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 17723426 : FlxX_renormalize(GEN /*in place*/ x, long lx)
31 : {
32 : long i;
33 22554186 : for (i = lx-1; i>1; i--)
34 21775037 : if (lgpol(gel(x,i))) break;
35 17723447 : stackdummy((pari_sp)(x + lg(x)), (pari_sp)(x + i+1));
36 17723985 : setlg(x, i+1); setsigne(x, i!=1); return x;
37 : }
38 :
39 : GEN
40 758614 : pol1_FlxX(long v, long sv)
41 : {
42 758614 : GEN z = cgetg(3, t_POL);
43 758613 : z[1] = evalsigne(1) | evalvarn(v);
44 758613 : 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 3079378 : FlxY_degreex(GEN b)
58 : {
59 3079378 : long deg = 0, i;
60 3079378 : if (!signe(b)) return -1;
61 11040763 : for (i = 2; i < lg(b); ++i)
62 7961352 : deg = maxss(deg, degpol(gel(b, i)));
63 3079411 : return deg;
64 : }
65 :
66 : /*Lift coefficient of B to constant Flx, to give a FlxY*/
67 : GEN
68 2510 : Fly_to_FlxY(GEN B, long sv)
69 : {
70 2510 : long lb=lg(B);
71 : long i;
72 2510 : GEN b=cgetg(lb,t_POL);
73 2510 : b[1]=evalsigne(1)|(((ulong)B[1])&VARNBITS);
74 65381 : for (i=2; i<lb; i++)
75 62876 : gel(b,i) = Fl_to_Flx(B[i], sv);
76 2505 : return FlxX_renormalize(b, lb);
77 : }
78 :
79 : GEN
80 2874917 : zxX_to_FlxX(GEN B, ulong p)
81 : {
82 2874917 : long i, lb = lg(B);
83 2874917 : GEN b = cgetg(lb,t_POL);
84 9384175 : for (i=2; i<lb; i++)
85 6514479 : gel(b,i) = zx_to_Flx(gel(B,i), p);
86 2869696 : b[1] = B[1]; return FlxX_renormalize(b, lb);
87 : }
88 :
89 : GEN
90 2771507 : FlxX_to_ZXX(GEN B)
91 : {
92 2771507 : long i, lb = lg(B);
93 2771507 : GEN b = cgetg(lb,t_POL);
94 8889418 : for (i=2; i<lb; i++)
95 : {
96 6118719 : GEN c = gel(B,i);
97 6118719 : switch(lgpol(c))
98 : {
99 267559 : case 0: c = gen_0; break;
100 796735 : case 1: c = utoi(c[2]); break;
101 5054502 : default: c = Flx_to_ZX(c); break;
102 : }
103 6117872 : gel(b,i) = c;
104 : }
105 2770699 : 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 4692416 : ZXX_to_FlxX(GEN B, ulong p, long v)
112 : {
113 4692416 : long lb=lg(B);
114 : long i;
115 4692416 : GEN b=cgetg(lb,t_POL);
116 4692487 : b[1]=evalsigne(1)|(((ulong)B[1])&VARNBITS);
117 21555190 : for (i=2; i<lb; i++)
118 16863766 : switch (typ(gel(B,i)))
119 : {
120 7105482 : case t_INT:
121 7105482 : gel(b,i) = Z_to_Flx(gel(B,i), p, evalvarn(v));
122 7105404 : break;
123 9759683 : case t_POL:
124 9759683 : gel(b,i) = ZX_to_Flx(gel(B,i), p);
125 9758698 : break;
126 : }
127 4691424 : 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 57625 : FlxX_to_Flm(GEN v, long n)
160 : {
161 57625 : long j, N = lg(v)-1;
162 57625 : GEN y = cgetg(N, t_MAT);
163 57625 : v++;
164 198629 : for (j=1; j<N; j++) gel(y,j) = Flx_to_Flv(gel(v,j), n);
165 57621 : return y;
166 : }
167 :
168 : GEN
169 375398 : FlxX_to_Flx(GEN f)
170 : {
171 375398 : long i, l = lg(f);
172 375398 : GEN V = cgetg(l, t_VECSMALL);
173 375398 : V[1] = ((ulong)f[1])&VARNBITS;
174 3548462 : for(i=2; i<l; i++)
175 3173064 : V[i] = lgpol(gel(f,i)) ? mael(f,i,2): 0L;
176 375398 : return V;
177 : }
178 :
179 : GEN
180 221464 : Flm_to_FlxX(GEN x, long v,long w)
181 : {
182 221464 : long j, lx = lg(x);
183 221464 : GEN y = cgetg(lx+1, t_POL);
184 221465 : y[1]=evalsigne(1) | v;
185 221465 : y++;
186 814303 : for (j=1; j<lx; j++) gel(y,j) = Flv_to_Flx(gel(x,j), w);
187 221447 : return FlxX_renormalize(--y, lx+1);
188 : }
189 :
190 : /* P(X,Y) --> P(Y,X), n is the degree in Y */
191 : GEN
192 181764 : FlxX_swap(GEN x, long n, long ws)
193 : {
194 181764 : long j, lx = lg(x), ly = n+3;
195 181764 : GEN y = cgetg(ly, t_POL);
196 181766 : y[1] = x[1];
197 1168694 : for (j=2; j<ly; j++)
198 : {
199 : long k;
200 986932 : GEN p1 = cgetg(lx, t_VECSMALL);
201 986928 : p1[1] = ws;
202 11225495 : for (k=2; k<lx; k++)
203 10238567 : if (j<lg(gel(x,k)))
204 7199154 : p1[k] = mael(x,k,j);
205 : else
206 3039413 : p1[k] = 0;
207 986928 : gel(y,j) = Flx_renormalize(p1,lx);
208 : }
209 181762 : return FlxX_renormalize(y,ly);
210 : }
211 :
212 : static GEN
213 4359697 : zxX_to_Kronecker_spec(GEN P, long lp, long n)
214 : { /* P(X) = sum Pi(Y) * X^i, return P( Y^(2n-1) ) */
215 4359697 : long i, j, k, l, N = (n<<1) + 1;
216 4359697 : GEN y = cgetg((N-2)*lp + 2, t_VECSMALL) + 2;
217 28820283 : for (k=i=0; i<lp; i++)
218 : {
219 28783781 : GEN c = gel(P,i);
220 28783781 : l = lg(c);
221 28783781 : if (l-3 >= n)
222 0 : pari_err_BUG("zxX_to_Kronecker, P is not reduced mod Q");
223 168688535 : for (j=2; j < l; j++) y[k++] = c[j];
224 28783863 : if (i == lp-1) break;
225 219122392 : for ( ; j < N; j++) y[k++] = 0;
226 : }
227 4359754 : y -= 2;
228 4359754 : y[1] = 0; setlg(y, k+2); return y;
229 : }
230 :
231 : GEN
232 3773438 : zxX_to_Kronecker(GEN P, GEN Q)
233 : {
234 3773438 : GEN z = zxX_to_Kronecker_spec(P+2, lg(P)-2, degpol(Q));
235 3773455 : z[1] = P[1]; return z;
236 : }
237 :
238 : GEN
239 348538 : FlxX_add(GEN x, GEN y, ulong p)
240 : {
241 : long i,lz;
242 : GEN z;
243 348538 : long lx=lg(x);
244 348538 : long ly=lg(y);
245 348538 : if (ly>lx) swapspec(x,y, lx,ly);
246 348538 : lz = lx; z = cgetg(lz, t_POL); z[1]=x[1];
247 3922261 : for (i=2; i<ly; i++) gel(z,i) = Flx_add(gel(x,i), gel(y,i), p);
248 2148285 : for ( ; i<lx; i++) gel(z,i) = Flx_copy(gel(x,i));
249 348518 : return FlxX_renormalize(z, lz);
250 : }
251 :
252 : GEN
253 245 : FlxY_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 : FlxY_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 84664 : FlxX_deriv(GEN z, ulong p)
322 : {
323 84664 : long i,l = lg(z)-1;
324 : GEN x;
325 84664 : if (l < 2) l = 2;
326 84664 : x = cgetg(l, t_POL); x[1] = z[1];
327 914734 : for (i=2; i<l; i++) gel(x,i) = Flx_mulu(gel(z,i+1), (ulong) i-1, p);
328 84659 : 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 623880 : FlxX_sub(GEN x, GEN y, ulong p)
380 : {
381 : long lx,ly,i,lz;
382 : GEN z;
383 623880 : lx = lg(x); ly = lg(y);
384 623880 : lz=maxss(lx,ly);
385 623880 : z = cgetg(lz,t_POL);
386 623879 : 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 513894 : z[1] = y[1];
396 1294771 : for (i=2; i<lx; i++) gel(z,i) = Flx_sub(gel(x,i),gel(y,i),p);
397 1381459 : for ( ; i<ly; i++) gel(z,i) = Flx_neg(gel(y,i),p);
398 : }
399 623852 : if (!lgpol(z)) { set_avma((pari_sp)(z + lz)); z = pol_0(varn(x)); }
400 623863 : return z;
401 : }
402 :
403 : GEN
404 0 : FlxY_Flx_mul_pre(GEN P, GEN U, ulong p, ulong pi)
405 : {
406 0 : long i, lP = lg(P);
407 0 : GEN res = cgetg(lP,t_POL);
408 0 : res[1] = P[1];
409 0 : for(i=2; i<lP; i++) gel(res,i) = Flx_mul_pre(U,gel(P,i), p, pi);
410 0 : return FlxX_renormalize(res, lP);
411 : }
412 :
413 : GEN
414 0 : FlxY_Flx_mul(GEN P, GEN U, ulong p)
415 0 : { return FlxY_Flx_mul_pre(P, U, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
416 :
417 : GEN
418 7500 : FlxY_Flx_div_pre(GEN x, GEN y, ulong p, ulong pi)
419 : {
420 : long i, l;
421 : GEN z;
422 7500 : if (degpol(y) == 0)
423 : {
424 5556 : ulong t = uel(y,2);
425 5556 : if (t == 1) return x;
426 0 : t = Fl_inv(t, p);
427 0 : z = cgetg_copy(x, &l); z[1] = x[1];
428 0 : for (i=2; i<l; i++) gel(z,i) = Flx_Fl_mul_pre(gel(x,i),t,p,pi);
429 : }
430 : else
431 : {
432 1944 : y = Flx_get_red_pre(y, p, pi);
433 1945 : z = cgetg_copy(x, &l); z[1] = x[1];
434 3890 : for (i=2; i<l; i++) gel(z,i) = Flx_div_pre(gel(x,i),y,p,pi);
435 : }
436 1945 : return z;
437 : }
438 : GEN
439 0 : FlxY_Flx_div(GEN P, GEN U, ulong p)
440 0 : { return FlxY_Flx_div_pre(P, U, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
441 :
442 : GEN
443 14274905 : FlxY_evalx_pre(GEN Q, ulong x, ulong p, ulong pi)
444 : {
445 14274905 : long i, lb = lg(Q);
446 : GEN z;
447 14274905 : z = cgetg(lb,t_VECSMALL); z[1] = evalvarn(varn(Q));
448 115807970 : for (i=2; i<lb; i++) z[i] = Flx_eval_pre(gel(Q,i), x, p, pi);
449 14278209 : return Flx_renormalize(z, lb);
450 : }
451 : GEN
452 231 : FlxY_evalx(GEN Q, ulong x, ulong p)
453 231 : { return FlxY_evalx_pre(Q, x, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
454 :
455 : GEN
456 0 : FlxY_Flx_translate(GEN P, GEN c, ulong p)
457 : {
458 0 : pari_sp av = avma;
459 0 : ulong pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
460 : GEN Q;
461 : long i, k, n;
462 :
463 0 : if (!signe(P) || gequal0(c)) return RgX_copy(P);
464 0 : Q = leafcopy(P); n = degpol(P);
465 0 : for (i=1; i<=n; i++)
466 : {
467 0 : for (k=n-i; k<n; k++)
468 0 : gel(Q,2+k) = Flx_add(gel(Q,2+k), Flx_mul_pre(gel(Q,2+k+1), c, p, pi), p);
469 0 : if (gc_needed(av,2))
470 : {
471 0 : if(DEBUGMEM>1)
472 0 : pari_warn(warnmem,"FlxY_Flx_translate, i = %ld/%ld", i,n);
473 0 : Q = gc_GEN(av, Q);
474 : }
475 : }
476 0 : return gc_GEN(av, Q);
477 : }
478 :
479 : /* allow pi = 0 */
480 : GEN
481 10977206 : FlxY_evalx_powers_pre(GEN pol, GEN ypowers, ulong p, ulong pi)
482 : {
483 10977206 : long i, len = lg(pol);
484 10977206 : GEN res = cgetg(len, t_VECSMALL);
485 10973637 : res[1] = pol[1] & VARNBITS;
486 37280921 : for (i = 2; i < len; ++i)
487 26288469 : res[i] = Flx_eval_powers_pre(gel(pol, i), ypowers, p, pi);
488 10992452 : return Flx_renormalize(res, len);
489 : }
490 :
491 : /* allow pi = 0 */
492 : ulong
493 7367069 : FlxY_eval_powers_pre(GEN pol, GEN ypowers, GEN xpowers, ulong p, ulong pi)
494 : {
495 7367069 : pari_sp av = avma;
496 7367069 : GEN t = FlxY_evalx_powers_pre(pol, ypowers, p, pi);
497 7363176 : return gc_ulong(av, Flx_eval_powers_pre(t, xpowers, p, pi));
498 : }
499 :
500 : GEN
501 136362 : FlxY_FlxqV_evalx_pre(GEN P, GEN x, GEN T, ulong p, ulong pi)
502 : {
503 136362 : long i, lP = lg(P);
504 136362 : GEN res = cgetg(lP,t_POL);
505 136362 : res[1] = P[1];
506 930268 : for(i=2; i<lP; i++)
507 793906 : gel(res,i) = Flx_FlxqV_eval_pre(gel(P,i), x, T, p, pi);
508 136362 : return FlxX_renormalize(res, lP);
509 : }
510 : GEN
511 0 : FlxY_FlxqV_evalx(GEN P, GEN x, GEN T, ulong p)
512 0 : { return FlxY_FlxqV_evalx_pre(P, x, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
513 :
514 : GEN
515 0 : FlxY_Flxq_evalx_pre(GEN P, GEN x, GEN T, ulong p, ulong pi)
516 : {
517 0 : pari_sp av = avma;
518 0 : long n = brent_kung_optpow(get_Flx_degree(T)-1,lgpol(P),1);
519 0 : GEN xp = Flxq_powers_pre(x, n, T, p, pi);
520 0 : return gc_upto(av, FlxY_FlxqV_evalx_pre(P, xp, T, p, pi));
521 : }
522 : GEN
523 0 : FlxY_Flxq_evalx(GEN P, GEN x, GEN T, ulong p)
524 0 : { return FlxY_Flxq_evalx_pre(P, x, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
525 :
526 : GEN
527 71618 : FlxX_shift(GEN a, long n, long vs)
528 : {
529 71618 : long i, l = lg(a);
530 : GEN b;
531 71618 : if (l == 2 || !n) return a;
532 64625 : l += n;
533 64625 : if (n < 0)
534 : {
535 35772 : if (l <= 2) return pol_0(varn(a));
536 29402 : b = cgetg(l, t_POL); b[1] = a[1];
537 29402 : a -= n;
538 612626 : for (i=2; i<l; i++) gel(b,i) = gel(a,i);
539 : } else {
540 28853 : b = cgetg(l, t_POL); b[1] = a[1];
541 28856 : a -= n; n += 2;
542 507079 : for (i=2; i<n; i++) gel(b,i) = pol0_Flx(vs);
543 365774 : for ( ; i<l; i++) gel(b,i) = gel(a,i);
544 : }
545 58245 : return b;
546 : }
547 :
548 : GEN
549 13195 : FlxX_blocks(GEN P, long n, long m, long vs)
550 : {
551 13195 : GEN z = cgetg(m+1,t_VEC);
552 13195 : long i,j, k=2, l = lg(P);
553 39585 : for(i=1; i<=m; i++)
554 : {
555 26390 : GEN zi = cgetg(n+2,t_POL);
556 26389 : zi[1] = P[1];
557 26389 : gel(z,i) = zi;
558 160427 : for(j=2; j<n+2; j++)
559 134091 : gel(zi, j) = k==l ? pol0_Flx(vs) : gel(P,k++);
560 26336 : zi = FlxX_renormalize(zi, n+2);
561 : }
562 13195 : return z;
563 : }
564 :
565 : static GEN
566 235489 : FlxX_recipspec(GEN x, long l, long n, long vs)
567 : {
568 : long i;
569 235489 : GEN z = cgetg(n+2,t_POL);
570 235489 : z[1] = 0; z += 2;
571 5279911 : for(i=0; i<l; i++)
572 5044423 : gel(z,n-i-1) = Flx_copy(gel(x,i));
573 242330 : for( ; i<n; i++)
574 6842 : gel(z,n-i-1) = pol0_Flx(vs);
575 235488 : return FlxX_renormalize(z-2,n+2);
576 : }
577 :
578 : GEN
579 2432 : FlxX_invLaplace(GEN x, ulong p)
580 : {
581 2432 : long i, d = degpol(x);
582 : GEN y;
583 : ulong t;
584 2432 : if (d <= 1) return gcopy(x);
585 2425 : t = Fl_inv(factorial_Fl(d, p), p);
586 2425 : y = cgetg(d+3, t_POL);
587 2425 : y[1] = x[1];
588 47537 : for (i=d; i>=2; i--)
589 : {
590 45112 : gel(y,i+2) = Flx_Fl_mul(gel(x,i+2), t, p);
591 45116 : t = Fl_mul(t, i, p);
592 : }
593 2425 : gel(y,3) = Flx_copy(gel(x,3));
594 2425 : gel(y,2) = Flx_copy(gel(x,2));
595 2425 : return FlxX_renormalize(y, d+3);
596 : }
597 :
598 : GEN
599 1216 : FlxX_Laplace(GEN x, ulong p)
600 : {
601 1216 : long i, d = degpol(x);
602 1216 : ulong t = 1;
603 : GEN y;
604 1216 : if (d <= 1) return gcopy(x);
605 1216 : y = cgetg(d+3, t_POL);
606 1216 : y[1] = x[1];
607 1216 : gel(y,2) = Flx_copy(gel(x,2));
608 1216 : gel(y,3) = Flx_copy(gel(x,3));
609 23850 : for (i=2; i<=d; i++)
610 : {
611 22634 : t = Fl_mul(t, i%p, p);
612 22634 : gel(y,i+2) = Flx_Fl_mul(gel(x,i+2), t, p);
613 : }
614 1216 : return FlxX_renormalize(y, d+3);
615 : }
616 :
617 : /***********************************************************************/
618 : /** **/
619 : /** FlxXV **/
620 : /** **/
621 : /***********************************************************************/
622 :
623 : GEN
624 0 : FlxXC_sub(GEN x, GEN y, ulong p)
625 0 : { pari_APPLY_same(FlxX_sub(gel(x, i), gel(y,i), p)) }
626 :
627 : static GEN
628 138362 : FlxXV_to_FlxM_lg(GEN x, long m, long n, long sv)
629 : {
630 : long i;
631 138362 : GEN y = cgetg(n+1, t_MAT);
632 458220 : for (i=1; i<=n; i++) gel(y,i) = FlxX_to_FlxC(gel(x,i), m, sv);
633 138362 : return y;
634 : }
635 :
636 : GEN
637 0 : FlxXV_to_FlxM(GEN v, long n, long sv)
638 0 : { return FlxXV_to_FlxM_lg(v, n, lg(v)-1, sv); }
639 :
640 : GEN
641 12607 : FlxXC_to_ZXXC(GEN x)
642 62885 : { pari_APPLY_type(t_COL, FlxX_to_ZXX(gel(x,i))) }
643 :
644 : GEN
645 0 : FlxXM_to_ZXXM(GEN x)
646 0 : { pari_APPLY_same(FlxXC_to_ZXXC(gel(x,i))) }
647 :
648 : /***********************************************************************/
649 : /** **/
650 : /** FlxqX **/
651 : /** **/
652 : /***********************************************************************/
653 :
654 : static GEN
655 3614359 : get_FlxqX_red(GEN T, GEN *B)
656 : {
657 3614359 : if (typ(T)!=t_VEC) { *B=NULL; return T; }
658 141827 : *B = gel(T,1); return gel(T,2);
659 : }
660 :
661 : GEN
662 162564 : RgX_to_FlxqX(GEN x, GEN T, ulong p)
663 : {
664 162564 : long i, l = lg(x);
665 162564 : GEN z = cgetg(l, t_POL); z[1] = x[1];
666 2376267 : for (i = 2; i < l; i++)
667 2213707 : gel(z,i) = Rg_to_Flxq(gel(x,i), T, p);
668 162560 : return FlxX_renormalize(z, l);
669 : }
670 :
671 : /* FlxqX are t_POL with Flxq coefficients.
672 : * Normally the variable ordering should be respected.*/
673 :
674 : GEN
675 590 : random_FlxqX(long d1, long v, GEN T, ulong p)
676 : {
677 590 : long dT = get_Flx_degree(T), vT = get_Flx_var(T);
678 590 : long i, d = d1+2;
679 590 : GEN y = cgetg(d,t_POL); y[1] = evalsigne(1) | evalvarn(v);
680 3124 : for (i=2; i<d; i++) gel(y,i) = random_Flx(dT, vT, p);
681 590 : return FlxX_renormalize(y,d);
682 : }
683 :
684 : /*Not stack clean*/
685 : GEN
686 2356838 : Kronecker_to_FlxqX_pre(GEN z, GEN T, ulong p, ulong pi)
687 : {
688 2356838 : long i,j,lx,l, N = (get_Flx_degree(T)<<1) + 1;
689 2356837 : GEN x, t = cgetg(N,t_VECSMALL);
690 2356834 : t[1] = get_Flx_var(T);
691 2356834 : l = lg(z); lx = (l-2) / (N-2);
692 2356834 : x = cgetg(lx+3,t_POL);
693 2356834 : x[1] = z[1];
694 28859944 : for (i=2; i<lx+2; i++)
695 : {
696 370679391 : for (j=2; j<N; j++) t[j] = z[j];
697 26503106 : z += (N-2);
698 26503106 : gel(x,i) = Flx_rem_pre(Flx_renormalize(t,N), T,p,pi);
699 : }
700 2356838 : N = (l-2) % (N-2) + 2;
701 7565875 : for (j=2; j<N; j++) t[j] = z[j];
702 2356838 : gel(x,i) = Flx_rem_pre(Flx_renormalize(t,N), T,p,pi);
703 2356805 : return FlxX_renormalize(x, i+1);
704 : }
705 : GEN
706 0 : Kronecker_to_FlxqX(GEN z, GEN T, ulong p)
707 0 : { return Kronecker_to_FlxqX_pre(z, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
708 :
709 : GEN
710 1264504 : FlxqX_red_pre(GEN z, GEN T, ulong p, ulong pi)
711 : {
712 : GEN res;
713 1264504 : long i, l = lg(z);
714 1264504 : res = cgetg(l,t_POL); res[1] = z[1];
715 13066969 : for(i=2;i<l;i++) gel(res,i) = Flx_rem_pre(gel(z,i),T,p,pi);
716 1264497 : return FlxX_renormalize(res,l);
717 : }
718 : GEN
719 0 : FlxqX_red(GEN z, GEN T, ulong p)
720 0 : { return FlxqX_red_pre(z, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
721 :
722 : static GEN
723 293138 : FlxqX_mulspec(GEN x, GEN y, GEN T, ulong p, ulong pi, long lx, long ly)
724 : {
725 293138 : pari_sp av = avma;
726 : GEN z,kx,ky;
727 293138 : long dT = get_Flx_degree(T);
728 293138 : kx= zxX_to_Kronecker_spec(x,lx,dT);
729 293138 : ky= zxX_to_Kronecker_spec(y,ly,dT);
730 293138 : z = Flx_mul_pre(ky, kx, p, pi);
731 293138 : z = Kronecker_to_FlxqX_pre(z,T,p,pi);
732 293138 : return gc_upto(av, z);
733 : }
734 :
735 : GEN
736 1709725 : FlxqX_mul_pre(GEN x, GEN y, GEN T, ulong p, ulong pi)
737 : {
738 1709725 : pari_sp av = avma;
739 1709725 : GEN z, kx, ky, Tm = get_Flx_mod(T);
740 1709724 : kx= zxX_to_Kronecker(x, Tm);
741 1709749 : ky= zxX_to_Kronecker(y, Tm);
742 1709753 : z = Flx_mul_pre(ky, kx, p, pi);
743 1709722 : z = Kronecker_to_FlxqX_pre(z, T, p, pi);
744 1709694 : return gc_upto(av, z);
745 : }
746 : GEN
747 63586 : FlxqX_mul(GEN x, GEN y, GEN T, ulong p)
748 63586 : { return FlxqX_mul_pre(x, y, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
749 :
750 : GEN
751 353990 : FlxqX_sqr_pre(GEN x, GEN T, ulong p, ulong pi)
752 : {
753 353990 : pari_sp av = avma;
754 : GEN z,kx;
755 353990 : kx= zxX_to_Kronecker(x,get_Flx_mod(T));
756 353990 : z = Flx_sqr_pre(kx, p, pi);
757 353990 : z = Kronecker_to_FlxqX_pre(z,T,p,pi);
758 353989 : return gc_upto(av, z);
759 : }
760 : GEN
761 1218 : FlxqX_sqr(GEN x, GEN T, ulong p)
762 1218 : { return FlxqX_sqr_pre(x, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
763 :
764 : GEN
765 155141 : FlxqX_Flxq_mul_pre(GEN P, GEN U, GEN T, ulong p, ulong pi)
766 : {
767 155141 : long i, lP = lg(P);
768 155141 : GEN res = cgetg(lP,t_POL);
769 155141 : res[1] = P[1];
770 554378 : for(i=2; i<lP; i++) gel(res,i) = Flxq_mul_pre(U,gel(P,i), T,p,pi);
771 155139 : return FlxX_renormalize(res, lP);
772 : }
773 : GEN
774 0 : FlxqX_Flxq_mul(GEN P, GEN U, GEN T, ulong p)
775 0 : { return FlxqX_Flxq_mul_pre(P, U, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
776 :
777 : GEN
778 664299 : FlxqX_Flxq_mul_to_monic_pre(GEN P, GEN U, GEN T, ulong p, ulong pi)
779 : {
780 664299 : long i, lP = lg(P);
781 664299 : GEN res = cgetg(lP,t_POL);
782 664290 : res[1] = P[1];
783 3550732 : for(i=2; i<lP-1; i++) gel(res,i) = Flxq_mul_pre(U,gel(P,i), T,p,pi);
784 663822 : gel(res,lP-1) = pol1_Flx(get_Flx_var(T));
785 664309 : return FlxX_renormalize(res, lP);
786 : }
787 : GEN
788 0 : FlxqX_Flxq_mul_to_monic(GEN P, GEN U, GEN T, ulong p)
789 : {
790 0 : ulong pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
791 0 : return FlxqX_Flxq_mul_to_monic_pre(P, U, T, p, pi);
792 : }
793 :
794 : GEN
795 190188 : FlxqX_normalize_pre(GEN z, GEN T, ulong p, ulong pi)
796 : {
797 190188 : GEN p1 = leading_coeff(z);
798 190188 : if (!lgpol(z) || (!degpol(p1) && p1[1] == 1)) return z;
799 190167 : return FlxqX_Flxq_mul_to_monic_pre(z, Flxq_inv_pre(p1,T,p,pi), T,p,pi);
800 : }
801 : GEN
802 133 : FlxqX_normalize(GEN z, GEN T, ulong p)
803 133 : { return FlxqX_normalize_pre(z, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
804 :
805 : struct _FlxqXQ {
806 : GEN T, S;
807 : ulong p, pi;
808 : };
809 :
810 538529 : static GEN _FlxqX_mul(void *data,GEN a,GEN b)
811 : {
812 538529 : struct _FlxqXQ *d=(struct _FlxqXQ*)data;
813 538529 : return FlxqX_mul_pre(a,b,d->T,d->p,d->pi);
814 : }
815 10283 : static GEN _FlxqX_sqr(void *data,GEN a)
816 : {
817 10283 : struct _FlxqXQ *d=(struct _FlxqXQ*)data;
818 10283 : return FlxqX_sqr_pre(a,d->T,d->p,d->pi);
819 : }
820 :
821 : GEN
822 10248 : FlxqX_powu_pre(GEN V, ulong n, GEN T, ulong p, ulong pi)
823 : {
824 10248 : struct _FlxqXQ d; d.p = p; d.pi = pi; d.T = T;
825 10248 : return gen_powu(V, n, (void*)&d, &_FlxqX_sqr, &_FlxqX_mul);
826 : }
827 : GEN
828 0 : FlxqX_powu(GEN V, ulong n, GEN T, ulong p)
829 0 : { return FlxqX_powu_pre(V, n, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
830 :
831 : /* x and y in Z[Y][X]. Assume T irreducible mod p */
832 : static GEN
833 3162404 : FlxqX_divrem_basecase(GEN x, GEN y, GEN T, ulong p, ulong pi, GEN *pr)
834 : {
835 3162404 : long vx = varn(x), dx = degpol(x), dy = degpol(y), dz, i, j, sx, lr;
836 : pari_sp av0, av;
837 : GEN z, p1, rem, lead;
838 :
839 3162402 : if (!signe(y)) pari_err_INV("FlxqX_divrem",y);
840 3162415 : if (dx < dy)
841 : {
842 21612 : if (pr)
843 : {
844 21360 : av0 = avma; x = FlxqX_red_pre(x, T, p, pi);
845 21360 : if (pr == ONLY_DIVIDES) { set_avma(av0); return signe(x)? NULL: pol_0(vx); }
846 21360 : if (pr == ONLY_REM) return x;
847 21360 : *pr = x;
848 : }
849 21612 : return pol_0(vx);
850 : }
851 3140803 : lead = leading_coeff(y);
852 3140808 : if (!dy) /* y is constant */
853 : {
854 330730 : if (pr && pr != ONLY_DIVIDES)
855 : {
856 326055 : if (pr == ONLY_REM) return pol_0(vx);
857 133822 : *pr = pol_0(vx);
858 : }
859 138497 : if (Flx_equal1(lead)) return gcopy(x);
860 134298 : av0 = avma; x = FlxqX_Flxq_mul_pre(x,Flxq_inv(lead,T,p),T,p,pi);
861 134300 : return gc_upto(av0,x);
862 : }
863 2810078 : av0 = avma; dz = dx-dy;
864 2810078 : lead = Flx_equal1(lead)? NULL: gclone(Flxq_inv_pre(lead,T,p,pi));
865 2810104 : set_avma(av0);
866 2810102 : z = cgetg(dz+3,t_POL); z[1] = x[1];
867 2810101 : x += 2; y += 2; z += 2;
868 :
869 2810101 : p1 = gel(x,dx); av = avma;
870 2810101 : gel(z,dz) = lead? gc_upto(av, Flxq_mul_pre(p1,lead, T,p,pi)): gcopy(p1);
871 6478303 : for (i=dx-1; i>=dy; i--)
872 : {
873 3668243 : av = avma; p1 = gel(x,i);
874 11940148 : for (j=i-dy+1; j<=i && j<=dz; j++)
875 8272078 : p1 = Flx_sub(p1, Flx_mul_pre(gel(z,j),gel(y,i-j),p,pi),p);
876 3668070 : if (lead) p1 = Flx_mul_pre(p1, lead,p,pi);
877 3668070 : gel(z,i-dy) = gc_leaf(av, Flx_rem_pre(p1,T,p,pi));
878 : }
879 2810060 : if (!pr) { guncloneNULL(lead); return z-2; }
880 :
881 2616004 : rem = (GEN)avma; av = (pari_sp)new_chunk(dx+3);
882 2937126 : for (sx=0; ; i--)
883 : {
884 2937126 : p1 = gel(x,i);
885 8684650 : for (j=0; j<=i && j<=dz; j++)
886 5747763 : p1 = Flx_sub(p1, Flx_mul_pre(gel(z,j),gel(y,i-j),p,pi),p);
887 2936887 : p1 = Flx_rem_pre(p1, T,p,pi); if (lgpol(p1)) { sx = 1; break; }
888 395366 : if (!i) break;
889 321076 : set_avma(av);
890 : }
891 2615909 : if (pr == ONLY_DIVIDES)
892 : {
893 0 : guncloneNULL(lead);
894 0 : if (sx) return gc_NULL(av0);
895 0 : return gc_const((pari_sp)rem, z-2);
896 : }
897 2615909 : lr=i+3; rem -= lr; av = (pari_sp)rem;
898 2615909 : rem[0] = evaltyp(t_POL) | _evallg(lr);
899 2615909 : rem[1] = z[-1];
900 2615909 : rem += 2; gel(rem,i) = gc_leaf(av, p1);
901 16341801 : for (i--; i>=0; i--)
902 : {
903 13725758 : av = avma; p1 = gel(x,i);
904 44865566 : for (j=0; j<=i && j<=dz; j++)
905 31145061 : p1 = Flx_sub(p1, Flx_mul_pre(gel(z,j),gel(y,i-j),p,pi), p);
906 13720505 : gel(rem,i) = gc_leaf(av, Flx_rem_pre(p1, T,p,pi));
907 : }
908 2616043 : rem -= 2;
909 2616043 : guncloneNULL(lead);
910 2616061 : if (!sx) (void)FlxX_renormalize(rem, lr);
911 2616067 : if (pr == ONLY_REM) return gc_upto(av0,rem);
912 1221227 : *pr = rem; return z-2;
913 : }
914 :
915 : static GEN
916 1419 : FlxqX_invBarrett_basecase(GEN T, GEN Q, ulong p, ulong pi)
917 : {
918 1419 : long i, l=lg(T)-1, lr = l-1, k;
919 1419 : long sv=Q[1];
920 1419 : GEN r=cgetg(lr,t_POL); r[1]=T[1];
921 1419 : gel(r,2) = pol1_Flx(sv);
922 16396 : for (i=3;i<lr;i++)
923 : {
924 14977 : pari_sp ltop=avma;
925 14977 : GEN u = Flx_neg(gel(T,l-i+2),p);
926 108758 : for (k=3;k<i;k++)
927 93781 : u = Flx_sub(u, Flxq_mul_pre(gel(T,l-i+k), gel(r,k), Q, p, pi), p);
928 14977 : gel(r,i) = gc_upto(ltop, u);
929 : }
930 1419 : r = FlxX_renormalize(r,lr);
931 1419 : return r;
932 : }
933 :
934 : /* Return new lgpol */
935 : static long
936 328043 : FlxX_lgrenormalizespec(GEN x, long lx)
937 : {
938 : long i;
939 359738 : for (i = lx-1; i>=0; i--)
940 359738 : if (lgpol(gel(x,i))) break;
941 328043 : return i+1;
942 : }
943 :
944 : static GEN
945 6711 : FlxqX_invBarrett_Newton(GEN S, GEN T, ulong p, ulong pi)
946 : {
947 6711 : pari_sp av = avma;
948 6711 : long nold, lx, lz, lq, l = degpol(S), i, lQ;
949 6711 : GEN q, y, z, x = cgetg(l+2, t_POL) + 2;
950 6711 : long dT = get_Flx_degree(T), vT = get_Flx_var(T);
951 6711 : ulong mask = quadratic_prec_mask(l-2); /* assume l > 2 */
952 273213 : for (i=0;i<l;i++) gel(x,i) = pol0_Flx(vT);
953 6711 : q = FlxX_recipspec(S+2,l+1,l+1,dT);
954 6711 : lQ = lgpol(q); q+=2;
955 : /* We work on _spec_ FlxX's, all the l[xzq] below are lgpol's */
956 :
957 : /* initialize */
958 6711 : gel(x,0) = Flxq_inv_pre(gel(q,0),T, p, pi);
959 6711 : if (lQ>1 && degpol(gel(q,1)) >= dT)
960 0 : gel(q,1) = Flx_rem_pre(gel(q,1), T, p, pi);
961 6711 : if (lQ>1 && lgpol(gel(q,1)))
962 5686 : {
963 5686 : GEN u = gel(q, 1);
964 5686 : if (!Flx_equal1(gel(x,0)))
965 7 : u = Flxq_mul_pre(u, Flxq_sqr_pre(gel(x,0), T,p,pi), T,p,pi);
966 5686 : gel(x,1) = Flx_neg(u, p); lx = 2;
967 : }
968 : else
969 1025 : lx = 1;
970 6711 : nold = 1;
971 43278 : for (; mask > 1; )
972 : { /* set x -= x(x*q - 1) + O(t^(nnew + 1)), knowing x*q = 1 + O(t^(nold+1)) */
973 36567 : long i, lnew, nnew = nold << 1;
974 :
975 36567 : if (mask & 1) nnew--;
976 36567 : mask >>= 1;
977 :
978 36567 : lnew = nnew + 1;
979 36567 : lq = FlxX_lgrenormalizespec(q, minss(lQ,lnew));
980 36567 : z = FlxqX_mulspec(x, q, T,p,pi, lx, lq); /* FIXME: high product */
981 36567 : lz = lgpol(z); if (lz > lnew) lz = lnew;
982 36567 : z += 2;
983 : /* subtract 1 [=>first nold words are 0]: renormalize so that z(0) != 0 */
984 74746 : for (i = nold; i < lz; i++) if (lgpol(gel(z,i))) break;
985 36567 : nold = nnew;
986 36567 : if (i >= lz) continue; /* z-1 = 0(t^(nnew + 1)) */
987 :
988 : /* z + i represents (x*q - 1) / t^i */
989 35664 : lz = FlxX_lgrenormalizespec (z+i, lz-i);
990 35664 : z = FlxqX_mulspec(x, z+i, T,p,pi, lx, lz); /* FIXME: low product */
991 35664 : lz = lgpol(z); z += 2;
992 35664 : if (lz > lnew-i) lz = FlxX_lgrenormalizespec(z, lnew-i);
993 :
994 35664 : lx = lz+ i;
995 35664 : y = x + i; /* x -= z * t^i, in place */
996 278801 : for (i = 0; i < lz; i++) gel(y,i) = Flx_neg(gel(z,i), p);
997 : }
998 6711 : x -= 2; setlg(x, lx + 2); x[1] = S[1];
999 6711 : return gc_GEN(av, x);
1000 : }
1001 :
1002 : GEN
1003 8130 : FlxqX_invBarrett_pre(GEN T, GEN Q, ulong p, ulong pi)
1004 : {
1005 8130 : pari_sp ltop=avma;
1006 8130 : long l=lg(T), v = varn(T);
1007 : GEN r;
1008 8130 : GEN c = gel(T,l-1);
1009 8130 : if (l<5) return pol_0(v);
1010 8130 : if (l<=FlxqX_INVBARRETT_LIMIT)
1011 : {
1012 1419 : if (!Flx_equal1(c))
1013 : {
1014 0 : GEN ci = Flxq_inv_pre(c,Q,p,pi);
1015 0 : T = FlxqX_Flxq_mul_pre(T, ci, Q, p, pi);
1016 0 : r = FlxqX_invBarrett_basecase(T,Q,p,pi);
1017 0 : r = FlxqX_Flxq_mul_pre(r,ci,Q,p,pi);
1018 : } else
1019 1419 : r = FlxqX_invBarrett_basecase(T,Q,p,pi);
1020 : } else
1021 6711 : r = FlxqX_invBarrett_Newton(T,Q,p,pi);
1022 8130 : return gc_upto(ltop, r);
1023 : }
1024 : GEN
1025 76 : FlxqX_invBarrett(GEN T, GEN Q, ulong p)
1026 76 : { return FlxqX_invBarrett_pre(T, Q, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
1027 :
1028 : GEN
1029 491659 : FlxqX_get_red_pre(GEN S, GEN T, ulong p, ulong pi)
1030 : {
1031 491659 : if (typ(S)==t_POL && lg(S)>FlxqX_BARRETT_LIMIT)
1032 6674 : retmkvec2(FlxqX_invBarrett_pre(S, T, p, pi), S);
1033 484985 : return S;
1034 : }
1035 : GEN
1036 371 : FlxqX_get_red(GEN S, GEN T, ulong p)
1037 : {
1038 371 : if (typ(S)==t_POL && lg(S)>FlxqX_BARRETT_LIMIT)
1039 76 : retmkvec2(FlxqX_invBarrett(S, T, p), S);
1040 295 : return S;
1041 : }
1042 :
1043 : /* Compute x mod S where 2 <= degpol(S) <= l+1 <= 2*(degpol(S)-1)
1044 : * * and mg is the Barrett inverse of S. */
1045 : static GEN
1046 110590 : FlxqX_divrem_Barrettspec(GEN x, long l, GEN mg, GEN S, GEN T, ulong p,
1047 : ulong pi, GEN *pr)
1048 : {
1049 : GEN q, r;
1050 110590 : long lt = degpol(S); /*We discard the leading term*/
1051 : long ld, lm, lT, lmg;
1052 110590 : ld = l-lt;
1053 110590 : lm = minss(ld, lgpol(mg));
1054 110590 : lT = FlxX_lgrenormalizespec(S+2,lt);
1055 110590 : lmg = FlxX_lgrenormalizespec(mg+2,lm);
1056 110590 : q = FlxX_recipspec(x+lt,ld,ld,0); /* = rec(x) lq<=ld*/
1057 110590 : q = FlxqX_mulspec(q+2,mg+2,T,p,pi,lgpol(q),lmg); /* = rec(x)*mg lq<=ld+lm*/
1058 110590 : q = FlxX_recipspec(q+2,minss(ld,lgpol(q)),ld,0); /* = rec(rec(x)*mg) lq<=ld*/
1059 110590 : if (!pr) return q;
1060 110317 : r = FlxqX_mulspec(q+2,S+2,T,p,pi,lgpol(q),lT); /* = q*pol lr<=ld+lt*/
1061 110317 : r = FlxX_subspec(x,r+2,p,lt,minss(lt,lgpol(r)));/* = x - r lr<=lt */
1062 110317 : if (pr == ONLY_REM) return r;
1063 7688 : *pr = r; return q;
1064 : }
1065 :
1066 : static GEN
1067 103701 : FlxqX_divrem_Barrett(GEN x, GEN mg, GEN S, GEN T, ulong p, ulong pi, GEN *pr)
1068 : {
1069 103701 : GEN q = NULL, r = FlxqX_red_pre(x, T, p, pi);
1070 103701 : long l = lgpol(r), lt = degpol(S), lm = 2*lt-1, v = varn(S);
1071 : long i;
1072 103701 : if (l <= lt)
1073 : {
1074 0 : if (pr == ONLY_REM) return r;
1075 0 : if (pr == ONLY_DIVIDES) return signe(r)? NULL: pol_0(v);
1076 0 : if (pr) *pr = r;
1077 0 : return pol_0(v);
1078 : }
1079 103701 : if (lt <= 1)
1080 0 : return FlxqX_divrem_basecase(x,S,T,p,pi,pr);
1081 103701 : if (pr != ONLY_REM && l>lm)
1082 : {
1083 764 : long vT = get_Flx_var(T);
1084 764 : q = cgetg(l-lt+2, t_POL); q[1] = S[1];
1085 56948 : for (i=0;i<l-lt;i++) gel(q+2,i) = pol0_Flx(vT);
1086 : }
1087 110672 : while (l>lm)
1088 : {
1089 6971 : GEN zr, zq = FlxqX_divrem_Barrettspec(r+2+l-lm,lm,mg,S,T,p,pi,&zr);
1090 6971 : long lz = lgpol(zr);
1091 6971 : if (pr != ONLY_REM)
1092 : {
1093 2582 : long lq = lgpol(zq);
1094 50816 : for(i=0; i<lq; i++) gel(q+2+l-lm,i) = gel(zq,2+i);
1095 : }
1096 72514 : for(i=0; i<lz; i++) gel(r+2+l-lm,i) = gel(zr,2+i);
1097 6971 : l = l-lm+lz;
1098 : }
1099 103701 : if (pr == ONLY_REM)
1100 : {
1101 102629 : if (l > lt)
1102 102629 : r = FlxqX_divrem_Barrettspec(r+2,l,mg,S,T,p,pi,ONLY_REM);
1103 : else
1104 0 : r = FlxX_renormalize(r, l+2);
1105 102629 : setvarn(r, v); return r;
1106 : }
1107 1072 : if (l > lt)
1108 : {
1109 990 : GEN zq = FlxqX_divrem_Barrettspec(r+2,l,mg,S,T,p,pi,pr? &r: NULL);
1110 990 : if (!q) q = zq;
1111 : else
1112 : {
1113 682 : long lq = lgpol(zq);
1114 6048 : for(i=0; i<lq; i++) gel(q+2,i) = gel(zq,2+i);
1115 : }
1116 : }
1117 82 : else if (pr)
1118 82 : r = FlxX_renormalize(r, l+2);
1119 1072 : setvarn(q, v); q = FlxX_renormalize(q, lg(q));
1120 1072 : if (pr == ONLY_DIVIDES) return signe(r)? NULL: q;
1121 1072 : if (pr) { setvarn(r, v); *pr = r; }
1122 1072 : return q;
1123 : }
1124 :
1125 : GEN
1126 1576374 : FlxqX_divrem_pre(GEN x, GEN S, GEN T, ulong p, long pi, GEN *pr)
1127 : {
1128 : GEN B, y;
1129 : long dy, dx, d;
1130 1576374 : if (pr==ONLY_REM) return FlxqX_rem_pre(x, S, T, p, pi);
1131 1576374 : y = get_FlxqX_red(S, &B);
1132 1576363 : dy = degpol(y); dx = degpol(x); d = dx-dy;
1133 1576323 : if (!B && d+3 < FlxqX_DIVREM_BARRETT_LIMIT)
1134 1575251 : return FlxqX_divrem_basecase(x,y,T,p,pi,pr);
1135 : else
1136 : {
1137 1072 : pari_sp av = avma;
1138 1072 : GEN mg = B? B: FlxqX_invBarrett_pre(y, T, p, pi);
1139 1072 : GEN q = FlxqX_divrem_Barrett(x,mg,y,T,p,pi,pr);
1140 1072 : if (!q) return gc_NULL(av);
1141 1072 : if (!pr || pr==ONLY_DIVIDES) return gc_GEN(av, q);
1142 799 : return gc_all(av, 2, &q, pr);
1143 : }
1144 : }
1145 : GEN
1146 1073763 : FlxqX_divrem(GEN x, GEN S, GEN T, ulong p, GEN *pr)
1147 : {
1148 1073763 : ulong pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
1149 1073763 : return FlxqX_divrem_pre(x, S, T, p, pi, pr);
1150 : }
1151 :
1152 : GEN
1153 2037479 : FlxqX_rem_pre(GEN x, GEN S, GEN T, ulong p, ulong pi)
1154 : {
1155 2037479 : GEN B, y = get_FlxqX_red(S, &B);
1156 2037481 : long dy = degpol(y), dx = degpol(x), d = dx-dy;
1157 2037477 : if (d < 0) return FlxqX_red_pre(x, T, p, pi);
1158 1689736 : if (!B && d+3 < FlxqX_REM_BARRETT_LIMIT)
1159 1587107 : return FlxqX_divrem_basecase(x,y, T, p, pi, ONLY_REM);
1160 : else
1161 : {
1162 102629 : pari_sp av=avma;
1163 102629 : GEN mg = B? B: FlxqX_invBarrett_pre(y, T, p, pi);
1164 102629 : GEN r = FlxqX_divrem_Barrett(x, mg, y, T, p, pi, ONLY_REM);
1165 102629 : return gc_upto(av, r);
1166 : }
1167 : }
1168 : GEN
1169 5949 : FlxqX_rem(GEN x, GEN S, GEN T, ulong p)
1170 5949 : { return FlxqX_rem_pre(x, S, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
1171 :
1172 : /* x + y*z mod p */
1173 : INLINE GEN
1174 103656 : Flxq_addmul_pre(GEN x, GEN y, GEN z, GEN T, ulong p, ulong pi)
1175 : {
1176 : pari_sp av;
1177 103656 : if (!lgpol(y) || !lgpol(z)) return Flx_rem_pre(x, T, p, pi);
1178 102125 : if (!lgpol(x)) return Flxq_mul_pre(z, y, T, p, pi);
1179 102021 : av = avma;
1180 102021 : return gc_upto(av, Flx_add(x, Flxq_mul_pre(y, z, T, p, pi), p));
1181 : }
1182 :
1183 : GEN
1184 51828 : FlxqX_div_by_X_x_pre(GEN a, GEN x, GEN T, ulong p, ulong pi, GEN *r)
1185 : {
1186 51828 : long l = lg(a), i;
1187 : GEN z;
1188 51828 : if (l <= 3)
1189 : {
1190 0 : if (r) *r = l == 2? pol0_Flx(get_Flx_var(T)): Flx_copy(gel(a,2));
1191 0 : return pol_0(varn(a));
1192 : }
1193 51828 : l--; z = cgetg(l, t_POL); z[1] = a[1];
1194 51828 : gel(z, l-1) = gel(a,l);
1195 155484 : for (i=l-2; i>1; i--) /* z[i] = a[i+1] + x*z[i+1] */
1196 103656 : gel(z, i) = Flxq_addmul_pre(gel(a,i+1), x, gel(z,i+1), T, p, pi);
1197 51828 : if (r) *r = Flxq_addmul_pre(gel(a,2), x, gel(z,2), T, p, pi);
1198 51828 : return z;
1199 : }
1200 :
1201 : GEN
1202 51828 : FlxqX_div_by_X_x(GEN a, GEN x, GEN T, ulong p, GEN *r)
1203 51828 : { return FlxqX_div_by_X_x_pre(a, x, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p), r); }
1204 :
1205 : static GEN
1206 13530 : FlxqX_addmulmul(GEN u, GEN v, GEN x, GEN y, GEN T, ulong p, ulong pi)
1207 : {
1208 13530 : return FlxX_add(FlxqX_mul_pre(u, x, T, p, pi),
1209 : FlxqX_mul_pre(v, y, T, p, pi), p);
1210 : }
1211 :
1212 : static GEN
1213 6626 : FlxqXM_FlxqX_mul2(GEN M, GEN x, GEN y, GEN T, ulong p, ulong pi)
1214 : {
1215 6626 : GEN res = cgetg(3, t_COL);
1216 6626 : gel(res, 1) = FlxqX_addmulmul(gcoeff(M,1,1), gcoeff(M,1,2), x, y, T, p, pi);
1217 6626 : gel(res, 2) = FlxqX_addmulmul(gcoeff(M,2,1), gcoeff(M,2,2), x, y, T, p, pi);
1218 6626 : return res;
1219 : }
1220 :
1221 : static GEN
1222 3276 : FlxqXM_mul2(GEN A, GEN B, GEN T, ulong p, ulong pi)
1223 : {
1224 3276 : GEN A11=gcoeff(A,1,1),A12=gcoeff(A,1,2), B11=gcoeff(B,1,1),B12=gcoeff(B,1,2);
1225 3276 : GEN A21=gcoeff(A,2,1),A22=gcoeff(A,2,2), B21=gcoeff(B,2,1),B22=gcoeff(B,2,2);
1226 3276 : GEN M1 = FlxqX_mul_pre(FlxX_add(A11,A22, p), FlxX_add(B11,B22, p), T, p, pi);
1227 3276 : GEN M2 = FlxqX_mul_pre(FlxX_add(A21,A22, p), B11, T, p, pi);
1228 3276 : GEN M3 = FlxqX_mul_pre(A11, FlxX_sub(B12,B22, p), T, p, pi);
1229 3276 : GEN M4 = FlxqX_mul_pre(A22, FlxX_sub(B21,B11, p), T, p, pi);
1230 3276 : GEN M5 = FlxqX_mul_pre(FlxX_add(A11,A12, p), B22, T, p, pi);
1231 3276 : GEN M6 = FlxqX_mul_pre(FlxX_sub(A21,A11, p), FlxX_add(B11,B12, p), T, p, pi);
1232 3276 : GEN M7 = FlxqX_mul_pre(FlxX_sub(A12,A22, p), FlxX_add(B21,B22, p), T, p, pi);
1233 3276 : GEN T1 = FlxX_add(M1,M4, p), T2 = FlxX_sub(M7,M5, p);
1234 3276 : GEN T3 = FlxX_sub(M1,M2, p), T4 = FlxX_add(M3,M6, p);
1235 3276 : retmkmat22(FlxX_add(T1,T2, p), FlxX_add(M3,M5, p),
1236 : FlxX_add(M2,M4, p), FlxX_add(T3,T4, p));
1237 : }
1238 :
1239 : /* Return [0,1;1,-q]*M */
1240 : static GEN
1241 3276 : FlxqX_FlxqXM_qmul(GEN q, GEN M, GEN T, ulong p, ulong pi)
1242 : {
1243 3276 : GEN u = FlxqX_mul_pre(gcoeff(M,2,1), q, T,p,pi);
1244 3276 : GEN v = FlxqX_mul_pre(gcoeff(M,2,2), q, T,p,pi);
1245 3276 : retmkmat22(gcoeff(M,2,1), gcoeff(M,2,2),
1246 : FlxX_sub(gcoeff(M,1,1), u, p), FlxX_sub(gcoeff(M,1,2), v, p));
1247 : }
1248 :
1249 : static GEN
1250 16 : matid2_FlxXM(long v, long sv)
1251 16 : { retmkmat22(pol1_FlxX(v, sv),pol_0(v),pol_0(v),pol1_FlxX(v, sv)); }
1252 :
1253 : static GEN
1254 0 : matJ2_FlxXM(long v, long sv)
1255 0 : { retmkmat22(pol_0(v),pol1_FlxX(v, sv),pol1_FlxX(v, sv),pol_0(v)); }
1256 :
1257 : struct FlxqX_res
1258 : {
1259 : GEN res, lc;
1260 : long deg0, deg1, off;
1261 : };
1262 :
1263 : INLINE void
1264 0 : FlxqX_halfres_update(long da, long db, long dr, GEN T, ulong p, ulong pi, struct FlxqX_res *res)
1265 : {
1266 0 : if (dr >= 0)
1267 : {
1268 0 : if (!Flx_equal1(res->lc))
1269 : {
1270 0 : res->lc = Flxq_powu_pre(res->lc, da - dr, T, p, pi);
1271 0 : res->res = Flxq_mul_pre(res->res, res->lc, T, p, pi);
1272 : }
1273 0 : if (both_odd(da + res->off, db + res->off))
1274 0 : res->res = Flx_neg(res->res, p);
1275 : } else
1276 : {
1277 0 : if (db == 0)
1278 : {
1279 0 : if (!Flx_equal1(res->lc))
1280 : {
1281 0 : res->lc = Flxq_powu_pre(res->lc, da, T, p, pi);
1282 0 : res->res = Flxq_mul_pre(res->res, res->lc, T, p, pi);
1283 : }
1284 : } else
1285 0 : res->res = pol0_Flx(get_Flx_var(T));
1286 : }
1287 0 : }
1288 :
1289 : static GEN
1290 4035 : FlxqX_halfres_basecase(GEN a, GEN b, GEN T, ulong p, ulong pi, GEN *pa, GEN *pb, struct FlxqX_res *res)
1291 : {
1292 4035 : pari_sp av=avma;
1293 : GEN u,u1,v,v1, M;
1294 4035 : long vx = varn(a), vT = get_Flx_var(T), n = lgpol(a)>>1;
1295 4035 : u1 = v = pol_0(vx);
1296 4035 : u = v1 = pol1_FlxX(vx, vT);
1297 22321 : while (lgpol(b)>n)
1298 : {
1299 : GEN r, q;
1300 18286 : q = FlxqX_divrem(a,b, T, p, &r);
1301 18286 : if (res)
1302 : {
1303 0 : long da = degpol(a), db = degpol(b), dr = degpol(r);
1304 0 : res->lc = gel(b,db+2);
1305 0 : if (dr >= n)
1306 0 : FlxqX_halfres_update(da, db, dr, T, p, pi, res);
1307 : else
1308 : {
1309 0 : res->deg0 = da;
1310 0 : res->deg1 = db;
1311 : }
1312 : }
1313 18286 : a = b; b = r; swap(u,u1); swap(v,v1);
1314 18286 : u1 = FlxX_sub(u1, FlxqX_mul_pre(u, q, T, p, pi), p);
1315 18286 : v1 = FlxX_sub(v1, FlxqX_mul_pre(v, q, T, p, pi), p);
1316 18286 : if (gc_needed(av,2))
1317 : {
1318 0 : if (DEBUGMEM>1) pari_warn(warnmem,"FlxqX_halfgcd (d = %ld)",degpol(b));
1319 0 : if (res)
1320 0 : (void)gc_all(av, 8, &a,&b,&u1,&v1,&u,&v,&res->res,&res->lc);
1321 : else
1322 0 : (void)gc_all(av, 6, &a,&b,&u1,&v1,&u,&v);
1323 : }
1324 : }
1325 4035 : M = mkmat22(u,v,u1,v1); *pa = a; *pb = b;
1326 0 : return res ? gc_all(av, 5, &M, pa, pb, &res->res, &res->lc)
1327 4035 : : gc_all(av, 3, &M, pa, pb);
1328 : }
1329 :
1330 : static GEN FlxqX_halfres_i(GEN x, GEN y, GEN T, ulong p, ulong pi, GEN *a, GEN *b, struct FlxqX_res *res);
1331 :
1332 : static GEN
1333 3366 : FlxqX_halfres_split(GEN x, GEN y, GEN T, ulong p, ulong pi, GEN *a, GEN *b, struct FlxqX_res *res)
1334 : {
1335 3366 : pari_sp av = avma;
1336 : GEN Q, R, S, V1, V2;
1337 : GEN x1, y1, r, q;
1338 3366 : long l = lgpol(x), n = l>>1, k, vT = get_Flx_var(T);
1339 3366 : if (lgpol(y) <= n)
1340 16 : { *a = RgX_copy(x); *b = RgX_copy(y); return matid2_FlxXM(varn(x), vT); }
1341 3350 : if (res)
1342 : {
1343 0 : res->lc = leading_coeff(y);
1344 0 : res->deg0 -= n;
1345 0 : res->deg1 -= n;
1346 0 : res->off += n;
1347 : }
1348 3350 : R = FlxqX_halfres_i(FlxX_shift(x,-n, vT),FlxX_shift(y,-n, vT), T, p, pi, a, b, res);
1349 3350 : if (res)
1350 : {
1351 0 : res->off -= n;
1352 0 : res->deg0 += n;
1353 0 : res->deg1 += n;
1354 : }
1355 3350 : V1 = FlxqXM_FlxqX_mul2(R, Flxn_red(x,n), Flxn_red(y,n), T, p, pi);
1356 3350 : x1 = FlxX_add(FlxX_shift(*a,n,vT), gel(V1,1), p);
1357 3350 : y1 = FlxX_add(FlxX_shift(*b,n,vT), gel(V1,2), p);
1358 3350 : if (lgpol(y1) <= n)
1359 : {
1360 74 : *a = x1; *b = y1;
1361 0 : return res ? gc_all(av, 5, &R, a, b, &res->res, &res->lc)
1362 74 : : gc_all(av, 3, &R, a, b);
1363 : }
1364 3276 : k = 2*n-degpol(y1);
1365 3276 : q = FlxqX_divrem(x1, y1, T, p, &r);
1366 3276 : if (res)
1367 : {
1368 0 : long dx1 = degpol(x1), dy1 = degpol(y1), dr = degpol(r);
1369 0 : if (dy1 < degpol(y))
1370 0 : FlxqX_halfres_update(res->deg0, res->deg1, dy1, T, p, pi, res);
1371 0 : res->lc = leading_coeff(y1);
1372 0 : res->deg0 = dx1;
1373 0 : res->deg1 = dy1;
1374 0 : if (dr >= n)
1375 : {
1376 0 : FlxqX_halfres_update(dx1, dy1, dr, T, p, pi, res);
1377 0 : res->deg0 = dy1;
1378 0 : res->deg1 = dr;
1379 : }
1380 0 : res->deg0 -= k;
1381 0 : res->deg1 -= k;
1382 0 : res->off += k;
1383 : }
1384 3276 : S = FlxqX_halfres_i(FlxX_shift(y1,-k, vT), FlxX_shift(r,-k, vT), T, p, pi, a, b, res);
1385 3276 : if (res)
1386 : {
1387 0 : res->deg0 += k;
1388 0 : res->deg1 += k;
1389 0 : res->off -= k;
1390 : }
1391 3276 : Q = FlxqXM_mul2(S, FlxqX_FlxqXM_qmul(q, R, T, p, pi), T, p, pi);
1392 3276 : V2 = FlxqXM_FlxqX_mul2(S, FlxXn_red(y1,k), FlxXn_red(r,k), T, p, pi);
1393 3276 : *a = FlxX_add(FlxX_shift(*a,k,vT), gel(V2,1), p);
1394 3276 : *b = FlxX_add(FlxX_shift(*b,k,vT), gel(V2,2), p);
1395 0 : return res ? gc_all(av, 5, &Q, a, b, &res->res, &res->lc)
1396 3276 : : gc_all(av, 3, &Q, a, b);
1397 : }
1398 :
1399 : static GEN
1400 7401 : FlxqX_halfres_i(GEN x, GEN y, GEN T, ulong p, ulong pi, GEN *a, GEN *b, struct FlxqX_res *res)
1401 : {
1402 7401 : if (lgpol(x) < FlxqX_HALFGCD_LIMIT)
1403 4035 : return FlxqX_halfres_basecase(x, y, T, p, pi, a, b, res);
1404 3366 : return FlxqX_halfres_split(x, y, T, p, pi, a, b, res);
1405 : }
1406 :
1407 : static GEN
1408 775 : FlxqX_halfgcd_all_i(GEN x, GEN y, GEN T, ulong p, ulong pi, GEN *pa, GEN *pb)
1409 : {
1410 : GEN a, b;
1411 775 : GEN R = FlxqX_halfres_i(x, y, T, p, pi, &a, &b, NULL);
1412 775 : if (pa) *pa = a;
1413 775 : if (pb) *pb = b;
1414 775 : return R;
1415 : }
1416 :
1417 : /* Return M in GL_2(Fp[X]/(T)[Y]) such that:
1418 : if [a',b']~=M*[a,b]~ then degpol(a')>= (lgpol(a)>>1) >degpol(b')
1419 : */
1420 :
1421 : GEN
1422 775 : FlxqX_halfgcd_all_pre(GEN x, GEN y, GEN T, ulong p, ulong pi, GEN *a, GEN *b)
1423 : {
1424 775 : pari_sp av = avma;
1425 : GEN R,q,r;
1426 775 : if (!signe(x))
1427 : {
1428 0 : if (a) *a = RgX_copy(y);
1429 0 : if (b) *b = RgX_copy(x);
1430 0 : return matJ2_FlxXM(varn(x),get_Flx_var(T));
1431 : }
1432 775 : if (degpol(y)<degpol(x)) return FlxqX_halfgcd_all_i(x, y, T, p, pi, a, b);
1433 180 : q = FlxqX_divrem_pre(y, x, T, p, pi, &r);
1434 180 : R = FlxqX_halfgcd_all_i(x, r, T, p, pi, a, b);
1435 180 : gcoeff(R,1,1) = FlxX_sub(gcoeff(R,1,1),
1436 180 : FlxqX_mul_pre(q, gcoeff(R,1,2), T, p, pi), p);
1437 180 : gcoeff(R,2,1) = FlxX_sub(gcoeff(R,2,1),
1438 180 : FlxqX_mul_pre(q, gcoeff(R,2,2), T, p, pi), p);
1439 180 : return !a && b ? gc_all(av, 2, &R, b): gc_all(av, 1+!!a+!!b, &R, a, b);
1440 : }
1441 : GEN
1442 7 : FlxqX_halfgcd_all(GEN x, GEN y, GEN T, ulong p, GEN *a, GEN *b)
1443 7 : { return FlxqX_halfgcd_all_pre(x, y, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p), a, b); }
1444 :
1445 : GEN
1446 253 : FlxqX_halfgcd_pre(GEN x, GEN y, GEN T, ulong p, ulong pi)
1447 253 : { return FlxqX_halfgcd_all_pre(x, y, T, p, pi, NULL, NULL); }
1448 :
1449 : GEN
1450 0 : FlxqX_halfgcd(GEN x, GEN y, GEN T, ulong p)
1451 0 : { return FlxqX_halfgcd_pre(x, y, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
1452 :
1453 : static GEN
1454 166770 : FlxqX_gcd_basecase(GEN a, GEN b, GEN T, ulong p, ulong pi)
1455 : {
1456 166770 : pari_sp av = avma, av0=avma;
1457 1076592 : while (signe(b))
1458 : {
1459 : GEN c;
1460 909822 : if (gc_needed(av0,2))
1461 : {
1462 0 : if (DEBUGMEM>1) pari_warn(warnmem,"FlxqX_gcd (d = %ld)",degpol(b));
1463 0 : (void)gc_all(av0,2, &a,&b);
1464 : }
1465 909822 : av = avma; c = FlxqX_rem_pre(a, b, T, p, pi); a=b; b=c;
1466 : }
1467 166770 : return gc_const(av, a);
1468 : }
1469 :
1470 : GEN
1471 175808 : FlxqX_gcd_pre(GEN x, GEN y, GEN T, ulong p, ulong pi)
1472 : {
1473 175808 : pari_sp av = avma;
1474 175808 : x = FlxqX_red_pre(x, T, p, pi);
1475 175808 : y = FlxqX_red_pre(y, T, p, pi);
1476 175808 : if (!signe(x)) return gc_upto(av, y);
1477 167146 : while (lgpol(y)>=FlxqX_GCD_LIMIT)
1478 : {
1479 376 : if (lgpol(y)<=(lgpol(x)>>1))
1480 : {
1481 0 : GEN r = FlxqX_rem_pre(x, y, T, p, pi);
1482 0 : x = y; y = r;
1483 : }
1484 376 : (void) FlxqX_halfgcd_all_pre(x,y, T, p, pi, &x, &y);
1485 376 : if (gc_needed(av,2))
1486 : {
1487 0 : if (DEBUGMEM>1) pari_warn(warnmem,"FlxqX_gcd (y = %ld)",degpol(y));
1488 0 : (void)gc_all(av,2,&x,&y);
1489 : }
1490 : }
1491 166770 : return gc_upto(av, FlxqX_gcd_basecase(x, y, T, p, pi));
1492 : }
1493 : GEN
1494 23458 : FlxqX_gcd(GEN x, GEN y, GEN T, ulong p)
1495 23458 : { return FlxqX_gcd_pre(x, y, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
1496 :
1497 : static GEN
1498 133829 : FlxqX_extgcd_basecase(GEN a, GEN b, GEN T, ulong p,ulong pi, GEN *ptu, GEN *ptv)
1499 : {
1500 133829 : pari_sp av=avma;
1501 : GEN u,v,d,d1,v1;
1502 133829 : long vx = varn(a);
1503 133829 : d = a; d1 = b;
1504 133829 : v = pol_0(vx); v1 = pol1_FlxX(vx, get_Flx_var(T));
1505 470920 : while (signe(d1))
1506 : {
1507 337095 : GEN r, q = FlxqX_divrem_pre(d, d1, T, p, pi, &r);
1508 337102 : v = FlxX_sub(v, FlxqX_mul_pre(q,v1,T, p, pi),p);
1509 337088 : u=v; v=v1; v1=u;
1510 337088 : u=r; d=d1; d1=u;
1511 337088 : if (gc_needed(av,2))
1512 : {
1513 0 : if (DEBUGMEM>1) pari_warn(warnmem,"FlxqX_extgcd (d = %ld)",degpol(d));
1514 0 : (void)gc_all(av,5, &d,&d1,&u,&v,&v1);
1515 : }
1516 : }
1517 133825 : if (ptu)
1518 133812 : *ptu = FlxqX_div_pre(FlxX_sub(d,FlxqX_mul_pre(b,v, T,p,pi), p), a, T,p,pi);
1519 133826 : *ptv = v; return d;
1520 : }
1521 :
1522 : static GEN
1523 130 : FlxqX_extgcd_halfgcd(GEN x, GEN y, GEN T, ulong p, ulong pi, GEN *ptu, GEN *ptv)
1524 : {
1525 : GEN u,v;
1526 130 : GEN V = cgetg(expu(lgpol(y))+2,t_VEC);
1527 130 : long i, n = 0, vs = varn(x), vT = get_Flx_var(T);
1528 269 : while (lgpol(y) >= FlxqX_EXTGCD_LIMIT)
1529 : {
1530 139 : if (lgpol(y)<=(lgpol(x)>>1))
1531 : {
1532 0 : GEN r, q = FlxqX_divrem_pre(x, y, T, p, pi, &r);
1533 0 : x = y; y = r;
1534 0 : gel(V,++n) = mkmat22(pol_0(vs),pol1_FlxX(vs,vT),pol1_FlxX(vs,vT),FlxX_neg(q,p));
1535 : } else
1536 139 : gel(V,++n) = FlxqX_halfgcd_all_pre(x, y, T, p, pi, &x, &y);
1537 : }
1538 130 : y = FlxqX_extgcd_basecase(x,y, T, p, pi, &u,&v);
1539 139 : for (i = n; i>1; i--)
1540 : {
1541 9 : GEN R = gel(V,i);
1542 9 : GEN u1 = FlxqX_addmulmul(u, v, gcoeff(R,1,1), gcoeff(R,2,1), T, p, pi);
1543 9 : GEN v1 = FlxqX_addmulmul(u, v, gcoeff(R,1,2), gcoeff(R,2,2), T, p, pi);
1544 9 : u = u1; v = v1;
1545 : }
1546 : {
1547 130 : GEN R = gel(V,1);
1548 130 : if (ptu)
1549 130 : *ptu = FlxqX_addmulmul(u, v, gcoeff(R,1,1), gcoeff(R,2,1), T, p, pi);
1550 130 : *ptv = FlxqX_addmulmul(u, v, gcoeff(R,1,2), gcoeff(R,2,2), T, p, pi);
1551 : }
1552 130 : return y;
1553 : }
1554 :
1555 : /* x and y in Z[Y][X], return lift(gcd(x mod T,p, y mod T,p)). Set u and v st
1556 : * ux + vy = gcd (mod T,p) */
1557 : GEN
1558 133827 : FlxqX_extgcd_pre(GEN x, GEN y, GEN T, ulong p, ulong pi, GEN *ptu, GEN *ptv)
1559 : {
1560 133827 : pari_sp av = avma;
1561 : GEN d;
1562 133827 : x = FlxqX_red_pre(x, T, p, pi);
1563 133826 : y = FlxqX_red_pre(y, T, p, pi);
1564 133828 : if (lgpol(y)>=FlxqX_EXTGCD_LIMIT)
1565 130 : d = FlxqX_extgcd_halfgcd(x, y, T, p, pi, ptu, ptv);
1566 : else
1567 133698 : d = FlxqX_extgcd_basecase(x, y, T, p, pi, ptu, ptv);
1568 133826 : return gc_all(av, ptu?3:2, &d, ptv, ptu);
1569 : }
1570 : GEN
1571 133813 : FlxqX_extgcd(GEN x, GEN y, GEN T, ulong p, GEN *ptu, GEN *ptv)
1572 : {
1573 133813 : ulong pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
1574 133813 : return FlxqX_extgcd_pre(x, y, T, p, pi, ptu, ptv);
1575 : }
1576 :
1577 : static GEN
1578 378263 : FlxqX_saferem(GEN P, GEN Q, GEN T, ulong p, ulong pi)
1579 : {
1580 378263 : GEN U = Flxq_invsafe_pre(leading_coeff(Q), T, p, pi);
1581 378260 : if (!U) return NULL;
1582 378260 : Q = FlxqX_Flxq_mul_to_monic_pre(Q,U,T,p,pi);
1583 378273 : return FlxqX_rem_pre(P,Q,T,p,pi);
1584 : }
1585 :
1586 : GEN
1587 0 : FlxqX_eval(GEN x, GEN y, GEN T, ulong p)
1588 : {
1589 : pari_sp av;
1590 : GEN p1, r;
1591 0 : long j, i=lg(x)-1;
1592 0 : if (i<=2)
1593 0 : return (i==2)? gcopy(gel(x,2)): pol0_Flx(get_Flx_var(T));
1594 0 : av=avma; p1=gel(x,i);
1595 : /* specific attention to sparse polynomials (see poleval)*/
1596 : /*You've guessed it! It's a copy-paste(tm)*/
1597 0 : for (i--; i>=2; i=j-1)
1598 : {
1599 0 : for (j=i; lg(gel(x,j))==1; j--)
1600 0 : if (j==2)
1601 : {
1602 0 : if (i!=j) y = Flxq_powu(y, i-j+1, T, p);
1603 0 : return gc_upto(av, Flxq_mul(p1,y, T, p));
1604 : }
1605 0 : r = (i==j)? y: Flxq_powu(y, i-j+1, T, p);
1606 0 : p1 = Flx_add(Flxq_mul(p1,r,T,p), gel(x,j), p);
1607 : }
1608 0 : return gc_upto(av, p1);
1609 : }
1610 :
1611 : GEN
1612 95876 : FlxqX_safegcd(GEN P, GEN Q, GEN T, ulong p)
1613 : {
1614 95876 : pari_sp av = avma;
1615 : ulong pi;
1616 : GEN U;
1617 95876 : if (!signe(P)) return gcopy(Q);
1618 95876 : if (!signe(Q)) return gcopy(P);
1619 95876 : pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
1620 95876 : T = Flx_get_red_pre(T,p,pi);
1621 : for(;;)
1622 : {
1623 324261 : P = FlxqX_saferem(P,Q,T,p,pi);
1624 324262 : if (!P) return gc_NULL(av);
1625 324262 : if (!signe(P)) break;
1626 228385 : if (gc_needed(av, 1))
1627 : {
1628 0 : if (DEBUGMEM>1) pari_warn(warnmem,"FlxqX_safegcd");
1629 0 : (void)gc_all(av, 2, &P,&Q);
1630 : }
1631 228385 : swap(P, Q);
1632 : }
1633 95877 : U = Flxq_invsafe_pre(leading_coeff(Q), T, p, pi);
1634 95877 : if (!U) return gc_NULL(av);
1635 95877 : Q = FlxqX_Flxq_mul_to_monic_pre(Q,U,T,p,pi);
1636 95877 : return gc_upto(av, Q);
1637 : }
1638 :
1639 : /* Res(A,B) = Res(B,R) * lc(B)^(a-r) * (-1)^(ab), with R=A%B, a=deg(A) ...*/
1640 : GEN
1641 11010 : FlxqX_saferesultant(GEN a, GEN b, GEN T, ulong p)
1642 : {
1643 11010 : long vT = get_Flx_var(T), da,db,dc;
1644 : ulong pi;
1645 : pari_sp av;
1646 11010 : GEN c,lb, res = pol1_Flx(vT);
1647 :
1648 11010 : if (!signe(a) || !signe(b)) return pol0_Flx(vT);
1649 :
1650 11010 : da = degpol(a);
1651 11010 : db = degpol(b);
1652 11010 : if (db > da)
1653 : {
1654 0 : swapspec(a,b, da,db);
1655 0 : if (both_odd(da,db)) res = Flx_neg(res, p);
1656 : }
1657 11010 : if (!da) return pol1_Flx(vT); /* = res * a[2] ^ db, since 0 <= db <= da = 0 */
1658 11010 : pi = SMALL_ULONG(p)? 0: get_Fl_red(p); av = avma;
1659 64981 : while (db)
1660 : {
1661 54000 : lb = gel(b,db+2);
1662 54000 : c = FlxqX_saferem(a,b, T,p,pi);
1663 54046 : if (!c) return gc_NULL(av);
1664 54046 : a = b; b = c; dc = degpol(c);
1665 54046 : if (dc < 0) { set_avma(av); return pol0_Flx(vT); }
1666 :
1667 54032 : if (both_odd(da,db)) res = Flx_neg(res, p);
1668 54030 : if (!Flx_equal1(lb))
1669 53966 : res = Flxq_mul_pre(res, Flxq_powu_pre(lb, da - dc, T, p, pi), T, p, pi);
1670 53971 : if (gc_needed(av,2))
1671 : {
1672 0 : if (DEBUGMEM>1) pari_warn(warnmem,"FlxqX_resultant (da = %ld)",da);
1673 0 : (void)gc_all(av,3, &a,&b,&res);
1674 : }
1675 53971 : da = db; /* = degpol(a) */
1676 53971 : db = dc; /* = degpol(b) */
1677 : }
1678 10981 : res = Flxq_mul_pre(res, Flxq_powu_pre(gel(b,2), da, T, p, pi), T, p, pi);
1679 10992 : return gc_upto(av, res);
1680 : }
1681 :
1682 : static GEN
1683 0 : FlxqX_halfres(GEN x, GEN y, GEN T, ulong p, ulong pi, GEN *a, GEN *b, GEN *r)
1684 : {
1685 : struct FlxqX_res res;
1686 : GEN V;
1687 : long dB;
1688 :
1689 0 : res.res = *r;
1690 0 : res.lc = leading_coeff(y);
1691 0 : res.deg0 = degpol(x);
1692 0 : res.deg1 = degpol(y);
1693 0 : res.off = 0;
1694 0 : V = FlxqX_halfres_i(x, y, T, p, pi, a, b, &res);
1695 0 : dB = degpol(*b);
1696 0 : if (dB < degpol(y))
1697 0 : FlxqX_halfres_update(res.deg0, res.deg1, dB, T, p, pi, &res);
1698 0 : *r = res.res;
1699 0 : return V;
1700 : }
1701 :
1702 : static GEN
1703 56 : FlxqX_resultant_basecase(GEN a, GEN b, GEN T, ulong p, ulong pi)
1704 : {
1705 56 : pari_sp av = avma;
1706 56 : long vT = get_Flx_var(T), da,db,dc;
1707 56 : GEN c,lb, res = pol1_Flx(vT);
1708 :
1709 56 : if (!signe(a) || !signe(b)) return pol0_Flx(vT);
1710 :
1711 56 : da = degpol(a);
1712 56 : db = degpol(b);
1713 56 : if (db > da)
1714 : {
1715 0 : swapspec(a,b, da,db);
1716 0 : if (both_odd(da,db)) res = Flx_neg(res, p);
1717 : }
1718 56 : if (!da) return pol1_Flx(vT); /* = res * a[2] ^ db, since 0 <= db <= da = 0 */
1719 147 : while (db)
1720 : {
1721 91 : lb = gel(b,db+2);
1722 91 : c = FlxqX_rem_pre(a,b, T,p,pi);
1723 91 : a = b; b = c; dc = degpol(c);
1724 91 : if (dc < 0) { set_avma(av); return pol0_Flx(vT); }
1725 :
1726 91 : if (both_odd(da,db)) res = Flx_neg(res, p);
1727 91 : if (!Flx_equal1(lb))
1728 63 : res = Flxq_mul_pre(res, Flxq_powu_pre(lb, da - dc, T,p,pi), T,p,pi);
1729 91 : if (gc_needed(av,2))
1730 : {
1731 0 : if (DEBUGMEM>1) pari_warn(warnmem,"FlxqX_resultant (da = %ld)",da);
1732 0 : (void)gc_all(av,3, &a,&b,&res);
1733 : }
1734 91 : da = db; /* = degpol(a) */
1735 91 : db = dc; /* = degpol(b) */
1736 : }
1737 56 : res = Flxq_mul_pre(res, Flxq_powu_pre(gel(b,2), da, T,p,pi), T,p,pi);
1738 56 : return gc_upto(av, res);
1739 : }
1740 :
1741 : /* Res(A,B) = Res(B,R) * lc(B)^(a-r) * (-1)^(ab), with R=A%B, a=deg(A) ...*/
1742 : GEN
1743 56 : FlxqX_resultant_pre(GEN x, GEN y, GEN T, ulong p, ulong pi)
1744 : {
1745 56 : pari_sp av = avma;
1746 56 : long dx, dy, vT = get_Flx_var(T);
1747 56 : GEN res = pol1_Flx(vT);
1748 56 : if (!signe(x) || !signe(y)) return pol0_Flx(vT);
1749 56 : dx = degpol(x); dy = degpol(y);
1750 56 : if (dx < dy)
1751 : {
1752 21 : swap(x,y);
1753 21 : if (both_odd(dx, dy))
1754 0 : res = Flx_neg(res, p);
1755 : }
1756 56 : while (lgpol(y) >= FlxqX_GCD_LIMIT)
1757 : {
1758 0 : if (lgpol(y)<=(lgpol(x)>>1))
1759 : {
1760 0 : GEN r = FlxqX_rem_pre(x, y, T, p, pi);
1761 0 : long dx = degpol(x), dy = degpol(y), dr = degpol(r);
1762 0 : GEN ly = gel(y,dy+2);
1763 0 : if (!Flx_equal1(ly))
1764 0 : res = Flxq_mul_pre(res, Flxq_powu_pre(ly, dx - dr, T, p, pi), T, p, pi);
1765 0 : if (both_odd(dx, dy))
1766 0 : res = Flx_neg(res, p);
1767 0 : x = y; y = r;
1768 : }
1769 0 : (void) FlxqX_halfres(x, y, T, p, pi, &x, &y, &res);
1770 0 : if (gc_needed(av,2))
1771 : {
1772 0 : if (DEBUGMEM>1) pari_warn(warnmem,"FlxqX_resultant (y = %ld)",degpol(y));
1773 0 : (void)gc_all(av,3,&x,&y,&res);
1774 : }
1775 : }
1776 56 : res = Flxq_mul_pre(res, FlxqX_resultant_basecase(x, y, T, p, pi), T, p, pi);
1777 56 : return gc_upto(av, res);
1778 : }
1779 : GEN
1780 56 : FlxqX_resultant(GEN x, GEN y, GEN T, ulong p)
1781 56 : { return FlxqX_resultant_pre(x, y, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
1782 :
1783 : /* disc P = (-1)^(n(n-1)/2) lc(P)^(n - deg P' - 2) Res(P,P'), n = deg P */
1784 : GEN
1785 14 : FlxqX_disc(GEN P, GEN T, ulong p)
1786 : {
1787 14 : pari_sp av = avma;
1788 14 : GEN L, dP = FlxX_deriv(P, p), D = FlxqX_resultant(P, dP, T, p);
1789 : long dd;
1790 14 : if (!lgpol(D)) return pol0_Flx(get_Flx_var(T));
1791 14 : dd = degpol(P) - 2 - degpol(dP); /* >= -1; > -1 iff p | deg(P) */
1792 14 : L = leading_coeff(P);
1793 14 : if (dd && !Flx_equal1(L))
1794 : {
1795 0 : ulong pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
1796 0 : D = (dd == -1)? Flxq_div_pre(D,L,T,p,pi)
1797 0 : : Flxq_mul_pre(D, Flxq_powu_pre(L, dd, T,p,pi), T,p,pi); }
1798 14 : if (degpol(P) & 2) D = Flx_neg(D, p);
1799 14 : return gc_upto(av, D);
1800 : }
1801 :
1802 : INLINE GEN
1803 6080 : FlxXn_recip(GEN x, long n, long v)
1804 6080 : { return FlxX_recipspec(x+2, minss(lgpol(x), n), n, v); }
1805 :
1806 : GEN
1807 2432 : FlxqX_Newton_pre(GEN P, long n, GEN T, ulong p, ulong pi)
1808 : {
1809 2432 : pari_sp av = avma;
1810 2432 : long d = degpol(P), vT = get_Flx_var(T);
1811 2432 : GEN dP = FlxXn_recip(FlxX_deriv(P, p), d, vT);
1812 2432 : GEN Q = FlxqXn_mul_pre(FlxqXn_inv_pre(FlxXn_recip(P, d+1, vT), n, T,p,pi),
1813 : dP, n, T, p, pi);
1814 2432 : return gc_GEN(av, Q);
1815 : }
1816 : GEN
1817 0 : FlxqX_Newton(GEN P, long n, GEN T, ulong p)
1818 0 : { return FlxqX_Newton_pre(P, n, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
1819 :
1820 : GEN
1821 1216 : FlxqX_fromNewton_pre(GEN P, GEN T, ulong p, ulong pi)
1822 : {
1823 1216 : pari_sp av = avma;
1824 1216 : long vT = get_Flx_var(T);
1825 1216 : long n = Flx_constant(constant_coeff(P))+1;
1826 1216 : GEN z = FlxX_neg(FlxX_shift(P, -1, vT), p);
1827 1216 : GEN Q = FlxXn_recip(FlxqXn_expint_pre(z, n, T, p, pi), n, vT);
1828 1216 : return gc_GEN(av, Q);
1829 : }
1830 : GEN
1831 0 : FlxqX_fromNewton(GEN P, GEN T, ulong p)
1832 0 : { return FlxqX_fromNewton_pre(P, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
1833 :
1834 : GEN
1835 1216 : FlxqX_composedsum(GEN P, GEN Q, GEN T, ulong p)
1836 : {
1837 1216 : pari_sp av = avma;
1838 1216 : ulong pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
1839 1216 : long n = 1+ degpol(P)*degpol(Q);
1840 1216 : GEN Pl = FlxX_invLaplace(FlxqX_Newton_pre(P,n, T,p,pi), p);
1841 1216 : GEN Ql = FlxX_invLaplace(FlxqX_Newton_pre(Q,n, T,p,pi), p);
1842 1216 : GEN L = FlxX_Laplace(FlxqXn_mul_pre(Pl, Ql, n, T,p,pi), p);
1843 1216 : GEN R = FlxqX_fromNewton_pre(L, T, p, pi);
1844 1216 : GEN lead = Flxq_mul_pre(Flxq_powu_pre(leading_coeff(P),degpol(Q), T,p,pi),
1845 1216 : Flxq_powu_pre(leading_coeff(Q),degpol(P), T,p,pi),
1846 : T, p, pi);
1847 1216 : return gc_upto(av, FlxqX_Flxq_mul_pre(R, lead, T, p, pi));
1848 : }
1849 :
1850 : GEN
1851 223093 : FlxqXV_prod(GEN V, GEN T, ulong p)
1852 : {
1853 223093 : struct _FlxqXQ d; d.p=p; d.T=T; d.pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
1854 223093 : return gen_product(V, (void*)&d, &_FlxqX_mul);
1855 : }
1856 :
1857 : static GEN
1858 32151 : FlxqV_roots_to_deg1(GEN x, GEN T, ulong p, long v)
1859 : {
1860 32151 : long sv = get_Flx_var(T);
1861 124249 : pari_APPLY_same(deg1pol_shallow(pol1_Flx(sv),Flx_neg(gel(x,i),p),v))
1862 : }
1863 :
1864 : GEN
1865 32151 : FlxqV_roots_to_pol(GEN V, GEN T, ulong p, long v)
1866 : {
1867 32151 : pari_sp ltop = avma;
1868 32151 : GEN W = FlxqV_roots_to_deg1(V, T, p, v);
1869 32151 : return gc_upto(ltop, FlxqXV_prod(W, T, p));
1870 : }
1871 :
1872 : /*******************************************************************/
1873 : /* */
1874 : /* (Fl[X]/T(X))[Y] / S(Y) */
1875 : /* */
1876 : /*******************************************************************/
1877 :
1878 : GEN
1879 470985 : FlxqXQ_mul_pre(GEN x, GEN y, GEN S, GEN T, ulong p, ulong pi)
1880 470985 : { return FlxqX_rem_pre(FlxqX_mul_pre(x,y,T,p,pi),S,T,p,pi); }
1881 : GEN
1882 1947 : FlxqXQ_mul(GEN x, GEN y, GEN S, GEN T, ulong p)
1883 1947 : { return FlxqXQ_mul_pre(x, y, S, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
1884 :
1885 : GEN
1886 261973 : FlxqXQ_sqr_pre(GEN x, GEN S, GEN T, ulong p, ulong pi)
1887 261973 : { return FlxqX_rem_pre(FlxqX_sqr_pre(x,T,p,pi),S,T,p,pi); }
1888 : GEN
1889 0 : FlxqXQ_sqr(GEN x, GEN S, GEN T, ulong p)
1890 0 : { return FlxqXQ_sqr_pre(x, S, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
1891 :
1892 : GEN
1893 14 : FlxqXQ_invsafe_pre(GEN x, GEN S, GEN T, ulong p, ulong pi)
1894 : {
1895 14 : GEN V, z = FlxqX_extgcd_pre(get_FlxqX_mod(S), x, T, p, pi, NULL, &V);
1896 14 : if (degpol(z)) return NULL;
1897 14 : z = Flxq_invsafe_pre(gel(z,2),T,p,pi);
1898 14 : if (!z) return NULL;
1899 14 : return FlxqX_Flxq_mul_pre(V, z, T, p, pi);
1900 : }
1901 : GEN
1902 0 : FlxqXQ_invsafe(GEN x, GEN S, GEN T, ulong p)
1903 0 : { return FlxqXQ_invsafe_pre(x, S, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
1904 :
1905 : GEN
1906 14 : FlxqXQ_inv_pre(GEN x, GEN S, GEN T, ulong p, ulong pi)
1907 : {
1908 14 : pari_sp av = avma;
1909 14 : GEN U = FlxqXQ_invsafe_pre(x, S, T, p, pi);
1910 14 : if (!U) pari_err_INV("FlxqXQ_inv",x);
1911 14 : return gc_upto(av, U);
1912 : }
1913 : GEN
1914 14 : FlxqXQ_inv(GEN x, GEN S, GEN T,ulong p)
1915 14 : { return FlxqXQ_inv_pre(x, S, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
1916 :
1917 : GEN
1918 0 : FlxqXQ_div_pre(GEN x, GEN y, GEN S, GEN T, ulong p, ulong pi)
1919 0 : { return FlxqXQ_mul_pre(x, FlxqXQ_inv_pre(y,S,T,p,pi),S,T,p,pi); }
1920 : GEN
1921 0 : FlxqXQ_div(GEN x, GEN y, GEN S, GEN T, ulong p)
1922 0 : { return FlxqXQ_div_pre(x, y, S, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
1923 :
1924 : static GEN
1925 0 : _FlxqX_add(void *data, GEN x, GEN y) {
1926 0 : struct _FlxqXQ *d = (struct _FlxqXQ*) data;
1927 0 : return FlxX_add(x,y, d->p);
1928 : }
1929 : static GEN
1930 5526 : _FlxqX_sub(void *data, GEN x, GEN y) {
1931 5526 : struct _FlxqXQ *d = (struct _FlxqXQ*) data;
1932 5526 : return FlxX_sub(x,y, d->p);
1933 : }
1934 : #if 0
1935 : static GEN
1936 : _FlxqXQ_cmul(void *data, GEN P, long a, GEN x) {
1937 : struct _FlxqXQ *d = (struct _FlxqXQ*) data;
1938 : return FlxY_Flx_mul_pre(x,gel(P,a+2), d->p, d->pi);
1939 : }
1940 : #endif
1941 : static GEN
1942 6044 : _FlxqXQ_red(void *data, GEN x) {
1943 6044 : struct _FlxqXQ *d = (struct _FlxqXQ*) data;
1944 6044 : return FlxqX_red_pre(x, d->T, d->p, d->pi);
1945 : }
1946 : static GEN
1947 179118 : _FlxqXQ_mul(void *data, GEN x, GEN y) {
1948 179118 : struct _FlxqXQ *d = (struct _FlxqXQ*) data;
1949 179118 : return FlxqXQ_mul_pre(x,y, d->S,d->T, d->p, d->pi);
1950 : }
1951 : static GEN
1952 261525 : _FlxqXQ_sqr(void *data, GEN x) {
1953 261525 : struct _FlxqXQ *d = (struct _FlxqXQ*) data;
1954 261525 : return FlxqXQ_sqr_pre(x, d->S,d->T, d->p, d->pi);
1955 : }
1956 :
1957 : static GEN
1958 111276 : _FlxqXQ_one(void *data) {
1959 111276 : struct _FlxqXQ *d = (struct _FlxqXQ*) data;
1960 111276 : return pol1_FlxX(get_FlxqX_var(d->S),get_Flx_var(d->T));
1961 : }
1962 :
1963 : static GEN
1964 316 : _FlxqXQ_zero(void *data) {
1965 316 : struct _FlxqXQ *d = (struct _FlxqXQ*) data;
1966 316 : return pol_0(get_FlxqX_var(d->S));
1967 : }
1968 :
1969 : static struct bb_algebra FlxqXQ_algebra = { _FlxqXQ_red, _FlxqX_add,
1970 : _FlxqX_sub, _FlxqXQ_mul, _FlxqXQ_sqr, _FlxqXQ_one, _FlxqXQ_zero };
1971 :
1972 : const struct bb_algebra *
1973 761 : get_FlxqXQ_algebra(void **E, GEN S, GEN T, ulong p)
1974 : {
1975 761 : ulong pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
1976 761 : GEN z = new_chunk(sizeof(struct _FlxqXQ));
1977 761 : struct _FlxqXQ *e = (struct _FlxqXQ *) z;
1978 761 : e->T = Flx_get_red_pre(T, p, pi);
1979 761 : e->S = FlxqX_get_red_pre(S, e->T, p, pi);
1980 761 : e->p = p;
1981 761 : e->pi= pi; *E = (void*)e;
1982 761 : return &FlxqXQ_algebra;
1983 : }
1984 :
1985 : static struct bb_algebra FlxqX_algebra = { _FlxqXQ_red, _FlxqX_add,
1986 : _FlxqX_sub, _FlxqX_mul, _FlxqX_sqr, _FlxqXQ_one, _FlxqXQ_zero };
1987 :
1988 : const struct bb_algebra *
1989 0 : get_FlxqX_algebra(void **E, GEN T, ulong p, long v)
1990 : {
1991 0 : ulong pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
1992 0 : GEN z = new_chunk(sizeof(struct _FlxqXQ));
1993 0 : struct _FlxqXQ *e = (struct _FlxqXQ *) z;
1994 0 : e->T = Flx_get_red(T, p);
1995 0 : e->S = pol_x(v);
1996 0 : e->p = p;
1997 0 : e->pi= pi; *E = (void*)e;
1998 0 : return &FlxqX_algebra;
1999 : }
2000 :
2001 : /* x over Fq, return lift(x^n) mod S */
2002 : GEN
2003 91 : FlxqXQ_pow_pre(GEN x, GEN n, GEN S, GEN T, ulong p, ulong pi)
2004 : {
2005 91 : pari_sp av = avma;
2006 : struct _FlxqXQ D;
2007 91 : long s = signe(n);
2008 91 : if (!s) return pol1_FlxX(get_FlxqX_var(S),get_Flx_var(T));
2009 91 : if (s < 0) x = FlxqXQ_inv_pre(x,S,T,p,pi);
2010 91 : if (is_pm1(n)) return s < 0 ? x : gcopy(x);
2011 91 : if (degpol(x) >= get_FlxqX_degree(S)) x = FlxqX_rem_pre(x,S,T,p,pi);
2012 91 : T = Flx_get_red_pre(T, p, pi);
2013 91 : S = FlxqX_get_red_pre(S, T, p, pi);
2014 91 : D.S = S; D.T = T; D.p = p; D.pi = pi;
2015 91 : x = gen_pow_i(x, n, (void*)&D, &_FlxqXQ_sqr, &_FlxqXQ_mul);
2016 91 : return gc_GEN(av, x);
2017 : }
2018 : GEN
2019 35 : FlxqXQ_pow(GEN x, GEN n, GEN S, GEN T, ulong p)
2020 35 : { return FlxqXQ_pow_pre(x, n, S, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
2021 :
2022 : /* x over Fq, return lift(x^n) mod S */
2023 : GEN
2024 82058 : FlxqXQ_powu_pre(GEN x, ulong n, GEN S, GEN T, ulong p, ulong pi)
2025 : {
2026 82058 : pari_sp av = avma;
2027 : struct _FlxqXQ D;
2028 82058 : switch(n)
2029 : {
2030 0 : case 0: return pol1_FlxX(get_FlxqX_var(S),get_Flx_var(T));
2031 7690 : case 1: return gcopy(x);
2032 448 : case 2: return FlxqXQ_sqr_pre(x, S, T, p, pi);
2033 : }
2034 73920 : T = Flx_get_red_pre(T, p, pi);
2035 73920 : S = FlxqX_get_red_pre(S, T, p, pi);
2036 73920 : D.S = S; D.T = T; D.p = p; D.pi = pi;
2037 73920 : x = gen_powu_i(x, n, (void*)&D, &_FlxqXQ_sqr, &_FlxqXQ_mul);
2038 73920 : return gc_GEN(av, x);
2039 : }
2040 : GEN
2041 0 : FlxqXQ_powu(GEN x, ulong n, GEN S, GEN T, ulong p)
2042 0 : { return FlxqXQ_powu_pre(x, n, S, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
2043 :
2044 : GEN
2045 108241 : FlxqXQ_powers_pre(GEN x, long l, GEN S, GEN T, ulong p, ulong pi)
2046 : {
2047 : struct _FlxqXQ D;
2048 108241 : int use_sqr = 2*degpol(x) >= get_FlxqX_degree(S);
2049 108241 : T = Flx_get_red_pre(T, p, pi);
2050 108241 : S = FlxqX_get_red_pre(S, T, p, pi);
2051 108241 : D.S = S; D.T = T; D.p = p; D.pi = pi;
2052 108241 : return gen_powers(x, l, use_sqr, (void*)&D, &_FlxqXQ_sqr, &_FlxqXQ_mul,&_FlxqXQ_one);
2053 : }
2054 : GEN
2055 0 : FlxqXQ_powers(GEN x, long l, GEN S, GEN T, ulong p)
2056 0 : { return FlxqXQ_powers_pre(x, l, S, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
2057 :
2058 : /* Let v a linear form, return the linear form z->v(tau*z)
2059 : that is, v*(M_tau) */
2060 : static GEN
2061 506 : FlxqXQ_transmul_init(GEN tau, GEN S, GEN T, ulong p, ulong pi)
2062 : {
2063 : GEN bht;
2064 506 : GEN h, Sp = get_FlxqX_red(S, &h);
2065 506 : long n = degpol(Sp), vS = varn(Sp), vT = get_Flx_var(T);
2066 506 : GEN ft = FlxX_recipspec(Sp+2, n+1, n+1, vT);
2067 506 : GEN bt = FlxX_recipspec(tau+2, lgpol(tau), n, vT);
2068 506 : setvarn(ft, vS); setvarn(bt, vS);
2069 506 : if (h)
2070 0 : bht = FlxqXn_mul_pre(bt, h, n-1, T, p, pi);
2071 : else
2072 : {
2073 506 : GEN bh = FlxqX_div_pre(FlxX_shift(tau, n-1, vT), S, T, p, pi);
2074 506 : bht = FlxX_recipspec(bh+2, lgpol(bh), n-1, vT);
2075 506 : setvarn(bht, vS);
2076 : }
2077 506 : return mkvec3(bt, bht, ft);
2078 : }
2079 :
2080 : static GEN
2081 1071 : FlxqXQ_transmul(GEN tau, GEN a, long n, GEN T, ulong p, ulong pi)
2082 : {
2083 1071 : pari_sp ltop = avma;
2084 : GEN t1, t2, t3, vec;
2085 1071 : GEN bt = gel(tau, 1), bht = gel(tau, 2), ft = gel(tau, 3);
2086 1071 : long vT = get_Flx_var(T);
2087 1071 : if (signe(a)==0) return pol_0(varn(a));
2088 1061 : t2 = FlxX_shift(FlxqX_mul_pre(bt, a, T, p, pi),1-n,vT);
2089 1061 : if (signe(bht)==0) return gc_GEN(ltop, t2);
2090 767 : t1 = FlxX_shift(FlxqX_mul_pre(ft, a, T, p, pi),-n,vT);
2091 767 : t3 = FlxqXn_mul_pre(t1, bht, n-1, T, p, pi);
2092 767 : vec = FlxX_sub(t2, FlxX_shift(t3, 1, vT), p);
2093 767 : return gc_upto(ltop, vec);
2094 : }
2095 :
2096 : static GEN
2097 253 : polxn_FlxX(long n, long v, long vT)
2098 : {
2099 253 : long i, a = n+2;
2100 253 : GEN p = cgetg(a+1, t_POL);
2101 253 : p[1] = evalsigne(1)|evalvarn(v);
2102 2171 : for (i = 2; i < a; i++) gel(p,i) = pol0_Flx(vT);
2103 253 : gel(p,a) = pol1_Flx(vT); return p;
2104 : }
2105 :
2106 : GEN
2107 224 : FlxqXQ_minpoly_pre(GEN x, GEN S, GEN T, ulong p, ulong pi)
2108 : {
2109 224 : pari_sp ltop = avma;
2110 : long vS, vT, n;
2111 : GEN v_x, g, tau;
2112 224 : vS = get_FlxqX_var(S);
2113 224 : vT = get_Flx_var(T);
2114 224 : n = get_FlxqX_degree(S);
2115 224 : g = pol1_FlxX(vS,vT);
2116 224 : tau = pol1_FlxX(vS,vT);
2117 224 : S = FlxqX_get_red_pre(S, T, p, pi);
2118 224 : v_x = FlxqXQ_powers_pre(x, usqrt(2*n), S, T, p, pi);
2119 477 : while(signe(tau) != 0)
2120 : {
2121 : long i, j, m, k1;
2122 : GEN M, v, tr;
2123 : GEN g_prime, c;
2124 253 : if (degpol(g) == n) { tau = pol1_FlxX(vS, vT); g = pol1_FlxX(vS, vT); }
2125 253 : v = random_FlxqX(n, vS, T, p);
2126 253 : tr = FlxqXQ_transmul_init(tau, S, T, p, pi);
2127 253 : v = FlxqXQ_transmul(tr, v, n, T, p, pi);
2128 253 : m = 2*(n-degpol(g));
2129 253 : k1 = usqrt(m);
2130 253 : tr = FlxqXQ_transmul_init(gel(v_x,k1+1), S, T, p, pi);
2131 253 : c = cgetg(m+2,t_POL);
2132 253 : c[1] = evalsigne(1)|evalvarn(vS);
2133 1071 : for (i=0; i<m; i+=k1)
2134 : {
2135 818 : long mj = minss(m-i, k1);
2136 2736 : for (j=0; j<mj; j++)
2137 1918 : gel(c,m+1-(i+j)) = FlxqX_dotproduct(v, gel(v_x,j+1), T, p);
2138 818 : v = FlxqXQ_transmul(tr, v, n, T, p, pi);
2139 : }
2140 253 : c = FlxX_renormalize(c, m+2);
2141 : /* now c contains <v,x^i> , i = 0..m-1 */
2142 253 : M = FlxqX_halfgcd_pre(polxn_FlxX(m, vS, vT), c, T, p, pi);
2143 253 : g_prime = gmael(M, 2, 2);
2144 253 : if (degpol(g_prime) < 1) continue;
2145 252 : g = FlxqX_mul_pre(g, g_prime, T, p, pi);
2146 252 : tau = FlxqXQ_mul_pre(tau, FlxqX_FlxqXQV_eval_pre(g_prime, v_x, S, T,p,pi),
2147 : S, T, p,pi);
2148 : }
2149 224 : g = FlxqX_normalize_pre(g,T,p,pi);
2150 224 : return gc_GEN(ltop,g);
2151 : }
2152 : GEN
2153 62 : FlxqXQ_minpoly(GEN x, GEN S, GEN T, ulong p)
2154 62 : { return FlxqXQ_minpoly_pre(x, S, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
2155 :
2156 : GEN
2157 0 : FlxqXQ_matrix_pow(GEN y, long n, long m, GEN S, GEN T, ulong p)
2158 0 : { return FlxXV_to_FlxM(FlxqXQ_powers(y,m-1,S,T,p), n, get_Flx_var(T)); }
2159 :
2160 : static GEN
2161 138362 : FlxX_blocks_FlxM(GEN P, long n, long m, long v)
2162 : {
2163 138362 : GEN z = cgetg(m+1,t_MAT);
2164 138362 : long i,j, k=2, l = lg(P);
2165 536339 : for(i=1; i<=m; i++)
2166 : {
2167 397977 : GEN zi = cgetg(n+1,t_COL);
2168 397977 : gel(z,i) = zi;
2169 1274305 : for(j=1; j<=n; j++)
2170 876328 : gel(zi, j) = k==l ? pol0_Flx(v) : gel(P,k++);
2171 : }
2172 138362 : return z;
2173 : }
2174 :
2175 : GEN
2176 138362 : FlxqX_FlxqXQV_eval_pre(GEN Q, GEN x, GEN S, GEN T, ulong p, ulong pi)
2177 : {
2178 138362 : pari_sp btop, av = avma;
2179 138362 : long v = get_FlxqX_var(S), m = get_FlxqX_degree(S);
2180 138362 : long vT = get_Flx_var(T);
2181 138362 : long i, l = lg(x)-1, lQ = lgpol(Q), n, d;
2182 : GEN A, B, C, R, g;
2183 138362 : if (lQ == 0) return pol_0(v);
2184 138362 : if (lQ <= l)
2185 : {
2186 43859 : n = l;
2187 43859 : d = 1;
2188 : }
2189 : else
2190 : {
2191 94503 : n = l-1;
2192 94503 : d = (lQ+n-1)/n;
2193 : }
2194 138362 : A = FlxXV_to_FlxM_lg(x, m, n, vT);
2195 138362 : B = FlxX_blocks_FlxM(Q, n, d, vT);
2196 138362 : C = gc_upto(av, FlxqM_mul(A, B, T, p));
2197 138362 : g = gel(x, l);
2198 138362 : T = Flx_get_red_pre(T, p, pi);
2199 138362 : S = FlxqX_get_red_pre(S, T, p, pi);
2200 138362 : btop = avma;
2201 138362 : R = FlxV_to_FlxX(gel(C, d), v);
2202 397977 : for (i = d-1; i>0; i--)
2203 : {
2204 259615 : R = FlxX_add(FlxqXQ_mul_pre(R, g, S, T,p,pi), FlxV_to_FlxX(gel(C,i), v), p);
2205 259615 : if (gc_needed(btop,1))
2206 6 : R = gc_upto(btop, R);
2207 : }
2208 138362 : return gc_GEN(av, R);
2209 : }
2210 : GEN
2211 0 : FlxqX_FlxqXQV_eval(GEN Q, GEN x, GEN S, GEN T, ulong p)
2212 0 : { return FlxqX_FlxqXQV_eval_pre(Q,x,S,T,p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
2213 :
2214 : GEN
2215 76758 : FlxqX_FlxqXQ_eval_pre(GEN Q, GEN x, GEN S, GEN T, ulong p, ulong pi)
2216 : {
2217 76758 : pari_sp av = avma;
2218 : GEN z, V;
2219 76758 : long d = degpol(Q), rtd;
2220 76758 : if (d < 0) return pol_0(get_FlxqX_var(S));
2221 76758 : rtd = (long) sqrt((double)d);
2222 76758 : T = Flx_get_red_pre(T, p, pi);
2223 76758 : S = FlxqX_get_red_pre(S, T, p, pi);
2224 76758 : V = FlxqXQ_powers_pre(x, rtd, S, T, p, pi);
2225 76758 : z = FlxqX_FlxqXQV_eval_pre(Q, V, S, T, p, pi);
2226 76758 : return gc_upto(av, z);
2227 : }
2228 : GEN
2229 0 : FlxqX_FlxqXQ_eval(GEN Q, GEN x, GEN S, GEN T, ulong p)
2230 0 : { return FlxqX_FlxqXQ_eval_pre(Q, x, S, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
2231 :
2232 : GEN
2233 0 : FlxqXC_FlxqXQV_eval_pre(GEN x, GEN v, GEN S, GEN T, ulong p, ulong pi)
2234 0 : { pari_APPLY_type(t_COL, FlxqX_FlxqXQV_eval_pre(gel(x,i), v, S, T, p, pi)) }
2235 : GEN
2236 0 : FlxqXC_FlxqXQV_eval(GEN x, GEN v, GEN S, GEN T, ulong p)
2237 0 : { return FlxqXC_FlxqXQV_eval_pre(x, v, S, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
2238 :
2239 : GEN
2240 0 : FlxqXC_FlxqXQ_eval(GEN x, GEN F, GEN S, GEN T, ulong p)
2241 : {
2242 0 : long d = brent_kung_optpow(get_FlxqX_degree(S)-1,lg(x)-1,1);
2243 0 : ulong pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
2244 0 : GEN Fp = FlxqXQ_powers_pre(F, d, S, T, p, pi);
2245 0 : return FlxqXC_FlxqXQV_eval_pre(x, Fp, S, T, p, pi);
2246 : }
2247 :
2248 : static GEN
2249 72682 : FlxqXQ_autpow_sqr(void * E, GEN x)
2250 : {
2251 72682 : struct _FlxqXQ *D = (struct _FlxqXQ *)E;
2252 72682 : GEN S = D->S, T = D->T;
2253 72682 : ulong p = D->p, pi = D->pi;
2254 72682 : GEN phi = gel(x,1), S1 = gel(x,2);
2255 72682 : long n = brent_kung_optpow(get_Flx_degree(T)-1,lgpol(S1)+1,1);
2256 72682 : GEN V = Flxq_powers_pre(phi, n, T, p, pi);
2257 72682 : GEN phi2 = Flx_FlxqV_eval_pre(phi, V, T, p, pi);
2258 72682 : GEN Sphi = FlxY_FlxqV_evalx_pre(S1, V, T, p, pi);
2259 72682 : GEN S2 = FlxqX_FlxqXQ_eval_pre(Sphi, S1, S, T, p, pi);
2260 72682 : return mkvec2(phi2, S2);
2261 : }
2262 :
2263 : static GEN
2264 3714 : FlxqXQ_autpow_mul(void * E, GEN x, GEN y)
2265 : {
2266 3714 : struct _FlxqXQ *D = (struct _FlxqXQ *)E;
2267 3714 : GEN S = D->S, T = D->T;
2268 3714 : ulong p = D->p, pi = D->pi;
2269 3714 : GEN phi1 = gel(x,1), S1 = gel(x,2);
2270 3714 : GEN phi2 = gel(y,1), S2 = gel(y,2);
2271 3714 : long n = brent_kung_optpow(get_Flx_degree(T)-1,lgpol(S1)+1,1);
2272 3714 : GEN V = Flxq_powers_pre(phi2, n, T, p, pi);
2273 3714 : GEN phi3 = Flx_FlxqV_eval_pre(phi1, V, T, p, pi);
2274 3714 : GEN Sphi = FlxY_FlxqV_evalx_pre(S1, V, T, p, pi);
2275 3714 : GEN S3 = FlxqX_FlxqXQ_eval_pre(Sphi, S2, S, T, p, pi);
2276 3714 : return mkvec2(phi3, S3);
2277 : }
2278 :
2279 : GEN
2280 69275 : FlxqXQ_autpow_pre(GEN aut, long n, GEN S, GEN T, ulong p, ulong pi)
2281 : {
2282 69275 : pari_sp av = avma;
2283 : struct _FlxqXQ D;
2284 69275 : T = Flx_get_red_pre(T, p, pi);
2285 69275 : S = FlxqX_get_red_pre(S, T, p, pi);
2286 69275 : D.S = S; D.T = T; D.p = p; D.pi = pi;
2287 69275 : aut = gen_powu_i(aut,n,&D,FlxqXQ_autpow_sqr,FlxqXQ_autpow_mul);
2288 69275 : return gc_GEN(av, aut);
2289 : }
2290 : GEN
2291 0 : FlxqXQ_autpow(GEN aut, long n, GEN S, GEN T, ulong p)
2292 0 : { return FlxqXQ_autpow_pre(aut, n, S, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
2293 :
2294 : static GEN
2295 29983 : FlxqXQ_autsum_mul(void *E, GEN x, GEN y)
2296 : {
2297 29983 : struct _FlxqXQ *D = (struct _FlxqXQ *)E;
2298 29983 : GEN S = D->S, T = D->T;
2299 29983 : ulong p = D->p, pi = D->pi;
2300 29983 : GEN phi1 = gel(x,1), S1 = gel(x,2), a1 = gel(x,3);
2301 29983 : GEN phi2 = gel(y,1), S2 = gel(y,2), a2 = gel(y,3);
2302 29983 : long n2 = brent_kung_optpow(get_Flx_degree(T)-1, lgpol(S1)+lgpol(a1)+1,1);
2303 29983 : GEN V2 = Flxq_powers_pre(phi2, n2, T, p, pi);
2304 29983 : GEN phi3 = Flx_FlxqV_eval_pre(phi1, V2, T, p, pi);
2305 29983 : GEN Sphi = FlxY_FlxqV_evalx_pre(S1, V2, T, p, pi);
2306 29983 : GEN aphi = FlxY_FlxqV_evalx_pre(a1, V2, T, p, pi);
2307 29983 : long n = brent_kung_optpow(maxss(degpol(Sphi),degpol(aphi)),2,1);
2308 29983 : GEN V = FlxqXQ_powers_pre(S2, n, S, T, p, pi);
2309 29983 : GEN S3 = FlxqX_FlxqXQV_eval_pre(Sphi, V, S, T, p, pi);
2310 29983 : GEN aS = FlxqX_FlxqXQV_eval_pre(aphi, V, S, T, p, pi);
2311 29983 : GEN a3 = FlxqXQ_mul_pre(aS, a2, S, T, p, pi);
2312 29983 : return mkvec3(phi3, S3, a3);
2313 : }
2314 :
2315 : static GEN
2316 18582 : FlxqXQ_autsum_sqr(void * T, GEN x)
2317 18582 : { return FlxqXQ_autsum_mul(T, x, x); }
2318 :
2319 : GEN
2320 12125 : FlxqXQ_autsum_pre(GEN aut, long n, GEN S, GEN T, ulong p, ulong pi)
2321 : {
2322 12125 : pari_sp av = avma;
2323 : struct _FlxqXQ D;
2324 12125 : T = Flx_get_red_pre(T, p, pi);
2325 12125 : S = FlxqX_get_red_pre(S, T, p, pi);
2326 12125 : D.S=S; D.T=T; D.p=p; D.pi=pi;
2327 12125 : aut = gen_powu_i(aut,n,&D,FlxqXQ_autsum_sqr,FlxqXQ_autsum_mul);
2328 12125 : return gc_GEN(av, aut);
2329 : }
2330 : GEN
2331 0 : FlxqXQ_autsum(GEN aut, long n, GEN S, GEN T, ulong p)
2332 0 : { return FlxqXQ_autsum_pre(aut, n, S, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
2333 :
2334 : static GEN
2335 27 : FlxqXQ_auttrace_mul(void *E, GEN x, GEN y)
2336 : {
2337 27 : struct _FlxqXQ *D = (struct _FlxqXQ *)E;
2338 27 : GEN S = D->S, T = D->T;
2339 27 : ulong p = D->p, pi = D->pi;
2340 27 : GEN S1 = gel(x,1), a1 = gel(x,2);
2341 27 : GEN S2 = gel(y,1), a2 = gel(y,2);
2342 27 : long n = brent_kung_optpow(maxss(degpol(S1),degpol(a1)),2,1);
2343 27 : GEN V = FlxqXQ_powers_pre(S2, n, S, T, p, pi);
2344 27 : GEN S3 = FlxqX_FlxqXQV_eval_pre(S1, V, S, T, p, pi);
2345 27 : GEN aS = FlxqX_FlxqXQV_eval_pre(a1, V, S, T, p, pi);
2346 27 : GEN a3 = FlxX_add(aS, a2, p);
2347 27 : return mkvec2(S3, a3);
2348 : }
2349 :
2350 : static GEN
2351 20 : FlxqXQ_auttrace_sqr(void *E, GEN x)
2352 20 : { return FlxqXQ_auttrace_mul(E, x, x); }
2353 :
2354 : GEN
2355 337 : FlxqXQ_auttrace_pre(GEN x, ulong n, GEN S, GEN T, ulong p, ulong pi)
2356 : {
2357 337 : pari_sp av = avma;
2358 : struct _FlxqXQ D;
2359 337 : T = Flx_get_red_pre(T, p, pi);
2360 337 : S = FlxqX_get_red_pre(S, T, p, pi);
2361 337 : D.S=S; D.T=T; D.p=p; D.pi = pi;
2362 337 : x = gen_powu_i(x,n,(void*)&D,FlxqXQ_auttrace_sqr,FlxqXQ_auttrace_mul);
2363 337 : return gc_GEN(av, x);
2364 : }
2365 : GEN
2366 0 : FlxqXQ_auttrace(GEN x, ulong n, GEN S, GEN T, ulong p)
2367 0 : { return FlxqXQ_auttrace_pre(x, n, S, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
2368 :
2369 : /*******************************************************************/
2370 : /* */
2371 : /* FlxYqQ */
2372 : /* */
2373 : /*******************************************************************/
2374 :
2375 : /*Preliminary implementation to speed up FpX_ffisom*/
2376 : typedef struct {
2377 : GEN S, T;
2378 : ulong p, pi;
2379 : } FlxYqq_muldata;
2380 :
2381 : /* reduce x in Fl[X, Y] in the algebra Fl[X, Y]/ (P(X),Q(Y)) */
2382 : static GEN
2383 90884 : FlxYqq_redswap(GEN x, GEN S, GEN T, ulong p, ulong pi)
2384 : {
2385 90884 : pari_sp ltop=avma;
2386 90884 : long n = get_Flx_degree(S);
2387 90884 : long m = get_Flx_degree(T);
2388 90883 : long w = get_Flx_var(T);
2389 90883 : GEN V = FlxX_swap(x,m,w);
2390 90883 : V = FlxqX_red_pre(V,S,p,pi);
2391 90881 : V = FlxX_swap(V,n,w);
2392 90883 : return gc_GEN(ltop,V);
2393 : }
2394 : static GEN
2395 80516 : FlxYqq_sqr(void *data, GEN x)
2396 : {
2397 80516 : FlxYqq_muldata *D = (FlxYqq_muldata*)data;
2398 80516 : return FlxYqq_redswap(FlxqX_sqr_pre(x,D->T,D->p,D->pi),D->S,D->T,D->p,D->pi);
2399 : }
2400 :
2401 : static GEN
2402 10368 : FlxYqq_mul(void *data, GEN x, GEN y)
2403 : {
2404 10368 : FlxYqq_muldata *D = (FlxYqq_muldata*)data;
2405 10368 : return FlxYqq_redswap(FlxqX_mul_pre(x,y, D->T,D->p,D->pi),D->S,D->T,D->p,D->pi);
2406 : }
2407 :
2408 : /* x in Z[X,Y], S in Z[X] over Fq = Z[Y]/(p,T); compute lift(x^n mod (S,T,p)) */
2409 : GEN
2410 39226 : FlxYqq_pow(GEN x, GEN n, GEN S, GEN T, ulong p)
2411 : {
2412 : FlxYqq_muldata D;
2413 39226 : D.S = S; D.T = T; D.p = p; D.pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
2414 39226 : return gen_pow(x, n, (void*)&D, &FlxYqq_sqr, &FlxYqq_mul);
2415 : }
2416 :
2417 : /*******************************************************************/
2418 : /* */
2419 : /* FlxqXn */
2420 : /* */
2421 : /*******************************************************************/
2422 :
2423 : GEN
2424 66176 : FlxXn_red(GEN a, long n)
2425 : {
2426 66176 : long i, L = n+2, l = lg(a);
2427 : GEN b;
2428 66176 : if (L >= l) return a; /* deg(x) < n */
2429 36738 : b = cgetg(L, t_POL); b[1] = a[1];
2430 391853 : for (i=2; i<L; i++) gel(b,i) = gel(a,i);
2431 36740 : return FlxX_renormalize(b,L);
2432 : }
2433 :
2434 : GEN
2435 40406 : FlxqXn_mul_pre(GEN a, GEN b, long n, GEN T, ulong p, ulong pi)
2436 40406 : { return FlxXn_red(FlxqX_mul_pre(a, b, T, p, pi), n); }
2437 : GEN
2438 0 : FlxqXn_mul(GEN a, GEN b, long n, GEN T, ulong p)
2439 0 : { return FlxqXn_mul_pre(a, b, n, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
2440 :
2441 : GEN
2442 0 : FlxqXn_sqr_pre(GEN a, long n, GEN T, ulong p, ulong pi)
2443 0 : { return FlxXn_red(FlxqX_sqr_pre(a, T, p, pi), n); }
2444 : GEN
2445 0 : FlxqXn_sqr(GEN a, long n, GEN T, ulong p)
2446 0 : { return FlxqXn_sqr_pre(a, n, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
2447 :
2448 : /* (f*g) \/ x^n */
2449 : static GEN
2450 17998 : FlxqX_mulhigh_i(GEN f, GEN g, long n, GEN T, ulong p, ulong pi)
2451 17998 : { return FlxX_shift(FlxqX_mul_pre(f, g, T, p, pi), -n , get_Flx_var(T)); }
2452 :
2453 : static GEN
2454 13195 : FlxqXn_mulhigh(GEN f, GEN g, long n2, long n, GEN T, ulong p, ulong pi)
2455 : {
2456 13195 : long vT = get_Flx_var(T);
2457 13195 : GEN F = FlxX_blocks(f, n2, 2, vT), fl = gel(F,1), fh = gel(F,2);
2458 13194 : return FlxX_add(FlxqX_mulhigh_i(fl, g, n2, T, p, pi),
2459 : FlxqXn_mul_pre(fh, g, n - n2, T, p, pi), p);
2460 : }
2461 :
2462 : GEN
2463 2432 : FlxqXn_inv_pre(GEN f, long e, GEN T, ulong p, ulong pi)
2464 : {
2465 2432 : pari_sp av = avma, av2;
2466 : ulong mask;
2467 : GEN W, a;
2468 2432 : long v = varn(f), n = 1, vT = get_Flx_var(T);
2469 :
2470 2432 : if (!signe(f)) pari_err_INV("FlxqXn_inv",f);
2471 2432 : a = Flxq_inv_pre(gel(f,2), T, p, pi);
2472 2432 : if (e == 1) return scalarpol(a, v);
2473 2432 : else if (e == 2)
2474 : {
2475 : GEN b;
2476 0 : if (degpol(f) <= 0) return scalarpol(a, v);
2477 0 : b = Flx_neg(gel(f,3), p);
2478 0 : if (lgpol(b)==0) return scalarpol(a, v);
2479 0 : b = Flxq_mul_pre(b, Flxq_sqr_pre(a, T, p, pi), T, p, pi);
2480 0 : W = deg1pol_shallow(b, a, v);
2481 0 : return gc_GEN(av, W);
2482 : }
2483 2432 : W = scalarpol_shallow(Flxq_inv_pre(gel(f,2), T, p, pi), v);
2484 2432 : mask = quadratic_prec_mask(e);
2485 2432 : av2 = avma;
2486 12040 : for (;mask>1;)
2487 : {
2488 : GEN u, fr;
2489 9608 : long n2 = n;
2490 9608 : n<<=1; if (mask & 1) n--;
2491 9608 : mask >>= 1;
2492 9608 : fr = FlxXn_red(f, n);
2493 9607 : u = FlxqXn_mul_pre(W, FlxqXn_mulhigh(fr, W, n2, n, T,p,pi), n-n2, T,p,pi);
2494 9608 : W = FlxX_sub(W, FlxX_shift(u, n2, vT), p);
2495 9608 : if (gc_needed(av2,2))
2496 : {
2497 0 : if(DEBUGMEM>1) pari_warn(warnmem,"FlxqXn_inv, e = %ld", n);
2498 0 : W = gc_upto(av2, W);
2499 : }
2500 : }
2501 2432 : return gc_upto(av, W);
2502 : }
2503 : GEN
2504 0 : FlxqXn_inv(GEN f, long e, GEN T, ulong p)
2505 0 : { return FlxqXn_inv_pre(f, e, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
2506 :
2507 : /* Compute intformal(x^n*S)/x^(n+1) */
2508 : static GEN
2509 4803 : FlxX_integXn(GEN x, long n, ulong p)
2510 : {
2511 4803 : long i, lx = lg(x);
2512 : GEN y;
2513 4803 : if (lx == 2) return gcopy(x);
2514 3997 : y = cgetg(lx, t_POL); y[1] = x[1];
2515 26729 : for (i=2; i<lx; i++)
2516 : {
2517 22731 : GEN xi = gel(x,i);
2518 22731 : gel(y,i) = Flx_Fl_mul(xi, Fl_inv((n+i-1)%p, p), p);
2519 : }
2520 3998 : return FlxX_renormalize(y, lx);;
2521 : }
2522 :
2523 : GEN
2524 1216 : FlxqXn_expint_pre(GEN h, long e, GEN T, ulong p, ulong pi)
2525 : {
2526 1216 : pari_sp av = avma, av2;
2527 1216 : long v = varn(h), n = 1, vT = get_Flx_var(T);
2528 1216 : GEN f = pol1_FlxX(v, vT), g = pol1_FlxX(v, vT);
2529 1216 : ulong mask = quadratic_prec_mask(e);
2530 1216 : av2 = avma;
2531 4804 : for (;mask>1;)
2532 : {
2533 : GEN u, w;
2534 4804 : long n2 = n;
2535 4804 : n<<=1; if (mask & 1) n--;
2536 4804 : mask >>= 1;
2537 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);
2538 4804 : u = FlxX_add(u, FlxX_shift(FlxXn_red(h, n-1), 1-n2, vT), p);
2539 4803 : w = FlxqXn_mul_pre(f, FlxX_integXn(u, n2-1, p), n-n2, T, p, pi);
2540 4804 : f = FlxX_add(f, FlxX_shift(w, n2, vT), p);
2541 4804 : if (mask<=1) break;
2542 3588 : u = FlxqXn_mul_pre(g, FlxqXn_mulhigh(f, g, n2, n, T,p,pi), n-n2, T,p,pi);
2543 3588 : g = FlxX_sub(g, FlxX_shift(u, n2, vT), p);
2544 3588 : if (gc_needed(av2,2))
2545 : {
2546 0 : if (DEBUGMEM>1) pari_warn(warnmem,"FlxqXn_exp, e = %ld", n);
2547 0 : (void)gc_all(av2, 2, &f, &g);
2548 : }
2549 : }
2550 1216 : return gc_upto(av, f);
2551 : }
2552 : GEN
2553 0 : FlxqXn_expint(GEN h, long e, GEN T, ulong p)
2554 0 : { return FlxqXn_expint_pre(h, e, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
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