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 17969390 : FlxX_renormalize(GEN /*in place*/ x, long lx)
31 : {
32 : long i;
33 22925112 : for (i = lx-1; i>1; i--)
34 22141416 : if (lgpol(gel(x,i))) break;
35 17969390 : stackdummy((pari_sp)(x + lg(x)), (pari_sp)(x + i+1));
36 17969390 : setlg(x, i+1); setsigne(x, i!=1); return x;
37 : }
38 :
39 : GEN
40 760668 : pol1_FlxX(long v, long sv)
41 : {
42 760668 : GEN z = cgetg(3, t_POL);
43 760668 : z[1] = evalsigne(1) | evalvarn(v);
44 760668 : gel(z,2) = pol1_Flx(sv); return z;
45 : }
46 :
47 : GEN
48 692005 : polx_FlxX(long v, long sv)
49 : {
50 692005 : GEN z = cgetg(4, t_POL);
51 692005 : z[1] = evalsigne(1) | evalvarn(v);
52 692005 : gel(z,2) = pol0_Flx(sv);
53 692005 : gel(z,3) = pol1_Flx(sv); return z;
54 : }
55 :
56 : long
57 3067261 : FlxY_degreex(GEN b)
58 : {
59 3067261 : long deg = 0, i;
60 3067261 : if (!signe(b)) return -1;
61 10993877 : for (i = 2; i < lg(b); ++i)
62 7926616 : deg = maxss(deg, degpol(gel(b, i)));
63 3067261 : return deg;
64 : }
65 :
66 : /*Lift coefficient of B to constant Flx, to give a FlxY*/
67 : GEN
68 2565 : Fly_to_FlxY(GEN B, long sv)
69 : {
70 2565 : long lb=lg(B);
71 : long i;
72 2565 : GEN b=cgetg(lb,t_POL);
73 2565 : b[1]=evalsigne(1)|(((ulong)B[1])&VARNBITS);
74 67006 : for (i=2; i<lb; i++)
75 64441 : gel(b,i) = Fl_to_Flx(B[i], sv);
76 2565 : return FlxX_renormalize(b, lb);
77 : }
78 :
79 : GEN
80 2864835 : zxX_to_FlxX(GEN B, ulong p)
81 : {
82 2864835 : long i, lb = lg(B);
83 2864835 : GEN b = cgetg(lb,t_POL);
84 9357831 : for (i=2; i<lb; i++)
85 6492996 : gel(b,i) = zx_to_Flx(gel(B,i), p);
86 2864835 : b[1] = B[1]; return FlxX_renormalize(b, lb);
87 : }
88 :
89 : GEN
90 2782427 : FlxX_to_ZXX(GEN B)
91 : {
92 2782427 : long i, lb = lg(B);
93 2782427 : GEN b = cgetg(lb,t_POL);
94 8935666 : for (i=2; i<lb; i++)
95 : {
96 6153239 : GEN c = gel(B,i);
97 6153239 : switch(lgpol(c))
98 : {
99 267910 : case 0: c = gen_0; break;
100 796757 : case 1: c = utoi(c[2]); break;
101 5088572 : default: c = Flx_to_ZX(c); break;
102 : }
103 6153239 : gel(b,i) = c;
104 : }
105 2782427 : 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 4706572 : ZXX_to_FlxX(GEN B, ulong p, long v)
112 : {
113 4706572 : long lb=lg(B);
114 : long i;
115 4706572 : GEN b=cgetg(lb,t_POL);
116 4706572 : b[1]=evalsigne(1)|(((ulong)B[1])&VARNBITS);
117 21634741 : for (i=2; i<lb; i++)
118 16928169 : switch (typ(gel(B,i)))
119 : {
120 7124923 : case t_INT:
121 7124923 : gel(b,i) = Z_to_Flx(gel(B,i), p, evalvarn(v));
122 7124923 : break;
123 9803246 : case t_POL:
124 9803246 : gel(b,i) = ZX_to_Flx(gel(B,i), p);
125 9803246 : break;
126 : }
127 4706572 : 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
135 442 : ZXXT_to_FlxXT(GEN x, ulong p, long v)
136 : {
137 442 : if (typ(x) == t_POL)
138 428 : return ZXX_to_FlxX(x, p, v);
139 : else
140 42 : pari_APPLY_type(t_VEC, ZXXT_to_FlxXT(gel(x,i), p, v))
141 : }
142 :
143 : GEN
144 328131 : FlxX_to_FlxC(GEN x, long N, long sv)
145 : {
146 : long i, l;
147 : GEN z;
148 328131 : l = lg(x)-1; x++;
149 328131 : if (l > N+1) l = N+1; /* truncate higher degree terms */
150 328131 : z = cgetg(N+1,t_COL);
151 2990274 : for (i=1; i<l ; i++) gel(z,i) = gel(x,i);
152 3601734 : for ( ; i<=N; i++) gel(z,i) = pol0_Flx(sv);
153 328131 : 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 58299 : FlxX_to_Flm(GEN v, long n)
160 : {
161 58299 : long j, N = lg(v)-1;
162 58299 : GEN y = cgetg(N, t_MAT);
163 58299 : v++;
164 204854 : for (j=1; j<N; j++) gel(y,j) = Flx_to_Flv(gel(v,j), n);
165 58299 : return y;
166 : }
167 :
168 : GEN
169 378159 : FlxX_to_Flx(GEN f)
170 : {
171 378159 : long i, l = lg(f);
172 378159 : GEN V = cgetg(l, t_VECSMALL);
173 378159 : V[1] = ((ulong)f[1])&VARNBITS;
174 3559405 : for(i=2; i<l; i++)
175 3181246 : V[i] = lgpol(gel(f,i)) ? mael(f,i,2): 0L;
176 378159 : return V;
177 : }
178 :
179 : GEN
180 221990 : Flm_to_FlxX(GEN x, long v,long w)
181 : {
182 221990 : long j, lx = lg(x);
183 221990 : GEN y = cgetg(lx+1, t_POL);
184 221990 : y[1]=evalsigne(1) | v;
185 221990 : y++;
186 816075 : for (j=1; j<lx; j++) gel(y,j) = Flv_to_Flx(gel(x,j), w);
187 221990 : return FlxX_renormalize(--y, lx+1);
188 : }
189 :
190 : /* P(X,Y) --> P(Y,X), n is the degree in Y */
191 : GEN
192 181920 : FlxX_swap(GEN x, long n, long ws)
193 : {
194 181920 : long j, lx = lg(x), ly = n+3;
195 181920 : GEN y = cgetg(ly, t_POL);
196 181920 : y[1] = x[1];
197 1169418 : for (j=2; j<ly; j++)
198 : {
199 : long k;
200 987498 : GEN p1 = cgetg(lx, t_VECSMALL);
201 987498 : p1[1] = ws;
202 11227877 : for (k=2; k<lx; k++)
203 10240379 : if (j<lg(gel(x,k)))
204 7199741 : p1[k] = mael(x,k,j);
205 : else
206 3040638 : p1[k] = 0;
207 987498 : gel(y,j) = Flx_renormalize(p1,lx);
208 : }
209 181920 : return FlxX_renormalize(y,ly);
210 : }
211 :
212 : static GEN
213 4537658 : zxX_to_Kronecker_spec(GEN P, long lp, long n)
214 : { /* P(X) = sum Pi(Y) * X^i, return P( Y^(2n-1) ) */
215 4537658 : long i, j, k, l, N = (n<<1) + 1;
216 4537658 : GEN y = cgetg((N-2)*lp + 2, t_VECSMALL) + 2;
217 37893800 : for (k=i=0; i<lp; i++)
218 : {
219 37857157 : GEN c = gel(P,i);
220 37857157 : l = lg(c);
221 37857157 : if (l-3 >= n)
222 0 : pari_err_BUG("zxX_to_Kronecker, P is not reduced mod Q");
223 169618382 : for (j=2; j < l; j++) y[k++] = c[j];
224 37857157 : if (i == lp-1) break;
225 275949064 : for ( ; j < N; j++) y[k++] = 0;
226 : }
227 4537658 : y -= 2;
228 4537658 : y[1] = 0; setlg(y, k+2); return y;
229 : }
230 :
231 : GEN
232 3822282 : zxX_to_Kronecker(GEN P, GEN Q)
233 : {
234 3822282 : GEN z = zxX_to_Kronecker_spec(P+2, lg(P)-2, degpol(Q));
235 3822282 : z[1] = P[1]; return z;
236 : }
237 :
238 : GEN
239 360094 : FlxX_add(GEN x, GEN y, ulong p)
240 : {
241 : long i,lz;
242 : GEN z;
243 360094 : long lx=lg(x);
244 360094 : long ly=lg(y);
245 360094 : if (ly>lx) swapspec(x,y, lx,ly);
246 360094 : lz = lx; z = cgetg(lz, t_POL); z[1]=x[1];
247 4720395 : for (i=2; i<ly; i++) gel(z,i) = Flx_add(gel(x,i), gel(y,i), p);
248 2185145 : for ( ; i<lx; i++) gel(z,i) = Flx_copy(gel(x,i));
249 360094 : 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 11703 : FlxY_Flx_sub(GEN y, GEN x, ulong p)
268 : {
269 11703 : long i, lz = lg(y);
270 : GEN z;
271 11703 : if (signe(y) == 0) return scalarpol(x, varn(y));
272 11703 : z = cgetg(lz,t_POL); z[1] = y[1];
273 11703 : gel(z,2) = Flx_sub(gel(y,2), x, p);
274 11703 : if (lz == 3) z = FlxX_renormalize(z,lz);
275 : else
276 84534 : for(i=3;i<lz;i++) gel(z,i) = Flx_copy(gel(y,i));
277 11703 : return z;
278 : }
279 :
280 : GEN
281 2538 : FlxX_neg(GEN x, ulong p)
282 : {
283 2538 : long i, lx=lg(x);
284 2538 : GEN z = cgetg(lx, t_POL);
285 2538 : z[1]=x[1];
286 43405 : for (i=2; i<lx; i++) gel(z,i) = Flx_neg(gel(x,i), p);
287 2538 : return z;
288 : }
289 :
290 : GEN
291 684 : FlxX_Fl_mul(GEN x, ulong y, ulong p)
292 : {
293 684 : long i, lx=lg(x);
294 684 : GEN z = cgetg(lx, t_POL);
295 684 : z[1]=x[1];
296 3296 : for (i=2; i<lx; i++) gel(z,i) = Flx_Fl_mul(gel(x,i), y, p);
297 684 : 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
311 684 : FlxX_double(GEN x, ulong p)
312 : {
313 684 : long i, lx=lg(x);
314 684 : GEN z = cgetg(lx, t_POL);
315 684 : z[1]=x[1];
316 5472 : for (i=2; i<lx; i++) gel(z,i) = Flx_double(gel(x,i), p);
317 684 : return FlxX_renormalize(z, lx);
318 : }
319 :
320 : GEN
321 85571 : FlxX_deriv(GEN z, ulong p)
322 : {
323 85571 : long i,l = lg(z)-1;
324 : GEN x;
325 85571 : if (l < 2) l = 2;
326 85571 : x = cgetg(l, t_POL); x[1] = z[1];
327 966413 : for (i=2; i<l; i++) gel(x,i) = Flx_mulu(gel(z,i+1), (ulong) i-1, p);
328 85571 : return FlxX_renormalize(x,l);
329 : }
330 :
331 : GEN
332 0 : FlxX_translate1(GEN P, ulong 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, ulong 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 132746 : FlxX_subspec(GEN x, GEN y, ulong p, long lx, long ly)
359 : {
360 : long i,lz;
361 : GEN z;
362 :
363 132746 : if (ly <= lx)
364 : {
365 132746 : lz = lx+2; z = cgetg(lz, t_POL);
366 4911339 : for (i=0; i<ly; i++) gel(z,i+2) = Flx_sub(gel(x,i),gel(y,i),p);
367 134609 : 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 132746 : z[1] = 0; return FlxX_renormalize(z, lz);
376 : }
377 :
378 : GEN
379 626217 : FlxX_sub(GEN x, GEN y, ulong p)
380 : {
381 : long lx,ly,i,lz;
382 : GEN z;
383 626217 : lx = lg(x); ly = lg(y);
384 626217 : lz=maxss(lx,ly);
385 626217 : z = cgetg(lz,t_POL);
386 626217 : if (lx >= ly)
387 : {
388 110106 : z[1] = x[1];
389 625856 : for (i=2; i<ly; i++) gel(z,i) = Flx_sub(gel(x,i),gel(y,i),p);
390 386849 : for ( ; i<lx; i++) gel(z,i) = Flx_copy(gel(x,i));
391 110106 : if (lx==ly) z = FlxX_renormalize(z, lz);
392 : }
393 : else
394 : {
395 516111 : z[1] = y[1];
396 1302112 : for (i=2; i<lx; i++) gel(z,i) = Flx_sub(gel(x,i),gel(y,i),p);
397 1388420 : for ( ; i<ly; i++) gel(z,i) = Flx_neg(gel(y,i),p);
398 : }
399 626217 : if (!lgpol(z)) { set_avma((pari_sp)(z + lz)); z = pol_0(varn(x)); }
400 626217 : 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 7667 : FlxY_Flx_div_pre(GEN x, GEN y, ulong p, ulong pi)
419 : {
420 : long i, l;
421 : GEN z;
422 7667 : if (degpol(y) == 0)
423 : {
424 5678 : ulong t = uel(y,2);
425 5678 : 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 1989 : y = Flx_get_red_pre(y, p, pi);
433 1989 : z = cgetg_copy(x, &l); z[1] = x[1];
434 3978 : for (i=2; i<l; i++) gel(z,i) = Flx_div_pre(gel(x,i),y,p,pi);
435 : }
436 1989 : 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 14263722 : FlxY_evalx_pre(GEN Q, ulong x, ulong p, ulong pi)
444 : {
445 14263722 : long i, lb = lg(Q);
446 : GEN z;
447 14263722 : z = cgetg(lb,t_VECSMALL); z[1] = evalvarn(varn(Q));
448 115619432 : for (i=2; i<lb; i++) z[i] = Flx_eval_pre(gel(Q,i), x, p, pi);
449 14263722 : return Flx_renormalize(z, lb);
450 : }
451 : GEN
452 238 : FlxY_evalx(GEN Q, ulong x, ulong p)
453 238 : { 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 11326857 : FlxY_evalx_powers_pre(GEN pol, GEN ypowers, ulong p, ulong pi)
482 : {
483 11326857 : long i, len = lg(pol);
484 11326857 : GEN res = cgetg(len, t_VECSMALL);
485 11326857 : res[1] = pol[1] & VARNBITS;
486 38456970 : for (i = 2; i < len; ++i)
487 27130113 : res[i] = Flx_eval_powers_pre(gel(pol, i), ypowers, p, pi);
488 11326857 : return Flx_renormalize(res, len);
489 : }
490 :
491 : /* allow pi = 0 */
492 : ulong
493 7591544 : FlxY_eval_powers_pre(GEN pol, GEN ypowers, GEN xpowers, ulong p, ulong pi)
494 : {
495 7591544 : pari_sp av = avma;
496 7591544 : GEN t = FlxY_evalx_powers_pre(pol, ypowers, p, pi);
497 7591544 : return gc_ulong(av, Flx_eval_powers_pre(t, xpowers, p, pi));
498 : }
499 :
500 : GEN
501 137237 : FlxY_FlxqV_evalx_pre(GEN P, GEN x, GEN T, ulong p, ulong pi)
502 : {
503 137237 : long i, lP = lg(P);
504 137237 : GEN res = cgetg(lP,t_POL);
505 137237 : res[1] = P[1];
506 1026715 : for(i=2; i<lP; i++)
507 889478 : gel(res,i) = Flx_FlxqV_eval_pre(gel(P,i), x, T, p, pi);
508 137237 : 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 71643 : FlxX_shift(GEN a, long n, long vs)
528 : {
529 71643 : long i, l = lg(a);
530 : GEN b;
531 71643 : if (l == 2 || !n) return a;
532 64649 : l += n;
533 64649 : if (n < 0)
534 : {
535 35785 : if (l <= 2) return pol_0(varn(a));
536 29415 : b = cgetg(l, t_POL); b[1] = a[1];
537 29415 : a -= n;
538 612756 : for (i=2; i<l; i++) gel(b,i) = gel(a,i);
539 : } else {
540 28864 : b = cgetg(l, t_POL); b[1] = a[1];
541 28864 : a -= n; n += 2;
542 507181 : for (i=2; i<n; i++) gel(b,i) = pol0_Flx(vs);
543 365846 : for ( ; i<l; i++) gel(b,i) = gel(a,i);
544 : }
545 58279 : return b;
546 : }
547 :
548 : GEN
549 13196 : FlxX_blocks(GEN P, long n, long m, long vs)
550 : {
551 13196 : GEN z = cgetg(m+1,t_VEC);
552 13196 : long i,j, k=2, l = lg(P);
553 39588 : for(i=1; i<=m; i++)
554 : {
555 26392 : GEN zi = cgetg(n+2,t_POL);
556 26392 : zi[1] = P[1];
557 26392 : gel(z,i) = zi;
558 160586 : for(j=2; j<n+2; j++)
559 134194 : gel(zi, j) = k==l ? pol0_Flx(vs) : gel(P,k++);
560 26392 : zi = FlxX_renormalize(zi, n+2);
561 : }
562 13196 : return z;
563 : }
564 :
565 : static GEN
566 281996 : FlxX_recipspec(GEN x, long l, long n, long vs)
567 : {
568 : long i;
569 281996 : GEN z = cgetg(n+2,t_POL);
570 281996 : z[1] = 0; z += 2;
571 8350838 : for(i=0; i<l; i++)
572 8068842 : gel(z,n-i-1) = Flx_copy(gel(x,i));
573 289060 : for( ; i<n; i++)
574 7064 : gel(z,n-i-1) = pol0_Flx(vs);
575 281996 : 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 47686 : for (i=d; i>=2; i--)
589 : {
590 45261 : gel(y,i+2) = Flx_Fl_mul(gel(x,i+2), t, p);
591 45261 : 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 139112 : FlxXV_to_FlxM_lg(GEN x, long m, long n, long sv)
629 : {
630 : long i;
631 139112 : GEN y = cgetg(n+1, t_MAT);
632 467243 : for (i=1; i<=n; i++) gel(y,i) = FlxX_to_FlxC(gel(x,i), m, sv);
633 139112 : 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 12516 : FlxXC_to_ZXXC(GEN x)
642 62621 : { 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 3700283 : get_FlxqX_red(GEN T, GEN *B)
656 : {
657 3700283 : if (typ(T)!=t_VEC) { *B=NULL; return T; }
658 170844 : *B = gel(T,1); return gel(T,2);
659 : }
660 :
661 : GEN
662 166250 : RgX_to_FlxqX(GEN x, GEN T, ulong p)
663 : {
664 166250 : long i, l = lg(x);
665 166250 : GEN z = cgetg(l, t_POL); z[1] = x[1];
666 2440082 : for (i = 2; i < l; i++)
667 2273832 : gel(z,i) = Rg_to_Flxq(gel(x,i), T, p);
668 166250 : 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
675 592 : random_FlxqX(long d1, long v, GEN T, ulong p)
676 : {
677 592 : long dT = get_Flx_degree(T), vT = get_Flx_var(T);
678 592 : long i, d = d1+2;
679 592 : GEN y = cgetg(d,t_POL); y[1] = evalsigne(1) | evalvarn(v);
680 3140 : for (i=2; i<d; i++) gel(y,i) = random_Flx(dT, vT, p);
681 592 : return FlxX_renormalize(y,d);
682 : }
683 :
684 : /*Not stack clean*/
685 : GEN
686 2450652 : Kronecker_to_FlxqX_pre(GEN z, GEN T, ulong p, ulong pi)
687 : {
688 2450652 : long i,j,lx,l, N = (get_Flx_degree(T)<<1) + 1;
689 2450652 : GEN x, t = cgetg(N,t_VECSMALL);
690 2450652 : t[1] = get_Flx_var(T);
691 2450652 : l = lg(z); lx = (l-2) / (N-2);
692 2450652 : x = cgetg(lx+3,t_POL);
693 2450652 : x[1] = z[1];
694 38267377 : for (i=2; i<lx+2; i++)
695 : {
696 421516380 : for (j=2; j<N; j++) t[j] = z[j];
697 35816725 : z += (N-2);
698 35816725 : gel(x,i) = Flx_rem_pre(Flx_renormalize(t,N), T,p,pi);
699 : }
700 2450652 : N = (l-2) % (N-2) + 2;
701 7645340 : for (j=2; j<N; j++) t[j] = z[j];
702 2450652 : gel(x,i) = Flx_rem_pre(Flx_renormalize(t,N), T,p,pi);
703 2450652 : 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 1294113 : FlxqX_red_pre(GEN z, GEN T, ulong p, ulong pi)
711 : {
712 : GEN res;
713 1294113 : long i, l = lg(z);
714 1294113 : res = cgetg(l,t_POL); res[1] = z[1];
715 16419539 : for(i=2;i<l;i++) gel(res,i) = Flx_rem_pre(gel(z,i),T,p,pi);
716 1294113 : 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 357688 : FlxqX_mulspec(GEN x, GEN y, GEN T, ulong p, ulong pi, long lx, long ly)
724 : {
725 357688 : pari_sp av = avma;
726 : GEN z,kx,ky;
727 357688 : long dT = get_Flx_degree(T);
728 357688 : kx= zxX_to_Kronecker_spec(x,lx,dT);
729 357688 : ky= zxX_to_Kronecker_spec(y,ly,dT);
730 357688 : z = Flx_mul_pre(ky, kx, p, pi);
731 357688 : z = Kronecker_to_FlxqX_pre(z,T,p,pi);
732 357688 : return gc_upto(av, z);
733 : }
734 :
735 : GEN
736 1729318 : FlxqX_mul_pre(GEN x, GEN y, GEN T, ulong p, ulong pi)
737 : {
738 1729318 : pari_sp av = avma;
739 1729318 : GEN z, kx, ky, Tm = get_Flx_mod(T);
740 1729318 : kx= zxX_to_Kronecker(x, Tm);
741 1729318 : ky= zxX_to_Kronecker(y, Tm);
742 1729318 : z = Flx_mul_pre(ky, kx, p, pi);
743 1729318 : z = Kronecker_to_FlxqX_pre(z, T, p, pi);
744 1729318 : return gc_upto(av, z);
745 : }
746 : GEN
747 63936 : FlxqX_mul(GEN x, GEN y, GEN T, ulong p)
748 63936 : { return FlxqX_mul_pre(x, y, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
749 :
750 : GEN
751 363646 : FlxqX_sqr_pre(GEN x, GEN T, ulong p, ulong pi)
752 : {
753 363646 : pari_sp av = avma;
754 : GEN z,kx;
755 363646 : kx= zxX_to_Kronecker(x,get_Flx_mod(T));
756 363646 : z = Flx_sqr_pre(kx, p, pi);
757 363646 : z = Kronecker_to_FlxqX_pre(z,T,p,pi);
758 363646 : 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 155542 : FlxqX_Flxq_mul_pre(GEN P, GEN U, GEN T, ulong p, ulong pi)
766 : {
767 155542 : long i, lP = lg(P);
768 155542 : GEN res = cgetg(lP,t_POL);
769 155542 : res[1] = P[1];
770 555675 : for(i=2; i<lP; i++) gel(res,i) = Flxq_mul_pre(U,gel(P,i), T,p,pi);
771 155542 : 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 673076 : FlxqX_Flxq_mul_to_monic_pre(GEN P, GEN U, GEN T, ulong p, ulong pi)
779 : {
780 673076 : long i, lP = lg(P);
781 673076 : GEN res = cgetg(lP,t_POL);
782 673076 : res[1] = P[1];
783 3635265 : for(i=2; i<lP-1; i++) gel(res,i) = Flxq_mul_pre(U,gel(P,i), T,p,pi);
784 673076 : gel(res,lP-1) = pol1_Flx(get_Flx_var(T));
785 673076 : 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 190026 : FlxqX_normalize_pre(GEN z, GEN T, ulong p, ulong pi)
796 : {
797 190026 : GEN p1 = leading_coeff(z);
798 190026 : if (!lgpol(z) || (!degpol(p1) && p1[1] == 1)) return z;
799 190005 : 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 : static GEN
811 538511 : _FlxqX_mul(void *data,GEN a,GEN b)
812 : {
813 538511 : struct _FlxqXQ *d=(struct _FlxqXQ*)data;
814 538511 : return FlxqX_mul_pre(a,b,d->T,d->p,d->pi);
815 : }
816 : static GEN
817 10339 : _FlxqX_sqr(void *data,GEN a)
818 : {
819 10339 : struct _FlxqXQ *d=(struct _FlxqXQ*)data;
820 10339 : return FlxqX_sqr_pre(a,d->T,d->p,d->pi);
821 : }
822 :
823 : GEN
824 10262 : FlxqX_powu_pre(GEN V, ulong n, GEN T, ulong p, ulong pi)
825 : {
826 10262 : struct _FlxqXQ d; d.p = p; d.pi = pi; d.T = T;
827 10262 : return gen_powu(V, n, (void*)&d, &_FlxqX_sqr, &_FlxqX_mul);
828 : }
829 : GEN
830 0 : FlxqX_powu(GEN V, ulong n, GEN T, ulong p)
831 0 : { return FlxqX_powu_pre(V, n, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
832 :
833 : /* x and y in Z[Y][X]. Assume T irreducible mod p */
834 : static GEN
835 3219762 : FlxqX_divrem_basecase(GEN x, GEN y, GEN T, ulong p, ulong pi, GEN *pr)
836 : {
837 3219762 : long vx = varn(x), dx = degpol(x), dy = degpol(y), dz, i, j, sx, lr;
838 : pari_sp av0, av;
839 : GEN z, p1, rem, lead;
840 :
841 3219762 : if (!signe(y)) pari_err_INV("FlxqX_divrem",y);
842 3219762 : if (dx < dy)
843 : {
844 21653 : if (pr)
845 : {
846 21400 : av0 = avma; x = FlxqX_red_pre(x, T, p, pi);
847 21400 : if (pr == ONLY_DIVIDES) { set_avma(av0); return signe(x)? NULL: pol_0(vx); }
848 21400 : if (pr == ONLY_REM) return x;
849 21400 : *pr = x;
850 : }
851 21653 : return pol_0(vx);
852 : }
853 3198109 : lead = leading_coeff(y);
854 3198109 : if (!dy) /* y is constant */
855 : {
856 333560 : if (pr && pr != ONLY_DIVIDES)
857 : {
858 328871 : if (pr == ONLY_REM) return pol_0(vx);
859 134239 : *pr = pol_0(vx);
860 : }
861 138928 : if (Flx_equal1(lead)) return gcopy(x);
862 134680 : av0 = avma; x = FlxqX_Flxq_mul_pre(x,Flxq_inv(lead,T,p),T,p,pi);
863 134680 : return gc_upto(av0,x);
864 : }
865 2864549 : av0 = avma; dz = dx-dy;
866 2864549 : lead = Flx_equal1(lead)? NULL: gclone(Flxq_inv_pre(lead,T,p,pi));
867 2864549 : set_avma(av0);
868 2864549 : z = cgetg(dz+3,t_POL); z[1] = x[1];
869 2864549 : x += 2; y += 2; z += 2;
870 :
871 2864549 : p1 = gel(x,dx); av = avma;
872 2864549 : gel(z,dz) = lead? gc_upto(av, Flxq_mul_pre(p1,lead, T,p,pi)): gcopy(p1);
873 6581331 : for (i=dx-1; i>=dy; i--)
874 : {
875 3716782 : av = avma; p1 = gel(x,i);
876 12024688 : for (j=i-dy+1; j<=i && j<=dz; j++)
877 8307906 : p1 = Flx_sub(p1, Flx_mul_pre(gel(z,j),gel(y,i-j),p,pi),p);
878 3716782 : if (lead) p1 = Flx_mul_pre(p1, lead,p,pi);
879 3716782 : gel(z,i-dy) = gc_leaf(av, Flx_rem_pre(p1,T,p,pi));
880 : }
881 2864549 : if (!pr) { guncloneNULL(lead); return z-2; }
882 :
883 2670003 : rem = (GEN)avma; av = (pari_sp)new_chunk(dx+3);
884 2997699 : for (sx=0; ; i--)
885 : {
886 2997699 : p1 = gel(x,i);
887 8857879 : for (j=0; j<=i && j<=dz; j++)
888 5860180 : p1 = Flx_sub(p1, Flx_mul_pre(gel(z,j),gel(y,i-j),p,pi),p);
889 2997699 : p1 = Flx_rem_pre(p1, T,p,pi); if (lgpol(p1)) { sx = 1; break; }
890 402680 : if (!i) break;
891 327696 : set_avma(av);
892 : }
893 2670003 : if (pr == ONLY_DIVIDES)
894 : {
895 0 : guncloneNULL(lead);
896 0 : if (sx) return gc_NULL(av0);
897 0 : return gc_const((pari_sp)rem, z-2);
898 : }
899 2670003 : lr=i+3; rem -= lr; av = (pari_sp)rem;
900 2670003 : rem[0] = evaltyp(t_POL) | _evallg(lr);
901 2670003 : rem[1] = z[-1];
902 2670003 : rem += 2; gel(rem,i) = gc_leaf(av, p1);
903 17798479 : for (i--; i>=0; i--)
904 : {
905 15128476 : av = avma; p1 = gel(x,i);
906 49009065 : for (j=0; j<=i && j<=dz; j++)
907 33880589 : p1 = Flx_sub(p1, Flx_mul_pre(gel(z,j),gel(y,i-j),p,pi), p);
908 15128476 : gel(rem,i) = gc_leaf(av, Flx_rem_pre(p1, T,p,pi));
909 : }
910 2670003 : rem -= 2;
911 2670003 : guncloneNULL(lead);
912 2670003 : if (!sx) (void)FlxX_renormalize(rem, lr);
913 2670003 : if (pr == ONLY_REM) return gc_upto(av0,rem);
914 1227146 : *pr = rem; return z-2;
915 : }
916 :
917 : static GEN
918 1391 : FlxqX_invBarrett_basecase(GEN T, GEN Q, ulong p, ulong pi)
919 : {
920 1391 : long i, l=lg(T)-1, lr = l-1, k;
921 1391 : long sv=Q[1];
922 1391 : GEN r=cgetg(lr,t_POL); r[1]=T[1];
923 1391 : gel(r,2) = pol1_Flx(sv);
924 15941 : for (i=3;i<lr;i++)
925 : {
926 14550 : pari_sp ltop=avma;
927 14550 : GEN u = Flx_neg(gel(T,l-i+2),p);
928 105265 : for (k=3;k<i;k++)
929 90715 : u = Flx_sub(u, Flxq_mul_pre(gel(T,l-i+k), gel(r,k), Q, p, pi), p);
930 14550 : gel(r,i) = gc_upto(ltop, u);
931 : }
932 1391 : r = FlxX_renormalize(r,lr);
933 1391 : return r;
934 : }
935 :
936 : /* Return new lgpol */
937 : static long
938 400717 : FlxX_lgrenormalizespec(GEN x, long lx)
939 : {
940 : long i;
941 485136 : for (i = lx-1; i>=0; i--)
942 485136 : if (lgpol(gel(x,i))) break;
943 400717 : return i+1;
944 : }
945 :
946 : static GEN
947 8354 : FlxqX_invBarrett_Newton(GEN S, GEN T, ulong p, ulong pi)
948 : {
949 8354 : pari_sp av = avma;
950 8354 : long nold, lx, lz, lq, l = degpol(S), i, lQ;
951 8354 : GEN q, y, z, x = cgetg(l+2, t_POL) + 2;
952 8354 : long dT = get_Flx_degree(T), vT = get_Flx_var(T);
953 8354 : ulong mask = quadratic_prec_mask(l-2); /* assume l > 2 */
954 374914 : for (i=0;i<l;i++) gel(x,i) = pol0_Flx(vT);
955 8354 : q = FlxX_recipspec(S+2,l+1,l+1,dT);
956 8354 : lQ = lgpol(q); q+=2;
957 : /* We work on _spec_ FlxX's, all the l[xzq] below are lgpol's */
958 :
959 : /* initialize */
960 8354 : gel(x,0) = Flxq_inv_pre(gel(q,0),T, p, pi);
961 8354 : if (lQ>1 && degpol(gel(q,1)) >= dT)
962 0 : gel(q,1) = Flx_rem_pre(gel(q,1), T, p, pi);
963 8354 : if (lQ>1 && lgpol(gel(q,1)))
964 5635 : {
965 5635 : GEN u = gel(q, 1);
966 5635 : if (!Flx_equal1(gel(x,0)))
967 7 : u = Flxq_mul_pre(u, Flxq_sqr_pre(gel(x,0), T,p,pi), T,p,pi);
968 5635 : gel(x,1) = Flx_neg(u, p); lx = 2;
969 : }
970 : else
971 2719 : lx = 1;
972 8354 : nold = 1;
973 54795 : for (; mask > 1; )
974 : { /* set x -= x(x*q - 1) + O(t^(nnew + 1)), knowing x*q = 1 + O(t^(nold+1)) */
975 46441 : long i, lnew, nnew = nold << 1;
976 :
977 46441 : if (mask & 1) nnew--;
978 46441 : mask >>= 1;
979 :
980 46441 : lnew = nnew + 1;
981 46441 : lq = FlxX_lgrenormalizespec(q, minss(lQ,lnew));
982 46441 : z = FlxqX_mulspec(x, q, T,p,pi, lx, lq); /* FIXME: high product */
983 46441 : lz = lgpol(z); if (lz > lnew) lz = lnew;
984 46441 : z += 2;
985 : /* subtract 1 [=>first nold words are 0]: renormalize so that z(0) != 0 */
986 99660 : for (i = nold; i < lz; i++) if (lgpol(gel(z,i))) break;
987 46441 : nold = nnew;
988 46441 : if (i >= lz) continue; /* z-1 = 0(t^(nnew + 1)) */
989 :
990 : /* z + i represents (x*q - 1) / t^i */
991 45482 : lz = FlxX_lgrenormalizespec (z+i, lz-i);
992 45482 : z = FlxqX_mulspec(x, z+i, T,p,pi, lx, lz); /* FIXME: low product */
993 45482 : lz = lgpol(z); z += 2;
994 45482 : if (lz > lnew-i) lz = FlxX_lgrenormalizespec(z, lnew-i);
995 :
996 45482 : lx = lz+ i;
997 45482 : y = x + i; /* x -= z * t^i, in place */
998 374886 : for (i = 0; i < lz; i++) gel(y,i) = Flx_neg(gel(z,i), p);
999 : }
1000 8354 : x -= 2; setlg(x, lx + 2); x[1] = S[1];
1001 8354 : return gc_GEN(av, x);
1002 : }
1003 :
1004 : GEN
1005 9745 : FlxqX_invBarrett_pre(GEN T, GEN Q, ulong p, ulong pi)
1006 : {
1007 9745 : pari_sp ltop=avma;
1008 9745 : long l=lg(T), v = varn(T);
1009 : GEN r;
1010 9745 : GEN c = gel(T,l-1);
1011 9745 : if (l<5) return pol_0(v);
1012 9745 : if (l<=FlxqX_INVBARRETT_LIMIT)
1013 : {
1014 1391 : if (!Flx_equal1(c))
1015 : {
1016 0 : GEN ci = Flxq_inv_pre(c,Q,p,pi);
1017 0 : T = FlxqX_Flxq_mul_pre(T, ci, Q, p, pi);
1018 0 : r = FlxqX_invBarrett_basecase(T,Q,p,pi);
1019 0 : r = FlxqX_Flxq_mul_pre(r,ci,Q,p,pi);
1020 : } else
1021 1391 : r = FlxqX_invBarrett_basecase(T,Q,p,pi);
1022 : } else
1023 8354 : r = FlxqX_invBarrett_Newton(T,Q,p,pi);
1024 9745 : return gc_upto(ltop, r);
1025 : }
1026 : GEN
1027 62 : FlxqX_invBarrett(GEN T, GEN Q, ulong p)
1028 62 : { return FlxqX_invBarrett_pre(T, Q, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
1029 :
1030 : GEN
1031 495992 : FlxqX_get_red_pre(GEN S, GEN T, ulong p, ulong pi)
1032 : {
1033 495992 : if (typ(S)==t_POL && lg(S)>FlxqX_BARRETT_LIMIT)
1034 8221 : retmkvec2(FlxqX_invBarrett_pre(S, T, p, pi), S);
1035 487771 : return S;
1036 : }
1037 : GEN
1038 336 : FlxqX_get_red(GEN S, GEN T, ulong p)
1039 : {
1040 336 : if (typ(S)==t_POL && lg(S)>FlxqX_BARRETT_LIMIT)
1041 62 : retmkvec2(FlxqX_invBarrett(S, T, p), S);
1042 274 : return S;
1043 : }
1044 :
1045 : /* Compute x mod S where 2 <= degpol(S) <= l+1 <= 2*(degpol(S)-1)
1046 : * * and mg is the Barrett inverse of S. */
1047 : static GEN
1048 133019 : FlxqX_divrem_Barrettspec(GEN x, long l, GEN mg, GEN S, GEN T, ulong p,
1049 : ulong pi, GEN *pr)
1050 : {
1051 : GEN q, r;
1052 133019 : long lt = degpol(S); /*We discard the leading term*/
1053 : long ld, lm, lT, lmg;
1054 133019 : ld = l-lt;
1055 133019 : lm = minss(ld, lgpol(mg));
1056 133019 : lT = FlxX_lgrenormalizespec(S+2,lt);
1057 133019 : lmg = FlxX_lgrenormalizespec(mg+2,lm);
1058 133019 : q = FlxX_recipspec(x+lt,ld,ld,0); /* = rec(x) lq<=ld*/
1059 133019 : q = FlxqX_mulspec(q+2,mg+2,T,p,pi,lgpol(q),lmg); /* = rec(x)*mg lq<=ld+lm*/
1060 133019 : q = FlxX_recipspec(q+2,minss(ld,lgpol(q)),ld,0); /* = rec(rec(x)*mg) lq<=ld*/
1061 133019 : if (!pr) return q;
1062 132746 : r = FlxqX_mulspec(q+2,S+2,T,p,pi,lgpol(q),lT); /* = q*pol lr<=ld+lt*/
1063 132746 : r = FlxX_subspec(x,r+2,p,lt,minss(lt,lgpol(r)));/* = x - r lr<=lt */
1064 132746 : if (pr == ONLY_REM) return r;
1065 7934 : *pr = r; return q;
1066 : }
1067 :
1068 : static GEN
1069 125966 : FlxqX_divrem_Barrett(GEN x, GEN mg, GEN S, GEN T, ulong p, ulong pi, GEN *pr)
1070 : {
1071 125966 : GEN q = NULL, r = FlxqX_red_pre(x, T, p, pi);
1072 125966 : long l = lgpol(r), lt = degpol(S), lm = 2*lt-1, v = varn(S);
1073 : long i;
1074 125966 : if (l <= lt)
1075 : {
1076 0 : if (pr == ONLY_REM) return r;
1077 0 : if (pr == ONLY_DIVIDES) return signe(r)? NULL: pol_0(v);
1078 0 : if (pr) *pr = r;
1079 0 : return pol_0(v);
1080 : }
1081 125966 : if (lt <= 1)
1082 0 : return FlxqX_divrem_basecase(x,S,T,p,pi,pr);
1083 125966 : if (pr != ONLY_REM && l>lm)
1084 : {
1085 846 : long vT = get_Flx_var(T);
1086 846 : q = cgetg(l-lt+2, t_POL); q[1] = S[1];
1087 61868 : for (i=0;i<l-lt;i++) gel(q+2,i) = pol0_Flx(vT);
1088 : }
1089 133101 : while (l>lm)
1090 : {
1091 7135 : GEN zr, zq = FlxqX_divrem_Barrettspec(r+2+l-lm,lm,mg,S,T,p,pi,&zr);
1092 7135 : long lz = lgpol(zr);
1093 7135 : if (pr != ONLY_REM)
1094 : {
1095 2746 : long lq = lgpol(zq);
1096 55408 : for(i=0; i<lq; i++) gel(q+2+l-lm,i) = gel(zq,2+i);
1097 : }
1098 77270 : for(i=0; i<lz; i++) gel(r+2+l-lm,i) = gel(zr,2+i);
1099 7135 : l = l-lm+lz;
1100 : }
1101 125966 : if (pr == ONLY_REM)
1102 : {
1103 124812 : if (l > lt)
1104 124812 : r = FlxqX_divrem_Barrettspec(r+2,l,mg,S,T,p,pi,ONLY_REM);
1105 : else
1106 0 : r = FlxX_renormalize(r, l+2);
1107 124812 : setvarn(r, v); return r;
1108 : }
1109 1154 : if (l > lt)
1110 : {
1111 1072 : GEN zq = FlxqX_divrem_Barrettspec(r+2,l,mg,S,T,p,pi,pr? &r: NULL);
1112 1072 : if (!q) q = zq;
1113 : else
1114 : {
1115 764 : long lq = lgpol(zq);
1116 6540 : for(i=0; i<lq; i++) gel(q+2,i) = gel(zq,2+i);
1117 : }
1118 : }
1119 82 : else if (pr)
1120 82 : r = FlxX_renormalize(r, l+2);
1121 1154 : setvarn(q, v); q = FlxX_renormalize(q, lg(q));
1122 1154 : if (pr == ONLY_DIVIDES) return signe(r)? NULL: q;
1123 1154 : if (pr) { setvarn(r, v); *pr = r; }
1124 1154 : return q;
1125 : }
1126 :
1127 : GEN
1128 1583427 : FlxqX_divrem_pre(GEN x, GEN S, GEN T, ulong p, ulong pi, GEN *pr)
1129 : {
1130 : GEN B, y;
1131 : long dy, dx, d;
1132 1583427 : if (pr==ONLY_REM) return FlxqX_rem_pre(x, S, T, p, pi);
1133 1583427 : y = get_FlxqX_red(S, &B);
1134 1583427 : dy = degpol(y); dx = degpol(x); d = dx-dy;
1135 1583427 : if (!B && d+3 < FlxqX_DIVREM_BARRETT_LIMIT)
1136 1582273 : return FlxqX_divrem_basecase(x,y,T,p,pi,pr);
1137 : else
1138 : {
1139 1154 : pari_sp av = avma;
1140 1154 : GEN mg = B? B: FlxqX_invBarrett_pre(y, T, p, pi);
1141 1154 : GEN q = FlxqX_divrem_Barrett(x,mg,y,T,p,pi,pr);
1142 1154 : if (!q) return gc_NULL(av);
1143 1154 : if (!pr || pr==ONLY_DIVIDES) return gc_GEN(av, q);
1144 881 : return gc_all(av, 2, &q, pr);
1145 : }
1146 : }
1147 : GEN
1148 1078751 : FlxqX_divrem(GEN x, GEN S, GEN T, ulong p, GEN *pr)
1149 : {
1150 1078751 : ulong pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
1151 1078751 : return FlxqX_divrem_pre(x, S, T, p, pi, pr);
1152 : }
1153 :
1154 : GEN
1155 2116348 : FlxqX_rem_pre(GEN x, GEN S, GEN T, ulong p, ulong pi)
1156 : {
1157 2116348 : GEN B, y = get_FlxqX_red(S, &B);
1158 2116348 : long dy = degpol(y), dx = degpol(x), d = dx-dy;
1159 2116348 : if (d < 0) return FlxqX_red_pre(x, T, p, pi);
1160 1762301 : if (!B && d+3 < FlxqX_REM_BARRETT_LIMIT)
1161 1637489 : return FlxqX_divrem_basecase(x,y, T, p, pi, ONLY_REM);
1162 : else
1163 : {
1164 124812 : pari_sp av=avma;
1165 124812 : GEN mg = B? B: FlxqX_invBarrett_pre(y, T, p, pi);
1166 124812 : GEN r = FlxqX_divrem_Barrett(x, mg, y, T, p, pi, ONLY_REM);
1167 124812 : return gc_upto(av, r);
1168 : }
1169 : }
1170 : GEN
1171 5109 : FlxqX_rem(GEN x, GEN S, GEN T, ulong p)
1172 5109 : { return FlxqX_rem_pre(x, S, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
1173 :
1174 : /* x + y*z mod p */
1175 : INLINE GEN
1176 103796 : Flxq_addmul_pre(GEN x, GEN y, GEN z, GEN T, ulong p, ulong pi)
1177 : {
1178 : pari_sp av;
1179 103796 : if (!lgpol(y) || !lgpol(z)) return Flx_rem_pre(x, T, p, pi);
1180 102265 : if (!lgpol(x)) return Flxq_mul_pre(z, y, T, p, pi);
1181 102161 : av = avma;
1182 102161 : return gc_upto(av, Flx_add(x, Flxq_mul_pre(y, z, T, p, pi), p));
1183 : }
1184 :
1185 : GEN
1186 51898 : FlxqX_div_by_X_x_pre(GEN a, GEN x, GEN T, ulong p, ulong pi, GEN *r)
1187 : {
1188 51898 : long l = lg(a), i;
1189 : GEN z;
1190 51898 : if (l <= 3)
1191 : {
1192 0 : if (r) *r = l == 2? pol0_Flx(get_Flx_var(T)): Flx_copy(gel(a,2));
1193 0 : return pol_0(varn(a));
1194 : }
1195 51898 : l--; z = cgetg(l, t_POL); z[1] = a[1];
1196 51898 : gel(z, l-1) = gel(a,l);
1197 155694 : for (i=l-2; i>1; i--) /* z[i] = a[i+1] + x*z[i+1] */
1198 103796 : gel(z, i) = Flxq_addmul_pre(gel(a,i+1), x, gel(z,i+1), T, p, pi);
1199 51898 : if (r) *r = Flxq_addmul_pre(gel(a,2), x, gel(z,2), T, p, pi);
1200 51898 : return z;
1201 : }
1202 :
1203 : GEN
1204 51898 : FlxqX_div_by_X_x(GEN a, GEN x, GEN T, ulong p, GEN *r)
1205 51898 : { return FlxqX_div_by_X_x_pre(a, x, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p), r); }
1206 :
1207 : static GEN
1208 13562 : FlxqX_addmulmul(GEN u, GEN v, GEN x, GEN y, GEN T, ulong p, ulong pi)
1209 : {
1210 13562 : return FlxX_add(FlxqX_mul_pre(u, x, T, p, pi),
1211 : FlxqX_mul_pre(v, y, T, p, pi), p);
1212 : }
1213 :
1214 : static GEN
1215 6626 : FlxqXM_FlxqX_mul2(GEN M, GEN x, GEN y, GEN T, ulong p, ulong pi)
1216 : {
1217 6626 : GEN res = cgetg(3, t_COL);
1218 6626 : gel(res, 1) = FlxqX_addmulmul(gcoeff(M,1,1), gcoeff(M,1,2), x, y, T, p, pi);
1219 6626 : gel(res, 2) = FlxqX_addmulmul(gcoeff(M,2,1), gcoeff(M,2,2), x, y, T, p, pi);
1220 6626 : return res;
1221 : }
1222 :
1223 : static GEN
1224 3276 : FlxqXM_mul2(GEN A, GEN B, GEN T, ulong p, ulong pi)
1225 : {
1226 3276 : GEN A11=gcoeff(A,1,1),A12=gcoeff(A,1,2), B11=gcoeff(B,1,1),B12=gcoeff(B,1,2);
1227 3276 : GEN A21=gcoeff(A,2,1),A22=gcoeff(A,2,2), B21=gcoeff(B,2,1),B22=gcoeff(B,2,2);
1228 3276 : GEN M1 = FlxqX_mul_pre(FlxX_add(A11,A22, p), FlxX_add(B11,B22, p), T, p, pi);
1229 3276 : GEN M2 = FlxqX_mul_pre(FlxX_add(A21,A22, p), B11, T, p, pi);
1230 3276 : GEN M3 = FlxqX_mul_pre(A11, FlxX_sub(B12,B22, p), T, p, pi);
1231 3276 : GEN M4 = FlxqX_mul_pre(A22, FlxX_sub(B21,B11, p), T, p, pi);
1232 3276 : GEN M5 = FlxqX_mul_pre(FlxX_add(A11,A12, p), B22, T, p, pi);
1233 3276 : GEN M6 = FlxqX_mul_pre(FlxX_sub(A21,A11, p), FlxX_add(B11,B12, p), T, p, pi);
1234 3276 : GEN M7 = FlxqX_mul_pre(FlxX_sub(A12,A22, p), FlxX_add(B21,B22, p), T, p, pi);
1235 3276 : GEN T1 = FlxX_add(M1,M4, p), T2 = FlxX_sub(M7,M5, p);
1236 3276 : GEN T3 = FlxX_sub(M1,M2, p), T4 = FlxX_add(M3,M6, p);
1237 3276 : retmkmat22(FlxX_add(T1,T2, p), FlxX_add(M3,M5, p),
1238 : FlxX_add(M2,M4, p), FlxX_add(T3,T4, p));
1239 : }
1240 :
1241 : /* Return [0,1;1,-q]*M */
1242 : static GEN
1243 3276 : FlxqX_FlxqXM_qmul(GEN q, GEN M, GEN T, ulong p, ulong pi)
1244 : {
1245 3276 : GEN u = FlxqX_mul_pre(gcoeff(M,2,1), q, T,p,pi);
1246 3276 : GEN v = FlxqX_mul_pre(gcoeff(M,2,2), q, T,p,pi);
1247 3276 : retmkmat22(gcoeff(M,2,1), gcoeff(M,2,2),
1248 : FlxX_sub(gcoeff(M,1,1), u, p), FlxX_sub(gcoeff(M,1,2), v, p));
1249 : }
1250 :
1251 : static GEN
1252 16 : matid2_FlxXM(long v, long sv)
1253 16 : { retmkmat22(pol1_FlxX(v, sv),pol_0(v),pol_0(v),pol1_FlxX(v, sv)); }
1254 :
1255 : static GEN
1256 0 : matJ2_FlxXM(long v, long sv)
1257 0 : { retmkmat22(pol_0(v),pol1_FlxX(v, sv),pol1_FlxX(v, sv),pol_0(v)); }
1258 :
1259 : struct FlxqX_res
1260 : {
1261 : GEN res, lc;
1262 : long deg0, deg1, off;
1263 : };
1264 :
1265 : INLINE void
1266 0 : FlxqX_halfres_update(long da, long db, long dr, GEN T, ulong p, ulong pi, struct FlxqX_res *res)
1267 : {
1268 0 : if (dr >= 0)
1269 : {
1270 0 : if (!Flx_equal1(res->lc))
1271 : {
1272 0 : res->lc = Flxq_powu_pre(res->lc, da - dr, T, p, pi);
1273 0 : res->res = Flxq_mul_pre(res->res, res->lc, T, p, pi);
1274 : }
1275 0 : if (both_odd(da + res->off, db + res->off))
1276 0 : res->res = Flx_neg(res->res, p);
1277 : } else
1278 : {
1279 0 : if (db == 0)
1280 : {
1281 0 : if (!Flx_equal1(res->lc))
1282 : {
1283 0 : res->lc = Flxq_powu_pre(res->lc, da, T, p, pi);
1284 0 : res->res = Flxq_mul_pre(res->res, res->lc, T, p, pi);
1285 : }
1286 : } else
1287 0 : res->res = pol0_Flx(get_Flx_var(T));
1288 : }
1289 0 : }
1290 :
1291 : static GEN
1292 4052 : FlxqX_halfres_basecase(GEN a, GEN b, GEN T, ulong p, ulong pi, GEN *pa, GEN *pb, struct FlxqX_res *res)
1293 : {
1294 4052 : pari_sp av=avma;
1295 : GEN u,u1,v,v1, M;
1296 4052 : long vx = varn(a), vT = get_Flx_var(T), n = lgpol(a)>>1;
1297 4052 : u1 = v = pol_0(vx);
1298 4052 : u = v1 = pol1_FlxX(vx, vT);
1299 22505 : while (lgpol(b)>n)
1300 : {
1301 : GEN r, q;
1302 18453 : q = FlxqX_divrem(a,b, T, p, &r);
1303 18453 : if (res)
1304 : {
1305 0 : long da = degpol(a), db = degpol(b), dr = degpol(r);
1306 0 : res->lc = gel(b,db+2);
1307 0 : if (dr >= n)
1308 0 : FlxqX_halfres_update(da, db, dr, T, p, pi, res);
1309 : else
1310 : {
1311 0 : res->deg0 = da;
1312 0 : res->deg1 = db;
1313 : }
1314 : }
1315 18453 : a = b; b = r; swap(u,u1); swap(v,v1);
1316 18453 : u1 = FlxX_sub(u1, FlxqX_mul_pre(u, q, T, p, pi), p);
1317 18453 : v1 = FlxX_sub(v1, FlxqX_mul_pre(v, q, T, p, pi), p);
1318 18453 : if (gc_needed(av,2))
1319 : {
1320 0 : if (DEBUGMEM>1) pari_warn(warnmem,"FlxqX_halfgcd (d = %ld)",degpol(b));
1321 0 : if (res)
1322 0 : (void)gc_all(av, 8, &a,&b,&u1,&v1,&u,&v,&res->res,&res->lc);
1323 : else
1324 0 : (void)gc_all(av, 6, &a,&b,&u1,&v1,&u,&v);
1325 : }
1326 : }
1327 4052 : M = mkmat22(u,v,u1,v1); *pa = a; *pb = b;
1328 0 : return res ? gc_all(av, 5, &M, pa, pb, &res->res, &res->lc)
1329 4052 : : gc_all(av, 3, &M, pa, pb);
1330 : }
1331 :
1332 : static GEN FlxqX_halfres_i(GEN x, GEN y, GEN T, ulong p, ulong pi, GEN *a, GEN *b, struct FlxqX_res *res);
1333 :
1334 : static GEN
1335 3366 : FlxqX_halfres_split(GEN x, GEN y, GEN T, ulong p, ulong pi, GEN *a, GEN *b, struct FlxqX_res *res)
1336 : {
1337 3366 : pari_sp av = avma;
1338 : GEN Q, R, S, V1, V2;
1339 : GEN x1, y1, r, q;
1340 3366 : long l = lgpol(x), n = l>>1, k, vT = get_Flx_var(T);
1341 3366 : if (lgpol(y) <= n)
1342 16 : { *a = RgX_copy(x); *b = RgX_copy(y); return matid2_FlxXM(varn(x), vT); }
1343 3350 : if (res)
1344 : {
1345 0 : res->lc = leading_coeff(y);
1346 0 : res->deg0 -= n;
1347 0 : res->deg1 -= n;
1348 0 : res->off += n;
1349 : }
1350 3350 : R = FlxqX_halfres_i(FlxX_shift(x,-n, vT),FlxX_shift(y,-n, vT), T, p, pi, a, b, res);
1351 3350 : if (res)
1352 : {
1353 0 : res->off -= n;
1354 0 : res->deg0 += n;
1355 0 : res->deg1 += n;
1356 : }
1357 3350 : V1 = FlxqXM_FlxqX_mul2(R, Flxn_red(x,n), Flxn_red(y,n), T, p, pi);
1358 3350 : x1 = FlxX_add(FlxX_shift(*a,n,vT), gel(V1,1), p);
1359 3350 : y1 = FlxX_add(FlxX_shift(*b,n,vT), gel(V1,2), p);
1360 3350 : if (lgpol(y1) <= n)
1361 : {
1362 74 : *a = x1; *b = y1;
1363 0 : return res ? gc_all(av, 5, &R, a, b, &res->res, &res->lc)
1364 74 : : gc_all(av, 3, &R, a, b);
1365 : }
1366 3276 : k = 2*n-degpol(y1);
1367 3276 : q = FlxqX_divrem(x1, y1, T, p, &r);
1368 3276 : if (res)
1369 : {
1370 0 : long dx1 = degpol(x1), dy1 = degpol(y1), dr = degpol(r);
1371 0 : if (dy1 < degpol(y))
1372 0 : FlxqX_halfres_update(res->deg0, res->deg1, dy1, T, p, pi, res);
1373 0 : res->lc = leading_coeff(y1);
1374 0 : res->deg0 = dx1;
1375 0 : res->deg1 = dy1;
1376 0 : if (dr >= n)
1377 : {
1378 0 : FlxqX_halfres_update(dx1, dy1, dr, T, p, pi, res);
1379 0 : res->deg0 = dy1;
1380 0 : res->deg1 = dr;
1381 : }
1382 0 : res->deg0 -= k;
1383 0 : res->deg1 -= k;
1384 0 : res->off += k;
1385 : }
1386 3276 : S = FlxqX_halfres_i(FlxX_shift(y1,-k, vT), FlxX_shift(r,-k, vT), T, p, pi, a, b, res);
1387 3276 : if (res)
1388 : {
1389 0 : res->deg0 += k;
1390 0 : res->deg1 += k;
1391 0 : res->off -= k;
1392 : }
1393 3276 : Q = FlxqXM_mul2(S, FlxqX_FlxqXM_qmul(q, R, T, p, pi), T, p, pi);
1394 3276 : V2 = FlxqXM_FlxqX_mul2(S, FlxXn_red(y1,k), FlxXn_red(r,k), T, p, pi);
1395 3276 : *a = FlxX_add(FlxX_shift(*a,k,vT), gel(V2,1), p);
1396 3276 : *b = FlxX_add(FlxX_shift(*b,k,vT), gel(V2,2), p);
1397 0 : return res ? gc_all(av, 5, &Q, a, b, &res->res, &res->lc)
1398 3276 : : gc_all(av, 3, &Q, a, b);
1399 : }
1400 :
1401 : static GEN
1402 7418 : FlxqX_halfres_i(GEN x, GEN y, GEN T, ulong p, ulong pi, GEN *a, GEN *b, struct FlxqX_res *res)
1403 : {
1404 7418 : if (lgpol(x) < FlxqX_HALFGCD_LIMIT)
1405 4052 : return FlxqX_halfres_basecase(x, y, T, p, pi, a, b, res);
1406 3366 : return FlxqX_halfres_split(x, y, T, p, pi, a, b, res);
1407 : }
1408 :
1409 : static GEN
1410 792 : FlxqX_halfgcd_all_i(GEN x, GEN y, GEN T, ulong p, ulong pi, GEN *pa, GEN *pb)
1411 : {
1412 : GEN a, b;
1413 792 : GEN R = FlxqX_halfres_i(x, y, T, p, pi, &a, &b, NULL);
1414 792 : if (pa) *pa = a;
1415 792 : if (pb) *pb = b;
1416 792 : return R;
1417 : }
1418 :
1419 : /* Return M in GL_2(Fp[X]/(T)[Y]) such that:
1420 : if [a',b']~=M*[a,b]~ then degpol(a')>= (lgpol(a)>>1) >degpol(b')
1421 : */
1422 :
1423 : GEN
1424 792 : FlxqX_halfgcd_all_pre(GEN x, GEN y, GEN T, ulong p, ulong pi, GEN *a, GEN *b)
1425 : {
1426 792 : pari_sp av = avma;
1427 : GEN R,q,r;
1428 792 : if (!signe(x))
1429 : {
1430 0 : if (a) *a = RgX_copy(y);
1431 0 : if (b) *b = RgX_copy(x);
1432 0 : return matJ2_FlxXM(varn(x),get_Flx_var(T));
1433 : }
1434 792 : if (degpol(y)<degpol(x)) return FlxqX_halfgcd_all_i(x, y, T, p, pi, a, b);
1435 193 : q = FlxqX_divrem_pre(y, x, T, p, pi, &r);
1436 193 : R = FlxqX_halfgcd_all_i(x, r, T, p, pi, a, b);
1437 193 : gcoeff(R,1,1) = FlxX_sub(gcoeff(R,1,1),
1438 193 : FlxqX_mul_pre(q, gcoeff(R,1,2), T, p, pi), p);
1439 193 : gcoeff(R,2,1) = FlxX_sub(gcoeff(R,2,1),
1440 193 : FlxqX_mul_pre(q, gcoeff(R,2,2), T, p, pi), p);
1441 193 : return !a && b ? gc_all(av, 2, &R, b): gc_all(av, 1+!!a+!!b, &R, a, b);
1442 : }
1443 : GEN
1444 7 : FlxqX_halfgcd_all(GEN x, GEN y, GEN T, ulong p, GEN *a, GEN *b)
1445 7 : { return FlxqX_halfgcd_all_pre(x, y, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p), a, b); }
1446 :
1447 : GEN
1448 254 : FlxqX_halfgcd_pre(GEN x, GEN y, GEN T, ulong p, ulong pi)
1449 254 : { return FlxqX_halfgcd_all_pre(x, y, T, p, pi, NULL, NULL); }
1450 :
1451 : GEN
1452 0 : FlxqX_halfgcd(GEN x, GEN y, GEN T, ulong p)
1453 0 : { return FlxqX_halfgcd_pre(x, y, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
1454 :
1455 : static GEN
1456 167928 : FlxqX_gcd_basecase(GEN a, GEN b, GEN T, ulong p, ulong pi)
1457 : {
1458 167928 : pari_sp av = avma, av0=avma;
1459 1124147 : while (signe(b))
1460 : {
1461 : GEN c;
1462 956219 : if (gc_needed(av0,2))
1463 : {
1464 0 : if (DEBUGMEM>1) pari_warn(warnmem,"FlxqX_gcd (d = %ld)",degpol(b));
1465 0 : (void)gc_all(av0,2, &a,&b);
1466 : }
1467 956219 : av = avma; c = FlxqX_rem_pre(a, b, T, p, pi); a=b; b=c;
1468 : }
1469 167928 : return gc_const(av, a);
1470 : }
1471 :
1472 : GEN
1473 177830 : FlxqX_gcd_pre(GEN x, GEN y, GEN T, ulong p, ulong pi)
1474 : {
1475 177830 : pari_sp av = avma;
1476 177830 : x = FlxqX_red_pre(x, T, p, pi);
1477 177830 : y = FlxqX_red_pre(y, T, p, pi);
1478 177830 : if (!signe(x)) return gc_upto(av, y);
1479 168304 : while (lgpol(y)>=FlxqX_GCD_LIMIT)
1480 : {
1481 376 : if (lgpol(y)<=(lgpol(x)>>1))
1482 : {
1483 0 : GEN r = FlxqX_rem_pre(x, y, T, p, pi);
1484 0 : x = y; y = r;
1485 : }
1486 376 : (void) FlxqX_halfgcd_all_pre(x,y, T, p, pi, &x, &y);
1487 376 : if (gc_needed(av,2))
1488 : {
1489 0 : if (DEBUGMEM>1) pari_warn(warnmem,"FlxqX_gcd (y = %ld)",degpol(y));
1490 0 : (void)gc_all(av,2,&x,&y);
1491 : }
1492 : }
1493 167928 : return gc_upto(av, FlxqX_gcd_basecase(x, y, T, p, pi));
1494 : }
1495 : GEN
1496 24557 : FlxqX_gcd(GEN x, GEN y, GEN T, ulong p)
1497 24557 : { return FlxqX_gcd_pre(x, y, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
1498 :
1499 : static GEN
1500 134246 : FlxqX_extgcd_basecase(GEN a, GEN b, GEN T, ulong p,ulong pi, GEN *ptu, GEN *ptv)
1501 : {
1502 134246 : pari_sp av=avma;
1503 : GEN u,v,d,d1,v1;
1504 134246 : long vx = varn(a);
1505 134246 : d = a; d1 = b;
1506 134246 : v = pol_0(vx); v1 = pol1_FlxX(vx, get_Flx_var(T));
1507 472812 : while (signe(d1))
1508 : {
1509 338566 : GEN r, q = FlxqX_divrem_pre(d, d1, T, p, pi, &r);
1510 338566 : v = FlxX_sub(v, FlxqX_mul_pre(q,v1,T, p, pi),p);
1511 338566 : u=v; v=v1; v1=u;
1512 338566 : u=r; d=d1; d1=u;
1513 338566 : if (gc_needed(av,2))
1514 : {
1515 0 : if (DEBUGMEM>1) pari_warn(warnmem,"FlxqX_extgcd (d = %ld)",degpol(d));
1516 0 : (void)gc_all(av,5, &d,&d1,&u,&v,&v1);
1517 : }
1518 : }
1519 134246 : if (ptu)
1520 134232 : *ptu = FlxqX_div_pre(FlxX_sub(d,FlxqX_mul_pre(b,v, T,p,pi), p), a, T,p,pi);
1521 134246 : *ptv = v; return d;
1522 : }
1523 :
1524 : static GEN
1525 143 : FlxqX_extgcd_halfgcd(GEN x, GEN y, GEN T, ulong p, ulong pi, GEN *ptu, GEN *ptv)
1526 : {
1527 : GEN u,v;
1528 143 : GEN V = cgetg(expu(lgpol(y))+2,t_VEC);
1529 143 : long i, n = 0, vs = varn(x), vT = get_Flx_var(T);
1530 298 : while (lgpol(y) >= FlxqX_EXTGCD_LIMIT)
1531 : {
1532 155 : if (lgpol(y)<=(lgpol(x)>>1))
1533 : {
1534 0 : GEN r, q = FlxqX_divrem_pre(x, y, T, p, pi, &r);
1535 0 : x = y; y = r;
1536 0 : gel(V,++n) = mkmat22(pol_0(vs),pol1_FlxX(vs,vT),pol1_FlxX(vs,vT),FlxX_neg(q,p));
1537 : } else
1538 155 : gel(V,++n) = FlxqX_halfgcd_all_pre(x, y, T, p, pi, &x, &y);
1539 : }
1540 143 : y = FlxqX_extgcd_basecase(x,y, T, p, pi, &u,&v);
1541 155 : for (i = n; i>1; i--)
1542 : {
1543 12 : GEN R = gel(V,i);
1544 12 : GEN u1 = FlxqX_addmulmul(u, v, gcoeff(R,1,1), gcoeff(R,2,1), T, p, pi);
1545 12 : GEN v1 = FlxqX_addmulmul(u, v, gcoeff(R,1,2), gcoeff(R,2,2), T, p, pi);
1546 12 : u = u1; v = v1;
1547 : }
1548 : {
1549 143 : GEN R = gel(V,1);
1550 143 : if (ptu)
1551 143 : *ptu = FlxqX_addmulmul(u, v, gcoeff(R,1,1), gcoeff(R,2,1), T, p, pi);
1552 143 : *ptv = FlxqX_addmulmul(u, v, gcoeff(R,1,2), gcoeff(R,2,2), T, p, pi);
1553 : }
1554 143 : return y;
1555 : }
1556 :
1557 : /* x and y in Z[Y][X], return lift(gcd(x mod T,p, y mod T,p)). Set u and v st
1558 : * ux + vy = gcd (mod T,p) */
1559 : GEN
1560 134246 : FlxqX_extgcd_pre(GEN x, GEN y, GEN T, ulong p, ulong pi, GEN *ptu, GEN *ptv)
1561 : {
1562 134246 : pari_sp av = avma;
1563 : GEN d;
1564 134246 : x = FlxqX_red_pre(x, T, p, pi);
1565 134246 : y = FlxqX_red_pre(y, T, p, pi);
1566 134246 : if (lgpol(y)>=FlxqX_EXTGCD_LIMIT)
1567 143 : d = FlxqX_extgcd_halfgcd(x, y, T, p, pi, ptu, ptv);
1568 : else
1569 134103 : d = FlxqX_extgcd_basecase(x, y, T, p, pi, ptu, ptv);
1570 134246 : return gc_all(av, ptu?3:2, &d, ptv, ptu);
1571 : }
1572 : GEN
1573 134232 : FlxqX_extgcd(GEN x, GEN y, GEN T, ulong p, GEN *ptu, GEN *ptv)
1574 : {
1575 134232 : ulong pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
1576 134232 : return FlxqX_extgcd_pre(x, y, T, p, pi, ptu, ptv);
1577 : }
1578 :
1579 : static GEN
1580 385148 : FlxqX_saferem(GEN P, GEN Q, GEN T, ulong p, ulong pi)
1581 : {
1582 385148 : GEN U = Flxq_invsafe_pre(leading_coeff(Q), T, p, pi);
1583 385148 : if (!U) return NULL;
1584 385148 : Q = FlxqX_Flxq_mul_to_monic_pre(Q,U,T,p,pi);
1585 385148 : return FlxqX_rem_pre(P,Q,T,p,pi);
1586 : }
1587 :
1588 : GEN
1589 0 : FlxqX_eval(GEN x, GEN y, GEN T, ulong p)
1590 : {
1591 : pari_sp av;
1592 : GEN p1, r;
1593 0 : long j, i=lg(x)-1;
1594 0 : if (i<=2)
1595 0 : return (i==2)? gcopy(gel(x,2)): pol0_Flx(get_Flx_var(T));
1596 0 : av=avma; p1=gel(x,i);
1597 : /* specific attention to sparse polynomials (see poleval)*/
1598 : /*You've guessed it! It's a copy-paste(tm)*/
1599 0 : for (i--; i>=2; i=j-1)
1600 : {
1601 0 : for (j=i; lg(gel(x,j))==1; j--)
1602 0 : if (j==2)
1603 : {
1604 0 : if (i!=j) y = Flxq_powu(y, i-j+1, T, p);
1605 0 : return gc_upto(av, Flxq_mul(p1,y, T, p));
1606 : }
1607 0 : r = (i==j)? y: Flxq_powu(y, i-j+1, T, p);
1608 0 : p1 = Flx_add(Flxq_mul(p1,r,T,p), gel(x,j), p);
1609 : }
1610 0 : return gc_upto(av, p1);
1611 : }
1612 :
1613 : GEN
1614 97923 : FlxqX_safegcd(GEN P, GEN Q, GEN T, ulong p)
1615 : {
1616 97923 : pari_sp av = avma;
1617 : ulong pi;
1618 : GEN U;
1619 97923 : if (!signe(P)) return gcopy(Q);
1620 97923 : if (!signe(Q)) return gcopy(P);
1621 97923 : pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
1622 97923 : T = Flx_get_red_pre(T,p,pi);
1623 : for(;;)
1624 : {
1625 331044 : P = FlxqX_saferem(P,Q,T,p,pi);
1626 331044 : if (!P) return gc_NULL(av);
1627 331044 : if (!signe(P)) break;
1628 233121 : if (gc_needed(av, 1))
1629 : {
1630 0 : if (DEBUGMEM>1) pari_warn(warnmem,"FlxqX_safegcd");
1631 0 : (void)gc_all(av, 2, &P,&Q);
1632 : }
1633 233121 : swap(P, Q);
1634 : }
1635 97923 : U = Flxq_invsafe_pre(leading_coeff(Q), T, p, pi);
1636 97923 : if (!U) return gc_NULL(av);
1637 97923 : Q = FlxqX_Flxq_mul_to_monic_pre(Q,U,T,p,pi);
1638 97923 : return gc_upto(av, Q);
1639 : }
1640 :
1641 : /* Res(A,B) = Res(B,R) * lc(B)^(a-r) * (-1)^(ab), with R=A%B, a=deg(A) ...*/
1642 : GEN
1643 11041 : FlxqX_saferesultant(GEN a, GEN b, GEN T, ulong p)
1644 : {
1645 11041 : long vT = get_Flx_var(T), da,db,dc;
1646 : ulong pi;
1647 : pari_sp av;
1648 11041 : GEN c,lb, res = pol1_Flx(vT);
1649 :
1650 11041 : if (!signe(a) || !signe(b)) return pol0_Flx(vT);
1651 :
1652 11041 : da = degpol(a);
1653 11041 : db = degpol(b);
1654 11041 : if (db > da)
1655 : {
1656 0 : swapspec(a,b, da,db);
1657 0 : if (both_odd(da,db)) res = Flx_neg(res, p);
1658 : }
1659 11041 : if (!da) return pol1_Flx(vT); /* = res * a[2] ^ db, since 0 <= db <= da = 0 */
1660 11041 : pi = SMALL_ULONG(p)? 0: get_Fl_red(p); av = avma;
1661 65131 : while (db)
1662 : {
1663 54104 : lb = gel(b,db+2);
1664 54104 : c = FlxqX_saferem(a,b, T,p,pi);
1665 54104 : if (!c) return gc_NULL(av);
1666 54104 : a = b; b = c; dc = degpol(c);
1667 54104 : if (dc < 0) { set_avma(av); return pol0_Flx(vT); }
1668 :
1669 54090 : if (both_odd(da,db)) res = Flx_neg(res, p);
1670 54090 : if (!Flx_equal1(lb))
1671 54034 : res = Flxq_mul_pre(res, Flxq_powu_pre(lb, da - dc, T, p, pi), T, p, pi);
1672 54090 : if (gc_needed(av,2))
1673 : {
1674 0 : if (DEBUGMEM>1) pari_warn(warnmem,"FlxqX_resultant (da = %ld)",da);
1675 0 : (void)gc_all(av,3, &a,&b,&res);
1676 : }
1677 54090 : da = db; /* = degpol(a) */
1678 54090 : db = dc; /* = degpol(b) */
1679 : }
1680 11027 : res = Flxq_mul_pre(res, Flxq_powu_pre(gel(b,2), da, T, p, pi), T, p, pi);
1681 11027 : return gc_upto(av, res);
1682 : }
1683 :
1684 : static GEN
1685 0 : FlxqX_halfres(GEN x, GEN y, GEN T, ulong p, ulong pi, GEN *a, GEN *b, GEN *r)
1686 : {
1687 : struct FlxqX_res res;
1688 : GEN V;
1689 : long dB;
1690 :
1691 0 : res.res = *r;
1692 0 : res.lc = leading_coeff(y);
1693 0 : res.deg0 = degpol(x);
1694 0 : res.deg1 = degpol(y);
1695 0 : res.off = 0;
1696 0 : V = FlxqX_halfres_i(x, y, T, p, pi, a, b, &res);
1697 0 : dB = degpol(*b);
1698 0 : if (dB < degpol(y))
1699 0 : FlxqX_halfres_update(res.deg0, res.deg1, dB, T, p, pi, &res);
1700 0 : *r = res.res;
1701 0 : return V;
1702 : }
1703 :
1704 : static GEN
1705 56 : FlxqX_resultant_basecase(GEN a, GEN b, GEN T, ulong p, ulong pi)
1706 : {
1707 56 : pari_sp av = avma;
1708 56 : long vT = get_Flx_var(T), da,db,dc;
1709 56 : GEN c,lb, res = pol1_Flx(vT);
1710 :
1711 56 : if (!signe(a) || !signe(b)) return pol0_Flx(vT);
1712 :
1713 56 : da = degpol(a);
1714 56 : db = degpol(b);
1715 56 : if (db > da)
1716 : {
1717 0 : swapspec(a,b, da,db);
1718 0 : if (both_odd(da,db)) res = Flx_neg(res, p);
1719 : }
1720 56 : if (!da) return pol1_Flx(vT); /* = res * a[2] ^ db, since 0 <= db <= da = 0 */
1721 147 : while (db)
1722 : {
1723 91 : lb = gel(b,db+2);
1724 91 : c = FlxqX_rem_pre(a,b, T,p,pi);
1725 91 : a = b; b = c; dc = degpol(c);
1726 91 : if (dc < 0) { set_avma(av); return pol0_Flx(vT); }
1727 :
1728 91 : if (both_odd(da,db)) res = Flx_neg(res, p);
1729 91 : if (!Flx_equal1(lb))
1730 63 : res = Flxq_mul_pre(res, Flxq_powu_pre(lb, da - dc, T,p,pi), T,p,pi);
1731 91 : if (gc_needed(av,2))
1732 : {
1733 0 : if (DEBUGMEM>1) pari_warn(warnmem,"FlxqX_resultant (da = %ld)",da);
1734 0 : (void)gc_all(av,3, &a,&b,&res);
1735 : }
1736 91 : da = db; /* = degpol(a) */
1737 91 : db = dc; /* = degpol(b) */
1738 : }
1739 56 : res = Flxq_mul_pre(res, Flxq_powu_pre(gel(b,2), da, T,p,pi), T,p,pi);
1740 56 : return gc_upto(av, res);
1741 : }
1742 :
1743 : /* Res(A,B) = Res(B,R) * lc(B)^(a-r) * (-1)^(ab), with R=A%B, a=deg(A) ...*/
1744 : GEN
1745 56 : FlxqX_resultant_pre(GEN x, GEN y, GEN T, ulong p, ulong pi)
1746 : {
1747 56 : pari_sp av = avma;
1748 56 : long dx, dy, vT = get_Flx_var(T);
1749 56 : GEN res = pol1_Flx(vT);
1750 56 : if (!signe(x) || !signe(y)) return pol0_Flx(vT);
1751 56 : dx = degpol(x); dy = degpol(y);
1752 56 : if (dx < dy)
1753 : {
1754 21 : swap(x,y);
1755 21 : if (both_odd(dx, dy))
1756 0 : res = Flx_neg(res, p);
1757 : }
1758 56 : while (lgpol(y) >= FlxqX_GCD_LIMIT)
1759 : {
1760 0 : if (lgpol(y)<=(lgpol(x)>>1))
1761 : {
1762 0 : GEN r = FlxqX_rem_pre(x, y, T, p, pi);
1763 0 : long dx = degpol(x), dy = degpol(y), dr = degpol(r);
1764 0 : GEN ly = gel(y,dy+2);
1765 0 : if (!Flx_equal1(ly))
1766 0 : res = Flxq_mul_pre(res, Flxq_powu_pre(ly, dx - dr, T, p, pi), T, p, pi);
1767 0 : if (both_odd(dx, dy))
1768 0 : res = Flx_neg(res, p);
1769 0 : x = y; y = r;
1770 : }
1771 0 : (void) FlxqX_halfres(x, y, T, p, pi, &x, &y, &res);
1772 0 : if (gc_needed(av,2))
1773 : {
1774 0 : if (DEBUGMEM>1) pari_warn(warnmem,"FlxqX_resultant (y = %ld)",degpol(y));
1775 0 : (void)gc_all(av,3,&x,&y,&res);
1776 : }
1777 : }
1778 56 : res = Flxq_mul_pre(res, FlxqX_resultant_basecase(x, y, T, p, pi), T, p, pi);
1779 56 : return gc_upto(av, res);
1780 : }
1781 : GEN
1782 56 : FlxqX_resultant(GEN x, GEN y, GEN T, ulong p)
1783 56 : { return FlxqX_resultant_pre(x, y, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
1784 :
1785 : /* disc P = (-1)^(n(n-1)/2) lc(P)^(n - deg P' - 2) Res(P,P'), n = deg P */
1786 : GEN
1787 14 : FlxqX_disc(GEN P, GEN T, ulong p)
1788 : {
1789 14 : pari_sp av = avma;
1790 14 : GEN L, dP = FlxX_deriv(P, p), D = FlxqX_resultant(P, dP, T, p);
1791 : long dd;
1792 14 : if (!lgpol(D)) return pol0_Flx(get_Flx_var(T));
1793 14 : dd = degpol(P) - 2 - degpol(dP); /* >= -1; > -1 iff p | deg(P) */
1794 14 : L = leading_coeff(P);
1795 14 : if (dd && !Flx_equal1(L))
1796 : {
1797 0 : ulong pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
1798 0 : D = (dd == -1)? Flxq_div_pre(D,L,T,p,pi)
1799 0 : : Flxq_mul_pre(D, Flxq_powu_pre(L, dd, T,p,pi), T,p,pi); }
1800 14 : if (degpol(P) & 2) D = Flx_neg(D, p);
1801 14 : return gc_upto(av, D);
1802 : }
1803 :
1804 : INLINE GEN
1805 6080 : FlxXn_recip(GEN x, long n, long v)
1806 6080 : { return FlxX_recipspec(x+2, minss(lgpol(x), n), n, v); }
1807 :
1808 : GEN
1809 2432 : FlxqX_Newton_pre(GEN P, long n, GEN T, ulong p, ulong pi)
1810 : {
1811 2432 : pari_sp av = avma;
1812 2432 : long d = degpol(P), vT = get_Flx_var(T);
1813 2432 : GEN dP = FlxXn_recip(FlxX_deriv(P, p), d, vT);
1814 2432 : GEN Q = FlxqXn_mul_pre(FlxqXn_inv_pre(FlxXn_recip(P, d+1, vT), n, T,p,pi),
1815 : dP, n, T, p, pi);
1816 2432 : return gc_GEN(av, Q);
1817 : }
1818 : GEN
1819 0 : FlxqX_Newton(GEN P, long n, GEN T, ulong p)
1820 0 : { return FlxqX_Newton_pre(P, n, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
1821 :
1822 : GEN
1823 1216 : FlxqX_fromNewton_pre(GEN P, GEN T, ulong p, ulong pi)
1824 : {
1825 1216 : pari_sp av = avma;
1826 1216 : long vT = get_Flx_var(T);
1827 1216 : long n = Flx_constant(constant_coeff(P))+1;
1828 1216 : GEN z = FlxX_neg(FlxX_shift(P, -1, vT), p);
1829 1216 : GEN Q = FlxXn_recip(FlxqXn_expint_pre(z, n, T, p, pi), n, vT);
1830 1216 : return gc_GEN(av, Q);
1831 : }
1832 : GEN
1833 0 : FlxqX_fromNewton(GEN P, GEN T, ulong p)
1834 0 : { return FlxqX_fromNewton_pre(P, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
1835 :
1836 : GEN
1837 1216 : FlxqX_composedsum(GEN P, GEN Q, GEN T, ulong p)
1838 : {
1839 1216 : pari_sp av = avma;
1840 1216 : ulong pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
1841 1216 : long n = 1+ degpol(P)*degpol(Q);
1842 1216 : GEN Pl = FlxX_invLaplace(FlxqX_Newton_pre(P,n, T,p,pi), p);
1843 1216 : GEN Ql = FlxX_invLaplace(FlxqX_Newton_pre(Q,n, T,p,pi), p);
1844 1216 : GEN L = FlxX_Laplace(FlxqXn_mul_pre(Pl, Ql, n, T,p,pi), p);
1845 1216 : GEN R = FlxqX_fromNewton_pre(L, T, p, pi);
1846 1216 : GEN lead = Flxq_mul_pre(Flxq_powu_pre(leading_coeff(P),degpol(Q), T,p,pi),
1847 1216 : Flxq_powu_pre(leading_coeff(Q),degpol(P), T,p,pi),
1848 : T, p, pi);
1849 1216 : return gc_upto(av, FlxqX_Flxq_mul_pre(R, lead, T, p, pi));
1850 : }
1851 :
1852 : GEN
1853 223086 : FlxqXV_prod(GEN V, GEN T, ulong p)
1854 : {
1855 223086 : struct _FlxqXQ d; d.p=p; d.T=T; d.pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
1856 223086 : return gen_product(V, (void*)&d, &_FlxqX_mul);
1857 : }
1858 :
1859 : static GEN
1860 32144 : FlxqV_roots_to_deg1(GEN x, GEN T, ulong p, long v)
1861 : {
1862 32144 : long sv = get_Flx_var(T);
1863 124197 : pari_APPLY_same(deg1pol_shallow(pol1_Flx(sv),Flx_neg(gel(x,i),p),v))
1864 : }
1865 :
1866 : GEN
1867 32144 : FlxqV_roots_to_pol(GEN V, GEN T, ulong p, long v)
1868 : {
1869 32144 : pari_sp ltop = avma;
1870 32144 : GEN W = FlxqV_roots_to_deg1(V, T, p, v);
1871 32144 : return gc_upto(ltop, FlxqXV_prod(W, T, p));
1872 : }
1873 :
1874 : /*******************************************************************/
1875 : /* */
1876 : /* (Fl[X]/T(X))[Y] / S(Y) */
1877 : /* */
1878 : /*******************************************************************/
1879 :
1880 : GEN
1881 487855 : FlxqXQ_mul_pre(GEN x, GEN y, GEN S, GEN T, ulong p, ulong pi)
1882 487855 : { return FlxqX_rem_pre(FlxqX_mul_pre(x,y,T,p,pi),S,T,p,pi); }
1883 : GEN
1884 1800 : FlxqXQ_mul(GEN x, GEN y, GEN S, GEN T, ulong p)
1885 1800 : { return FlxqXQ_mul_pre(x, y, S, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
1886 :
1887 : GEN
1888 271535 : FlxqXQ_sqr_pre(GEN x, GEN S, GEN T, ulong p, ulong pi)
1889 271535 : { return FlxqX_rem_pre(FlxqX_sqr_pre(x,T,p,pi),S,T,p,pi); }
1890 : GEN
1891 0 : FlxqXQ_sqr(GEN x, GEN S, GEN T, ulong p)
1892 0 : { return FlxqXQ_sqr_pre(x, S, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
1893 :
1894 : GEN
1895 14 : FlxqXQ_invsafe_pre(GEN x, GEN S, GEN T, ulong p, ulong pi)
1896 : {
1897 14 : GEN V, z = FlxqX_extgcd_pre(get_FlxqX_mod(S), x, T, p, pi, NULL, &V);
1898 14 : if (degpol(z)) return NULL;
1899 14 : z = Flxq_invsafe_pre(gel(z,2),T,p,pi);
1900 14 : if (!z) return NULL;
1901 14 : return FlxqX_Flxq_mul_pre(V, z, T, p, pi);
1902 : }
1903 : GEN
1904 0 : FlxqXQ_invsafe(GEN x, GEN S, GEN T, ulong p)
1905 0 : { return FlxqXQ_invsafe_pre(x, S, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
1906 :
1907 : GEN
1908 14 : FlxqXQ_inv_pre(GEN x, GEN S, GEN T, ulong p, ulong pi)
1909 : {
1910 14 : pari_sp av = avma;
1911 14 : GEN U = FlxqXQ_invsafe_pre(x, S, T, p, pi);
1912 14 : if (!U) pari_err_INV("FlxqXQ_inv",x);
1913 14 : return gc_upto(av, U);
1914 : }
1915 : GEN
1916 14 : FlxqXQ_inv(GEN x, GEN S, GEN T,ulong p)
1917 14 : { return FlxqXQ_inv_pre(x, S, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
1918 :
1919 : GEN
1920 0 : FlxqXQ_div_pre(GEN x, GEN y, GEN S, GEN T, ulong p, ulong pi)
1921 0 : { return FlxqXQ_mul_pre(x, FlxqXQ_inv_pre(y,S,T,p,pi),S,T,p,pi); }
1922 : GEN
1923 0 : FlxqXQ_div(GEN x, GEN y, GEN S, GEN T, ulong p)
1924 0 : { return FlxqXQ_div_pre(x, y, S, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
1925 :
1926 : static GEN
1927 0 : _FlxqX_add(void *data, GEN x, GEN y) {
1928 0 : struct _FlxqXQ *d = (struct _FlxqXQ*) data;
1929 0 : return FlxX_add(x,y, d->p);
1930 : }
1931 : static GEN
1932 4868 : _FlxqX_sub(void *data, GEN x, GEN y) {
1933 4868 : struct _FlxqXQ *d = (struct _FlxqXQ*) data;
1934 4868 : return FlxX_sub(x,y, d->p);
1935 : }
1936 : #if 0
1937 : static GEN
1938 : _FlxqXQ_cmul(void *data, GEN P, long a, GEN x) {
1939 : struct _FlxqXQ *d = (struct _FlxqXQ*) data;
1940 : return FlxY_Flx_mul_pre(x,gel(P,a+2), d->p, d->pi);
1941 : }
1942 : #endif
1943 : static GEN
1944 1248 : _FlxqXQ_red(void *data, GEN x) {
1945 1248 : struct _FlxqXQ *d = (struct _FlxqXQ*) data;
1946 1248 : return FlxqX_red_pre(x, d->T, d->p, d->pi);
1947 : }
1948 : static GEN
1949 184836 : _FlxqXQ_mul(void *data, GEN x, GEN y) {
1950 184836 : struct _FlxqXQ *d = (struct _FlxqXQ*) data;
1951 184836 : return FlxqXQ_mul_pre(x,y, d->S,d->T, d->p, d->pi);
1952 : }
1953 : static GEN
1954 271087 : _FlxqXQ_sqr(void *data, GEN x) {
1955 271087 : struct _FlxqXQ *d = (struct _FlxqXQ*) data;
1956 271087 : return FlxqXQ_sqr_pre(x, d->S,d->T, d->p, d->pi);
1957 : }
1958 :
1959 : static GEN
1960 112026 : _FlxqXQ_one(void *data) {
1961 112026 : struct _FlxqXQ *d = (struct _FlxqXQ*) data;
1962 112026 : return pol1_FlxX(get_FlxqX_var(d->S),get_Flx_var(d->T));
1963 : }
1964 :
1965 : static GEN
1966 281 : _FlxqXQ_zero(void *data) {
1967 281 : struct _FlxqXQ *d = (struct _FlxqXQ*) data;
1968 281 : return pol_0(get_FlxqX_var(d->S));
1969 : }
1970 :
1971 : static struct bb_algebra FlxqXQ_algebra = { _FlxqXQ_red, _FlxqX_add,
1972 : _FlxqX_sub, _FlxqXQ_mul, _FlxqXQ_sqr, _FlxqXQ_one, _FlxqXQ_zero };
1973 :
1974 : const struct bb_algebra *
1975 684 : get_FlxqXQ_algebra(void **E, GEN S, GEN T, ulong p)
1976 : {
1977 684 : ulong pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
1978 684 : GEN z = new_chunk(sizeof(struct _FlxqXQ));
1979 684 : struct _FlxqXQ *e = (struct _FlxqXQ *) z;
1980 684 : e->T = Flx_get_red_pre(T, p, pi);
1981 684 : e->S = FlxqX_get_red_pre(S, e->T, p, pi);
1982 684 : e->p = p;
1983 684 : e->pi= pi; *E = (void*)e;
1984 684 : return &FlxqXQ_algebra;
1985 : }
1986 :
1987 : static struct bb_algebra FlxqX_algebra = { _FlxqXQ_red, _FlxqX_add,
1988 : _FlxqX_sub, _FlxqX_mul, _FlxqX_sqr, _FlxqXQ_one, _FlxqXQ_zero };
1989 :
1990 : const struct bb_algebra *
1991 0 : get_FlxqX_algebra(void **E, GEN T, ulong p, long v)
1992 : {
1993 0 : ulong pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
1994 0 : GEN z = new_chunk(sizeof(struct _FlxqXQ));
1995 0 : struct _FlxqXQ *e = (struct _FlxqXQ *) z;
1996 0 : e->T = Flx_get_red(T, p);
1997 0 : e->S = pol_x(v);
1998 0 : e->p = p;
1999 0 : e->pi= pi; *E = (void*)e;
2000 0 : return &FlxqX_algebra;
2001 : }
2002 :
2003 : /* x over Fq, return lift(x^n) mod S */
2004 : GEN
2005 105 : FlxqXQ_pow_pre(GEN x, GEN n, GEN S, GEN T, ulong p, ulong pi)
2006 : {
2007 105 : pari_sp av = avma;
2008 : struct _FlxqXQ D;
2009 105 : long s = signe(n);
2010 105 : if (!s) return pol1_FlxX(get_FlxqX_var(S),get_Flx_var(T));
2011 105 : if (s < 0) x = FlxqXQ_inv_pre(x,S,T,p,pi);
2012 105 : if (is_pm1(n)) return s < 0 ? x : gcopy(x);
2013 105 : if (degpol(x) >= get_FlxqX_degree(S)) x = FlxqX_rem_pre(x,S,T,p,pi);
2014 105 : T = Flx_get_red_pre(T, p, pi);
2015 105 : S = FlxqX_get_red_pre(S, T, p, pi);
2016 105 : D.S = S; D.T = T; D.p = p; D.pi = pi;
2017 105 : x = gen_pow_i(x, n, (void*)&D, &_FlxqXQ_sqr, &_FlxqXQ_mul);
2018 105 : return gc_GEN(av, x);
2019 : }
2020 : GEN
2021 35 : FlxqXQ_pow(GEN x, GEN n, GEN S, GEN T, ulong p)
2022 35 : { return FlxqXQ_pow_pre(x, n, S, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
2023 :
2024 : /* x over Fq, return lift(x^n) mod S */
2025 : GEN
2026 82722 : FlxqXQ_powu_pre(GEN x, ulong n, GEN S, GEN T, ulong p, ulong pi)
2027 : {
2028 82722 : pari_sp av = avma;
2029 : struct _FlxqXQ D;
2030 82722 : switch(n)
2031 : {
2032 0 : case 0: return pol1_FlxX(get_FlxqX_var(S),get_Flx_var(T));
2033 7690 : case 1: return gcopy(x);
2034 448 : case 2: return FlxqXQ_sqr_pre(x, S, T, p, pi);
2035 : }
2036 74584 : T = Flx_get_red_pre(T, p, pi);
2037 74584 : S = FlxqX_get_red_pre(S, T, p, pi);
2038 74584 : D.S = S; D.T = T; D.p = p; D.pi = pi;
2039 74584 : x = gen_powu_i(x, n, (void*)&D, &_FlxqXQ_sqr, &_FlxqXQ_mul);
2040 74584 : return gc_GEN(av, x);
2041 : }
2042 : GEN
2043 0 : FlxqXQ_powu(GEN x, ulong n, GEN S, GEN T, ulong p)
2044 0 : { return FlxqXQ_powu_pre(x, n, S, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
2045 :
2046 : GEN
2047 109278 : FlxqXQ_powers_pre(GEN x, long l, GEN S, GEN T, ulong p, ulong pi)
2048 : {
2049 : struct _FlxqXQ D;
2050 109278 : int use_sqr = 2*degpol(x) >= get_FlxqX_degree(S);
2051 109278 : T = Flx_get_red_pre(T, p, pi);
2052 109278 : S = FlxqX_get_red_pre(S, T, p, pi);
2053 109278 : D.S = S; D.T = T; D.p = p; D.pi = pi;
2054 109278 : return gen_powers(x, l, use_sqr, (void*)&D, &_FlxqXQ_sqr, &_FlxqXQ_mul,&_FlxqXQ_one);
2055 : }
2056 : GEN
2057 0 : FlxqXQ_powers(GEN x, long l, GEN S, GEN T, ulong p)
2058 0 : { return FlxqXQ_powers_pre(x, l, S, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
2059 :
2060 : /* Let v a linear form, return the linear form z->v(tau*z)
2061 : that is, v*(M_tau) */
2062 : static GEN
2063 508 : FlxqXQ_transmul_init(GEN tau, GEN S, GEN T, ulong p, ulong pi)
2064 : {
2065 : GEN bht;
2066 508 : GEN h, Sp = get_FlxqX_red(S, &h);
2067 508 : long n = degpol(Sp), vS = varn(Sp), vT = get_Flx_var(T);
2068 508 : GEN ft = FlxX_recipspec(Sp+2, n+1, n+1, vT);
2069 508 : GEN bt = FlxX_recipspec(tau+2, lgpol(tau), n, vT);
2070 508 : setvarn(ft, vS); setvarn(bt, vS);
2071 508 : if (h)
2072 0 : bht = FlxqXn_mul_pre(bt, h, n-1, T, p, pi);
2073 : else
2074 : {
2075 508 : GEN bh = FlxqX_div_pre(FlxX_shift(tau, n-1, vT), S, T, p, pi);
2076 508 : bht = FlxX_recipspec(bh+2, lgpol(bh), n-1, vT);
2077 508 : setvarn(bht, vS);
2078 : }
2079 508 : return mkvec3(bt, bht, ft);
2080 : }
2081 :
2082 : static GEN
2083 1077 : FlxqXQ_transmul(GEN tau, GEN a, long n, GEN T, ulong p, ulong pi)
2084 : {
2085 1077 : pari_sp ltop = avma;
2086 : GEN t1, t2, t3, vec;
2087 1077 : GEN bt = gel(tau, 1), bht = gel(tau, 2), ft = gel(tau, 3);
2088 1077 : long vT = get_Flx_var(T);
2089 1077 : if (signe(a)==0) return pol_0(varn(a));
2090 1067 : t2 = FlxX_shift(FlxqX_mul_pre(bt, a, T, p, pi),1-n,vT);
2091 1067 : if (signe(bht)==0) return gc_GEN(ltop, t2);
2092 772 : t1 = FlxX_shift(FlxqX_mul_pre(ft, a, T, p, pi),-n,vT);
2093 772 : t3 = FlxqXn_mul_pre(t1, bht, n-1, T, p, pi);
2094 772 : vec = FlxX_sub(t2, FlxX_shift(t3, 1, vT), p);
2095 772 : return gc_upto(ltop, vec);
2096 : }
2097 :
2098 : static GEN
2099 254 : polxn_FlxX(long n, long v, long vT)
2100 : {
2101 254 : long i, a = n+2;
2102 254 : GEN p = cgetg(a+1, t_POL);
2103 254 : p[1] = evalsigne(1)|evalvarn(v);
2104 2186 : for (i = 2; i < a; i++) gel(p,i) = pol0_Flx(vT);
2105 254 : gel(p,a) = pol1_Flx(vT); return p;
2106 : }
2107 :
2108 : GEN
2109 225 : FlxqXQ_minpoly_pre(GEN x, GEN S, GEN T, ulong p, ulong pi)
2110 : {
2111 225 : pari_sp ltop = avma;
2112 : long vS, vT, n;
2113 : GEN v_x, g, tau;
2114 225 : vS = get_FlxqX_var(S);
2115 225 : vT = get_Flx_var(T);
2116 225 : n = get_FlxqX_degree(S);
2117 225 : g = pol1_FlxX(vS,vT);
2118 225 : tau = pol1_FlxX(vS,vT);
2119 225 : S = FlxqX_get_red_pre(S, T, p, pi);
2120 225 : v_x = FlxqXQ_powers_pre(x, usqrt(2*n), S, T, p, pi);
2121 479 : while(signe(tau) != 0)
2122 : {
2123 : long i, j, m, k1;
2124 : GEN M, v, tr;
2125 : GEN g_prime, c;
2126 254 : if (degpol(g) == n) { tau = pol1_FlxX(vS, vT); g = pol1_FlxX(vS, vT); }
2127 254 : v = random_FlxqX(n, vS, T, p);
2128 254 : tr = FlxqXQ_transmul_init(tau, S, T, p, pi);
2129 254 : v = FlxqXQ_transmul(tr, v, n, T, p, pi);
2130 254 : m = 2*(n-degpol(g));
2131 254 : k1 = usqrt(m);
2132 254 : tr = FlxqXQ_transmul_init(gel(v_x,k1+1), S, T, p, pi);
2133 254 : c = cgetg(m+2,t_POL);
2134 254 : c[1] = evalsigne(1)|evalvarn(vS);
2135 1077 : for (i=0; i<m; i+=k1)
2136 : {
2137 823 : long mj = minss(m-i, k1);
2138 2755 : for (j=0; j<mj; j++)
2139 1932 : gel(c,m+1-(i+j)) = FlxqX_dotproduct(v, gel(v_x,j+1), T, p);
2140 823 : v = FlxqXQ_transmul(tr, v, n, T, p, pi);
2141 : }
2142 254 : c = FlxX_renormalize(c, m+2);
2143 : /* now c contains <v,x^i>, i = 0..m-1 */
2144 254 : M = FlxqX_halfgcd_pre(polxn_FlxX(m, vS, vT), c, T, p, pi);
2145 254 : g_prime = gmael(M, 2, 2);
2146 254 : if (degpol(g_prime) < 1) continue;
2147 253 : g = FlxqX_mul_pre(g, g_prime, T, p, pi);
2148 253 : tau = FlxqXQ_mul_pre(tau, FlxqX_FlxqXQV_eval_pre(g_prime, v_x, S, T,p,pi),
2149 : S, T, p,pi);
2150 : }
2151 225 : g = FlxqX_normalize_pre(g,T,p,pi);
2152 225 : return gc_GEN(ltop,g);
2153 : }
2154 : GEN
2155 62 : FlxqXQ_minpoly(GEN x, GEN S, GEN T, ulong p)
2156 62 : { return FlxqXQ_minpoly_pre(x, S, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
2157 :
2158 : GEN
2159 0 : FlxqXQ_matrix_pow(GEN y, long n, long m, GEN S, GEN T, ulong p)
2160 0 : { return FlxXV_to_FlxM(FlxqXQ_powers(y,m-1,S,T,p), n, get_Flx_var(T)); }
2161 :
2162 : static GEN
2163 139112 : FlxX_blocks_FlxM(GEN P, long n, long m, long v)
2164 : {
2165 139112 : GEN z = cgetg(m+1,t_MAT);
2166 139112 : long i,j, k=2, l = lg(P);
2167 549361 : for(i=1; i<=m; i++)
2168 : {
2169 410249 : GEN zi = cgetg(n+1,t_COL);
2170 410249 : gel(z,i) = zi;
2171 1383145 : for(j=1; j<=n; j++)
2172 972896 : gel(zi, j) = k==l ? pol0_Flx(v) : gel(P,k++);
2173 : }
2174 139112 : return z;
2175 : }
2176 :
2177 : GEN
2178 139112 : FlxqX_FlxqXQV_eval_pre(GEN Q, GEN x, GEN S, GEN T, ulong p, ulong pi)
2179 : {
2180 139112 : pari_sp btop, av = avma;
2181 139112 : long v = get_FlxqX_var(S), m = get_FlxqX_degree(S);
2182 139112 : long vT = get_Flx_var(T);
2183 139112 : long i, l = lg(x)-1, lQ = lgpol(Q), n, d;
2184 : GEN A, B, C, R, g;
2185 139112 : if (lQ == 0) return pol_0(v);
2186 139112 : if (lQ <= l)
2187 : {
2188 43778 : n = l;
2189 43778 : d = 1;
2190 : }
2191 : else
2192 : {
2193 95334 : n = l-1;
2194 95334 : d = (lQ+n-1)/n;
2195 : }
2196 139112 : A = FlxXV_to_FlxM_lg(x, m, n, vT);
2197 139112 : B = FlxX_blocks_FlxM(Q, n, d, vT);
2198 139112 : C = gc_upto(av, FlxqM_mul(A, B, T, p));
2199 139112 : g = gel(x, l);
2200 139112 : T = Flx_get_red_pre(T, p, pi);
2201 139112 : S = FlxqX_get_red_pre(S, T, p, pi);
2202 139112 : btop = avma;
2203 139112 : R = FlxV_to_FlxX(gel(C, d), v);
2204 410249 : for (i = d-1; i>0; i--)
2205 : {
2206 271137 : R = FlxX_add(FlxqXQ_mul_pre(R, g, S, T,p,pi), FlxV_to_FlxX(gel(C,i), v), p);
2207 271137 : if (gc_needed(btop,1))
2208 6 : R = gc_upto(btop, R);
2209 : }
2210 139112 : return gc_GEN(av, R);
2211 : }
2212 : GEN
2213 0 : FlxqX_FlxqXQV_eval(GEN Q, GEN x, GEN S, GEN T, ulong p)
2214 0 : { return FlxqX_FlxqXQV_eval_pre(Q,x,S,T,p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
2215 :
2216 : GEN
2217 78081 : FlxqX_FlxqXQ_eval_pre(GEN Q, GEN x, GEN S, GEN T, ulong p, ulong pi)
2218 : {
2219 78081 : pari_sp av = avma;
2220 : GEN z, V;
2221 78081 : long d = degpol(Q), rtd;
2222 78081 : if (d < 0) return pol_0(get_FlxqX_var(S));
2223 78081 : rtd = (long) sqrt((double)d);
2224 78081 : T = Flx_get_red_pre(T, p, pi);
2225 78081 : S = FlxqX_get_red_pre(S, T, p, pi);
2226 78081 : V = FlxqXQ_powers_pre(x, rtd, S, T, p, pi);
2227 78081 : z = FlxqX_FlxqXQV_eval_pre(Q, V, S, T, p, pi);
2228 78081 : return gc_upto(av, z);
2229 : }
2230 : GEN
2231 0 : FlxqX_FlxqXQ_eval(GEN Q, GEN x, GEN S, GEN T, ulong p)
2232 0 : { return FlxqX_FlxqXQ_eval_pre(Q, x, S, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
2233 :
2234 : GEN
2235 0 : FlxqXC_FlxqXQV_eval_pre(GEN x, GEN v, GEN S, GEN T, ulong p, ulong pi)
2236 0 : { pari_APPLY_type(t_COL, FlxqX_FlxqXQV_eval_pre(gel(x,i), v, S, T, p, pi)) }
2237 : GEN
2238 0 : FlxqXC_FlxqXQV_eval(GEN x, GEN v, GEN S, GEN T, ulong p)
2239 0 : { return FlxqXC_FlxqXQV_eval_pre(x, v, S, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
2240 :
2241 : GEN
2242 0 : FlxqXC_FlxqXQ_eval(GEN x, GEN F, GEN S, GEN T, ulong p)
2243 : {
2244 0 : long d = brent_kung_optpow(get_FlxqX_degree(S)-1,lg(x)-1,1);
2245 0 : ulong pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
2246 0 : GEN Fp = FlxqXQ_powers_pre(F, d, S, T, p, pi);
2247 0 : return FlxqXC_FlxqXQV_eval_pre(x, Fp, S, T, p, pi);
2248 : }
2249 :
2250 : static GEN
2251 73445 : FlxqXQ_autpow_sqr(void * E, GEN x)
2252 : {
2253 73445 : struct _FlxqXQ *D = (struct _FlxqXQ *)E;
2254 73445 : GEN S = D->S, T = D->T;
2255 73445 : ulong p = D->p, pi = D->pi;
2256 73445 : GEN phi = gel(x,1), S1 = gel(x,2);
2257 73445 : long n = brent_kung_optpow(get_Flx_degree(T)-1,lgpol(S1)+1,1);
2258 73445 : GEN V = Flxq_powers_pre(phi, n, T, p, pi);
2259 73445 : GEN phi2 = Flx_FlxqV_eval_pre(phi, V, T, p, pi);
2260 73445 : GEN Sphi = FlxY_FlxqV_evalx_pre(S1, V, T, p, pi);
2261 73445 : GEN S2 = FlxqX_FlxqXQ_eval_pre(Sphi, S1, S, T, p, pi);
2262 73445 : return mkvec2(phi2, S2);
2263 : }
2264 :
2265 : static GEN
2266 4274 : FlxqXQ_autpow_mul(void * E, GEN x, GEN y)
2267 : {
2268 4274 : struct _FlxqXQ *D = (struct _FlxqXQ *)E;
2269 4274 : GEN S = D->S, T = D->T;
2270 4274 : ulong p = D->p, pi = D->pi;
2271 4274 : GEN phi1 = gel(x,1), S1 = gel(x,2);
2272 4274 : GEN phi2 = gel(y,1), S2 = gel(y,2);
2273 4274 : long n = brent_kung_optpow(get_Flx_degree(T)-1,lgpol(S1)+1,1);
2274 4274 : GEN V = Flxq_powers_pre(phi2, n, T, p, pi);
2275 4274 : GEN phi3 = Flx_FlxqV_eval_pre(phi1, V, T, p, pi);
2276 4274 : GEN Sphi = FlxY_FlxqV_evalx_pre(S1, V, T, p, pi);
2277 4274 : GEN S3 = FlxqX_FlxqXQ_eval_pre(Sphi, S2, S, T, p, pi);
2278 4274 : return mkvec2(phi3, S3);
2279 : }
2280 :
2281 : GEN
2282 69996 : FlxqXQ_autpow_pre(GEN aut, long n, GEN S, GEN T, ulong p, ulong pi)
2283 : {
2284 69996 : pari_sp av = avma;
2285 : struct _FlxqXQ D;
2286 69996 : T = Flx_get_red_pre(T, p, pi);
2287 69996 : S = FlxqX_get_red_pre(S, T, p, pi);
2288 69996 : D.S = S; D.T = T; D.p = p; D.pi = pi;
2289 69996 : aut = gen_powu_i(aut,n,&D,FlxqXQ_autpow_sqr,FlxqXQ_autpow_mul);
2290 69996 : return gc_GEN(av, aut);
2291 : }
2292 : GEN
2293 0 : FlxqXQ_autpow(GEN aut, long n, GEN S, GEN T, ulong p)
2294 0 : { return FlxqXQ_autpow_pre(aut, n, S, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
2295 :
2296 : static GEN
2297 29759 : FlxqXQ_autsum_mul(void *E, GEN x, GEN y)
2298 : {
2299 29759 : struct _FlxqXQ *D = (struct _FlxqXQ *)E;
2300 29759 : GEN S = D->S, T = D->T;
2301 29759 : ulong p = D->p, pi = D->pi;
2302 29759 : GEN phi1 = gel(x,1), S1 = gel(x,2), a1 = gel(x,3);
2303 29759 : GEN phi2 = gel(y,1), S2 = gel(y,2), a2 = gel(y,3);
2304 29759 : long n2 = brent_kung_optpow(get_Flx_degree(T)-1, lgpol(S1)+lgpol(a1)+1,1);
2305 29759 : GEN V2 = Flxq_powers_pre(phi2, n2, T, p, pi);
2306 29759 : GEN phi3 = Flx_FlxqV_eval_pre(phi1, V2, T, p, pi);
2307 29759 : GEN Sphi = FlxY_FlxqV_evalx_pre(S1, V2, T, p, pi);
2308 29759 : GEN aphi = FlxY_FlxqV_evalx_pre(a1, V2, T, p, pi);
2309 29759 : long n = brent_kung_optpow(maxss(degpol(Sphi),degpol(aphi)),2,1);
2310 29759 : GEN V = FlxqXQ_powers_pre(S2, n, S, T, p, pi);
2311 29759 : GEN S3 = FlxqX_FlxqXQV_eval_pre(Sphi, V, S, T, p, pi);
2312 29759 : GEN aS = FlxqX_FlxqXQV_eval_pre(aphi, V, S, T, p, pi);
2313 29759 : GEN a3 = FlxqXQ_mul_pre(aS, a2, S, T, p, pi);
2314 29759 : return mkvec3(phi3, S3, a3);
2315 : }
2316 :
2317 : static GEN
2318 18401 : FlxqXQ_autsum_sqr(void * T, GEN x)
2319 18401 : { return FlxqXQ_autsum_mul(T, x, x); }
2320 :
2321 : GEN
2322 12110 : FlxqXQ_autsum_pre(GEN aut, long n, GEN S, GEN T, ulong p, ulong pi)
2323 : {
2324 12110 : pari_sp av = avma;
2325 : struct _FlxqXQ D;
2326 12110 : T = Flx_get_red_pre(T, p, pi);
2327 12110 : S = FlxqX_get_red_pre(S, T, p, pi);
2328 12110 : D.S=S; D.T=T; D.p=p; D.pi=pi;
2329 12110 : aut = gen_powu_i(aut,n,&D,FlxqXQ_autsum_sqr,FlxqXQ_autsum_mul);
2330 12110 : return gc_GEN(av, aut);
2331 : }
2332 : GEN
2333 0 : FlxqXQ_autsum(GEN aut, long n, GEN S, GEN T, ulong p)
2334 0 : { return FlxqXQ_autsum_pre(aut, n, S, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
2335 :
2336 : static GEN
2337 27 : FlxqXQ_auttrace_mul(void *E, GEN x, GEN y)
2338 : {
2339 27 : struct _FlxqXQ *D = (struct _FlxqXQ *)E;
2340 27 : GEN S = D->S, T = D->T;
2341 27 : ulong p = D->p, pi = D->pi;
2342 27 : GEN S1 = gel(x,1), a1 = gel(x,2);
2343 27 : GEN S2 = gel(y,1), a2 = gel(y,2);
2344 27 : long n = brent_kung_optpow(maxss(degpol(S1),degpol(a1)),2,1);
2345 27 : GEN V = FlxqXQ_powers_pre(S2, n, S, T, p, pi);
2346 27 : GEN S3 = FlxqX_FlxqXQV_eval_pre(S1, V, S, T, p, pi);
2347 27 : GEN aS = FlxqX_FlxqXQV_eval_pre(a1, V, S, T, p, pi);
2348 27 : GEN a3 = FlxX_add(aS, a2, p);
2349 27 : return mkvec2(S3, a3);
2350 : }
2351 :
2352 : static GEN
2353 20 : FlxqXQ_auttrace_sqr(void *E, GEN x)
2354 20 : { return FlxqXQ_auttrace_mul(E, x, x); }
2355 :
2356 : GEN
2357 338 : FlxqXQ_auttrace_pre(GEN x, ulong n, GEN S, GEN T, ulong p, ulong pi)
2358 : {
2359 338 : pari_sp av = avma;
2360 : struct _FlxqXQ D;
2361 338 : T = Flx_get_red_pre(T, p, pi);
2362 338 : S = FlxqX_get_red_pre(S, T, p, pi);
2363 338 : D.S=S; D.T=T; D.p=p; D.pi = pi;
2364 338 : x = gen_powu_i(x,n,(void*)&D,FlxqXQ_auttrace_sqr,FlxqXQ_auttrace_mul);
2365 338 : return gc_GEN(av, x);
2366 : }
2367 : GEN
2368 0 : FlxqXQ_auttrace(GEN x, ulong n, GEN S, GEN T, ulong p)
2369 0 : { return FlxqXQ_auttrace_pre(x, n, S, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
2370 :
2371 : /*******************************************************************/
2372 : /* */
2373 : /* FlxYqQ */
2374 : /* */
2375 : /*******************************************************************/
2376 :
2377 : /*Preliminary implementation to speed up FpX_ffisom*/
2378 : typedef struct {
2379 : GEN S, T;
2380 : ulong p, pi;
2381 : } FlxYqq_muldata;
2382 :
2383 : /* reduce x in Fl[X, Y] in the algebra Fl[X, Y]/ (P(X),Q(Y)) */
2384 : static GEN
2385 90960 : FlxYqq_redswap(GEN x, GEN S, GEN T, ulong p, ulong pi)
2386 : {
2387 90960 : pari_sp ltop=avma;
2388 90960 : long n = get_Flx_degree(S);
2389 90960 : long m = get_Flx_degree(T);
2390 90960 : long w = get_Flx_var(T);
2391 90960 : GEN V = FlxX_swap(x,m,w);
2392 90960 : V = FlxqX_red_pre(V,S,p,pi);
2393 90960 : V = FlxX_swap(V,n,w);
2394 90960 : return gc_GEN(ltop,V);
2395 : }
2396 : static GEN
2397 80554 : FlxYqq_sqr(void *data, GEN x)
2398 : {
2399 80554 : FlxYqq_muldata *D = (FlxYqq_muldata*)data;
2400 80554 : return FlxYqq_redswap(FlxqX_sqr_pre(x,D->T,D->p,D->pi),D->S,D->T,D->p,D->pi);
2401 : }
2402 :
2403 : static GEN
2404 10406 : FlxYqq_mul(void *data, GEN x, GEN y)
2405 : {
2406 10406 : FlxYqq_muldata *D = (FlxYqq_muldata*)data;
2407 10406 : return FlxYqq_redswap(FlxqX_mul_pre(x,y, D->T,D->p,D->pi),D->S,D->T,D->p,D->pi);
2408 : }
2409 :
2410 : /* x in Z[X,Y], S in Z[X] over Fq = Z[Y]/(p,T); compute lift(x^n mod (S,T,p)) */
2411 : GEN
2412 39264 : FlxYqq_pow(GEN x, GEN n, GEN S, GEN T, ulong p)
2413 : {
2414 : FlxYqq_muldata D;
2415 39264 : D.S = S; D.T = T; D.p = p; D.pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
2416 39264 : return gen_pow(x, n, (void*)&D, &FlxYqq_sqr, &FlxYqq_mul);
2417 : }
2418 :
2419 : /*******************************************************************/
2420 : /* */
2421 : /* FlxqXn */
2422 : /* */
2423 : /*******************************************************************/
2424 :
2425 : GEN
2426 66188 : FlxXn_red(GEN a, long n)
2427 : {
2428 66188 : long i, L = n+2, l = lg(a);
2429 : GEN b;
2430 66188 : if (L >= l) return a; /* deg(x) < n */
2431 36749 : b = cgetg(L, t_POL); b[1] = a[1];
2432 392028 : for (i=2; i<L; i++) gel(b,i) = gel(a,i);
2433 36749 : return FlxX_renormalize(b,L);
2434 : }
2435 :
2436 : GEN
2437 40420 : FlxqXn_mul_pre(GEN a, GEN b, long n, GEN T, ulong p, ulong pi)
2438 40420 : { return FlxXn_red(FlxqX_mul_pre(a, b, T, p, pi), n); }
2439 : GEN
2440 0 : FlxqXn_mul(GEN a, GEN b, long n, GEN T, ulong p)
2441 0 : { return FlxqXn_mul_pre(a, b, n, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
2442 :
2443 : GEN
2444 0 : FlxqXn_sqr_pre(GEN a, long n, GEN T, ulong p, ulong pi)
2445 0 : { return FlxXn_red(FlxqX_sqr_pre(a, T, p, pi), n); }
2446 : GEN
2447 0 : FlxqXn_sqr(GEN a, long n, GEN T, ulong p)
2448 0 : { return FlxqXn_sqr_pre(a, n, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
2449 :
2450 : /* (f*g) \/ x^n */
2451 : static GEN
2452 18000 : FlxqX_mulhigh_i(GEN f, GEN g, long n, GEN T, ulong p, ulong pi)
2453 18000 : { return FlxX_shift(FlxqX_mul_pre(f, g, T, p, pi), -n, get_Flx_var(T)); }
2454 :
2455 : static GEN
2456 13196 : FlxqXn_mulhigh(GEN f, GEN g, long n2, long n, GEN T, ulong p, ulong pi)
2457 : {
2458 13196 : long vT = get_Flx_var(T);
2459 13196 : GEN F = FlxX_blocks(f, n2, 2, vT), fl = gel(F,1), fh = gel(F,2);
2460 13196 : return FlxX_add(FlxqX_mulhigh_i(fl, g, n2, T, p, pi),
2461 : FlxqXn_mul_pre(fh, g, n - n2, T, p, pi), p);
2462 : }
2463 :
2464 : GEN
2465 2432 : FlxqXn_div_pre(GEN g, GEN f, long e, GEN T, ulong p, ulong pi)
2466 : {
2467 2432 : pari_sp av = avma, av2;
2468 : ulong mask;
2469 : GEN W, a;
2470 2432 : long v = varn(f), n = 1, vT = get_Flx_var(T);
2471 :
2472 2432 : if (!signe(f)) pari_err_INV("FlxqXn_inv",f);
2473 2432 : a = Flxq_inv_pre(gel(f,2), T, p, pi);
2474 2432 : if (e == 1 && !g) return scalarpol(a, v);
2475 2432 : else if (e == 2 && !g)
2476 : {
2477 : GEN b;
2478 0 : if (degpol(f) <= 0) return scalarpol(a, v);
2479 0 : b = Flx_neg(gel(f,3), p);
2480 0 : if (lgpol(b)==0) return scalarpol(a, v);
2481 0 : b = Flxq_mul_pre(b, Flxq_sqr_pre(a, T, p, pi), T, p, pi);
2482 0 : W = deg1pol_shallow(b, a, v);
2483 0 : return gc_GEN(av, W);
2484 : }
2485 2432 : W = scalarpol_shallow(Flxq_inv_pre(gel(f,2), T, p, pi), v);
2486 2432 : mask = quadratic_prec_mask(e);
2487 2432 : av2 = avma;
2488 12040 : for (;mask>1;)
2489 : {
2490 : GEN u, fr;
2491 9608 : long n2 = n;
2492 9608 : n<<=1; if (mask & 1) n--;
2493 9608 : mask >>= 1;
2494 9608 : fr = FlxXn_red(f, n);
2495 9608 : if (mask>1 || !g)
2496 : {
2497 9608 : u = FlxqXn_mul_pre(W, FlxqXn_mulhigh(fr, W, n2, n, T, p, pi), n-n2, T, p, pi);
2498 9608 : W = FlxX_sub(W, FlxX_shift(u, n2, vT), p);
2499 : }
2500 : else
2501 : {
2502 0 : GEN y = FlxqXn_mul_pre(g, W, n, T, p, pi), yt = FlxXn_red(y, n-n2);
2503 0 : u = FlxqXn_mul_pre(yt, FlxqXn_mulhigh(fr, W, n2, n, T, p, pi), n-n2, T, p, pi);
2504 0 : W = FlxX_sub(y, FlxX_shift(u, n2, vT), p);
2505 : }
2506 9608 : if (gc_needed(av2,2))
2507 : {
2508 0 : if(DEBUGMEM>1) pari_warn(warnmem,"FlxqXn_inv, e = %ld", n);
2509 0 : W = gc_upto(av2, W);
2510 : }
2511 : }
2512 2432 : return gc_upto(av, W);
2513 : }
2514 :
2515 : GEN
2516 0 : FlxqXn_div(GEN f, GEN g, long e, GEN T, ulong p)
2517 0 : { return FlxqXn_div_pre(f, g, e, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
2518 :
2519 : GEN
2520 2432 : FlxqXn_inv_pre(GEN f, long e, GEN T, ulong p, ulong pi)
2521 2432 : { return FlxqXn_div_pre(NULL, f, e, T, p, pi); }
2522 :
2523 : GEN
2524 0 : FlxqXn_inv(GEN f, long e, GEN T, ulong p)
2525 0 : { return FlxqXn_div_pre(NULL, f, e, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
2526 :
2527 : /* Compute intformal(x^n*S)/x^(n+1) */
2528 : static GEN
2529 4804 : FlxX_integXn(GEN x, long n, ulong p)
2530 : {
2531 4804 : long i, lx = lg(x);
2532 : GEN y;
2533 4804 : if (lx == 2) return gcopy(x);
2534 3998 : y = cgetg(lx, t_POL); y[1] = x[1];
2535 26760 : for (i=2; i<lx; i++)
2536 : {
2537 22762 : GEN xi = gel(x,i);
2538 22762 : gel(y,i) = Flx_Fl_mul(xi, Fl_inv((n+i-1)%p, p), p);
2539 : }
2540 3998 : return FlxX_renormalize(y, lx);;
2541 : }
2542 :
2543 : GEN
2544 1216 : FlxqXn_expint_pre(GEN h, long e, GEN T, ulong p, ulong pi)
2545 : {
2546 1216 : pari_sp av = avma, av2;
2547 1216 : long v = varn(h), n = 1, vT = get_Flx_var(T);
2548 1216 : GEN f = pol1_FlxX(v, vT), g = pol1_FlxX(v, vT);
2549 1216 : ulong mask = quadratic_prec_mask(e);
2550 1216 : av2 = avma;
2551 4804 : for (;mask>1;)
2552 : {
2553 : GEN u, w;
2554 4804 : long n2 = n;
2555 4804 : n<<=1; if (mask & 1) n--;
2556 4804 : mask >>= 1;
2557 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);
2558 4804 : u = FlxX_add(u, FlxX_shift(FlxXn_red(h, n-1), 1-n2, vT), p);
2559 4804 : w = FlxqXn_mul_pre(f, FlxX_integXn(u, n2-1, p), n-n2, T, p, pi);
2560 4804 : f = FlxX_add(f, FlxX_shift(w, n2, vT), p);
2561 4804 : if (mask<=1) break;
2562 3588 : u = FlxqXn_mul_pre(g, FlxqXn_mulhigh(f, g, n2, n, T,p,pi), n-n2, T,p,pi);
2563 3588 : g = FlxX_sub(g, FlxX_shift(u, n2, vT), p);
2564 3588 : if (gc_needed(av2,2))
2565 : {
2566 0 : if (DEBUGMEM>1) pari_warn(warnmem,"FlxqXn_exp, e = %ld", n);
2567 0 : (void)gc_all(av2, 2, &f, &g);
2568 : }
2569 : }
2570 1216 : return gc_upto(av, f);
2571 : }
2572 : GEN
2573 0 : FlxqXn_expint(GEN h, long e, GEN T, ulong p)
2574 0 : { return FlxqXn_expint_pre(h, e, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
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