(gel(z,i), p);
994 : }
995 6711 : x -= 2; setlg(x, lx + 2); x[1] = S[1];
996 6711 : return gc_GEN(av, x);
997 : }
998 :
999 : GEN
1000 8130 : FlxqX_invBarrett_pre(GEN T, GEN Q, ulong p, ulong pi)
1001 : {
1002 8130 : pari_sp ltop=avma;
1003 8130 : long l=lg(T), v = varn(T);
1004 : GEN r;
1005 8130 : GEN c = gel(T,l-1);
1006 8130 : if (l<5) return pol_0(v);
1007 8130 : if (l<=FlxqX_INVBARRETT_LIMIT)
1008 : {
1009 1419 : if (!Flx_equal1(c))
1010 : {
1011 0 : GEN ci = Flxq_inv_pre(c,Q,p,pi);
1012 0 : T = FlxqX_Flxq_mul_pre(T, ci, Q, p, pi);
1013 0 : r = FlxqX_invBarrett_basecase(T,Q,p,pi);
1014 0 : r = FlxqX_Flxq_mul_pre(r,ci,Q,p,pi);
1015 : } else
1016 1419 : r = FlxqX_invBarrett_basecase(T,Q,p,pi);
1017 : } else
1018 6711 : r = FlxqX_invBarrett_Newton(T,Q,p,pi);
1019 8130 : return gerepileupto(ltop, r);
1020 : }
1021 : GEN
1022 76 : FlxqX_invBarrett(GEN T, GEN Q, ulong p)
1023 76 : { return FlxqX_invBarrett_pre(T, Q, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
1024 :
1025 : GEN
1026 491659 : FlxqX_get_red_pre(GEN S, GEN T, ulong p, ulong pi)
1027 : {
1028 491659 : if (typ(S)==t_POL && lg(S)>FlxqX_BARRETT_LIMIT)
1029 6674 : retmkvec2(FlxqX_invBarrett_pre(S, T, p, pi), S);
1030 484985 : return S;
1031 : }
1032 : GEN
1033 371 : FlxqX_get_red(GEN S, GEN T, ulong p)
1034 : {
1035 371 : if (typ(S)==t_POL && lg(S)>FlxqX_BARRETT_LIMIT)
1036 76 : retmkvec2(FlxqX_invBarrett(S, T, p), S);
1037 295 : return S;
1038 : }
1039 :
1040 : /* Compute x mod S where 2 <= degpol(S) <= l+1 <= 2*(degpol(S)-1)
1041 : * * and mg is the Barrett inverse of S. */
1042 : static GEN
1043 110590 : FlxqX_divrem_Barrettspec(GEN x, long l, GEN mg, GEN S, GEN T, ulong p,
1044 : ulong pi, GEN *pr)
1045 : {
1046 : GEN q, r;
1047 110590 : long lt = degpol(S); /*We discard the leading term*/
1048 : long ld, lm, lT, lmg;
1049 110590 : ld = l-lt;
1050 110590 : lm = minss(ld, lgpol(mg));
1051 110590 : lT = FlxX_lgrenormalizespec(S+2,lt);
1052 110590 : lmg = FlxX_lgrenormalizespec(mg+2,lm);
1053 110590 : q = FlxX_recipspec(x+lt,ld,ld,0); /* = rec(x) lq<=ld*/
1054 110590 : q = FlxqX_mulspec(q+2,mg+2,T,p,pi,lgpol(q),lmg); /* = rec(x)*mg lq<=ld+lm*/
1055 110590 : q = FlxX_recipspec(q+2,minss(ld,lgpol(q)),ld,0); /* = rec(rec(x)*mg) lq<=ld*/
1056 110590 : if (!pr) return q;
1057 110317 : r = FlxqX_mulspec(q+2,S+2,T,p,pi,lgpol(q),lT); /* = q*pol lr<=ld+lt*/
1058 110317 : r = FlxX_subspec(x,r+2,p,lt,minss(lt,lgpol(r)));/* = x - r lr<=lt */
1059 110317 : if (pr == ONLY_REM) return r;
1060 7688 : *pr = r; return q;
1061 : }
1062 :
1063 : static GEN
1064 103701 : FlxqX_divrem_Barrett(GEN x, GEN mg, GEN S, GEN T, ulong p, ulong pi, GEN *pr)
1065 : {
1066 103701 : GEN q = NULL, r = FlxqX_red_pre(x, T, p, pi);
1067 103701 : long l = lgpol(r), lt = degpol(S), lm = 2*lt-1, v = varn(S);
1068 : long i;
1069 103701 : if (l <= lt)
1070 : {
1071 0 : if (pr == ONLY_REM) return r;
1072 0 : if (pr == ONLY_DIVIDES) return signe(r)? NULL: pol_0(v);
1073 0 : if (pr) *pr = r;
1074 0 : return pol_0(v);
1075 : }
1076 103701 : if (lt <= 1)
1077 0 : return FlxqX_divrem_basecase(x,S,T,p,pi,pr);
1078 103701 : if (pr != ONLY_REM && l>lm)
1079 : {
1080 764 : long vT = get_Flx_var(T);
1081 764 : q = cgetg(l-lt+2, t_POL); q[1] = S[1];
1082 56948 : for (i=0;i<l-lt;i++) gel(q+2,i) = pol0_Flx(vT);
1083 : }
1084 110672 : while (l>lm)
1085 : {
1086 6971 : GEN zr, zq = FlxqX_divrem_Barrettspec(r+2+l-lm,lm,mg,S,T,p,pi,&zr);
1087 6971 : long lz = lgpol(zr);
1088 6971 : if (pr != ONLY_REM)
1089 : {
1090 2582 : long lq = lgpol(zq);
1091 50816 : for(i=0; i<lq; i++) gel(q+2+l-lm,i) = gel(zq,2+i);
1092 : }
1093 72514 : for(i=0; i<lz; i++) gel(r+2+l-lm,i) = gel(zr,2+i);
1094 6971 : l = l-lm+lz;
1095 : }
1096 103701 : if (pr == ONLY_REM)
1097 : {
1098 102629 : if (l > lt)
1099 102629 : r = FlxqX_divrem_Barrettspec(r+2,l,mg,S,T,p,pi,ONLY_REM);
1100 : else
1101 0 : r = FlxX_renormalize(r, l+2);
1102 102629 : setvarn(r, v); return r;
1103 : }
1104 1072 : if (l > lt)
1105 : {
1106 990 : GEN zq = FlxqX_divrem_Barrettspec(r+2,l,mg,S,T,p,pi,pr? &r: NULL);
1107 990 : if (!q) q = zq;
1108 : else
1109 : {
1110 682 : long lq = lgpol(zq);
1111 6048 : for(i=0; i<lq; i++) gel(q+2,i) = gel(zq,2+i);
1112 : }
1113 : }
1114 82 : else if (pr)
1115 82 : r = FlxX_renormalize(r, l+2);
1116 1072 : setvarn(q, v); q = FlxX_renormalize(q, lg(q));
1117 1072 : if (pr == ONLY_DIVIDES) return signe(r)? NULL: q;
1118 1072 : if (pr) { setvarn(r, v); *pr = r; }
1119 1072 : return q;
1120 : }
1121 :
1122 : GEN
1123 1576269 : FlxqX_divrem_pre(GEN x, GEN S, GEN T, ulong p, long pi, GEN *pr)
1124 : {
1125 : GEN B, y;
1126 : long dy, dx, d;
1127 1576269 : if (pr==ONLY_REM) return FlxqX_rem_pre(x, S, T, p, pi);
1128 1576269 : y = get_FlxqX_red(S, &B);
1129 1576263 : dy = degpol(y); dx = degpol(x); d = dx-dy;
1130 1576219 : if (!B && d+3 < FlxqX_DIVREM_BARRETT_LIMIT)
1131 1575147 : return FlxqX_divrem_basecase(x,y,T,p,pi,pr);
1132 : else
1133 : {
1134 1072 : pari_sp av = avma;
1135 1072 : GEN mg = B? B: FlxqX_invBarrett_pre(y, T, p, pi);
1136 1072 : GEN q = FlxqX_divrem_Barrett(x,mg,y,T,p,pi,pr);
1137 1072 : if (!q) return gc_NULL(av);
1138 1072 : if (!pr || pr==ONLY_DIVIDES) return gc_GEN(av, q);
1139 799 : return gc_all(av, 2, &q, pr);
1140 : }
1141 : }
1142 : GEN
1143 1073724 : FlxqX_divrem(GEN x, GEN S, GEN T, ulong p, GEN *pr)
1144 : {
1145 1073724 : ulong pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
1146 1073724 : return FlxqX_divrem_pre(x, S, T, p, pi, pr);
1147 : }
1148 :
1149 : GEN
1150 2025925 : FlxqX_rem_pre(GEN x, GEN S, GEN T, ulong p, ulong pi)
1151 : {
1152 2025925 : GEN B, y = get_FlxqX_red(S, &B);
1153 2025923 : long dy = degpol(y), dx = degpol(x), d = dx-dy;
1154 2025919 : if (d < 0) return FlxqX_red_pre(x, T, p, pi);
1155 1677968 : if (!B && d+3 < FlxqX_REM_BARRETT_LIMIT)
1156 1575339 : return FlxqX_divrem_basecase(x,y, T, p, pi, ONLY_REM);
1157 : else
1158 : {
1159 102629 : pari_sp av=avma;
1160 102629 : GEN mg = B? B: FlxqX_invBarrett_pre(y, T, p, pi);
1161 102629 : GEN r = FlxqX_divrem_Barrett(x, mg, y, T, p, pi, ONLY_REM);
1162 102629 : return gerepileupto(av, r);
1163 : }
1164 : }
1165 : GEN
1166 5949 : FlxqX_rem(GEN x, GEN S, GEN T, ulong p)
1167 5949 : { return FlxqX_rem_pre(x, S, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
1168 :
1169 : /* x + y*z mod p */
1170 : INLINE GEN
1171 103656 : Flxq_addmul_pre(GEN x, GEN y, GEN z, GEN T, ulong p, ulong pi)
1172 : {
1173 : pari_sp av;
1174 103656 : if (!lgpol(y) || !lgpol(z)) return Flx_rem_pre(x, T, p, pi);
1175 102125 : if (!lgpol(x)) return Flxq_mul_pre(z, y, T, p, pi);
1176 102021 : av = avma;
1177 102021 : return gerepileupto(av, Flx_add(x, Flxq_mul_pre(y, z, T, p, pi), p));
1178 : }
1179 :
1180 : GEN
1181 51828 : FlxqX_div_by_X_x_pre(GEN a, GEN x, GEN T, ulong p, ulong pi, GEN *r)
1182 : {
1183 51828 : long l = lg(a), i;
1184 : GEN z;
1185 51828 : if (l <= 3)
1186 : {
1187 0 : if (r) *r = l == 2? pol0_Flx(get_Flx_var(T)): Flx_copy(gel(a,2));
1188 0 : return pol_0(varn(a));
1189 : }
1190 51828 : l--; z = cgetg(l, t_POL); z[1] = a[1];
1191 51828 : gel(z, l-1) = gel(a,l);
1192 155484 : for (i=l-2; i>1; i--) /* z[i] = a[i+1] + x*z[i+1] */
1193 103656 : gel(z, i) = Flxq_addmul_pre(gel(a,i+1), x, gel(z,i+1), T, p, pi);
1194 51828 : if (r) *r = Flxq_addmul_pre(gel(a,2), x, gel(z,2), T, p, pi);
1195 51828 : return z;
1196 : }
1197 :
1198 : GEN
1199 51828 : FlxqX_div_by_X_x(GEN a, GEN x, GEN T, ulong p, GEN *r)
1200 51828 : { return FlxqX_div_by_X_x_pre(a, x, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p), r); }
1201 :
1202 : static GEN
1203 13530 : FlxqX_addmulmul(GEN u, GEN v, GEN x, GEN y, GEN T, ulong p, ulong pi)
1204 : {
1205 13530 : return FlxX_add(FlxqX_mul_pre(u, x, T, p, pi),
1206 : FlxqX_mul_pre(v, y, T, p, pi), p);
1207 : }
1208 :
1209 : static GEN
1210 6626 : FlxqXM_FlxqX_mul2(GEN M, GEN x, GEN y, GEN T, ulong p, ulong pi)
1211 : {
1212 6626 : GEN res = cgetg(3, t_COL);
1213 6626 : gel(res, 1) = FlxqX_addmulmul(gcoeff(M,1,1), gcoeff(M,1,2), x, y, T, p, pi);
1214 6626 : gel(res, 2) = FlxqX_addmulmul(gcoeff(M,2,1), gcoeff(M,2,2), x, y, T, p, pi);
1215 6626 : return res;
1216 : }
1217 :
1218 : static GEN
1219 3276 : FlxqXM_mul2(GEN A, GEN B, GEN T, ulong p, ulong pi)
1220 : {
1221 3276 : GEN A11=gcoeff(A,1,1),A12=gcoeff(A,1,2), B11=gcoeff(B,1,1),B12=gcoeff(B,1,2);
1222 3276 : GEN A21=gcoeff(A,2,1),A22=gcoeff(A,2,2), B21=gcoeff(B,2,1),B22=gcoeff(B,2,2);
1223 3276 : GEN M1 = FlxqX_mul_pre(FlxX_add(A11,A22, p), FlxX_add(B11,B22, p), T, p, pi);
1224 3276 : GEN M2 = FlxqX_mul_pre(FlxX_add(A21,A22, p), B11, T, p, pi);
1225 3276 : GEN M3 = FlxqX_mul_pre(A11, FlxX_sub(B12,B22, p), T, p, pi);
1226 3276 : GEN M4 = FlxqX_mul_pre(A22, FlxX_sub(B21,B11, p), T, p, pi);
1227 3276 : GEN M5 = FlxqX_mul_pre(FlxX_add(A11,A12, p), B22, T, p, pi);
1228 3276 : GEN M6 = FlxqX_mul_pre(FlxX_sub(A21,A11, p), FlxX_add(B11,B12, p), T, p, pi);
1229 3276 : GEN M7 = FlxqX_mul_pre(FlxX_sub(A12,A22, p), FlxX_add(B21,B22, p), T, p, pi);
1230 3276 : GEN T1 = FlxX_add(M1,M4, p), T2 = FlxX_sub(M7,M5, p);
1231 3276 : GEN T3 = FlxX_sub(M1,M2, p), T4 = FlxX_add(M3,M6, p);
1232 3276 : retmkmat22(FlxX_add(T1,T2, p), FlxX_add(M3,M5, p),
1233 : FlxX_add(M2,M4, p), FlxX_add(T3,T4, p));
1234 : }
1235 :
1236 : /* Return [0,1;1,-q]*M */
1237 : static GEN
1238 3276 : FlxqX_FlxqXM_qmul(GEN q, GEN M, GEN T, ulong p, ulong pi)
1239 : {
1240 3276 : GEN u = FlxqX_mul_pre(gcoeff(M,2,1), q, T,p,pi);
1241 3276 : GEN v = FlxqX_mul_pre(gcoeff(M,2,2), q, T,p,pi);
1242 3276 : retmkmat22(gcoeff(M,2,1), gcoeff(M,2,2),
1243 : FlxX_sub(gcoeff(M,1,1), u, p), FlxX_sub(gcoeff(M,1,2), v, p));
1244 : }
1245 :
1246 : static GEN
1247 16 : matid2_FlxXM(long v, long sv)
1248 16 : { retmkmat22(pol1_FlxX(v, sv),pol_0(v),pol_0(v),pol1_FlxX(v, sv)); }
1249 :
1250 : static GEN
1251 0 : matJ2_FlxXM(long v, long sv)
1252 0 : { retmkmat22(pol_0(v),pol1_FlxX(v, sv),pol1_FlxX(v, sv),pol_0(v)); }
1253 :
1254 : struct FlxqX_res
1255 : {
1256 : GEN res, lc;
1257 : long deg0, deg1, off;
1258 : };
1259 :
1260 : INLINE void
1261 0 : FlxqX_halfres_update(long da, long db, long dr, GEN T, ulong p, ulong pi, struct FlxqX_res *res)
1262 : {
1263 0 : if (dr >= 0)
1264 : {
1265 0 : if (!Flx_equal1(res->lc))
1266 : {
1267 0 : res->lc = Flxq_powu_pre(res->lc, da - dr, T, p, pi);
1268 0 : res->res = Flxq_mul_pre(res->res, res->lc, T, p, pi);
1269 : }
1270 0 : if (both_odd(da + res->off, db + res->off))
1271 0 : res->res = Flx_neg(res->res, p);
1272 : } else
1273 : {
1274 0 : if (db == 0)
1275 : {
1276 0 : if (!Flx_equal1(res->lc))
1277 : {
1278 0 : res->lc = Flxq_powu_pre(res->lc, da, T, p, pi);
1279 0 : res->res = Flxq_mul_pre(res->res, res->lc, T, p, pi);
1280 : }
1281 : } else
1282 0 : res->res = pol0_Flx(get_Flx_var(T));
1283 : }
1284 0 : }
1285 :
1286 : static GEN
1287 4035 : FlxqX_halfres_basecase(GEN a, GEN b, GEN T, ulong p, ulong pi, GEN *pa, GEN *pb, struct FlxqX_res *res)
1288 : {
1289 4035 : pari_sp av=avma;
1290 : GEN u,u1,v,v1, M;
1291 4035 : long vx = varn(a), vT = get_Flx_var(T), n = lgpol(a)>>1;
1292 4035 : u1 = v = pol_0(vx);
1293 4035 : u = v1 = pol1_FlxX(vx, vT);
1294 22321 : while (lgpol(b)>n)
1295 : {
1296 : GEN r, q;
1297 18286 : q = FlxqX_divrem(a,b, T, p, &r);
1298 18286 : if (res)
1299 : {
1300 0 : long da = degpol(a), db = degpol(b), dr = degpol(r);
1301 0 : res->lc = gel(b,db+2);
1302 0 : if (dr >= n)
1303 0 : FlxqX_halfres_update(da, db, dr, T, p, pi, res);
1304 : else
1305 : {
1306 0 : res->deg0 = da;
1307 0 : res->deg1 = db;
1308 : }
1309 : }
1310 18286 : a = b; b = r; swap(u,u1); swap(v,v1);
1311 18286 : u1 = FlxX_sub(u1, FlxqX_mul_pre(u, q, T, p, pi), p);
1312 18286 : v1 = FlxX_sub(v1, FlxqX_mul_pre(v, q, T, p, pi), p);
1313 18286 : if (gc_needed(av,2))
1314 : {
1315 0 : if (DEBUGMEM>1) pari_warn(warnmem,"FlxqX_halfgcd (d = %ld)",degpol(b));
1316 0 : if (res)
1317 0 : gerepileall(av, 8, &a,&b,&u1,&v1,&u,&v,&res->res,&res->lc);
1318 : else
1319 0 : gerepileall(av, 6, &a,&b,&u1,&v1,&u,&v);
1320 : }
1321 : }
1322 4035 : M = mkmat22(u,v,u1,v1); *pa = a; *pb = b;
1323 0 : return res ? gc_all(av, 5, &M, pa, pb, &res->res, &res->lc)
1324 4035 : : gc_all(av, 3, &M, pa, pb);
1325 : }
1326 :
1327 : static GEN FlxqX_halfres_i(GEN x, GEN y, GEN T, ulong p, ulong pi, GEN *a, GEN *b, struct FlxqX_res *res);
1328 :
1329 : static GEN
1330 3366 : FlxqX_halfres_split(GEN x, GEN y, GEN T, ulong p, ulong pi, GEN *a, GEN *b, struct FlxqX_res *res)
1331 : {
1332 3366 : pari_sp av = avma;
1333 : GEN Q, R, S, V1, V2;
1334 : GEN x1, y1, r, q;
1335 3366 : long l = lgpol(x), n = l>>1, k, vT = get_Flx_var(T);
1336 3366 : if (lgpol(y) <= n)
1337 16 : { *a = RgX_copy(x); *b = RgX_copy(y); return matid2_FlxXM(varn(x), vT); }
1338 3350 : if (res)
1339 : {
1340 0 : res->lc = leading_coeff(y);
1341 0 : res->deg0 -= n;
1342 0 : res->deg1 -= n;
1343 0 : res->off += n;
1344 : }
1345 3350 : R = FlxqX_halfres_i(FlxX_shift(x,-n, vT),FlxX_shift(y,-n, vT), T, p, pi, a, b, res);
1346 3350 : if (res)
1347 : {
1348 0 : res->off -= n;
1349 0 : res->deg0 += n;
1350 0 : res->deg1 += n;
1351 : }
1352 3350 : V1 = FlxqXM_FlxqX_mul2(R, Flxn_red(x,n), Flxn_red(y,n), T, p, pi);
1353 3350 : x1 = FlxX_add(FlxX_shift(*a,n,vT), gel(V1,1), p);
1354 3350 : y1 = FlxX_add(FlxX_shift(*b,n,vT), gel(V1,2), p);
1355 3350 : if (lgpol(y1) <= n)
1356 : {
1357 74 : *a = x1; *b = y1;
1358 0 : return res ? gc_all(av, 5, &R, a, b, &res->res, &res->lc)
1359 74 : : gc_all(av, 3, &R, a, b);
1360 : }
1361 3276 : k = 2*n-degpol(y1);
1362 3276 : q = FlxqX_divrem(x1, y1, T, p, &r);
1363 3276 : if (res)
1364 : {
1365 0 : long dx1 = degpol(x1), dy1 = degpol(y1), dr = degpol(r);
1366 0 : if (dy1 < degpol(y))
1367 0 : FlxqX_halfres_update(res->deg0, res->deg1, dy1, T, p, pi, res);
1368 0 : res->lc = leading_coeff(y1);
1369 0 : res->deg0 = dx1;
1370 0 : res->deg1 = dy1;
1371 0 : if (dr >= n)
1372 : {
1373 0 : FlxqX_halfres_update(dx1, dy1, dr, T, p, pi, res);
1374 0 : res->deg0 = dy1;
1375 0 : res->deg1 = dr;
1376 : }
1377 0 : res->deg0 -= k;
1378 0 : res->deg1 -= k;
1379 0 : res->off += k;
1380 : }
1381 3276 : S = FlxqX_halfres_i(FlxX_shift(y1,-k, vT), FlxX_shift(r,-k, vT), T, p, pi, a, b, res);
1382 3276 : if (res)
1383 : {
1384 0 : res->deg0 += k;
1385 0 : res->deg1 += k;
1386 0 : res->off -= k;
1387 : }
1388 3276 : Q = FlxqXM_mul2(S, FlxqX_FlxqXM_qmul(q, R, T, p, pi), T, p, pi);
1389 3276 : V2 = FlxqXM_FlxqX_mul2(S, FlxXn_red(y1,k), FlxXn_red(r,k), T, p, pi);
1390 3276 : *a = FlxX_add(FlxX_shift(*a,k,vT), gel(V2,1), p);
1391 3276 : *b = FlxX_add(FlxX_shift(*b,k,vT), gel(V2,2), p);
1392 0 : return res ? gc_all(av, 5, &Q, a, b, &res->res, &res->lc)
1393 3276 : : gc_all(av, 3, &Q, a, b);
1394 : }
1395 :
1396 : static GEN
1397 7401 : FlxqX_halfres_i(GEN x, GEN y, GEN T, ulong p, ulong pi, GEN *a, GEN *b, struct FlxqX_res *res)
1398 : {
1399 7401 : if (lgpol(x) < FlxqX_HALFGCD_LIMIT)
1400 4035 : return FlxqX_halfres_basecase(x, y, T, p, pi, a, b, res);
1401 3366 : return FlxqX_halfres_split(x, y, T, p, pi, a, b, res);
1402 : }
1403 :
1404 : static GEN
1405 775 : FlxqX_halfgcd_all_i(GEN x, GEN y, GEN T, ulong p, ulong pi, GEN *pa, GEN *pb)
1406 : {
1407 : GEN a, b;
1408 775 : GEN R = FlxqX_halfres_i(x, y, T, p, pi, &a, &b, NULL);
1409 775 : if (pa) *pa = a;
1410 775 : if (pb) *pb = b;
1411 775 : return R;
1412 : }
1413 :
1414 : /* Return M in GL_2(Fp[X]/(T)[Y]) such that:
1415 : if [a',b']~=M*[a,b]~ then degpol(a')>= (lgpol(a)>>1) >degpol(b')
1416 : */
1417 :
1418 : GEN
1419 775 : FlxqX_halfgcd_all_pre(GEN x, GEN y, GEN T, ulong p, ulong pi, GEN *a, GEN *b)
1420 : {
1421 775 : pari_sp av = avma;
1422 : GEN R,q,r;
1423 775 : if (!signe(x))
1424 : {
1425 0 : if (a) *a = RgX_copy(y);
1426 0 : if (b) *b = RgX_copy(x);
1427 0 : return matJ2_FlxXM(varn(x),get_Flx_var(T));
1428 : }
1429 775 : if (degpol(y)<degpol(x)) return FlxqX_halfgcd_all_i(x, y, T, p, pi, a, b);
1430 180 : q = FlxqX_divrem_pre(y, x, T, p, pi, &r);
1431 180 : R = FlxqX_halfgcd_all_i(x, r, T, p, pi, a, b);
1432 180 : gcoeff(R,1,1) = FlxX_sub(gcoeff(R,1,1),
1433 180 : FlxqX_mul_pre(q, gcoeff(R,1,2), T, p, pi), p);
1434 180 : gcoeff(R,2,1) = FlxX_sub(gcoeff(R,2,1),
1435 180 : FlxqX_mul_pre(q, gcoeff(R,2,2), T, p, pi), p);
1436 180 : return !a && b ? gc_all(av, 2, &R, b): gc_all(av, 1+!!a+!!b, &R, a, b);
1437 : }
1438 : GEN
1439 7 : FlxqX_halfgcd_all(GEN x, GEN y, GEN T, ulong p, GEN *a, GEN *b)
1440 7 : { return FlxqX_halfgcd_all_pre(x, y, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p), a, b); }
1441 :
1442 : GEN
1443 253 : FlxqX_halfgcd_pre(GEN x, GEN y, GEN T, ulong p, ulong pi)
1444 253 : { return FlxqX_halfgcd_all_pre(x, y, T, p, pi, NULL, NULL); }
1445 :
1446 : GEN
1447 0 : FlxqX_halfgcd(GEN x, GEN y, GEN T, ulong p)
1448 0 : { return FlxqX_halfgcd_pre(x, y, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
1449 :
1450 : static GEN
1451 166770 : FlxqX_gcd_basecase(GEN a, GEN b, GEN T, ulong p, ulong pi)
1452 : {
1453 166770 : pari_sp av = avma, av0=avma;
1454 1076592 : while (signe(b))
1455 : {
1456 : GEN c;
1457 909822 : if (gc_needed(av0,2))
1458 : {
1459 0 : if (DEBUGMEM>1) pari_warn(warnmem,"FlxqX_gcd (d = %ld)",degpol(b));
1460 0 : gerepileall(av0,2, &a,&b);
1461 : }
1462 909822 : av = avma; c = FlxqX_rem_pre(a, b, T, p, pi); a=b; b=c;
1463 : }
1464 166770 : return gc_const(av, a);
1465 : }
1466 :
1467 : GEN
1468 175808 : FlxqX_gcd_pre(GEN x, GEN y, GEN T, ulong p, ulong pi)
1469 : {
1470 175808 : pari_sp av = avma;
1471 175808 : x = FlxqX_red_pre(x, T, p, pi);
1472 175808 : y = FlxqX_red_pre(y, T, p, pi);
1473 175808 : if (!signe(x)) return gerepileupto(av, y);
1474 167146 : while (lgpol(y)>=FlxqX_GCD_LIMIT)
1475 : {
1476 376 : if (lgpol(y)<=(lgpol(x)>>1))
1477 : {
1478 0 : GEN r = FlxqX_rem_pre(x, y, T, p, pi);
1479 0 : x = y; y = r;
1480 : }
1481 376 : (void) FlxqX_halfgcd_all_pre(x,y, T, p, pi, &x, &y);
1482 376 : if (gc_needed(av,2))
1483 : {
1484 0 : if (DEBUGMEM>1) pari_warn(warnmem,"FlxqX_gcd (y = %ld)",degpol(y));
1485 0 : gerepileall(av,2,&x,&y);
1486 : }
1487 : }
1488 166770 : return gerepileupto(av, FlxqX_gcd_basecase(x, y, T, p, pi));
1489 : }
1490 : GEN
1491 23458 : FlxqX_gcd(GEN x, GEN y, GEN T, ulong p)
1492 23458 : { return FlxqX_gcd_pre(x, y, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
1493 :
1494 : static GEN
1495 133824 : FlxqX_extgcd_basecase(GEN a, GEN b, GEN T, ulong p,ulong pi, GEN *ptu, GEN *ptv)
1496 : {
1497 133824 : pari_sp av=avma;
1498 : GEN u,v,d,d1,v1;
1499 133824 : long vx = varn(a);
1500 133824 : d = a; d1 = b;
1501 133824 : v = pol_0(vx); v1 = pol1_FlxX(vx, get_Flx_var(T));
1502 470908 : while (signe(d1))
1503 : {
1504 337079 : GEN r, q = FlxqX_divrem_pre(d, d1, T, p, pi, &r);
1505 337095 : v = FlxX_sub(v, FlxqX_mul_pre(q,v1,T, p, pi),p);
1506 337081 : u=v; v=v1; v1=u;
1507 337081 : u=r; d=d1; d1=u;
1508 337081 : if (gc_needed(av,2))
1509 : {
1510 0 : if (DEBUGMEM>1) pari_warn(warnmem,"FlxqX_extgcd (d = %ld)",degpol(d));
1511 0 : gerepileall(av,5, &d,&d1,&u,&v,&v1);
1512 : }
1513 : }
1514 133829 : if (ptu)
1515 133815 : *ptu = FlxqX_div_pre(FlxX_sub(d,FlxqX_mul_pre(b,v, T,p,pi), p), a, T,p,pi);
1516 133829 : *ptv = v; return d;
1517 : }
1518 :
1519 : static GEN
1520 130 : FlxqX_extgcd_halfgcd(GEN x, GEN y, GEN T, ulong p, ulong pi, GEN *ptu, GEN *ptv)
1521 : {
1522 : GEN u,v;
1523 130 : GEN V = cgetg(expu(lgpol(y))+2,t_VEC);
1524 130 : long i, n = 0, vs = varn(x), vT = get_Flx_var(T);
1525 269 : while (lgpol(y) >= FlxqX_EXTGCD_LIMIT)
1526 : {
1527 139 : if (lgpol(y)<=(lgpol(x)>>1))
1528 : {
1529 0 : GEN r, q = FlxqX_divrem_pre(x, y, T, p, pi, &r);
1530 0 : x = y; y = r;
1531 0 : gel(V,++n) = mkmat22(pol_0(vs),pol1_FlxX(vs,vT),pol1_FlxX(vs,vT),FlxX_neg(q,p));
1532 : } else
1533 139 : gel(V,++n) = FlxqX_halfgcd_all_pre(x, y, T, p, pi, &x, &y);
1534 : }
1535 130 : y = FlxqX_extgcd_basecase(x,y, T, p, pi, &u,&v);
1536 139 : for (i = n; i>1; i--)
1537 : {
1538 9 : GEN R = gel(V,i);
1539 9 : GEN u1 = FlxqX_addmulmul(u, v, gcoeff(R,1,1), gcoeff(R,2,1), T, p, pi);
1540 9 : GEN v1 = FlxqX_addmulmul(u, v, gcoeff(R,1,2), gcoeff(R,2,2), T, p, pi);
1541 9 : u = u1; v = v1;
1542 : }
1543 : {
1544 130 : GEN R = gel(V,1);
1545 130 : if (ptu)
1546 130 : *ptu = FlxqX_addmulmul(u, v, gcoeff(R,1,1), gcoeff(R,2,1), T, p, pi);
1547 130 : *ptv = FlxqX_addmulmul(u, v, gcoeff(R,1,2), gcoeff(R,2,2), T, p, pi);
1548 : }
1549 130 : return y;
1550 : }
1551 :
1552 : /* x and y in Z[Y][X], return lift(gcd(x mod T,p, y mod T,p)). Set u and v st
1553 : * ux + vy = gcd (mod T,p) */
1554 : GEN
1555 133826 : FlxqX_extgcd_pre(GEN x, GEN y, GEN T, ulong p, ulong pi, GEN *ptu, GEN *ptv)
1556 : {
1557 133826 : pari_sp av = avma;
1558 : GEN d;
1559 133826 : x = FlxqX_red_pre(x, T, p, pi);
1560 133824 : y = FlxqX_red_pre(y, T, p, pi);
1561 133824 : if (lgpol(y)>=FlxqX_EXTGCD_LIMIT)
1562 130 : d = FlxqX_extgcd_halfgcd(x, y, T, p, pi, ptu, ptv);
1563 : else
1564 133694 : d = FlxqX_extgcd_basecase(x, y, T, p, pi, ptu, ptv);
1565 133829 : return gc_all(av, ptu?3:2, &d, ptv, ptu);
1566 : }
1567 : GEN
1568 133811 : FlxqX_extgcd(GEN x, GEN y, GEN T, ulong p, GEN *ptu, GEN *ptv)
1569 : {
1570 133811 : ulong pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
1571 133811 : return FlxqX_extgcd_pre(x, y, T, p, pi, ptu, ptv);
1572 : }
1573 :
1574 : static GEN
1575 366700 : FlxqX_saferem(GEN P, GEN Q, GEN T, ulong p, ulong pi)
1576 : {
1577 366700 : GEN U = Flxq_invsafe_pre(leading_coeff(Q), T, p, pi);
1578 366712 : if (!U) return NULL;
1579 366712 : Q = FlxqX_Flxq_mul_to_monic_pre(Q,U,T,p,pi);
1580 366719 : return FlxqX_rem_pre(P,Q,T,p,pi);
1581 : }
1582 :
1583 : GEN
1584 0 : FlxqX_eval(GEN x, GEN y, GEN T, ulong p)
1585 : {
1586 : pari_sp av;
1587 : GEN p1, r;
1588 0 : long j, i=lg(x)-1;
1589 0 : if (i<=2)
1590 0 : return (i==2)? gcopy(gel(x,2)): pol0_Flx(get_Flx_var(T));
1591 0 : av=avma; p1=gel(x,i);
1592 : /* specific attention to sparse polynomials (see poleval)*/
1593 : /*You've guessed it! It's a copy-paste(tm)*/
1594 0 : for (i--; i>=2; i=j-1)
1595 : {
1596 0 : for (j=i; lg(gel(x,j))==1; j--)
1597 0 : if (j==2)
1598 : {
1599 0 : if (i!=j) y = Flxq_powu(y, i-j+1, T, p);
1600 0 : return gerepileupto(av, Flxq_mul(p1,y, T, p));
1601 : }
1602 0 : r = (i==j)? y: Flxq_powu(y, i-j+1, T, p);
1603 0 : p1 = Flx_add(Flxq_mul(p1,r,T,p), gel(x,j), p);
1604 : }
1605 0 : return gerepileupto(av, p1);
1606 : }
1607 :
1608 : GEN
1609 91184 : FlxqX_safegcd(GEN P, GEN Q, GEN T, ulong p)
1610 : {
1611 91184 : pari_sp av = avma;
1612 : ulong pi;
1613 : GEN U;
1614 91184 : if (!signe(P)) return gcopy(Q);
1615 91184 : if (!signe(Q)) return gcopy(P);
1616 91184 : pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
1617 91184 : T = Flx_get_red_pre(T,p,pi);
1618 : for(;;)
1619 : {
1620 313494 : P = FlxqX_saferem(P,Q,T,p,pi);
1621 313496 : if (!P) return gc_NULL(av);
1622 313496 : if (!signe(P)) break;
1623 222310 : if (gc_needed(av, 1))
1624 : {
1625 0 : if (DEBUGMEM>1) pari_warn(warnmem,"FlxqX_safegcd");
1626 0 : gerepileall(av, 2, &P,&Q);
1627 : }
1628 222310 : swap(P, Q);
1629 : }
1630 91186 : U = Flxq_invsafe_pre(leading_coeff(Q), T, p, pi);
1631 91185 : if (!U) return gc_NULL(av);
1632 91185 : Q = FlxqX_Flxq_mul_to_monic_pre(Q,U,T,p,pi);
1633 91186 : return gerepileupto(av, Q);
1634 : }
1635 :
1636 : /* Res(A,B) = Res(B,R) * lc(B)^(a-r) * (-1)^(ab), with R=A%B, a=deg(A) ...*/
1637 : GEN
1638 10588 : FlxqX_saferesultant(GEN a, GEN b, GEN T, ulong p)
1639 : {
1640 10588 : long vT = get_Flx_var(T), da,db,dc;
1641 : ulong pi;
1642 : pari_sp av;
1643 10588 : GEN c,lb, res = pol1_Flx(vT);
1644 :
1645 10588 : if (!signe(a) || !signe(b)) return pol0_Flx(vT);
1646 :
1647 10588 : da = degpol(a);
1648 10588 : db = degpol(b);
1649 10588 : if (db > da)
1650 : {
1651 0 : swapspec(a,b, da,db);
1652 0 : if (both_odd(da,db)) res = Flx_neg(res, p);
1653 : }
1654 10588 : if (!da) return pol1_Flx(vT); /* = res * a[2] ^ db, since 0 <= db <= da = 0 */
1655 10588 : pi = SMALL_ULONG(p)? 0: get_Fl_red(p); av = avma;
1656 63762 : while (db)
1657 : {
1658 53202 : lb = gel(b,db+2);
1659 53202 : c = FlxqX_saferem(a,b, T,p,pi);
1660 53264 : if (!c) return gc_NULL(av);
1661 53264 : a = b; b = c; dc = degpol(c);
1662 53260 : if (dc < 0) { set_avma(av); return pol0_Flx(vT); }
1663 :
1664 53246 : if (both_odd(da,db)) res = Flx_neg(res, p);
1665 53244 : if (!Flx_equal1(lb))
1666 53186 : res = Flxq_mul_pre(res, Flxq_powu_pre(lb, da - dc, T, p, pi), T, p, pi);
1667 53174 : if (gc_needed(av,2))
1668 : {
1669 0 : if (DEBUGMEM>1) pari_warn(warnmem,"FlxqX_resultant (da = %ld)",da);
1670 0 : gerepileall(av,3, &a,&b,&res);
1671 : }
1672 53174 : da = db; /* = degpol(a) */
1673 53174 : db = dc; /* = degpol(b) */
1674 : }
1675 10560 : res = Flxq_mul_pre(res, Flxq_powu_pre(gel(b,2), da, T, p, pi), T, p, pi);
1676 10574 : return gerepileupto(av, res);
1677 : }
1678 :
1679 : static GEN
1680 0 : FlxqX_halfres(GEN x, GEN y, GEN T, ulong p, ulong pi, GEN *a, GEN *b, GEN *r)
1681 : {
1682 : struct FlxqX_res res;
1683 : GEN V;
1684 : long dB;
1685 :
1686 0 : res.res = *r;
1687 0 : res.lc = leading_coeff(y);
1688 0 : res.deg0 = degpol(x);
1689 0 : res.deg1 = degpol(y);
1690 0 : res.off = 0;
1691 0 : V = FlxqX_halfres_i(x, y, T, p, pi, a, b, &res);
1692 0 : dB = degpol(*b);
1693 0 : if (dB < degpol(y))
1694 0 : FlxqX_halfres_update(res.deg0, res.deg1, dB, T, p, pi, &res);
1695 0 : *r = res.res;
1696 0 : return V;
1697 : }
1698 :
1699 : static GEN
1700 56 : FlxqX_resultant_basecase(GEN a, GEN b, GEN T, ulong p, ulong pi)
1701 : {
1702 56 : pari_sp av = avma;
1703 56 : long vT = get_Flx_var(T), da,db,dc;
1704 56 : GEN c,lb, res = pol1_Flx(vT);
1705 :
1706 56 : if (!signe(a) || !signe(b)) return pol0_Flx(vT);
1707 :
1708 56 : da = degpol(a);
1709 56 : db = degpol(b);
1710 56 : if (db > da)
1711 : {
1712 0 : swapspec(a,b, da,db);
1713 0 : if (both_odd(da,db)) res = Flx_neg(res, p);
1714 : }
1715 56 : if (!da) return pol1_Flx(vT); /* = res * a[2] ^ db, since 0 <= db <= da = 0 */
1716 147 : while (db)
1717 : {
1718 91 : lb = gel(b,db+2);
1719 91 : c = FlxqX_rem_pre(a,b, T,p,pi);
1720 91 : a = b; b = c; dc = degpol(c);
1721 91 : if (dc < 0) { set_avma(av); return pol0_Flx(vT); }
1722 :
1723 91 : if (both_odd(da,db)) res = Flx_neg(res, p);
1724 91 : if (!Flx_equal1(lb))
1725 63 : res = Flxq_mul_pre(res, Flxq_powu_pre(lb, da - dc, T,p,pi), T,p,pi);
1726 91 : if (gc_needed(av,2))
1727 : {
1728 0 : if (DEBUGMEM>1) pari_warn(warnmem,"FlxqX_resultant (da = %ld)",da);
1729 0 : gerepileall(av,3, &a,&b,&res);
1730 : }
1731 91 : da = db; /* = degpol(a) */
1732 91 : db = dc; /* = degpol(b) */
1733 : }
1734 56 : res = Flxq_mul_pre(res, Flxq_powu_pre(gel(b,2), da, T,p,pi), T,p,pi);
1735 56 : return gerepileupto(av, res);
1736 : }
1737 :
1738 : /* Res(A,B) = Res(B,R) * lc(B)^(a-r) * (-1)^(ab), with R=A%B, a=deg(A) ...*/
1739 : GEN
1740 56 : FlxqX_resultant_pre(GEN x, GEN y, GEN T, ulong p, ulong pi)
1741 : {
1742 56 : pari_sp av = avma;
1743 56 : long dx, dy, vT = get_Flx_var(T);
1744 56 : GEN res = pol1_Flx(vT);
1745 56 : if (!signe(x) || !signe(y)) return pol0_Flx(vT);
1746 56 : dx = degpol(x); dy = degpol(y);
1747 56 : if (dx < dy)
1748 : {
1749 21 : swap(x,y);
1750 21 : if (both_odd(dx, dy))
1751 0 : res = Flx_neg(res, p);
1752 : }
1753 56 : while (lgpol(y) >= FlxqX_GCD_LIMIT)
1754 : {
1755 0 : if (lgpol(y)<=(lgpol(x)>>1))
1756 : {
1757 0 : GEN r = FlxqX_rem_pre(x, y, T, p, pi);
1758 0 : long dx = degpol(x), dy = degpol(y), dr = degpol(r);
1759 0 : GEN ly = gel(y,dy+2);
1760 0 : if (!Flx_equal1(ly))
1761 0 : res = Flxq_mul_pre(res, Flxq_powu_pre(ly, dx - dr, T, p, pi), T, p, pi);
1762 0 : if (both_odd(dx, dy))
1763 0 : res = Flx_neg(res, p);
1764 0 : x = y; y = r;
1765 : }
1766 0 : (void) FlxqX_halfres(x, y, T, p, pi, &x, &y, &res);
1767 0 : if (gc_needed(av,2))
1768 : {
1769 0 : if (DEBUGMEM>1) pari_warn(warnmem,"FlxqX_resultant (y = %ld)",degpol(y));
1770 0 : gerepileall(av,3,&x,&y,&res);
1771 : }
1772 : }
1773 56 : res = Flxq_mul_pre(res, FlxqX_resultant_basecase(x, y, T, p, pi), T, p, pi);
1774 56 : return gerepileupto(av, res);
1775 : }
1776 : GEN
1777 56 : FlxqX_resultant(GEN x, GEN y, GEN T, ulong p)
1778 56 : { return FlxqX_resultant_pre(x, y, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
1779 :
1780 : /* disc P = (-1)^(n(n-1)/2) lc(P)^(n - deg P' - 2) Res(P,P'), n = deg P */
1781 : GEN
1782 14 : FlxqX_disc(GEN P, GEN T, ulong p)
1783 : {
1784 14 : pari_sp av = avma;
1785 14 : GEN L, dP = FlxX_deriv(P, p), D = FlxqX_resultant(P, dP, T, p);
1786 : long dd;
1787 14 : if (!lgpol(D)) return pol0_Flx(get_Flx_var(T));
1788 14 : dd = degpol(P) - 2 - degpol(dP); /* >= -1; > -1 iff p | deg(P) */
1789 14 : L = leading_coeff(P);
1790 14 : if (dd && !Flx_equal1(L))
1791 : {
1792 0 : ulong pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
1793 0 : D = (dd == -1)? Flxq_div_pre(D,L,T,p,pi)
1794 0 : : Flxq_mul_pre(D, Flxq_powu_pre(L, dd, T,p,pi), T,p,pi); }
1795 14 : if (degpol(P) & 2) D = Flx_neg(D, p);
1796 14 : return gerepileupto(av, D);
1797 : }
1798 :
1799 : INLINE GEN
1800 6080 : FlxXn_recip(GEN x, long n, long v)
1801 6080 : { return FlxX_recipspec(x+2, minss(lgpol(x), n), n, v); }
1802 :
1803 : GEN
1804 2432 : FlxqX_Newton_pre(GEN P, long n, GEN T, ulong p, ulong pi)
1805 : {
1806 2432 : pari_sp av = avma;
1807 2432 : long d = degpol(P), vT = get_Flx_var(T);
1808 2432 : GEN dP = FlxXn_recip(FlxX_deriv(P, p), d, vT);
1809 2432 : GEN Q = FlxqXn_mul_pre(FlxqXn_inv_pre(FlxXn_recip(P, d+1, vT), n, T,p,pi),
1810 : dP, n, T, p, pi);
1811 2432 : return gc_GEN(av, Q);
1812 : }
1813 : GEN
1814 0 : FlxqX_Newton(GEN P, long n, GEN T, ulong p)
1815 0 : { return FlxqX_Newton_pre(P, n, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
1816 :
1817 : GEN
1818 1216 : FlxqX_fromNewton_pre(GEN P, GEN T, ulong p, ulong pi)
1819 : {
1820 1216 : pari_sp av = avma;
1821 1216 : long vT = get_Flx_var(T);
1822 1216 : long n = Flx_constant(constant_coeff(P))+1;
1823 1216 : GEN z = FlxX_neg(FlxX_shift(P, -1, vT), p);
1824 1216 : GEN Q = FlxXn_recip(FlxqXn_expint_pre(z, n, T, p, pi), n, vT);
1825 1216 : return gc_GEN(av, Q);
1826 : }
1827 : GEN
1828 0 : FlxqX_fromNewton(GEN P, GEN T, ulong p)
1829 0 : { return FlxqX_fromNewton_pre(P, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
1830 :
1831 : GEN
1832 1216 : FlxqX_composedsum(GEN P, GEN Q, GEN T, ulong p)
1833 : {
1834 1216 : pari_sp av = avma;
1835 1216 : ulong pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
1836 1216 : long n = 1+ degpol(P)*degpol(Q);
1837 1216 : GEN Pl = FlxX_invLaplace(FlxqX_Newton_pre(P,n, T,p,pi), p);
1838 1216 : GEN Ql = FlxX_invLaplace(FlxqX_Newton_pre(Q,n, T,p,pi), p);
1839 1216 : GEN L = FlxX_Laplace(FlxqXn_mul_pre(Pl, Ql, n, T,p,pi), p);
1840 1216 : GEN R = FlxqX_fromNewton_pre(L, T, p, pi);
1841 1216 : GEN lead = Flxq_mul_pre(Flxq_powu_pre(leading_coeff(P),degpol(Q), T,p,pi),
1842 1216 : Flxq_powu_pre(leading_coeff(Q),degpol(P), T,p,pi),
1843 : T, p, pi);
1844 1216 : return gerepileupto(av, FlxqX_Flxq_mul_pre(R, lead, T, p, pi));
1845 : }
1846 :
1847 : GEN
1848 223094 : FlxqXV_prod(GEN V, GEN T, ulong p)
1849 : {
1850 223094 : struct _FlxqXQ d; d.p=p; d.T=T; d.pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
1851 223094 : return gen_product(V, (void*)&d, &_FlxqX_mul);
1852 : }
1853 :
1854 : static GEN
1855 32152 : FlxqV_roots_to_deg1(GEN x, GEN T, ulong p, long v)
1856 : {
1857 32152 : long sv = get_Flx_var(T);
1858 124251 : pari_APPLY_same(deg1pol_shallow(pol1_Flx(sv),Flx_neg(gel(x,i),p),v))
1859 : }
1860 :
1861 : GEN
1862 32152 : FlxqV_roots_to_pol(GEN V, GEN T, ulong p, long v)
1863 : {
1864 32152 : pari_sp ltop = avma;
1865 32152 : GEN W = FlxqV_roots_to_deg1(V, T, p, v);
1866 32152 : return gerepileupto(ltop, FlxqXV_prod(W, T, p));
1867 : }
1868 :
1869 : /*******************************************************************/
1870 : /* */
1871 : /* (Fl[X]/T(X))[Y] / S(Y) */
1872 : /* */
1873 : /*******************************************************************/
1874 :
1875 : GEN
1876 470985 : FlxqXQ_mul_pre(GEN x, GEN y, GEN S, GEN T, ulong p, ulong pi)
1877 470985 : { return FlxqX_rem_pre(FlxqX_mul_pre(x,y,T,p,pi),S,T,p,pi); }
1878 : GEN
1879 1947 : FlxqXQ_mul(GEN x, GEN y, GEN S, GEN T, ulong p)
1880 1947 : { return FlxqXQ_mul_pre(x, y, S, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
1881 :
1882 : GEN
1883 261973 : FlxqXQ_sqr_pre(GEN x, GEN S, GEN T, ulong p, ulong pi)
1884 261973 : { return FlxqX_rem_pre(FlxqX_sqr_pre(x,T,p,pi),S,T,p,pi); }
1885 : GEN
1886 0 : FlxqXQ_sqr(GEN x, GEN S, GEN T, ulong p)
1887 0 : { return FlxqXQ_sqr_pre(x, S, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
1888 :
1889 : GEN
1890 14 : FlxqXQ_invsafe_pre(GEN x, GEN S, GEN T, ulong p, ulong pi)
1891 : {
1892 14 : GEN V, z = FlxqX_extgcd_pre(get_FlxqX_mod(S), x, T, p, pi, NULL, &V);
1893 14 : if (degpol(z)) return NULL;
1894 14 : z = Flxq_invsafe_pre(gel(z,2),T,p,pi);
1895 14 : if (!z) return NULL;
1896 14 : return FlxqX_Flxq_mul_pre(V, z, T, p, pi);
1897 : }
1898 : GEN
1899 0 : FlxqXQ_invsafe(GEN x, GEN S, GEN T, ulong p)
1900 0 : { return FlxqXQ_invsafe_pre(x, S, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
1901 :
1902 : GEN
1903 14 : FlxqXQ_inv_pre(GEN x, GEN S, GEN T, ulong p, ulong pi)
1904 : {
1905 14 : pari_sp av = avma;
1906 14 : GEN U = FlxqXQ_invsafe_pre(x, S, T, p, pi);
1907 14 : if (!U) pari_err_INV("FlxqXQ_inv",x);
1908 14 : return gerepileupto(av, U);
1909 : }
1910 : GEN
1911 14 : FlxqXQ_inv(GEN x, GEN S, GEN T,ulong p)
1912 14 : { return FlxqXQ_inv_pre(x, S, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
1913 :
1914 : GEN
1915 0 : FlxqXQ_div_pre(GEN x, GEN y, GEN S, GEN T, ulong p, ulong pi)
1916 0 : { return FlxqXQ_mul_pre(x, FlxqXQ_inv_pre(y,S,T,p,pi),S,T,p,pi); }
1917 : GEN
1918 0 : FlxqXQ_div(GEN x, GEN y, GEN S, GEN T, ulong p)
1919 0 : { return FlxqXQ_div_pre(x, y, S, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
1920 :
1921 : static GEN
1922 0 : _FlxqX_add(void *data, GEN x, GEN y) {
1923 0 : struct _FlxqXQ *d = (struct _FlxqXQ*) data;
1924 0 : return FlxX_add(x,y, d->p);
1925 : }
1926 : static GEN
1927 5526 : _FlxqX_sub(void *data, GEN x, GEN y) {
1928 5526 : struct _FlxqXQ *d = (struct _FlxqXQ*) data;
1929 5526 : return FlxX_sub(x,y, d->p);
1930 : }
1931 : #if 0
1932 : static GEN
1933 : _FlxqXQ_cmul(void *data, GEN P, long a, GEN x) {
1934 : struct _FlxqXQ *d = (struct _FlxqXQ*) data;
1935 : return FlxX_Flx_mul(x,gel(P,a+2), d->p);
1936 : }
1937 : #endif
1938 : static GEN
1939 6044 : _FlxqXQ_red(void *data, GEN x) {
1940 6044 : struct _FlxqXQ *d = (struct _FlxqXQ*) data;
1941 6044 : return FlxqX_red_pre(x, d->T, d->p, d->pi);
1942 : }
1943 : static GEN
1944 179118 : _FlxqXQ_mul(void *data, GEN x, GEN y) {
1945 179118 : struct _FlxqXQ *d = (struct _FlxqXQ*) data;
1946 179118 : return FlxqXQ_mul_pre(x,y, d->S,d->T, d->p, d->pi);
1947 : }
1948 : static GEN
1949 261525 : _FlxqXQ_sqr(void *data, GEN x) {
1950 261525 : struct _FlxqXQ *d = (struct _FlxqXQ*) data;
1951 261525 : return FlxqXQ_sqr_pre(x, d->S,d->T, d->p, d->pi);
1952 : }
1953 :
1954 : static GEN
1955 111276 : _FlxqXQ_one(void *data) {
1956 111276 : struct _FlxqXQ *d = (struct _FlxqXQ*) data;
1957 111276 : return pol1_FlxX(get_FlxqX_var(d->S),get_Flx_var(d->T));
1958 : }
1959 :
1960 : static GEN
1961 316 : _FlxqXQ_zero(void *data) {
1962 316 : struct _FlxqXQ *d = (struct _FlxqXQ*) data;
1963 316 : return pol_0(get_FlxqX_var(d->S));
1964 : }
1965 :
1966 : static struct bb_algebra FlxqXQ_algebra = { _FlxqXQ_red, _FlxqX_add,
1967 : _FlxqX_sub, _FlxqXQ_mul, _FlxqXQ_sqr, _FlxqXQ_one, _FlxqXQ_zero };
1968 :
1969 : const struct bb_algebra *
1970 761 : get_FlxqXQ_algebra(void **E, GEN S, GEN T, ulong p)
1971 : {
1972 761 : ulong pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
1973 761 : GEN z = new_chunk(sizeof(struct _FlxqXQ));
1974 761 : struct _FlxqXQ *e = (struct _FlxqXQ *) z;
1975 761 : e->T = Flx_get_red_pre(T, p, pi);
1976 761 : e->S = FlxqX_get_red_pre(S, e->T, p, pi);
1977 761 : e->p = p;
1978 761 : e->pi= pi; *E = (void*)e;
1979 761 : return &FlxqXQ_algebra;
1980 : }
1981 :
1982 : static struct bb_algebra FlxqX_algebra = { _FlxqXQ_red, _FlxqX_add,
1983 : _FlxqX_sub, _FlxqX_mul, _FlxqX_sqr, _FlxqXQ_one, _FlxqXQ_zero };
1984 :
1985 : const struct bb_algebra *
1986 0 : get_FlxqX_algebra(void **E, GEN T, ulong p, long v)
1987 : {
1988 0 : ulong pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
1989 0 : GEN z = new_chunk(sizeof(struct _FlxqXQ));
1990 0 : struct _FlxqXQ *e = (struct _FlxqXQ *) z;
1991 0 : e->T = Flx_get_red(T, p);
1992 0 : e->S = pol_x(v);
1993 0 : e->p = p;
1994 0 : e->pi= pi; *E = (void*)e;
1995 0 : return &FlxqX_algebra;
1996 : }
1997 :
1998 : /* x over Fq, return lift(x^n) mod S */
1999 : GEN
2000 91 : FlxqXQ_pow_pre(GEN x, GEN n, GEN S, GEN T, ulong p, ulong pi)
2001 : {
2002 91 : pari_sp av = avma;
2003 : struct _FlxqXQ D;
2004 91 : long s = signe(n);
2005 91 : if (!s) return pol1_FlxX(get_FlxqX_var(S),get_Flx_var(T));
2006 91 : if (s < 0) x = FlxqXQ_inv_pre(x,S,T,p,pi);
2007 91 : if (is_pm1(n)) return s < 0 ? x : gcopy(x);
2008 91 : if (degpol(x) >= get_FlxqX_degree(S)) x = FlxqX_rem_pre(x,S,T,p,pi);
2009 91 : T = Flx_get_red_pre(T, p, pi);
2010 91 : S = FlxqX_get_red_pre(S, T, p, pi);
2011 91 : D.S = S; D.T = T; D.p = p; D.pi = pi;
2012 91 : x = gen_pow_i(x, n, (void*)&D, &_FlxqXQ_sqr, &_FlxqXQ_mul);
2013 91 : return gc_GEN(av, x);
2014 : }
2015 : GEN
2016 35 : FlxqXQ_pow(GEN x, GEN n, GEN S, GEN T, ulong p)
2017 35 : { return FlxqXQ_pow_pre(x, n, S, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
2018 :
2019 : /* x over Fq, return lift(x^n) mod S */
2020 : GEN
2021 82058 : FlxqXQ_powu_pre(GEN x, ulong n, GEN S, GEN T, ulong p, ulong pi)
2022 : {
2023 82058 : pari_sp av = avma;
2024 : struct _FlxqXQ D;
2025 82058 : switch(n)
2026 : {
2027 0 : case 0: return pol1_FlxX(get_FlxqX_var(S),get_Flx_var(T));
2028 7690 : case 1: return gcopy(x);
2029 448 : case 2: return FlxqXQ_sqr_pre(x, S, T, p, pi);
2030 : }
2031 73920 : T = Flx_get_red_pre(T, p, pi);
2032 73920 : S = FlxqX_get_red_pre(S, T, p, pi);
2033 73920 : D.S = S; D.T = T; D.p = p; D.pi = pi;
2034 73920 : x = gen_powu_i(x, n, (void*)&D, &_FlxqXQ_sqr, &_FlxqXQ_mul);
2035 73920 : return gc_GEN(av, x);
2036 : }
2037 : GEN
2038 0 : FlxqXQ_powu(GEN x, ulong n, GEN S, GEN T, ulong p)
2039 0 : { return FlxqXQ_powu_pre(x, n, S, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
2040 :
2041 : GEN
2042 108241 : FlxqXQ_powers_pre(GEN x, long l, GEN S, GEN T, ulong p, ulong pi)
2043 : {
2044 : struct _FlxqXQ D;
2045 108241 : int use_sqr = 2*degpol(x) >= get_FlxqX_degree(S);
2046 108241 : T = Flx_get_red_pre(T, p, pi);
2047 108241 : S = FlxqX_get_red_pre(S, T, p, pi);
2048 108241 : D.S = S; D.T = T; D.p = p; D.pi = pi;
2049 108241 : return gen_powers(x, l, use_sqr, (void*)&D, &_FlxqXQ_sqr, &_FlxqXQ_mul,&_FlxqXQ_one);
2050 : }
2051 : GEN
2052 0 : FlxqXQ_powers(GEN x, long l, GEN S, GEN T, ulong p)
2053 0 : { return FlxqXQ_powers_pre(x, l, S, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
2054 :
2055 : /* Let v a linear form, return the linear form z->v(tau*z)
2056 : that is, v*(M_tau) */
2057 : static GEN
2058 506 : FlxqXQ_transmul_init(GEN tau, GEN S, GEN T, ulong p, ulong pi)
2059 : {
2060 : GEN bht;
2061 506 : GEN h, Sp = get_FlxqX_red(S, &h);
2062 506 : long n = degpol(Sp), vS = varn(Sp), vT = get_Flx_var(T);
2063 506 : GEN ft = FlxX_recipspec(Sp+2, n+1, n+1, vT);
2064 506 : GEN bt = FlxX_recipspec(tau+2, lgpol(tau), n, vT);
2065 506 : setvarn(ft, vS); setvarn(bt, vS);
2066 506 : if (h)
2067 0 : bht = FlxqXn_mul_pre(bt, h, n-1, T, p, pi);
2068 : else
2069 : {
2070 506 : GEN bh = FlxqX_div_pre(FlxX_shift(tau, n-1, vT), S, T, p, pi);
2071 506 : bht = FlxX_recipspec(bh+2, lgpol(bh), n-1, vT);
2072 506 : setvarn(bht, vS);
2073 : }
2074 506 : return mkvec3(bt, bht, ft);
2075 : }
2076 :
2077 : static GEN
2078 1071 : FlxqXQ_transmul(GEN tau, GEN a, long n, GEN T, ulong p, ulong pi)
2079 : {
2080 1071 : pari_sp ltop = avma;
2081 : GEN t1, t2, t3, vec;
2082 1071 : GEN bt = gel(tau, 1), bht = gel(tau, 2), ft = gel(tau, 3);
2083 1071 : long vT = get_Flx_var(T);
2084 1071 : if (signe(a)==0) return pol_0(varn(a));
2085 1061 : t2 = FlxX_shift(FlxqX_mul_pre(bt, a, T, p, pi),1-n,vT);
2086 1061 : if (signe(bht)==0) return gc_GEN(ltop, t2);
2087 767 : t1 = FlxX_shift(FlxqX_mul_pre(ft, a, T, p, pi),-n,vT);
2088 767 : t3 = FlxqXn_mul_pre(t1, bht, n-1, T, p, pi);
2089 767 : vec = FlxX_sub(t2, FlxX_shift(t3, 1, vT), p);
2090 767 : return gerepileupto(ltop, vec);
2091 : }
2092 :
2093 : static GEN
2094 253 : polxn_FlxX(long n, long v, long vT)
2095 : {
2096 253 : long i, a = n+2;
2097 253 : GEN p = cgetg(a+1, t_POL);
2098 253 : p[1] = evalsigne(1)|evalvarn(v);
2099 2171 : for (i = 2; i < a; i++) gel(p,i) = pol0_Flx(vT);
2100 253 : gel(p,a) = pol1_Flx(vT); return p;
2101 : }
2102 :
2103 : GEN
2104 224 : FlxqXQ_minpoly_pre(GEN x, GEN S, GEN T, ulong p, ulong pi)
2105 : {
2106 224 : pari_sp ltop = avma;
2107 : long vS, vT, n;
2108 : GEN v_x, g, tau;
2109 224 : vS = get_FlxqX_var(S);
2110 224 : vT = get_Flx_var(T);
2111 224 : n = get_FlxqX_degree(S);
2112 224 : g = pol1_FlxX(vS,vT);
2113 224 : tau = pol1_FlxX(vS,vT);
2114 224 : S = FlxqX_get_red_pre(S, T, p, pi);
2115 224 : v_x = FlxqXQ_powers_pre(x, usqrt(2*n), S, T, p, pi);
2116 477 : while(signe(tau) != 0)
2117 : {
2118 : long i, j, m, k1;
2119 : GEN M, v, tr;
2120 : GEN g_prime, c;
2121 253 : if (degpol(g) == n) { tau = pol1_FlxX(vS, vT); g = pol1_FlxX(vS, vT); }
2122 253 : v = random_FlxqX(n, vS, T, p);
2123 253 : tr = FlxqXQ_transmul_init(tau, S, T, p, pi);
2124 253 : v = FlxqXQ_transmul(tr, v, n, T, p, pi);
2125 253 : m = 2*(n-degpol(g));
2126 253 : k1 = usqrt(m);
2127 253 : tr = FlxqXQ_transmul_init(gel(v_x,k1+1), S, T, p, pi);
2128 253 : c = cgetg(m+2,t_POL);
2129 253 : c[1] = evalsigne(1)|evalvarn(vS);
2130 1071 : for (i=0; i<m; i+=k1)
2131 : {
2132 818 : long mj = minss(m-i, k1);
2133 2736 : for (j=0; j<mj; j++)
2134 1918 : gel(c,m+1-(i+j)) = FlxqX_dotproduct(v, gel(v_x,j+1), T, p);
2135 818 : v = FlxqXQ_transmul(tr, v, n, T, p, pi);
2136 : }
2137 253 : c = FlxX_renormalize(c, m+2);
2138 : /* now c contains <v,x^i> , i = 0..m-1 */
2139 253 : M = FlxqX_halfgcd_pre(polxn_FlxX(m, vS, vT), c, T, p, pi);
2140 253 : g_prime = gmael(M, 2, 2);
2141 253 : if (degpol(g_prime) < 1) continue;
2142 252 : g = FlxqX_mul_pre(g, g_prime, T, p, pi);
2143 252 : tau = FlxqXQ_mul_pre(tau, FlxqX_FlxqXQV_eval_pre(g_prime, v_x, S, T,p,pi),
2144 : S, T, p,pi);
2145 : }
2146 224 : g = FlxqX_normalize_pre(g,T,p,pi);
2147 224 : return gc_GEN(ltop,g);
2148 : }
2149 : GEN
2150 62 : FlxqXQ_minpoly(GEN x, GEN S, GEN T, ulong p)
2151 62 : { return FlxqXQ_minpoly_pre(x, S, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
2152 :
2153 : GEN
2154 0 : FlxqXQ_matrix_pow(GEN y, long n, long m, GEN S, GEN T, ulong p)
2155 0 : { return FlxXV_to_FlxM(FlxqXQ_powers(y,m-1,S,T,p), n, get_Flx_var(T)); }
2156 :
2157 : static GEN
2158 138362 : FlxX_blocks_FlxM(GEN P, long n, long m, long v)
2159 : {
2160 138362 : GEN z = cgetg(m+1,t_MAT);
2161 138362 : long i,j, k=2, l = lg(P);
2162 536339 : for(i=1; i<=m; i++)
2163 : {
2164 397977 : GEN zi = cgetg(n+1,t_COL);
2165 397977 : gel(z,i) = zi;
2166 1274305 : for(j=1; j<=n; j++)
2167 876328 : gel(zi, j) = k==l ? pol0_Flx(v) : gel(P,k++);
2168 : }
2169 138362 : return z;
2170 : }
2171 :
2172 : GEN
2173 138362 : FlxqX_FlxqXQV_eval_pre(GEN Q, GEN x, GEN S, GEN T, ulong p, ulong pi)
2174 : {
2175 138362 : pari_sp btop, av = avma;
2176 138362 : long v = get_FlxqX_var(S), m = get_FlxqX_degree(S);
2177 138362 : long vT = get_Flx_var(T);
2178 138362 : long i, l = lg(x)-1, lQ = lgpol(Q), n, d;
2179 : GEN A, B, C, R, g;
2180 138362 : if (lQ == 0) return pol_0(v);
2181 138362 : if (lQ <= l)
2182 : {
2183 43859 : n = l;
2184 43859 : d = 1;
2185 : }
2186 : else
2187 : {
2188 94503 : n = l-1;
2189 94503 : d = (lQ+n-1)/n;
2190 : }
2191 138362 : A = FlxXV_to_FlxM_lg(x, m, n, vT);
2192 138362 : B = FlxX_blocks_FlxM(Q, n, d, vT);
2193 138362 : C = gerepileupto(av, FlxqM_mul(A, B, T, p));
2194 138362 : g = gel(x, l);
2195 138362 : T = Flx_get_red_pre(T, p, pi);
2196 138362 : S = FlxqX_get_red_pre(S, T, p, pi);
2197 138362 : btop = avma;
2198 138362 : R = FlxV_to_FlxX(gel(C, d), v);
2199 397977 : for (i = d-1; i>0; i--)
2200 : {
2201 259615 : R = FlxX_add(FlxqXQ_mul_pre(R, g, S, T,p,pi), FlxV_to_FlxX(gel(C,i), v), p);
2202 259615 : if (gc_needed(btop,1))
2203 6 : R = gerepileupto(btop, R);
2204 : }
2205 138362 : return gc_GEN(av, R);
2206 : }
2207 : GEN
2208 0 : FlxqX_FlxqXQV_eval(GEN Q, GEN x, GEN S, GEN T, ulong p)
2209 0 : { return FlxqX_FlxqXQV_eval_pre(Q,x,S,T,p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
2210 :
2211 : GEN
2212 76758 : FlxqX_FlxqXQ_eval_pre(GEN Q, GEN x, GEN S, GEN T, ulong p, ulong pi)
2213 : {
2214 76758 : pari_sp av = avma;
2215 : GEN z, V;
2216 76758 : long d = degpol(Q), rtd;
2217 76758 : if (d < 0) return pol_0(get_FlxqX_var(S));
2218 76758 : rtd = (long) sqrt((double)d);
2219 76758 : T = Flx_get_red_pre(T, p, pi);
2220 76758 : S = FlxqX_get_red_pre(S, T, p, pi);
2221 76758 : V = FlxqXQ_powers_pre(x, rtd, S, T, p, pi);
2222 76758 : z = FlxqX_FlxqXQV_eval_pre(Q, V, S, T, p, pi);
2223 76758 : return gerepileupto(av, z);
2224 : }
2225 : GEN
2226 0 : FlxqX_FlxqXQ_eval(GEN Q, GEN x, GEN S, GEN T, ulong p)
2227 0 : { return FlxqX_FlxqXQ_eval_pre(Q, x, S, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
2228 :
2229 : GEN
2230 0 : FlxqXC_FlxqXQV_eval_pre(GEN x, GEN v, GEN S, GEN T, ulong p, ulong pi)
2231 0 : { pari_APPLY_type(t_COL, FlxqX_FlxqXQV_eval_pre(gel(x,i), v, S, T, p, pi)) }
2232 : GEN
2233 0 : FlxqXC_FlxqXQV_eval(GEN x, GEN v, GEN S, GEN T, ulong p)
2234 0 : { return FlxqXC_FlxqXQV_eval_pre(x, v, S, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
2235 :
2236 : GEN
2237 0 : FlxqXC_FlxqXQ_eval(GEN x, GEN F, GEN S, GEN T, ulong p)
2238 : {
2239 0 : long d = brent_kung_optpow(get_FlxqX_degree(S)-1,lg(x)-1,1);
2240 0 : ulong pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
2241 0 : GEN Fp = FlxqXQ_powers_pre(F, d, S, T, p, pi);
2242 0 : return FlxqXC_FlxqXQV_eval_pre(x, Fp, S, T, p, pi);
2243 : }
2244 :
2245 : static GEN
2246 72682 : FlxqXQ_autpow_sqr(void * E, GEN x)
2247 : {
2248 72682 : struct _FlxqXQ *D = (struct _FlxqXQ *)E;
2249 72682 : GEN S = D->S, T = D->T;
2250 72682 : ulong p = D->p, pi = D->pi;
2251 72682 : GEN phi = gel(x,1), S1 = gel(x,2);
2252 72682 : long n = brent_kung_optpow(get_Flx_degree(T)-1,lgpol(S1)+1,1);
2253 72682 : GEN V = Flxq_powers_pre(phi, n, T, p, pi);
2254 72682 : GEN phi2 = Flx_FlxqV_eval_pre(phi, V, T, p, pi);
2255 72682 : GEN Sphi = FlxY_FlxqV_evalx_pre(S1, V, T, p, pi);
2256 72682 : GEN S2 = FlxqX_FlxqXQ_eval_pre(Sphi, S1, S, T, p, pi);
2257 72682 : return mkvec2(phi2, S2);
2258 : }
2259 :
2260 : static GEN
2261 3714 : FlxqXQ_autpow_mul(void * E, GEN x, GEN y)
2262 : {
2263 3714 : struct _FlxqXQ *D = (struct _FlxqXQ *)E;
2264 3714 : GEN S = D->S, T = D->T;
2265 3714 : ulong p = D->p, pi = D->pi;
2266 3714 : GEN phi1 = gel(x,1), S1 = gel(x,2);
2267 3714 : GEN phi2 = gel(y,1), S2 = gel(y,2);
2268 3714 : long n = brent_kung_optpow(get_Flx_degree(T)-1,lgpol(S1)+1,1);
2269 3714 : GEN V = Flxq_powers_pre(phi2, n, T, p, pi);
2270 3714 : GEN phi3 = Flx_FlxqV_eval_pre(phi1, V, T, p, pi);
2271 3714 : GEN Sphi = FlxY_FlxqV_evalx_pre(S1, V, T, p, pi);
2272 3714 : GEN S3 = FlxqX_FlxqXQ_eval_pre(Sphi, S2, S, T, p, pi);
2273 3714 : return mkvec2(phi3, S3);
2274 : }
2275 :
2276 : GEN
2277 69275 : FlxqXQ_autpow_pre(GEN aut, long n, GEN S, GEN T, ulong p, ulong pi)
2278 : {
2279 69275 : pari_sp av = avma;
2280 : struct _FlxqXQ D;
2281 69275 : T = Flx_get_red_pre(T, p, pi);
2282 69275 : S = FlxqX_get_red_pre(S, T, p, pi);
2283 69275 : D.S = S; D.T = T; D.p = p; D.pi = pi;
2284 69275 : aut = gen_powu_i(aut,n,&D,FlxqXQ_autpow_sqr,FlxqXQ_autpow_mul);
2285 69275 : return gc_GEN(av, aut);
2286 : }
2287 : GEN
2288 0 : FlxqXQ_autpow(GEN aut, long n, GEN S, GEN T, ulong p)
2289 0 : { return FlxqXQ_autpow_pre(aut, n, S, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
2290 :
2291 : static GEN
2292 29983 : FlxqXQ_autsum_mul(void *E, GEN x, GEN y)
2293 : {
2294 29983 : struct _FlxqXQ *D = (struct _FlxqXQ *)E;
2295 29983 : GEN S = D->S, T = D->T;
2296 29983 : ulong p = D->p, pi = D->pi;
2297 29983 : GEN phi1 = gel(x,1), S1 = gel(x,2), a1 = gel(x,3);
2298 29983 : GEN phi2 = gel(y,1), S2 = gel(y,2), a2 = gel(y,3);
2299 29983 : long n2 = brent_kung_optpow(get_Flx_degree(T)-1, lgpol(S1)+lgpol(a1)+1,1);
2300 29983 : GEN V2 = Flxq_powers_pre(phi2, n2, T, p, pi);
2301 29983 : GEN phi3 = Flx_FlxqV_eval_pre(phi1, V2, T, p, pi);
2302 29983 : GEN Sphi = FlxY_FlxqV_evalx_pre(S1, V2, T, p, pi);
2303 29983 : GEN aphi = FlxY_FlxqV_evalx_pre(a1, V2, T, p, pi);
2304 29983 : long n = brent_kung_optpow(maxss(degpol(Sphi),degpol(aphi)),2,1);
2305 29983 : GEN V = FlxqXQ_powers_pre(S2, n, S, T, p, pi);
2306 29983 : GEN S3 = FlxqX_FlxqXQV_eval_pre(Sphi, V, S, T, p, pi);
2307 29983 : GEN aS = FlxqX_FlxqXQV_eval_pre(aphi, V, S, T, p, pi);
2308 29983 : GEN a3 = FlxqXQ_mul_pre(aS, a2, S, T, p, pi);
2309 29983 : return mkvec3(phi3, S3, a3);
2310 : }
2311 :
2312 : static GEN
2313 18582 : FlxqXQ_autsum_sqr(void * T, GEN x)
2314 18582 : { return FlxqXQ_autsum_mul(T, x, x); }
2315 :
2316 : GEN
2317 12125 : FlxqXQ_autsum_pre(GEN aut, long n, GEN S, GEN T, ulong p, ulong pi)
2318 : {
2319 12125 : pari_sp av = avma;
2320 : struct _FlxqXQ D;
2321 12125 : T = Flx_get_red_pre(T, p, pi);
2322 12125 : S = FlxqX_get_red_pre(S, T, p, pi);
2323 12125 : D.S=S; D.T=T; D.p=p; D.pi=pi;
2324 12125 : aut = gen_powu_i(aut,n,&D,FlxqXQ_autsum_sqr,FlxqXQ_autsum_mul);
2325 12125 : return gc_GEN(av, aut);
2326 : }
2327 : GEN
2328 0 : FlxqXQ_autsum(GEN aut, long n, GEN S, GEN T, ulong p)
2329 0 : { return FlxqXQ_autsum_pre(aut, n, S, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
2330 :
2331 : static GEN
2332 27 : FlxqXQ_auttrace_mul(void *E, GEN x, GEN y)
2333 : {
2334 27 : struct _FlxqXQ *D = (struct _FlxqXQ *)E;
2335 27 : GEN S = D->S, T = D->T;
2336 27 : ulong p = D->p, pi = D->pi;
2337 27 : GEN S1 = gel(x,1), a1 = gel(x,2);
2338 27 : GEN S2 = gel(y,1), a2 = gel(y,2);
2339 27 : long n = brent_kung_optpow(maxss(degpol(S1),degpol(a1)),2,1);
2340 27 : GEN V = FlxqXQ_powers_pre(S2, n, S, T, p, pi);
2341 27 : GEN S3 = FlxqX_FlxqXQV_eval_pre(S1, V, S, T, p, pi);
2342 27 : GEN aS = FlxqX_FlxqXQV_eval_pre(a1, V, S, T, p, pi);
2343 27 : GEN a3 = FlxX_add(aS, a2, p);
2344 27 : return mkvec2(S3, a3);
2345 : }
2346 :
2347 : static GEN
2348 20 : FlxqXQ_auttrace_sqr(void *E, GEN x)
2349 20 : { return FlxqXQ_auttrace_mul(E, x, x); }
2350 :
2351 : GEN
2352 337 : FlxqXQ_auttrace_pre(GEN x, ulong n, GEN S, GEN T, ulong p, ulong pi)
2353 : {
2354 337 : pari_sp av = avma;
2355 : struct _FlxqXQ D;
2356 337 : T = Flx_get_red_pre(T, p, pi);
2357 337 : S = FlxqX_get_red_pre(S, T, p, pi);
2358 337 : D.S=S; D.T=T; D.p=p; D.pi = pi;
2359 337 : x = gen_powu_i(x,n,(void*)&D,FlxqXQ_auttrace_sqr,FlxqXQ_auttrace_mul);
2360 337 : return gc_GEN(av, x);
2361 : }
2362 : GEN
2363 0 : FlxqXQ_auttrace(GEN x, ulong n, GEN S, GEN T, ulong p)
2364 0 : { return FlxqXQ_auttrace_pre(x, n, S, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
2365 :
2366 : /*******************************************************************/
2367 : /* */
2368 : /* FlxYqQ */
2369 : /* */
2370 : /*******************************************************************/
2371 :
2372 : /*Preliminary implementation to speed up FpX_ffisom*/
2373 : typedef struct {
2374 : GEN S, T;
2375 : ulong p, pi;
2376 : } FlxYqq_muldata;
2377 :
2378 : /* reduce x in Fl[X, Y] in the algebra Fl[X, Y]/ (P(X),Q(Y)) */
2379 : static GEN
2380 90880 : FlxYqq_redswap(GEN x, GEN S, GEN T, ulong p, ulong pi)
2381 : {
2382 90880 : pari_sp ltop=avma;
2383 90880 : long n = get_Flx_degree(S);
2384 90881 : long m = get_Flx_degree(T);
2385 90880 : long w = get_Flx_var(T);
2386 90879 : GEN V = FlxX_swap(x,m,w);
2387 90878 : V = FlxqX_red_pre(V,S,p,pi);
2388 90876 : V = FlxX_swap(V,n,w);
2389 90881 : return gc_GEN(ltop,V);
2390 : }
2391 : static GEN
2392 80515 : FlxYqq_sqr(void *data, GEN x)
2393 : {
2394 80515 : FlxYqq_muldata *D = (FlxYqq_muldata*)data;
2395 80515 : return FlxYqq_redswap(FlxqX_sqr_pre(x,D->T,D->p,D->pi),D->S,D->T,D->p,D->pi);
2396 : }
2397 :
2398 : static GEN
2399 10368 : FlxYqq_mul(void *data, GEN x, GEN y)
2400 : {
2401 10368 : FlxYqq_muldata *D = (FlxYqq_muldata*)data;
2402 10368 : return FlxYqq_redswap(FlxqX_mul_pre(x,y, D->T,D->p,D->pi),D->S,D->T,D->p,D->pi);
2403 : }
2404 :
2405 : /* x in Z[X,Y], S in Z[X] over Fq = Z[Y]/(p,T); compute lift(x^n mod (S,T,p)) */
2406 : GEN
2407 39226 : FlxYqq_pow(GEN x, GEN n, GEN S, GEN T, ulong p)
2408 : {
2409 : FlxYqq_muldata D;
2410 39226 : D.S = S; D.T = T; D.p = p; D.pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
2411 39226 : return gen_pow(x, n, (void*)&D, &FlxYqq_sqr, &FlxYqq_mul);
2412 : }
2413 :
2414 : /*******************************************************************/
2415 : /* */
2416 : /* FlxqXn */
2417 : /* */
2418 : /*******************************************************************/
2419 :
2420 : GEN
2421 66180 : FlxXn_red(GEN a, long n)
2422 : {
2423 66180 : long i, L = n+2, l = lg(a);
2424 : GEN b;
2425 66180 : if (L >= l) return a; /* deg(x) < n */
2426 36741 : b = cgetg(L, t_POL); b[1] = a[1];
2427 391987 : for (i=2; i<L; i++) gel(b,i) = gel(a,i);
2428 36743 : return FlxX_renormalize(b,L);
2429 : }
2430 :
2431 : GEN
2432 40412 : FlxqXn_mul_pre(GEN a, GEN b, long n, GEN T, ulong p, ulong pi)
2433 40412 : { return FlxXn_red(FlxqX_mul_pre(a, b, T, p, pi), n); }
2434 : GEN
2435 0 : FlxqXn_mul(GEN a, GEN b, long n, GEN T, ulong p)
2436 0 : { return FlxqXn_mul_pre(a, b, n, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
2437 :
2438 : GEN
2439 0 : FlxqXn_sqr_pre(GEN a, long n, GEN T, ulong p, ulong pi)
2440 0 : { return FlxXn_red(FlxqX_sqr_pre(a, T, p, pi), n); }
2441 : GEN
2442 0 : FlxqXn_sqr(GEN a, long n, GEN T, ulong p)
2443 0 : { return FlxqXn_sqr_pre(a, n, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
2444 :
2445 : /* (f*g) \/ x^n */
2446 : static GEN
2447 18000 : FlxqX_mulhigh_i(GEN f, GEN g, long n, GEN T, ulong p, ulong pi)
2448 18000 : { return FlxX_shift(FlxqX_mul_pre(f, g, T, p, pi), -n , get_Flx_var(T)); }
2449 :
2450 : static GEN
2451 13194 : FlxqXn_mulhigh(GEN f, GEN g, long n2, long n, GEN T, ulong p, ulong pi)
2452 : {
2453 13194 : long vT = get_Flx_var(T);
2454 13194 : GEN F = FlxX_blocks(f, n2, 2, vT), fl = gel(F,1), fh = gel(F,2);
2455 13196 : return FlxX_add(FlxqX_mulhigh_i(fl, g, n2, T, p, pi),
2456 : FlxqXn_mul_pre(fh, g, n - n2, T, p, pi), p);
2457 : }
2458 :
2459 : GEN
2460 2432 : FlxqXn_inv_pre(GEN f, long e, GEN T, ulong p, ulong pi)
2461 : {
2462 2432 : pari_sp av = avma, av2;
2463 : ulong mask;
2464 : GEN W, a;
2465 2432 : long v = varn(f), n = 1, vT = get_Flx_var(T);
2466 :
2467 2432 : if (!signe(f)) pari_err_INV("FlxqXn_inv",f);
2468 2432 : a = Flxq_inv_pre(gel(f,2), T, p, pi);
2469 2432 : if (e == 1) return scalarpol(a, v);
2470 2432 : else if (e == 2)
2471 : {
2472 : GEN b;
2473 0 : if (degpol(f) <= 0) return scalarpol(a, v);
2474 0 : b = Flx_neg(gel(f,3), p);
2475 0 : if (lgpol(b)==0) return scalarpol(a, v);
2476 0 : b = Flxq_mul_pre(b, Flxq_sqr_pre(a, T, p, pi), T, p, pi);
2477 0 : W = deg1pol_shallow(b, a, v);
2478 0 : return gc_GEN(av, W);
2479 : }
2480 2432 : W = scalarpol_shallow(Flxq_inv_pre(gel(f,2), T, p, pi), v);
2481 2432 : mask = quadratic_prec_mask(e);
2482 2432 : av2 = avma;
2483 12039 : for (;mask>1;)
2484 : {
2485 : GEN u, fr;
2486 9607 : long n2 = n;
2487 9607 : n<<=1; if (mask & 1) n--;
2488 9607 : mask >>= 1;
2489 9607 : fr = FlxXn_red(f, n);
2490 9607 : u = FlxqXn_mul_pre(W, FlxqXn_mulhigh(fr, W, n2, n, T,p,pi), n-n2, T,p,pi);
2491 9608 : W = FlxX_sub(W, FlxX_shift(u, n2, vT), p);
2492 9608 : if (gc_needed(av2,2))
2493 : {
2494 0 : if(DEBUGMEM>1) pari_warn(warnmem,"FlxqXn_inv, e = %ld", n);
2495 0 : W = gerepileupto(av2, W);
2496 : }
2497 : }
2498 2432 : return gerepileupto(av, W);
2499 : }
2500 : GEN
2501 0 : FlxqXn_inv(GEN f, long e, GEN T, ulong p)
2502 0 : { return FlxqXn_inv_pre(f, e, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
2503 :
2504 : /* Compute intformal(x^n*S)/x^(n+1) */
2505 : static GEN
2506 4804 : FlxX_integXn(GEN x, long n, ulong p)
2507 : {
2508 4804 : long i, lx = lg(x);
2509 : GEN y;
2510 4804 : if (lx == 2) return gcopy(x);
2511 3998 : y = cgetg(lx, t_POL); y[1] = x[1];
2512 26742 : for (i=2; i<lx; i++)
2513 : {
2514 22744 : GEN xi = gel(x,i);
2515 22744 : gel(y,i) = Flx_Fl_mul(xi, Fl_inv((n+i-1)%p, p), p);
2516 : }
2517 3998 : return FlxX_renormalize(y, lx);;
2518 : }
2519 :
2520 : GEN
2521 1216 : FlxqXn_expint_pre(GEN h, long e, GEN T, ulong p, ulong pi)
2522 : {
2523 1216 : pari_sp av = avma, av2;
2524 1216 : long v = varn(h), n = 1, vT = get_Flx_var(T);
2525 1216 : GEN f = pol1_FlxX(v, vT), g = pol1_FlxX(v, vT);
2526 1216 : ulong mask = quadratic_prec_mask(e);
2527 1216 : av2 = avma;
2528 4804 : for (;mask>1;)
2529 : {
2530 : GEN u, w;
2531 4804 : long n2 = n;
2532 4804 : n<<=1; if (mask & 1) n--;
2533 4804 : mask >>= 1;
2534 4804 : u = FlxqXn_mul_pre(g, FlxqX_mulhigh_i(f, FlxXn_red(h, n2-1), n2-1, T,p,pi), n-n2, T,p,pi);
2535 4804 : u = FlxX_add(u, FlxX_shift(FlxXn_red(h, n-1), 1-n2, vT), p);
2536 4804 : w = FlxqXn_mul_pre(f, FlxX_integXn(u, n2-1, p), n-n2, T, p, pi);
2537 4804 : f = FlxX_add(f, FlxX_shift(w, n2, vT), p);
2538 4804 : if (mask<=1) break;
2539 3588 : u = FlxqXn_mul_pre(g, FlxqXn_mulhigh(f, g, n2, n, T,p,pi), n-n2, T,p,pi);
2540 3588 : g = FlxX_sub(g, FlxX_shift(u, n2, vT), p);
2541 3588 : if (gc_needed(av2,2))
2542 : {
2543 0 : if (DEBUGMEM>1) pari_warn(warnmem,"FlxqXn_exp, e = %ld", n);
2544 0 : gerepileall(av2, 2, &f, &g);
2545 : }
2546 : }
2547 1216 : return gerepileupto(av, f);
2548 : }
2549 : GEN
2550 0 : FlxqXn_expint(GEN h, long e, GEN T, ulong p)
2551 0 : { return FlxqXn_expint_pre(h, e, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
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