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 15241667 : FlxX_renormalize(GEN /*in place*/ x, long lx)
31 : {
32 : long i;
33 20071998 : for (i = lx-1; i>1; i--)
34 19293221 : if (lgpol(gel(x,i))) break;
35 15241717 : stackdummy((pari_sp)(x + lg(x)), (pari_sp)(x + i+1));
36 15242283 : 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 2872020 : FlxY_degreex(GEN b)
58 : {
59 2872020 : long deg = 0, i;
60 2872020 : if (!signe(b)) return -1;
61 10351332 : for (i = 2; i < lg(b); ++i)
62 7479299 : deg = maxss(deg, degpol(gel(b, i)));
63 2872033 : return deg;
64 : }
65 :
66 : /*Lift coefficient of B to constant Flx, to give a FlxY*/
67 : GEN
68 2522 : Fly_to_FlxY(GEN B, long sv)
69 : {
70 2522 : long lb=lg(B);
71 : long i;
72 2522 : GEN b=cgetg(lb,t_POL);
73 2522 : b[1]=evalsigne(1)|(((ulong)B[1])&VARNBITS);
74 65641 : for (i=2; i<lb; i++)
75 63127 : gel(b,i) = Fl_to_Flx(B[i], sv);
76 2514 : return FlxX_renormalize(b, lb);
77 : }
78 :
79 : GEN
80 2667684 : zxX_to_FlxX(GEN B, ulong p)
81 : {
82 2667684 : long i, lb = lg(B);
83 2667684 : GEN b = cgetg(lb,t_POL);
84 8696774 : for (i=2; i<lb; i++)
85 6034628 : gel(b,i) = zx_to_Flx(gel(B,i), p);
86 2662146 : b[1] = B[1]; return FlxX_renormalize(b, lb);
87 : }
88 :
89 : GEN
90 2771129 : FlxX_to_ZXX(GEN B)
91 : {
92 2771129 : long i, lb = lg(B);
93 2771129 : GEN b = cgetg(lb,t_POL);
94 8886893 : for (i=2; i<lb; i++)
95 : {
96 6116516 : GEN c = gel(B,i);
97 6116516 : switch(lgpol(c))
98 : {
99 267411 : case 0: c = gen_0; break;
100 795340 : case 1: c = utoi(c[2]); break;
101 5054176 : default: c = Flx_to_ZX(c); break;
102 : }
103 6115695 : gel(b,i) = c;
104 : }
105 2770377 : 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 2818364 : ZXX_to_FlxX(GEN B, ulong p, long v)
112 : {
113 2818364 : long lb=lg(B);
114 : long i;
115 2818364 : GEN b=cgetg(lb,t_POL);
116 2818457 : b[1]=evalsigne(1)|(((ulong)B[1])&VARNBITS);
117 13783670 : for (i=2; i<lb; i++)
118 10966338 : switch (typ(gel(B,i)))
119 : {
120 2144048 : case t_INT:
121 2144048 : gel(b,i) = Z_to_Flx(gel(B,i), p, evalvarn(v));
122 2143975 : break;
123 8823793 : case t_POL:
124 8823793 : gel(b,i) = ZX_to_Flx(gel(B,i), p);
125 8822741 : break;
126 : }
127 2817332 : 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 57258 : FlxX_to_Flm(GEN v, long n)
160 : {
161 57258 : long j, N = lg(v)-1;
162 57258 : GEN y = cgetg(N, t_MAT);
163 57259 : v++;
164 196196 : for (j=1; j<N; j++) gel(y,j) = Flx_to_Flv(gel(v,j), n);
165 57256 : return y;
166 : }
167 :
168 : GEN
169 364765 : FlxX_to_Flx(GEN f)
170 : {
171 364765 : long i, l = lg(f);
172 364765 : GEN V = cgetg(l, t_VECSMALL);
173 364765 : V[1] = ((ulong)f[1])&VARNBITS;
174 3497323 : for(i=2; i<l; i++)
175 3132558 : V[i] = lgpol(gel(f,i)) ? mael(f,i,2): 0L;
176 364765 : return V;
177 : }
178 :
179 : GEN
180 221475 : Flm_to_FlxX(GEN x, long v,long w)
181 : {
182 221475 : long j, lx = lg(x);
183 221475 : GEN y = cgetg(lx+1, t_POL);
184 221480 : y[1]=evalsigne(1) | v;
185 221480 : y++;
186 814344 : for (j=1; j<lx; j++) gel(y,j) = Flv_to_Flx(gel(x,j), w);
187 221456 : return FlxX_renormalize(--y, lx+1);
188 : }
189 :
190 : /* P(X,Y) --> P(Y,X), n is the degree in Y */
191 : GEN
192 181759 : FlxX_swap(GEN x, long n, long ws)
193 : {
194 181759 : long j, lx = lg(x), ly = n+3;
195 181759 : GEN y = cgetg(ly, t_POL);
196 181760 : y[1] = x[1];
197 1168627 : for (j=2; j<ly; j++)
198 : {
199 : long k;
200 986866 : GEN p1 = cgetg(lx, t_VECSMALL);
201 986865 : p1[1] = ws;
202 11225243 : for (k=2; k<lx; k++)
203 10238378 : if (j<lg(gel(x,k)))
204 7199130 : p1[k] = mael(x,k,j);
205 : else
206 3039248 : p1[k] = 0;
207 986865 : gel(y,j) = Flx_renormalize(p1,lx);
208 : }
209 181761 : return FlxX_renormalize(y,ly);
210 : }
211 :
212 : static GEN
213 4359698 : zxX_to_Kronecker_spec(GEN P, long lp, long n)
214 : { /* P(X) = sum Pi(Y) * X^i, return P( Y^(2n-1) ) */
215 4359698 : long i, j, k, l, N = (n<<1) + 1;
216 4359698 : GEN y = cgetg((N-2)*lp + 2, t_VECSMALL) + 2;
217 28820326 : for (k=i=0; i<lp; i++)
218 : {
219 28783869 : GEN c = gel(P,i);
220 28783869 : l = lg(c);
221 28783869 : if (l-3 >= n)
222 0 : pari_err_BUG("zxX_to_Kronecker, P is not reduced mod Q");
223 168688961 : for (j=2; j < l; j++) y[k++] = c[j];
224 28783888 : if (i == lp-1) break;
225 219122331 : for ( ; j < N; j++) y[k++] = 0;
226 : }
227 4359700 : y -= 2;
228 4359700 : y[1] = 0; setlg(y, k+2); return y;
229 : }
230 :
231 : GEN
232 3773428 : zxX_to_Kronecker(GEN P, GEN Q)
233 : {
234 3773428 : GEN z = zxX_to_Kronecker_spec(P+2, lg(P)-2, degpol(Q));
235 3773442 : z[1] = P[1]; return z;
236 : }
237 :
238 : GEN
239 348539 : FlxX_add(GEN x, GEN y, ulong p)
240 : {
241 : long i,lz;
242 : GEN z;
243 348539 : long lx=lg(x);
244 348539 : long ly=lg(y);
245 348539 : if (ly>lx) swapspec(x,y, lx,ly);
246 348539 : lz = lx; z = cgetg(lz, t_POL); z[1]=x[1];
247 3922266 : for (i=2; i<ly; i++) gel(z,i) = Flx_add(gel(x,i), gel(y,i), p);
248 2148326 : for ( ; i<lx; i++) gel(z,i) = Flx_copy(gel(x,i));
249 348536 : return FlxX_renormalize(z, lz);
250 : }
251 :
252 : GEN
253 245 : FlxX_Flx_add(GEN y, GEN x, ulong p)
254 : {
255 245 : long i, lz = lg(y);
256 : GEN z;
257 245 : if (signe(y) == 0) return scalarpol(x, varn(y));
258 245 : z = cgetg(lz,t_POL); z[1] = y[1];
259 245 : gel(z,2) = Flx_add(gel(y,2), x, p);
260 245 : if (lz == 3) z = FlxX_renormalize(z,lz);
261 : else
262 1071 : for(i=3;i<lz;i++) gel(z,i) = Flx_copy(gel(y,i));
263 245 : return z;
264 : }
265 :
266 : GEN
267 11662 : FlxX_Flx_sub(GEN y, GEN x, ulong p)
268 : {
269 11662 : long i, lz = lg(y);
270 : GEN z;
271 11662 : if (signe(y) == 0) return scalarpol(x, varn(y));
272 11662 : z = cgetg(lz,t_POL); z[1] = y[1];
273 11662 : gel(z,2) = Flx_sub(gel(y,2), x, p);
274 11662 : if (lz == 3) z = FlxX_renormalize(z,lz);
275 : else
276 84532 : for(i=3;i<lz;i++) gel(z,i) = Flx_copy(gel(y,i));
277 11662 : return z;
278 : }
279 :
280 : GEN
281 2657 : FlxX_neg(GEN x, ulong p)
282 : {
283 2657 : long i, lx=lg(x);
284 2657 : GEN z = cgetg(lx, t_POL);
285 2657 : z[1]=x[1];
286 45554 : for (i=2; i<lx; i++) gel(z,i) = Flx_neg(gel(x,i), p);
287 2657 : return z;
288 : }
289 :
290 : GEN
291 761 : FlxX_Fl_mul(GEN x, ulong y, ulong p)
292 : {
293 761 : long i, lx=lg(x);
294 761 : GEN z = cgetg(lx, t_POL);
295 761 : z[1]=x[1];
296 3667 : for (i=2; i<lx; i++) gel(z,i) = Flx_Fl_mul(gel(x,i), y, p);
297 761 : return FlxX_renormalize(z, lx);
298 : }
299 :
300 : GEN
301 0 : FlxX_triple(GEN x, ulong p)
302 : {
303 0 : long i, lx=lg(x);
304 0 : GEN z = cgetg(lx, t_POL);
305 0 : z[1]=x[1];
306 0 : for (i=2; i<lx; i++) gel(z,i) = Flx_triple(gel(x,i), p);
307 0 : return FlxX_renormalize(z, lx);
308 : }
309 :
310 : GEN
311 761 : FlxX_double(GEN x, ulong p)
312 : {
313 761 : long i, lx=lg(x);
314 761 : GEN z = cgetg(lx, t_POL);
315 761 : z[1]=x[1];
316 6088 : for (i=2; i<lx; i++) gel(z,i) = Flx_double(gel(x,i), p);
317 761 : return FlxX_renormalize(z, lx);
318 : }
319 :
320 : GEN
321 84257 : FlxX_deriv(GEN z, ulong p)
322 : {
323 84257 : long i,l = lg(z)-1;
324 : GEN x;
325 84257 : if (l < 2) l = 2;
326 84257 : x = cgetg(l, t_POL); x[1] = z[1];
327 903962 : for (i=2; i<l; i++) gel(x,i) = Flx_mulu(gel(z,i+1), (ulong) i-1, p);
328 84255 : 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 623867 : FlxX_sub(GEN x, GEN y, ulong p)
380 : {
381 : long lx,ly,i,lz;
382 : GEN z;
383 623867 : lx = lg(x); ly = lg(y);
384 623867 : lz=maxss(lx,ly);
385 623867 : z = cgetg(lz,t_POL);
386 623865 : 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 513880 : z[1] = y[1];
396 1294796 : for (i=2; i<lx; i++) gel(z,i) = Flx_sub(gel(x,i),gel(y,i),p);
397 1381515 : for ( ; i<ly; i++) gel(z,i) = Flx_neg(gel(y,i),p);
398 : }
399 623841 : if (!lgpol(z)) { set_avma((pari_sp)(z + lz)); z = pol_0(varn(x)); }
400 623853 : return z;
401 : }
402 :
403 : GEN
404 0 : FlxX_Flx_mul(GEN P, GEN U, ulong p)
405 : {
406 0 : long i, lP = lg(P);
407 0 : GEN res = cgetg(lP,t_POL);
408 0 : ulong pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
409 0 : res[1] = P[1];
410 0 : for(i=2; i<lP; i++) gel(res,i) = Flx_mul_pre(U,gel(P,i), p, pi);
411 0 : return FlxX_renormalize(res, lP);
412 : }
413 :
414 : GEN
415 5576928 : FlxY_evalx_pre(GEN Q, ulong x, ulong p, ulong pi)
416 : {
417 5576928 : long i, lb = lg(Q);
418 : GEN z;
419 5576928 : z = cgetg(lb,t_VECSMALL); z[1] = evalvarn(varn(Q));
420 75824181 : for (i=2; i<lb; i++) z[i] = Flx_eval_pre(gel(Q,i), x, p, pi);
421 5581341 : return Flx_renormalize(z, lb);
422 : }
423 : GEN
424 231 : FlxY_evalx(GEN Q, ulong x, ulong p)
425 231 : { return FlxY_evalx_pre(Q, x, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
426 :
427 : GEN
428 0 : FlxY_Flx_translate(GEN P, GEN c, ulong p)
429 : {
430 0 : pari_sp av = avma;
431 0 : ulong pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
432 : GEN Q;
433 : long i, k, n;
434 :
435 0 : if (!signe(P) || gequal0(c)) return RgX_copy(P);
436 0 : Q = leafcopy(P); n = degpol(P);
437 0 : for (i=1; i<=n; i++)
438 : {
439 0 : for (k=n-i; k<n; k++)
440 0 : gel(Q,2+k) = Flx_add(gel(Q,2+k), Flx_mul_pre(gel(Q,2+k+1), c, p, pi), p);
441 0 : if (gc_needed(av,2))
442 : {
443 0 : if(DEBUGMEM>1)
444 0 : pari_warn(warnmem,"FlxY_Flx_translate, i = %ld/%ld", i,n);
445 0 : Q = gc_GEN(av, Q);
446 : }
447 : }
448 0 : return gc_GEN(av, Q);
449 : }
450 :
451 : /* allow pi = 0 */
452 : GEN
453 10099318 : FlxY_evalx_powers_pre(GEN pol, GEN ypowers, ulong p, ulong pi)
454 : {
455 10099318 : long i, len = lg(pol);
456 10099318 : GEN res = cgetg(len, t_VECSMALL);
457 10096504 : res[1] = pol[1] & VARNBITS;
458 34235286 : for (i = 2; i < len; ++i)
459 24129237 : res[i] = Flx_eval_powers_pre(gel(pol, i), ypowers, p, pi);
460 10106049 : return Flx_renormalize(res, len);
461 : }
462 :
463 : /* allow pi = 0 */
464 : ulong
465 6769093 : FlxY_eval_powers_pre(GEN pol, GEN ypowers, GEN xpowers, ulong p, ulong pi)
466 : {
467 6769093 : pari_sp av = avma;
468 6769093 : GEN t = FlxY_evalx_powers_pre(pol, ypowers, p, pi);
469 6765638 : return gc_ulong(av, Flx_eval_powers_pre(t, xpowers, p, pi));
470 : }
471 :
472 : GEN
473 136362 : FlxY_FlxqV_evalx_pre(GEN P, GEN x, GEN T, ulong p, ulong pi)
474 : {
475 136362 : long i, lP = lg(P);
476 136362 : GEN res = cgetg(lP,t_POL);
477 136362 : res[1] = P[1];
478 930268 : for(i=2; i<lP; i++)
479 793906 : gel(res,i) = Flx_FlxqV_eval_pre(gel(P,i), x, T, p, pi);
480 136362 : return FlxX_renormalize(res, lP);
481 : }
482 : GEN
483 0 : FlxY_FlxqV_evalx(GEN P, GEN x, GEN T, ulong p)
484 0 : { return FlxY_FlxqV_evalx_pre(P, x, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
485 :
486 : GEN
487 0 : FlxY_Flxq_evalx_pre(GEN P, GEN x, GEN T, ulong p, ulong pi)
488 : {
489 0 : pari_sp av = avma;
490 0 : long n = brent_kung_optpow(get_Flx_degree(T)-1,lgpol(P),1);
491 0 : GEN xp = Flxq_powers_pre(x, n, T, p, pi);
492 0 : return gc_upto(av, FlxY_FlxqV_evalx_pre(P, xp, T, p, pi));
493 : }
494 : GEN
495 0 : FlxY_Flxq_evalx(GEN P, GEN x, GEN T, ulong p)
496 0 : { return FlxY_Flxq_evalx_pre(P, x, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
497 :
498 : GEN
499 7540 : FlxY_Flx_div(GEN x, GEN y, ulong p)
500 : {
501 : long i, l;
502 : GEN z;
503 7540 : if (degpol(y) == 0)
504 : {
505 5586 : ulong t = uel(y,2);
506 5586 : if (t == 1) return x;
507 0 : t = Fl_inv(t, p);
508 0 : z = cgetg_copy(x, &l); z[1] = x[1];
509 0 : for (i=2; i<l; i++) gel(z,i) = Flx_Fl_mul(gel(x,i),t,p);
510 : }
511 : else
512 : {
513 1954 : ulong pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
514 1954 : z = cgetg_copy(x, &l); z[1] = x[1];
515 3912 : for (i=2; i<l; i++) gel(z,i) = Flx_div_pre(gel(x,i),y,p,pi);
516 : }
517 1956 : return z;
518 : }
519 :
520 : GEN
521 71623 : FlxX_shift(GEN a, long n, long vs)
522 : {
523 71623 : long i, l = lg(a);
524 : GEN b;
525 71623 : if (l == 2 || !n) return a;
526 64630 : l += n;
527 64630 : if (n < 0)
528 : {
529 35774 : if (l <= 2) return pol_0(varn(a));
530 29404 : b = cgetg(l, t_POL); b[1] = a[1];
531 29404 : a -= n;
532 612651 : for (i=2; i<l; i++) gel(b,i) = gel(a,i);
533 : } else {
534 28856 : b = cgetg(l, t_POL); b[1] = a[1];
535 28857 : a -= n; n += 2;
536 507097 : for (i=2; i<n; i++) gel(b,i) = pol0_Flx(vs);
537 365759 : for ( ; i<l; i++) gel(b,i) = gel(a,i);
538 : }
539 58261 : return b;
540 : }
541 :
542 : GEN
543 13195 : FlxX_blocks(GEN P, long n, long m, long vs)
544 : {
545 13195 : GEN z = cgetg(m+1,t_VEC);
546 13195 : long i,j, k=2, l = lg(P);
547 39586 : for(i=1; i<=m; i++)
548 : {
549 26390 : GEN zi = cgetg(n+2,t_POL);
550 26391 : zi[1] = P[1];
551 26391 : gel(z,i) = zi;
552 160549 : for(j=2; j<n+2; j++)
553 134174 : gel(zi, j) = k==l ? pol0_Flx(vs) : gel(P,k++);
554 26375 : zi = FlxX_renormalize(zi, n+2);
555 : }
556 13196 : return z;
557 : }
558 :
559 : static GEN
560 235489 : FlxX_recipspec(GEN x, long l, long n, long vs)
561 : {
562 : long i;
563 235489 : GEN z = cgetg(n+2,t_POL);
564 235489 : z[1] = 0; z += 2;
565 5279930 : for(i=0; i<l; i++)
566 5044441 : gel(z,n-i-1) = Flx_copy(gel(x,i));
567 242331 : for( ; i<n; i++)
568 6842 : gel(z,n-i-1) = pol0_Flx(vs);
569 235489 : return FlxX_renormalize(z-2,n+2);
570 : }
571 :
572 : GEN
573 2432 : FlxX_invLaplace(GEN x, ulong p)
574 : {
575 2432 : long i, d = degpol(x);
576 : GEN y;
577 : ulong t;
578 2432 : if (d <= 1) return gcopy(x);
579 2425 : t = Fl_inv(factorial_Fl(d, p), p);
580 2425 : y = cgetg(d+3, t_POL);
581 2425 : y[1] = x[1];
582 47583 : for (i=d; i>=2; i--)
583 : {
584 45158 : gel(y,i+2) = Flx_Fl_mul(gel(x,i+2), t, p);
585 45157 : t = Fl_mul(t, i, p);
586 : }
587 2425 : gel(y,3) = Flx_copy(gel(x,3));
588 2425 : gel(y,2) = Flx_copy(gel(x,2));
589 2425 : return FlxX_renormalize(y, d+3);
590 : }
591 :
592 : GEN
593 1216 : FlxX_Laplace(GEN x, ulong p)
594 : {
595 1216 : long i, d = degpol(x);
596 1216 : ulong t = 1;
597 : GEN y;
598 1216 : if (d <= 1) return gcopy(x);
599 1216 : y = cgetg(d+3, t_POL);
600 1216 : y[1] = x[1];
601 1216 : gel(y,2) = Flx_copy(gel(x,2));
602 1216 : gel(y,3) = Flx_copy(gel(x,3));
603 23850 : for (i=2; i<=d; i++)
604 : {
605 22634 : t = Fl_mul(t, i%p, p);
606 22634 : gel(y,i+2) = Flx_Fl_mul(gel(x,i+2), t, p);
607 : }
608 1216 : return FlxX_renormalize(y, d+3);
609 : }
610 :
611 : /***********************************************************************/
612 : /** **/
613 : /** FlxXV **/
614 : /** **/
615 : /***********************************************************************/
616 :
617 : GEN
618 0 : FlxXC_sub(GEN x, GEN y, ulong p)
619 0 : { pari_APPLY_same(FlxX_sub(gel(x, i), gel(y,i), p)) }
620 :
621 : static GEN
622 138362 : FlxXV_to_FlxM_lg(GEN x, long m, long n, long sv)
623 : {
624 : long i;
625 138362 : GEN y = cgetg(n+1, t_MAT);
626 458220 : for (i=1; i<=n; i++) gel(y,i) = FlxX_to_FlxC(gel(x,i), m, sv);
627 138362 : return y;
628 : }
629 :
630 : GEN
631 0 : FlxXV_to_FlxM(GEN v, long n, long sv)
632 0 : { return FlxXV_to_FlxM_lg(v, n, lg(v)-1, sv); }
633 :
634 : GEN
635 12481 : FlxXC_to_ZXXC(GEN x)
636 62479 : { pari_APPLY_type(t_COL, FlxX_to_ZXX(gel(x,i))) }
637 :
638 : GEN
639 0 : FlxXM_to_ZXXM(GEN x)
640 0 : { pari_APPLY_same(FlxXC_to_ZXXC(gel(x,i))) }
641 :
642 : /***********************************************************************/
643 : /** **/
644 : /** FlxqX **/
645 : /** **/
646 : /***********************************************************************/
647 :
648 : static GEN
649 3602847 : get_FlxqX_red(GEN T, GEN *B)
650 : {
651 3602847 : if (typ(T)!=t_VEC) { *B=NULL; return T; }
652 141826 : *B = gel(T,1); return gel(T,2);
653 : }
654 :
655 : GEN
656 152094 : RgX_to_FlxqX(GEN x, GEN T, ulong p)
657 : {
658 152094 : long i, l = lg(x);
659 152094 : GEN z = cgetg(l, t_POL); z[1] = x[1];
660 2326823 : for (i = 2; i < l; i++)
661 2174730 : gel(z,i) = Rg_to_Flxq(gel(x,i), T, p);
662 152093 : return FlxX_renormalize(z, l);
663 : }
664 :
665 : /* FlxqX are t_POL with Flxq coefficients.
666 : * Normally the variable ordering should be respected.*/
667 :
668 : GEN
669 590 : random_FlxqX(long d1, long v, GEN T, ulong p)
670 : {
671 590 : long dT = get_Flx_degree(T), vT = get_Flx_var(T);
672 590 : long i, d = d1+2;
673 590 : GEN y = cgetg(d,t_POL); y[1] = evalsigne(1) | evalvarn(v);
674 3124 : for (i=2; i<d; i++) gel(y,i) = random_Flx(dT, vT, p);
675 590 : return FlxX_renormalize(y,d);
676 : }
677 :
678 : /*Not stack clean*/
679 : GEN
680 2356837 : Kronecker_to_FlxqX_pre(GEN z, GEN T, ulong p, ulong pi)
681 : {
682 2356837 : long i,j,lx,l, N = (get_Flx_degree(T)<<1) + 1;
683 2356835 : GEN x, t = cgetg(N,t_VECSMALL);
684 2356832 : t[1] = get_Flx_var(T);
685 2356835 : l = lg(z); lx = (l-2) / (N-2);
686 2356835 : x = cgetg(lx+3,t_POL);
687 2356832 : x[1] = z[1];
688 28858763 : for (i=2; i<lx+2; i++)
689 : {
690 370676278 : for (j=2; j<N; j++) t[j] = z[j];
691 26501960 : z += (N-2);
692 26501960 : gel(x,i) = Flx_rem_pre(Flx_renormalize(t,N), T,p,pi);
693 : }
694 2356803 : N = (l-2) % (N-2) + 2;
695 7566114 : for (j=2; j<N; j++) t[j] = z[j];
696 2356803 : gel(x,i) = Flx_rem_pre(Flx_renormalize(t,N), T,p,pi);
697 2356766 : return FlxX_renormalize(x, i+1);
698 : }
699 : GEN
700 0 : Kronecker_to_FlxqX(GEN z, GEN T, ulong p)
701 0 : { return Kronecker_to_FlxqX_pre(z, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
702 :
703 : GEN
704 1264728 : FlxqX_red_pre(GEN z, GEN T, ulong p, ulong pi)
705 : {
706 : GEN res;
707 1264728 : long i, l = lg(z);
708 1264728 : res = cgetg(l,t_POL); res[1] = z[1];
709 13067594 : for(i=2;i<l;i++) gel(res,i) = Flx_rem_pre(gel(z,i),T,p,pi);
710 1264708 : return FlxX_renormalize(res,l);
711 : }
712 : GEN
713 0 : FlxqX_red(GEN z, GEN T, ulong p)
714 0 : { return FlxqX_red_pre(z, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
715 :
716 : static GEN
717 293138 : FlxqX_mulspec(GEN x, GEN y, GEN T, ulong p, ulong pi, long lx, long ly)
718 : {
719 293138 : pari_sp av = avma;
720 : GEN z,kx,ky;
721 293138 : long dT = get_Flx_degree(T);
722 293138 : kx= zxX_to_Kronecker_spec(x,lx,dT);
723 293138 : ky= zxX_to_Kronecker_spec(y,ly,dT);
724 293138 : z = Flx_mul_pre(ky, kx, p, pi);
725 293138 : z = Kronecker_to_FlxqX_pre(z,T,p,pi);
726 293138 : return gc_upto(av, z);
727 : }
728 :
729 : GEN
730 1709735 : FlxqX_mul_pre(GEN x, GEN y, GEN T, ulong p, ulong pi)
731 : {
732 1709735 : pari_sp av = avma;
733 1709735 : GEN z, kx, ky, Tm = get_Flx_mod(T);
734 1709734 : kx= zxX_to_Kronecker(x, Tm);
735 1709741 : ky= zxX_to_Kronecker(y, Tm);
736 1709732 : z = Flx_mul_pre(ky, kx, p, pi);
737 1709724 : z = Kronecker_to_FlxqX_pre(z, T, p, pi);
738 1709676 : return gc_upto(av, z);
739 : }
740 : GEN
741 63586 : FlxqX_mul(GEN x, GEN y, GEN T, ulong p)
742 63586 : { return FlxqX_mul_pre(x, y, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
743 :
744 : GEN
745 353990 : FlxqX_sqr_pre(GEN x, GEN T, ulong p, ulong pi)
746 : {
747 353990 : pari_sp av = avma;
748 : GEN z,kx;
749 353990 : kx= zxX_to_Kronecker(x,get_Flx_mod(T));
750 353990 : z = Flx_sqr_pre(kx, p, pi);
751 353989 : z = Kronecker_to_FlxqX_pre(z,T,p,pi);
752 353985 : return gc_upto(av, z);
753 : }
754 : GEN
755 1218 : FlxqX_sqr(GEN x, GEN T, ulong p)
756 1218 : { return FlxqX_sqr_pre(x, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
757 :
758 : GEN
759 155142 : FlxqX_Flxq_mul_pre(GEN P, GEN U, GEN T, ulong p, ulong pi)
760 : {
761 155142 : long i, lP = lg(P);
762 155142 : GEN res = cgetg(lP,t_POL);
763 155143 : res[1] = P[1];
764 554427 : for(i=2; i<lP; i++) gel(res,i) = Flxq_mul_pre(U,gel(P,i), T,p,pi);
765 155132 : return FlxX_renormalize(res, lP);
766 : }
767 : GEN
768 0 : FlxqX_Flxq_mul(GEN P, GEN U, GEN T, ulong p)
769 0 : { return FlxqX_Flxq_mul_pre(P, U, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
770 :
771 : GEN
772 648053 : FlxqX_Flxq_mul_to_monic_pre(GEN P, GEN U, GEN T, ulong p, ulong pi)
773 : {
774 648053 : long i, lP = lg(P);
775 648053 : GEN res = cgetg(lP,t_POL);
776 648049 : res[1] = P[1];
777 3487114 : for(i=2; i<lP-1; i++) gel(res,i) = Flxq_mul_pre(U,gel(P,i), T,p,pi);
778 647640 : gel(res,lP-1) = pol1_Flx(get_Flx_var(T));
779 648052 : return FlxX_renormalize(res, lP);
780 : }
781 : GEN
782 0 : FlxqX_Flxq_mul_to_monic(GEN P, GEN U, GEN T, ulong p)
783 : {
784 0 : ulong pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
785 0 : return FlxqX_Flxq_mul_to_monic_pre(P, U, T, p, pi);
786 : }
787 :
788 : GEN
789 190062 : FlxqX_normalize_pre(GEN z, GEN T, ulong p, ulong pi)
790 : {
791 190062 : GEN p1 = leading_coeff(z);
792 190062 : if (!lgpol(z) || (!degpol(p1) && p1[1] == 1)) return z;
793 190041 : return FlxqX_Flxq_mul_to_monic_pre(z, Flxq_inv_pre(p1,T,p,pi), T,p,pi);
794 : }
795 : GEN
796 133 : FlxqX_normalize(GEN z, GEN T, ulong p)
797 133 : { return FlxqX_normalize_pre(z, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
798 :
799 : struct _FlxqXQ {
800 : GEN T, S;
801 : ulong p, pi;
802 : };
803 :
804 538529 : static GEN _FlxqX_mul(void *data,GEN a,GEN b)
805 : {
806 538529 : struct _FlxqXQ *d=(struct _FlxqXQ*)data;
807 538529 : return FlxqX_mul_pre(a,b,d->T,d->p,d->pi);
808 : }
809 10283 : static GEN _FlxqX_sqr(void *data,GEN a)
810 : {
811 10283 : struct _FlxqXQ *d=(struct _FlxqXQ*)data;
812 10283 : return FlxqX_sqr_pre(a,d->T,d->p,d->pi);
813 : }
814 :
815 : GEN
816 10248 : FlxqX_powu_pre(GEN V, ulong n, GEN T, ulong p, ulong pi)
817 : {
818 10248 : struct _FlxqXQ d; d.p = p; d.pi = pi; d.T = T;
819 10248 : return gen_powu(V, n, (void*)&d, &_FlxqX_sqr, &_FlxqX_mul);
820 : }
821 : GEN
822 0 : FlxqX_powu(GEN V, ulong n, GEN T, ulong p)
823 0 : { return FlxqX_powu_pre(V, n, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
824 :
825 : /* x and y in Z[Y][X]. Assume T irreducible mod p */
826 : static GEN
827 3150719 : FlxqX_divrem_basecase(GEN x, GEN y, GEN T, ulong p, ulong pi, GEN *pr)
828 : {
829 3150719 : long vx = varn(x), dx = degpol(x), dy = degpol(y), dz, i, j, sx, lr;
830 : pari_sp av0, av;
831 : GEN z, p1, rem, lead;
832 :
833 3150731 : if (!signe(y)) pari_err_INV("FlxqX_divrem",y);
834 3150734 : if (dx < dy)
835 : {
836 21625 : if (pr)
837 : {
838 21373 : av0 = avma; x = FlxqX_red_pre(x, T, p, pi);
839 21373 : if (pr == ONLY_DIVIDES) { set_avma(av0); return signe(x)? NULL: pol_0(vx); }
840 21373 : if (pr == ONLY_REM) return x;
841 21373 : *pr = x;
842 : }
843 21625 : return pol_0(vx);
844 : }
845 3129109 : lead = leading_coeff(y);
846 3129106 : if (!dy) /* y is constant */
847 : {
848 326452 : if (pr && pr != ONLY_DIVIDES)
849 : {
850 321777 : if (pr == ONLY_REM) return pol_0(vx);
851 133820 : *pr = pol_0(vx);
852 : }
853 138496 : if (Flx_equal1(lead)) return gcopy(x);
854 134296 : av0 = avma; x = FlxqX_Flxq_mul_pre(x,Flxq_inv(lead,T,p),T,p,pi);
855 134298 : return gc_upto(av0,x);
856 : }
857 2802654 : av0 = avma; dz = dx-dy;
858 2802654 : lead = Flx_equal1(lead)? NULL: gclone(Flxq_inv_pre(lead,T,p,pi));
859 2802688 : set_avma(av0);
860 2802686 : z = cgetg(dz+3,t_POL); z[1] = x[1];
861 2802680 : x += 2; y += 2; z += 2;
862 :
863 2802680 : p1 = gel(x,dx); av = avma;
864 2802680 : gel(z,dz) = lead? gc_upto(av, Flxq_mul_pre(p1,lead, T,p,pi)): gcopy(p1);
865 6460756 : for (i=dx-1; i>=dy; i--)
866 : {
867 3658168 : av = avma; p1 = gel(x,i);
868 11904638 : for (j=i-dy+1; j<=i && j<=dz; j++)
869 8246659 : p1 = Flx_sub(p1, Flx_mul_pre(gel(z,j),gel(y,i-j),p,pi),p);
870 3657979 : if (lead) p1 = Flx_mul_pre(p1, lead,p,pi);
871 3657980 : gel(z,i-dy) = gc_uptoleaf(av, Flx_rem_pre(p1,T,p,pi));
872 : }
873 2802588 : if (!pr) { guncloneNULL(lead); return z-2; }
874 :
875 2608534 : rem = (GEN)avma; av = (pari_sp)new_chunk(dx+3);
876 2918768 : for (sx=0; ; i--)
877 : {
878 2918768 : p1 = gel(x,i);
879 8631064 : for (j=0; j<=i && j<=dz; j++)
880 5712556 : p1 = Flx_sub(p1, Flx_mul_pre(gel(z,j),gel(y,i-j),p,pi),p);
881 2918508 : p1 = Flx_rem_pre(p1, T,p,pi); if (lgpol(p1)) { sx = 1; break; }
882 384053 : if (!i) break;
883 310130 : set_avma(av);
884 : }
885 2608382 : if (pr == ONLY_DIVIDES)
886 : {
887 0 : guncloneNULL(lead);
888 0 : if (sx) return gc_NULL(av0);
889 0 : return gc_const((pari_sp)rem, z-2);
890 : }
891 2608382 : lr=i+3; rem -= lr; av = (pari_sp)rem;
892 2608382 : rem[0] = evaltyp(t_POL) | _evallg(lr);
893 2608382 : rem[1] = z[-1];
894 2608382 : rem += 2; gel(rem,i) = gc_uptoleaf(av, p1);
895 16308473 : for (i--; i>=0; i--)
896 : {
897 13699922 : av = avma; p1 = gel(x,i);
898 44717729 : for (j=0; j<=i && j<=dz; j++)
899 31021679 : p1 = Flx_sub(p1, Flx_mul_pre(gel(z,j),gel(y,i-j),p,pi), p);
900 13696050 : gel(rem,i) = gc_uptoleaf(av, Flx_rem_pre(p1, T,p,pi));
901 : }
902 2608551 : rem -= 2;
903 2608551 : guncloneNULL(lead);
904 2608597 : if (!sx) (void)FlxX_renormalize(rem, lr);
905 2608609 : if (pr == ONLY_REM) return gc_upto(av0,rem);
906 1221172 : *pr = rem; return z-2;
907 : }
908 :
909 : static GEN
910 1419 : FlxqX_invBarrett_basecase(GEN T, GEN Q, ulong p, ulong pi)
911 : {
912 1419 : long i, l=lg(T)-1, lr = l-1, k;
913 1419 : long sv=Q[1];
914 1419 : GEN r=cgetg(lr,t_POL); r[1]=T[1];
915 1419 : gel(r,2) = pol1_Flx(sv);
916 16396 : for (i=3;i<lr;i++)
917 : {
918 14977 : pari_sp ltop=avma;
919 14977 : GEN u = Flx_neg(gel(T,l-i+2),p);
920 108758 : for (k=3;k<i;k++)
921 93781 : u = Flx_sub(u, Flxq_mul_pre(gel(T,l-i+k), gel(r,k), Q, p, pi), p);
922 14977 : gel(r,i) = gc_upto(ltop, u);
923 : }
924 1419 : r = FlxX_renormalize(r,lr);
925 1419 : return r;
926 : }
927 :
928 : /* Return new lgpol */
929 : static long
930 328043 : FlxX_lgrenormalizespec(GEN x, long lx)
931 : {
932 : long i;
933 359738 : for (i = lx-1; i>=0; i--)
934 359738 : if (lgpol(gel(x,i))) break;
935 328043 : return i+1;
936 : }
937 :
938 : static GEN
939 6711 : FlxqX_invBarrett_Newton(GEN S, GEN T, ulong p, ulong pi)
940 : {
941 6711 : pari_sp av = avma;
942 6711 : long nold, lx, lz, lq, l = degpol(S), i, lQ;
943 6711 : GEN q, y, z, x = cgetg(l+2, t_POL) + 2;
944 6711 : long dT = get_Flx_degree(T), vT = get_Flx_var(T);
945 6711 : ulong mask = quadratic_prec_mask(l-2); /* assume l > 2 */
946 273213 : for (i=0;i<l;i++) gel(x,i) = pol0_Flx(vT);
947 6711 : q = FlxX_recipspec(S+2,l+1,l+1,dT);
948 6711 : lQ = lgpol(q); q+=2;
949 : /* We work on _spec_ FlxX's, all the l[xzq] below are lgpol's */
950 :
951 : /* initialize */
952 6711 : gel(x,0) = Flxq_inv_pre(gel(q,0),T, p, pi);
953 6711 : if (lQ>1 && degpol(gel(q,1)) >= dT)
954 0 : gel(q,1) = Flx_rem_pre(gel(q,1), T, p, pi);
955 6711 : if (lQ>1 && lgpol(gel(q,1)))
956 5686 : {
957 5686 : GEN u = gel(q, 1);
958 5686 : if (!Flx_equal1(gel(x,0)))
959 7 : u = Flxq_mul_pre(u, Flxq_sqr_pre(gel(x,0), T,p,pi), T,p,pi);
960 5686 : gel(x,1) = Flx_neg(u, p); lx = 2;
961 : }
962 : else
963 1025 : lx = 1;
964 6711 : nold = 1;
965 43278 : for (; mask > 1; )
966 : { /* set x -= x(x*q - 1) + O(t^(nnew + 1)), knowing x*q = 1 + O(t^(nold+1)) */
967 36567 : long i, lnew, nnew = nold << 1;
968 :
969 36567 : if (mask & 1) nnew--;
970 36567 : mask >>= 1;
971 :
972 36567 : lnew = nnew + 1;
973 36567 : lq = FlxX_lgrenormalizespec(q, minss(lQ,lnew));
974 36567 : z = FlxqX_mulspec(x, q, T,p,pi, lx, lq); /* FIXME: high product */
975 36567 : lz = lgpol(z); if (lz > lnew) lz = lnew;
976 36567 : z += 2;
977 : /* subtract 1 [=>first nold words are 0]: renormalize so that z(0) != 0 */
978 74746 : for (i = nold; i < lz; i++) if (lgpol(gel(z,i))) break;
979 36567 : nold = nnew;
980 36567 : if (i >= lz) continue; /* z-1 = 0(t^(nnew + 1)) */
981 :
982 : /* z + i represents (x*q - 1) / t^i */
983 35664 : lz = FlxX_lgrenormalizespec (z+i, lz-i);
984 35664 : z = FlxqX_mulspec(x, z+i, T,p,pi, lx, lz); /* FIXME: low product */
985 35664 : lz = lgpol(z); z += 2;
986 35664 : if (lz > lnew-i) lz = FlxX_lgrenormalizespec(z, lnew-i);
987 :
988 35664 : lx = lz+ i;
989 35664 : y = x + i; /* x -= z * t^i, in place */
990 278801 : for (i = 0; i < lz; i++) gel(y,i) = Flx_neg(gel(z,i), p);
991 : }
992 6711 : x -= 2; setlg(x, lx + 2); x[1] = S[1];
993 6711 : return gc_GEN(av, x);
994 : }
995 :
996 : GEN
997 8130 : FlxqX_invBarrett_pre(GEN T, GEN Q, ulong p, ulong pi)
998 : {
999 8130 : pari_sp ltop=avma;
1000 8130 : long l=lg(T), v = varn(T);
1001 : GEN r;
1002 8130 : GEN c = gel(T,l-1);
1003 8130 : if (l<5) return pol_0(v);
1004 8130 : if (l<=FlxqX_INVBARRETT_LIMIT)
1005 : {
1006 1419 : if (!Flx_equal1(c))
1007 : {
1008 0 : GEN ci = Flxq_inv_pre(c,Q,p,pi);
1009 0 : T = FlxqX_Flxq_mul_pre(T, ci, Q, p, pi);
1010 0 : r = FlxqX_invBarrett_basecase(T,Q,p,pi);
1011 0 : r = FlxqX_Flxq_mul_pre(r,ci,Q,p,pi);
1012 : } else
1013 1419 : r = FlxqX_invBarrett_basecase(T,Q,p,pi);
1014 : } else
1015 6711 : r = FlxqX_invBarrett_Newton(T,Q,p,pi);
1016 8130 : return gc_upto(ltop, r);
1017 : }
1018 : GEN
1019 76 : FlxqX_invBarrett(GEN T, GEN Q, ulong p)
1020 76 : { return FlxqX_invBarrett_pre(T, Q, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
1021 :
1022 : GEN
1023 491659 : FlxqX_get_red_pre(GEN S, GEN T, ulong p, ulong pi)
1024 : {
1025 491659 : if (typ(S)==t_POL && lg(S)>FlxqX_BARRETT_LIMIT)
1026 6674 : retmkvec2(FlxqX_invBarrett_pre(S, T, p, pi), S);
1027 484985 : return S;
1028 : }
1029 : GEN
1030 371 : FlxqX_get_red(GEN S, GEN T, ulong p)
1031 : {
1032 371 : if (typ(S)==t_POL && lg(S)>FlxqX_BARRETT_LIMIT)
1033 76 : retmkvec2(FlxqX_invBarrett(S, T, p), S);
1034 295 : return S;
1035 : }
1036 :
1037 : /* Compute x mod S where 2 <= degpol(S) <= l+1 <= 2*(degpol(S)-1)
1038 : * * and mg is the Barrett inverse of S. */
1039 : static GEN
1040 110590 : FlxqX_divrem_Barrettspec(GEN x, long l, GEN mg, GEN S, GEN T, ulong p,
1041 : ulong pi, GEN *pr)
1042 : {
1043 : GEN q, r;
1044 110590 : long lt = degpol(S); /*We discard the leading term*/
1045 : long ld, lm, lT, lmg;
1046 110590 : ld = l-lt;
1047 110590 : lm = minss(ld, lgpol(mg));
1048 110590 : lT = FlxX_lgrenormalizespec(S+2,lt);
1049 110590 : lmg = FlxX_lgrenormalizespec(mg+2,lm);
1050 110590 : q = FlxX_recipspec(x+lt,ld,ld,0); /* = rec(x) lq<=ld*/
1051 110590 : q = FlxqX_mulspec(q+2,mg+2,T,p,pi,lgpol(q),lmg); /* = rec(x)*mg lq<=ld+lm*/
1052 110590 : q = FlxX_recipspec(q+2,minss(ld,lgpol(q)),ld,0); /* = rec(rec(x)*mg) lq<=ld*/
1053 110590 : if (!pr) return q;
1054 110317 : r = FlxqX_mulspec(q+2,S+2,T,p,pi,lgpol(q),lT); /* = q*pol lr<=ld+lt*/
1055 110317 : r = FlxX_subspec(x,r+2,p,lt,minss(lt,lgpol(r)));/* = x - r lr<=lt */
1056 110317 : if (pr == ONLY_REM) return r;
1057 7688 : *pr = r; return q;
1058 : }
1059 :
1060 : static GEN
1061 103701 : FlxqX_divrem_Barrett(GEN x, GEN mg, GEN S, GEN T, ulong p, ulong pi, GEN *pr)
1062 : {
1063 103701 : GEN q = NULL, r = FlxqX_red_pre(x, T, p, pi);
1064 103701 : long l = lgpol(r), lt = degpol(S), lm = 2*lt-1, v = varn(S);
1065 : long i;
1066 103701 : if (l <= lt)
1067 : {
1068 0 : if (pr == ONLY_REM) return r;
1069 0 : if (pr == ONLY_DIVIDES) return signe(r)? NULL: pol_0(v);
1070 0 : if (pr) *pr = r;
1071 0 : return pol_0(v);
1072 : }
1073 103701 : if (lt <= 1)
1074 0 : return FlxqX_divrem_basecase(x,S,T,p,pi,pr);
1075 103701 : if (pr != ONLY_REM && l>lm)
1076 : {
1077 764 : long vT = get_Flx_var(T);
1078 764 : q = cgetg(l-lt+2, t_POL); q[1] = S[1];
1079 56948 : for (i=0;i<l-lt;i++) gel(q+2,i) = pol0_Flx(vT);
1080 : }
1081 110672 : while (l>lm)
1082 : {
1083 6971 : GEN zr, zq = FlxqX_divrem_Barrettspec(r+2+l-lm,lm,mg,S,T,p,pi,&zr);
1084 6971 : long lz = lgpol(zr);
1085 6971 : if (pr != ONLY_REM)
1086 : {
1087 2582 : long lq = lgpol(zq);
1088 50816 : for(i=0; i<lq; i++) gel(q+2+l-lm,i) = gel(zq,2+i);
1089 : }
1090 72514 : for(i=0; i<lz; i++) gel(r+2+l-lm,i) = gel(zr,2+i);
1091 6971 : l = l-lm+lz;
1092 : }
1093 103701 : if (pr == ONLY_REM)
1094 : {
1095 102629 : if (l > lt)
1096 102629 : r = FlxqX_divrem_Barrettspec(r+2,l,mg,S,T,p,pi,ONLY_REM);
1097 : else
1098 0 : r = FlxX_renormalize(r, l+2);
1099 102629 : setvarn(r, v); return r;
1100 : }
1101 1072 : if (l > lt)
1102 : {
1103 990 : GEN zq = FlxqX_divrem_Barrettspec(r+2,l,mg,S,T,p,pi,pr? &r: NULL);
1104 990 : if (!q) q = zq;
1105 : else
1106 : {
1107 682 : long lq = lgpol(zq);
1108 6048 : for(i=0; i<lq; i++) gel(q+2,i) = gel(zq,2+i);
1109 : }
1110 : }
1111 82 : else if (pr)
1112 82 : r = FlxX_renormalize(r, l+2);
1113 1072 : setvarn(q, v); q = FlxX_renormalize(q, lg(q));
1114 1072 : if (pr == ONLY_DIVIDES) return signe(r)? NULL: q;
1115 1072 : if (pr) { setvarn(r, v); *pr = r; }
1116 1072 : return q;
1117 : }
1118 :
1119 : GEN
1120 1576323 : FlxqX_divrem_pre(GEN x, GEN S, GEN T, ulong p, long pi, GEN *pr)
1121 : {
1122 : GEN B, y;
1123 : long dy, dx, d;
1124 1576323 : if (pr==ONLY_REM) return FlxqX_rem_pre(x, S, T, p, pi);
1125 1576323 : y = get_FlxqX_red(S, &B);
1126 1576319 : dy = degpol(y); dx = degpol(x); d = dx-dy;
1127 1576297 : if (!B && d+3 < FlxqX_DIVREM_BARRETT_LIMIT)
1128 1575225 : return FlxqX_divrem_basecase(x,y,T,p,pi,pr);
1129 : else
1130 : {
1131 1072 : pari_sp av = avma;
1132 1072 : GEN mg = B? B: FlxqX_invBarrett_pre(y, T, p, pi);
1133 1072 : GEN q = FlxqX_divrem_Barrett(x,mg,y,T,p,pi,pr);
1134 1072 : if (!q) return gc_NULL(av);
1135 1072 : if (!pr || pr==ONLY_DIVIDES) return gc_GEN(av, q);
1136 799 : return gc_all(av, 2, &q, pr);
1137 : }
1138 : }
1139 : GEN
1140 1073758 : FlxqX_divrem(GEN x, GEN S, GEN T, ulong p, GEN *pr)
1141 : {
1142 1073758 : ulong pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
1143 1073758 : return FlxqX_divrem_pre(x, S, T, p, pi, pr);
1144 : }
1145 :
1146 : GEN
1147 2026016 : FlxqX_rem_pre(GEN x, GEN S, GEN T, ulong p, ulong pi)
1148 : {
1149 2026016 : GEN B, y = get_FlxqX_red(S, &B);
1150 2026016 : long dy = degpol(y), dx = degpol(x), d = dx-dy;
1151 2026011 : if (d < 0) return FlxqX_red_pre(x, T, p, pi);
1152 1678060 : if (!B && d+3 < FlxqX_REM_BARRETT_LIMIT)
1153 1575431 : return FlxqX_divrem_basecase(x,y, T, p, pi, ONLY_REM);
1154 : else
1155 : {
1156 102629 : pari_sp av=avma;
1157 102629 : GEN mg = B? B: FlxqX_invBarrett_pre(y, T, p, pi);
1158 102629 : GEN r = FlxqX_divrem_Barrett(x, mg, y, T, p, pi, ONLY_REM);
1159 102629 : return gc_upto(av, r);
1160 : }
1161 : }
1162 : GEN
1163 5949 : FlxqX_rem(GEN x, GEN S, GEN T, ulong p)
1164 5949 : { return FlxqX_rem_pre(x, S, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
1165 :
1166 : /* x + y*z mod p */
1167 : INLINE GEN
1168 103656 : Flxq_addmul_pre(GEN x, GEN y, GEN z, GEN T, ulong p, ulong pi)
1169 : {
1170 : pari_sp av;
1171 103656 : if (!lgpol(y) || !lgpol(z)) return Flx_rem_pre(x, T, p, pi);
1172 102125 : if (!lgpol(x)) return Flxq_mul_pre(z, y, T, p, pi);
1173 102021 : av = avma;
1174 102021 : return gc_upto(av, Flx_add(x, Flxq_mul_pre(y, z, T, p, pi), p));
1175 : }
1176 :
1177 : GEN
1178 51828 : FlxqX_div_by_X_x_pre(GEN a, GEN x, GEN T, ulong p, ulong pi, GEN *r)
1179 : {
1180 51828 : long l = lg(a), i;
1181 : GEN z;
1182 51828 : if (l <= 3)
1183 : {
1184 0 : if (r) *r = l == 2? pol0_Flx(get_Flx_var(T)): Flx_copy(gel(a,2));
1185 0 : return pol_0(varn(a));
1186 : }
1187 51828 : l--; z = cgetg(l, t_POL); z[1] = a[1];
1188 51828 : gel(z, l-1) = gel(a,l);
1189 155484 : for (i=l-2; i>1; i--) /* z[i] = a[i+1] + x*z[i+1] */
1190 103656 : gel(z, i) = Flxq_addmul_pre(gel(a,i+1), x, gel(z,i+1), T, p, pi);
1191 51828 : if (r) *r = Flxq_addmul_pre(gel(a,2), x, gel(z,2), T, p, pi);
1192 51828 : return z;
1193 : }
1194 :
1195 : GEN
1196 51828 : FlxqX_div_by_X_x(GEN a, GEN x, GEN T, ulong p, GEN *r)
1197 51828 : { return FlxqX_div_by_X_x_pre(a, x, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p), r); }
1198 :
1199 : static GEN
1200 13530 : FlxqX_addmulmul(GEN u, GEN v, GEN x, GEN y, GEN T, ulong p, ulong pi)
1201 : {
1202 13530 : return FlxX_add(FlxqX_mul_pre(u, x, T, p, pi),
1203 : FlxqX_mul_pre(v, y, T, p, pi), p);
1204 : }
1205 :
1206 : static GEN
1207 6626 : FlxqXM_FlxqX_mul2(GEN M, GEN x, GEN y, GEN T, ulong p, ulong pi)
1208 : {
1209 6626 : GEN res = cgetg(3, t_COL);
1210 6626 : gel(res, 1) = FlxqX_addmulmul(gcoeff(M,1,1), gcoeff(M,1,2), x, y, T, p, pi);
1211 6626 : gel(res, 2) = FlxqX_addmulmul(gcoeff(M,2,1), gcoeff(M,2,2), x, y, T, p, pi);
1212 6626 : return res;
1213 : }
1214 :
1215 : static GEN
1216 3276 : FlxqXM_mul2(GEN A, GEN B, GEN T, ulong p, ulong pi)
1217 : {
1218 3276 : GEN A11=gcoeff(A,1,1),A12=gcoeff(A,1,2), B11=gcoeff(B,1,1),B12=gcoeff(B,1,2);
1219 3276 : GEN A21=gcoeff(A,2,1),A22=gcoeff(A,2,2), B21=gcoeff(B,2,1),B22=gcoeff(B,2,2);
1220 3276 : GEN M1 = FlxqX_mul_pre(FlxX_add(A11,A22, p), FlxX_add(B11,B22, p), T, p, pi);
1221 3276 : GEN M2 = FlxqX_mul_pre(FlxX_add(A21,A22, p), B11, T, p, pi);
1222 3276 : GEN M3 = FlxqX_mul_pre(A11, FlxX_sub(B12,B22, p), T, p, pi);
1223 3276 : GEN M4 = FlxqX_mul_pre(A22, FlxX_sub(B21,B11, p), T, p, pi);
1224 3276 : GEN M5 = FlxqX_mul_pre(FlxX_add(A11,A12, p), B22, T, p, pi);
1225 3276 : GEN M6 = FlxqX_mul_pre(FlxX_sub(A21,A11, p), FlxX_add(B11,B12, p), T, p, pi);
1226 3276 : GEN M7 = FlxqX_mul_pre(FlxX_sub(A12,A22, p), FlxX_add(B21,B22, p), T, p, pi);
1227 3276 : GEN T1 = FlxX_add(M1,M4, p), T2 = FlxX_sub(M7,M5, p);
1228 3276 : GEN T3 = FlxX_sub(M1,M2, p), T4 = FlxX_add(M3,M6, p);
1229 3276 : retmkmat22(FlxX_add(T1,T2, p), FlxX_add(M3,M5, p),
1230 : FlxX_add(M2,M4, p), FlxX_add(T3,T4, p));
1231 : }
1232 :
1233 : /* Return [0,1;1,-q]*M */
1234 : static GEN
1235 3276 : FlxqX_FlxqXM_qmul(GEN q, GEN M, GEN T, ulong p, ulong pi)
1236 : {
1237 3276 : GEN u = FlxqX_mul_pre(gcoeff(M,2,1), q, T,p,pi);
1238 3276 : GEN v = FlxqX_mul_pre(gcoeff(M,2,2), q, T,p,pi);
1239 3276 : retmkmat22(gcoeff(M,2,1), gcoeff(M,2,2),
1240 : FlxX_sub(gcoeff(M,1,1), u, p), FlxX_sub(gcoeff(M,1,2), v, p));
1241 : }
1242 :
1243 : static GEN
1244 16 : matid2_FlxXM(long v, long sv)
1245 16 : { retmkmat22(pol1_FlxX(v, sv),pol_0(v),pol_0(v),pol1_FlxX(v, sv)); }
1246 :
1247 : static GEN
1248 0 : matJ2_FlxXM(long v, long sv)
1249 0 : { retmkmat22(pol_0(v),pol1_FlxX(v, sv),pol1_FlxX(v, sv),pol_0(v)); }
1250 :
1251 : struct FlxqX_res
1252 : {
1253 : GEN res, lc;
1254 : long deg0, deg1, off;
1255 : };
1256 :
1257 : INLINE void
1258 0 : FlxqX_halfres_update(long da, long db, long dr, GEN T, ulong p, ulong pi, struct FlxqX_res *res)
1259 : {
1260 0 : if (dr >= 0)
1261 : {
1262 0 : if (!Flx_equal1(res->lc))
1263 : {
1264 0 : res->lc = Flxq_powu_pre(res->lc, da - dr, T, p, pi);
1265 0 : res->res = Flxq_mul_pre(res->res, res->lc, T, p, pi);
1266 : }
1267 0 : if (both_odd(da + res->off, db + res->off))
1268 0 : res->res = Flx_neg(res->res, p);
1269 : } else
1270 : {
1271 0 : if (db == 0)
1272 : {
1273 0 : if (!Flx_equal1(res->lc))
1274 : {
1275 0 : res->lc = Flxq_powu_pre(res->lc, da, T, p, pi);
1276 0 : res->res = Flxq_mul_pre(res->res, res->lc, T, p, pi);
1277 : }
1278 : } else
1279 0 : res->res = pol0_Flx(get_Flx_var(T));
1280 : }
1281 0 : }
1282 :
1283 : static GEN
1284 4035 : FlxqX_halfres_basecase(GEN a, GEN b, GEN T, ulong p, ulong pi, GEN *pa, GEN *pb, struct FlxqX_res *res)
1285 : {
1286 4035 : pari_sp av=avma;
1287 : GEN u,u1,v,v1, M;
1288 4035 : long vx = varn(a), vT = get_Flx_var(T), n = lgpol(a)>>1;
1289 4035 : u1 = v = pol_0(vx);
1290 4035 : u = v1 = pol1_FlxX(vx, vT);
1291 22321 : while (lgpol(b)>n)
1292 : {
1293 : GEN r, q;
1294 18286 : q = FlxqX_divrem(a,b, T, p, &r);
1295 18286 : if (res)
1296 : {
1297 0 : long da = degpol(a), db = degpol(b), dr = degpol(r);
1298 0 : res->lc = gel(b,db+2);
1299 0 : if (dr >= n)
1300 0 : FlxqX_halfres_update(da, db, dr, T, p, pi, res);
1301 : else
1302 : {
1303 0 : res->deg0 = da;
1304 0 : res->deg1 = db;
1305 : }
1306 : }
1307 18286 : a = b; b = r; swap(u,u1); swap(v,v1);
1308 18286 : u1 = FlxX_sub(u1, FlxqX_mul_pre(u, q, T, p, pi), p);
1309 18286 : v1 = FlxX_sub(v1, FlxqX_mul_pre(v, q, T, p, pi), p);
1310 18286 : if (gc_needed(av,2))
1311 : {
1312 0 : if (DEBUGMEM>1) pari_warn(warnmem,"FlxqX_halfgcd (d = %ld)",degpol(b));
1313 0 : if (res)
1314 0 : (void)gc_all(av, 8, &a,&b,&u1,&v1,&u,&v,&res->res,&res->lc);
1315 : else
1316 0 : (void)gc_all(av, 6, &a,&b,&u1,&v1,&u,&v);
1317 : }
1318 : }
1319 4035 : M = mkmat22(u,v,u1,v1); *pa = a; *pb = b;
1320 0 : return res ? gc_all(av, 5, &M, pa, pb, &res->res, &res->lc)
1321 4035 : : gc_all(av, 3, &M, pa, pb);
1322 : }
1323 :
1324 : static GEN FlxqX_halfres_i(GEN x, GEN y, GEN T, ulong p, ulong pi, GEN *a, GEN *b, struct FlxqX_res *res);
1325 :
1326 : static GEN
1327 3366 : FlxqX_halfres_split(GEN x, GEN y, GEN T, ulong p, ulong pi, GEN *a, GEN *b, struct FlxqX_res *res)
1328 : {
1329 3366 : pari_sp av = avma;
1330 : GEN Q, R, S, V1, V2;
1331 : GEN x1, y1, r, q;
1332 3366 : long l = lgpol(x), n = l>>1, k, vT = get_Flx_var(T);
1333 3366 : if (lgpol(y) <= n)
1334 16 : { *a = RgX_copy(x); *b = RgX_copy(y); return matid2_FlxXM(varn(x), vT); }
1335 3350 : if (res)
1336 : {
1337 0 : res->lc = leading_coeff(y);
1338 0 : res->deg0 -= n;
1339 0 : res->deg1 -= n;
1340 0 : res->off += n;
1341 : }
1342 3350 : R = FlxqX_halfres_i(FlxX_shift(x,-n, vT),FlxX_shift(y,-n, vT), T, p, pi, a, b, res);
1343 3350 : if (res)
1344 : {
1345 0 : res->off -= n;
1346 0 : res->deg0 += n;
1347 0 : res->deg1 += n;
1348 : }
1349 3350 : V1 = FlxqXM_FlxqX_mul2(R, Flxn_red(x,n), Flxn_red(y,n), T, p, pi);
1350 3350 : x1 = FlxX_add(FlxX_shift(*a,n,vT), gel(V1,1), p);
1351 3350 : y1 = FlxX_add(FlxX_shift(*b,n,vT), gel(V1,2), p);
1352 3350 : if (lgpol(y1) <= n)
1353 : {
1354 74 : *a = x1; *b = y1;
1355 0 : return res ? gc_all(av, 5, &R, a, b, &res->res, &res->lc)
1356 74 : : gc_all(av, 3, &R, a, b);
1357 : }
1358 3276 : k = 2*n-degpol(y1);
1359 3276 : q = FlxqX_divrem(x1, y1, T, p, &r);
1360 3276 : if (res)
1361 : {
1362 0 : long dx1 = degpol(x1), dy1 = degpol(y1), dr = degpol(r);
1363 0 : if (dy1 < degpol(y))
1364 0 : FlxqX_halfres_update(res->deg0, res->deg1, dy1, T, p, pi, res);
1365 0 : res->lc = leading_coeff(y1);
1366 0 : res->deg0 = dx1;
1367 0 : res->deg1 = dy1;
1368 0 : if (dr >= n)
1369 : {
1370 0 : FlxqX_halfres_update(dx1, dy1, dr, T, p, pi, res);
1371 0 : res->deg0 = dy1;
1372 0 : res->deg1 = dr;
1373 : }
1374 0 : res->deg0 -= k;
1375 0 : res->deg1 -= k;
1376 0 : res->off += k;
1377 : }
1378 3276 : S = FlxqX_halfres_i(FlxX_shift(y1,-k, vT), FlxX_shift(r,-k, vT), T, p, pi, a, b, res);
1379 3276 : if (res)
1380 : {
1381 0 : res->deg0 += k;
1382 0 : res->deg1 += k;
1383 0 : res->off -= k;
1384 : }
1385 3276 : Q = FlxqXM_mul2(S, FlxqX_FlxqXM_qmul(q, R, T, p, pi), T, p, pi);
1386 3276 : V2 = FlxqXM_FlxqX_mul2(S, FlxXn_red(y1,k), FlxXn_red(r,k), T, p, pi);
1387 3276 : *a = FlxX_add(FlxX_shift(*a,k,vT), gel(V2,1), p);
1388 3276 : *b = FlxX_add(FlxX_shift(*b,k,vT), gel(V2,2), p);
1389 0 : return res ? gc_all(av, 5, &Q, a, b, &res->res, &res->lc)
1390 3276 : : gc_all(av, 3, &Q, a, b);
1391 : }
1392 :
1393 : static GEN
1394 7401 : FlxqX_halfres_i(GEN x, GEN y, GEN T, ulong p, ulong pi, GEN *a, GEN *b, struct FlxqX_res *res)
1395 : {
1396 7401 : if (lgpol(x) < FlxqX_HALFGCD_LIMIT)
1397 4035 : return FlxqX_halfres_basecase(x, y, T, p, pi, a, b, res);
1398 3366 : return FlxqX_halfres_split(x, y, T, p, pi, a, b, res);
1399 : }
1400 :
1401 : static GEN
1402 775 : FlxqX_halfgcd_all_i(GEN x, GEN y, GEN T, ulong p, ulong pi, GEN *pa, GEN *pb)
1403 : {
1404 : GEN a, b;
1405 775 : GEN R = FlxqX_halfres_i(x, y, T, p, pi, &a, &b, NULL);
1406 775 : if (pa) *pa = a;
1407 775 : if (pb) *pb = b;
1408 775 : return R;
1409 : }
1410 :
1411 : /* Return M in GL_2(Fp[X]/(T)[Y]) such that:
1412 : if [a',b']~=M*[a,b]~ then degpol(a')>= (lgpol(a)>>1) >degpol(b')
1413 : */
1414 :
1415 : GEN
1416 775 : FlxqX_halfgcd_all_pre(GEN x, GEN y, GEN T, ulong p, ulong pi, GEN *a, GEN *b)
1417 : {
1418 775 : pari_sp av = avma;
1419 : GEN R,q,r;
1420 775 : if (!signe(x))
1421 : {
1422 0 : if (a) *a = RgX_copy(y);
1423 0 : if (b) *b = RgX_copy(x);
1424 0 : return matJ2_FlxXM(varn(x),get_Flx_var(T));
1425 : }
1426 775 : if (degpol(y)<degpol(x)) return FlxqX_halfgcd_all_i(x, y, T, p, pi, a, b);
1427 180 : q = FlxqX_divrem_pre(y, x, T, p, pi, &r);
1428 180 : R = FlxqX_halfgcd_all_i(x, r, T, p, pi, a, b);
1429 180 : gcoeff(R,1,1) = FlxX_sub(gcoeff(R,1,1),
1430 180 : FlxqX_mul_pre(q, gcoeff(R,1,2), T, p, pi), p);
1431 180 : gcoeff(R,2,1) = FlxX_sub(gcoeff(R,2,1),
1432 180 : FlxqX_mul_pre(q, gcoeff(R,2,2), T, p, pi), p);
1433 180 : return !a && b ? gc_all(av, 2, &R, b): gc_all(av, 1+!!a+!!b, &R, a, b);
1434 : }
1435 : GEN
1436 7 : FlxqX_halfgcd_all(GEN x, GEN y, GEN T, ulong p, GEN *a, GEN *b)
1437 7 : { return FlxqX_halfgcd_all_pre(x, y, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p), a, b); }
1438 :
1439 : GEN
1440 253 : FlxqX_halfgcd_pre(GEN x, GEN y, GEN T, ulong p, ulong pi)
1441 253 : { return FlxqX_halfgcd_all_pre(x, y, T, p, pi, NULL, NULL); }
1442 :
1443 : GEN
1444 0 : FlxqX_halfgcd(GEN x, GEN y, GEN T, ulong p)
1445 0 : { return FlxqX_halfgcd_pre(x, y, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
1446 :
1447 : static GEN
1448 166770 : FlxqX_gcd_basecase(GEN a, GEN b, GEN T, ulong p, ulong pi)
1449 : {
1450 166770 : pari_sp av = avma, av0=avma;
1451 1076592 : while (signe(b))
1452 : {
1453 : GEN c;
1454 909822 : if (gc_needed(av0,2))
1455 : {
1456 0 : if (DEBUGMEM>1) pari_warn(warnmem,"FlxqX_gcd (d = %ld)",degpol(b));
1457 0 : (void)gc_all(av0,2, &a,&b);
1458 : }
1459 909822 : av = avma; c = FlxqX_rem_pre(a, b, T, p, pi); a=b; b=c;
1460 : }
1461 166770 : return gc_const(av, a);
1462 : }
1463 :
1464 : GEN
1465 175808 : FlxqX_gcd_pre(GEN x, GEN y, GEN T, ulong p, ulong pi)
1466 : {
1467 175808 : pari_sp av = avma;
1468 175808 : x = FlxqX_red_pre(x, T, p, pi);
1469 175808 : y = FlxqX_red_pre(y, T, p, pi);
1470 175808 : if (!signe(x)) return gc_upto(av, y);
1471 167146 : while (lgpol(y)>=FlxqX_GCD_LIMIT)
1472 : {
1473 376 : if (lgpol(y)<=(lgpol(x)>>1))
1474 : {
1475 0 : GEN r = FlxqX_rem_pre(x, y, T, p, pi);
1476 0 : x = y; y = r;
1477 : }
1478 376 : (void) FlxqX_halfgcd_all_pre(x,y, T, p, pi, &x, &y);
1479 376 : if (gc_needed(av,2))
1480 : {
1481 0 : if (DEBUGMEM>1) pari_warn(warnmem,"FlxqX_gcd (y = %ld)",degpol(y));
1482 0 : (void)gc_all(av,2,&x,&y);
1483 : }
1484 : }
1485 166770 : return gc_upto(av, FlxqX_gcd_basecase(x, y, T, p, pi));
1486 : }
1487 : GEN
1488 23458 : FlxqX_gcd(GEN x, GEN y, GEN T, ulong p)
1489 23458 : { return FlxqX_gcd_pre(x, y, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
1490 :
1491 : static GEN
1492 133829 : FlxqX_extgcd_basecase(GEN a, GEN b, GEN T, ulong p,ulong pi, GEN *ptu, GEN *ptv)
1493 : {
1494 133829 : pari_sp av=avma;
1495 : GEN u,v,d,d1,v1;
1496 133829 : long vx = varn(a);
1497 133829 : d = a; d1 = b;
1498 133829 : v = pol_0(vx); v1 = pol1_FlxX(vx, get_Flx_var(T));
1499 470914 : while (signe(d1))
1500 : {
1501 337088 : GEN r, q = FlxqX_divrem_pre(d, d1, T, p, pi, &r);
1502 337093 : v = FlxX_sub(v, FlxqX_mul_pre(q,v1,T, p, pi),p);
1503 337085 : u=v; v=v1; v1=u;
1504 337085 : u=r; d=d1; d1=u;
1505 337085 : if (gc_needed(av,2))
1506 : {
1507 0 : if (DEBUGMEM>1) pari_warn(warnmem,"FlxqX_extgcd (d = %ld)",degpol(d));
1508 0 : (void)gc_all(av,5, &d,&d1,&u,&v,&v1);
1509 : }
1510 : }
1511 133826 : if (ptu)
1512 133812 : *ptu = FlxqX_div_pre(FlxX_sub(d,FlxqX_mul_pre(b,v, T,p,pi), p), a, T,p,pi);
1513 133824 : *ptv = v; return d;
1514 : }
1515 :
1516 : static GEN
1517 130 : FlxqX_extgcd_halfgcd(GEN x, GEN y, GEN T, ulong p, ulong pi, GEN *ptu, GEN *ptv)
1518 : {
1519 : GEN u,v;
1520 130 : GEN V = cgetg(expu(lgpol(y))+2,t_VEC);
1521 130 : long i, n = 0, vs = varn(x), vT = get_Flx_var(T);
1522 269 : while (lgpol(y) >= FlxqX_EXTGCD_LIMIT)
1523 : {
1524 139 : if (lgpol(y)<=(lgpol(x)>>1))
1525 : {
1526 0 : GEN r, q = FlxqX_divrem_pre(x, y, T, p, pi, &r);
1527 0 : x = y; y = r;
1528 0 : gel(V,++n) = mkmat22(pol_0(vs),pol1_FlxX(vs,vT),pol1_FlxX(vs,vT),FlxX_neg(q,p));
1529 : } else
1530 139 : gel(V,++n) = FlxqX_halfgcd_all_pre(x, y, T, p, pi, &x, &y);
1531 : }
1532 130 : y = FlxqX_extgcd_basecase(x,y, T, p, pi, &u,&v);
1533 139 : for (i = n; i>1; i--)
1534 : {
1535 9 : GEN R = gel(V,i);
1536 9 : GEN u1 = FlxqX_addmulmul(u, v, gcoeff(R,1,1), gcoeff(R,2,1), T, p, pi);
1537 9 : GEN v1 = FlxqX_addmulmul(u, v, gcoeff(R,1,2), gcoeff(R,2,2), T, p, pi);
1538 9 : u = u1; v = v1;
1539 : }
1540 : {
1541 130 : GEN R = gel(V,1);
1542 130 : if (ptu)
1543 130 : *ptu = FlxqX_addmulmul(u, v, gcoeff(R,1,1), gcoeff(R,2,1), T, p, pi);
1544 130 : *ptv = FlxqX_addmulmul(u, v, gcoeff(R,1,2), gcoeff(R,2,2), T, p, pi);
1545 : }
1546 130 : return y;
1547 : }
1548 :
1549 : /* x and y in Z[Y][X], return lift(gcd(x mod T,p, y mod T,p)). Set u and v st
1550 : * ux + vy = gcd (mod T,p) */
1551 : GEN
1552 133829 : FlxqX_extgcd_pre(GEN x, GEN y, GEN T, ulong p, ulong pi, GEN *ptu, GEN *ptv)
1553 : {
1554 133829 : pari_sp av = avma;
1555 : GEN d;
1556 133829 : x = FlxqX_red_pre(x, T, p, pi);
1557 133824 : y = FlxqX_red_pre(y, T, p, pi);
1558 133827 : if (lgpol(y)>=FlxqX_EXTGCD_LIMIT)
1559 130 : d = FlxqX_extgcd_halfgcd(x, y, T, p, pi, ptu, ptv);
1560 : else
1561 133697 : d = FlxqX_extgcd_basecase(x, y, T, p, pi, ptu, ptv);
1562 133824 : return gc_all(av, ptu?3:2, &d, ptv, ptu);
1563 : }
1564 : GEN
1565 133815 : FlxqX_extgcd(GEN x, GEN y, GEN T, ulong p, GEN *ptu, GEN *ptv)
1566 : {
1567 133815 : ulong pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
1568 133815 : return FlxqX_extgcd_pre(x, y, T, p, pi, ptu, ptv);
1569 : }
1570 :
1571 : static GEN
1572 366782 : FlxqX_saferem(GEN P, GEN Q, GEN T, ulong p, ulong pi)
1573 : {
1574 366782 : GEN U = Flxq_invsafe_pre(leading_coeff(Q), T, p, pi);
1575 366795 : if (!U) return NULL;
1576 366795 : Q = FlxqX_Flxq_mul_to_monic_pre(Q,U,T,p,pi);
1577 366809 : return FlxqX_rem_pre(P,Q,T,p,pi);
1578 : }
1579 :
1580 : GEN
1581 0 : FlxqX_eval(GEN x, GEN y, GEN T, ulong p)
1582 : {
1583 : pari_sp av;
1584 : GEN p1, r;
1585 0 : long j, i=lg(x)-1;
1586 0 : if (i<=2)
1587 0 : return (i==2)? gcopy(gel(x,2)): pol0_Flx(get_Flx_var(T));
1588 0 : av=avma; p1=gel(x,i);
1589 : /* specific attention to sparse polynomials (see poleval)*/
1590 : /*You've guessed it! It's a copy-paste(tm)*/
1591 0 : for (i--; i>=2; i=j-1)
1592 : {
1593 0 : for (j=i; lg(gel(x,j))==1; j--)
1594 0 : if (j==2)
1595 : {
1596 0 : if (i!=j) y = Flxq_powu(y, i-j+1, T, p);
1597 0 : return gc_upto(av, Flxq_mul(p1,y, T, p));
1598 : }
1599 0 : r = (i==j)? y: Flxq_powu(y, i-j+1, T, p);
1600 0 : p1 = Flx_add(Flxq_mul(p1,r,T,p), gel(x,j), p);
1601 : }
1602 0 : return gc_upto(av, p1);
1603 : }
1604 :
1605 : GEN
1606 91222 : FlxqX_safegcd(GEN P, GEN Q, GEN T, ulong p)
1607 : {
1608 91222 : pari_sp av = avma;
1609 : ulong pi;
1610 : GEN U;
1611 91222 : if (!signe(P)) return gcopy(Q);
1612 91222 : if (!signe(Q)) return gcopy(P);
1613 91222 : pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
1614 91222 : T = Flx_get_red_pre(T,p,pi);
1615 : for(;;)
1616 : {
1617 313573 : P = FlxqX_saferem(P,Q,T,p,pi);
1618 313573 : if (!P) return gc_NULL(av);
1619 313573 : if (!signe(P)) break;
1620 222351 : if (gc_needed(av, 1))
1621 : {
1622 0 : if (DEBUGMEM>1) pari_warn(warnmem,"FlxqX_safegcd");
1623 0 : (void)gc_all(av, 2, &P,&Q);
1624 : }
1625 222351 : swap(P, Q);
1626 : }
1627 91222 : U = Flxq_invsafe_pre(leading_coeff(Q), T, p, pi);
1628 91222 : if (!U) return gc_NULL(av);
1629 91222 : Q = FlxqX_Flxq_mul_to_monic_pre(Q,U,T,p,pi);
1630 91222 : return gc_upto(av, Q);
1631 : }
1632 :
1633 : /* Res(A,B) = Res(B,R) * lc(B)^(a-r) * (-1)^(ab), with R=A%B, a=deg(A) ...*/
1634 : GEN
1635 10602 : FlxqX_saferesultant(GEN a, GEN b, GEN T, ulong p)
1636 : {
1637 10602 : long vT = get_Flx_var(T), da,db,dc;
1638 : ulong pi;
1639 : pari_sp av;
1640 10602 : GEN c,lb, res = pol1_Flx(vT);
1641 :
1642 10602 : if (!signe(a) || !signe(b)) return pol0_Flx(vT);
1643 :
1644 10602 : da = degpol(a);
1645 10602 : db = degpol(b);
1646 10602 : if (db > da)
1647 : {
1648 0 : swapspec(a,b, da,db);
1649 0 : if (both_odd(da,db)) res = Flx_neg(res, p);
1650 : }
1651 10602 : if (!da) return pol1_Flx(vT); /* = res * a[2] ^ db, since 0 <= db <= da = 0 */
1652 10602 : pi = SMALL_ULONG(p)? 0: get_Fl_red(p); av = avma;
1653 63779 : while (db)
1654 : {
1655 53206 : lb = gel(b,db+2);
1656 53206 : c = FlxqX_saferem(a,b, T,p,pi);
1657 53263 : if (!c) return gc_NULL(av);
1658 53263 : a = b; b = c; dc = degpol(c);
1659 53261 : if (dc < 0) { set_avma(av); return pol0_Flx(vT); }
1660 :
1661 53247 : if (both_odd(da,db)) res = Flx_neg(res, p);
1662 53245 : if (!Flx_equal1(lb))
1663 53182 : res = Flxq_mul_pre(res, Flxq_powu_pre(lb, da - dc, T, p, pi), T, p, pi);
1664 53177 : if (gc_needed(av,2))
1665 : {
1666 0 : if (DEBUGMEM>1) pari_warn(warnmem,"FlxqX_resultant (da = %ld)",da);
1667 0 : (void)gc_all(av,3, &a,&b,&res);
1668 : }
1669 53177 : da = db; /* = degpol(a) */
1670 53177 : db = dc; /* = degpol(b) */
1671 : }
1672 10573 : res = Flxq_mul_pre(res, Flxq_powu_pre(gel(b,2), da, T, p, pi), T, p, pi);
1673 10587 : return gc_upto(av, res);
1674 : }
1675 :
1676 : static GEN
1677 0 : FlxqX_halfres(GEN x, GEN y, GEN T, ulong p, ulong pi, GEN *a, GEN *b, GEN *r)
1678 : {
1679 : struct FlxqX_res res;
1680 : GEN V;
1681 : long dB;
1682 :
1683 0 : res.res = *r;
1684 0 : res.lc = leading_coeff(y);
1685 0 : res.deg0 = degpol(x);
1686 0 : res.deg1 = degpol(y);
1687 0 : res.off = 0;
1688 0 : V = FlxqX_halfres_i(x, y, T, p, pi, a, b, &res);
1689 0 : dB = degpol(*b);
1690 0 : if (dB < degpol(y))
1691 0 : FlxqX_halfres_update(res.deg0, res.deg1, dB, T, p, pi, &res);
1692 0 : *r = res.res;
1693 0 : return V;
1694 : }
1695 :
1696 : static GEN
1697 56 : FlxqX_resultant_basecase(GEN a, GEN b, GEN T, ulong p, ulong pi)
1698 : {
1699 56 : pari_sp av = avma;
1700 56 : long vT = get_Flx_var(T), da,db,dc;
1701 56 : GEN c,lb, res = pol1_Flx(vT);
1702 :
1703 56 : if (!signe(a) || !signe(b)) return pol0_Flx(vT);
1704 :
1705 56 : da = degpol(a);
1706 56 : db = degpol(b);
1707 56 : if (db > da)
1708 : {
1709 0 : swapspec(a,b, da,db);
1710 0 : if (both_odd(da,db)) res = Flx_neg(res, p);
1711 : }
1712 56 : if (!da) return pol1_Flx(vT); /* = res * a[2] ^ db, since 0 <= db <= da = 0 */
1713 147 : while (db)
1714 : {
1715 91 : lb = gel(b,db+2);
1716 91 : c = FlxqX_rem_pre(a,b, T,p,pi);
1717 91 : a = b; b = c; dc = degpol(c);
1718 91 : if (dc < 0) { set_avma(av); return pol0_Flx(vT); }
1719 :
1720 91 : if (both_odd(da,db)) res = Flx_neg(res, p);
1721 91 : if (!Flx_equal1(lb))
1722 63 : res = Flxq_mul_pre(res, Flxq_powu_pre(lb, da - dc, T,p,pi), T,p,pi);
1723 91 : if (gc_needed(av,2))
1724 : {
1725 0 : if (DEBUGMEM>1) pari_warn(warnmem,"FlxqX_resultant (da = %ld)",da);
1726 0 : (void)gc_all(av,3, &a,&b,&res);
1727 : }
1728 91 : da = db; /* = degpol(a) */
1729 91 : db = dc; /* = degpol(b) */
1730 : }
1731 56 : res = Flxq_mul_pre(res, Flxq_powu_pre(gel(b,2), da, T,p,pi), T,p,pi);
1732 56 : return gc_upto(av, res);
1733 : }
1734 :
1735 : /* Res(A,B) = Res(B,R) * lc(B)^(a-r) * (-1)^(ab), with R=A%B, a=deg(A) ...*/
1736 : GEN
1737 56 : FlxqX_resultant_pre(GEN x, GEN y, GEN T, ulong p, ulong pi)
1738 : {
1739 56 : pari_sp av = avma;
1740 56 : long dx, dy, vT = get_Flx_var(T);
1741 56 : GEN res = pol1_Flx(vT);
1742 56 : if (!signe(x) || !signe(y)) return pol0_Flx(vT);
1743 56 : dx = degpol(x); dy = degpol(y);
1744 56 : if (dx < dy)
1745 : {
1746 21 : swap(x,y);
1747 21 : if (both_odd(dx, dy))
1748 0 : res = Flx_neg(res, p);
1749 : }
1750 56 : while (lgpol(y) >= FlxqX_GCD_LIMIT)
1751 : {
1752 0 : if (lgpol(y)<=(lgpol(x)>>1))
1753 : {
1754 0 : GEN r = FlxqX_rem_pre(x, y, T, p, pi);
1755 0 : long dx = degpol(x), dy = degpol(y), dr = degpol(r);
1756 0 : GEN ly = gel(y,dy+2);
1757 0 : if (!Flx_equal1(ly))
1758 0 : res = Flxq_mul_pre(res, Flxq_powu_pre(ly, dx - dr, T, p, pi), T, p, pi);
1759 0 : if (both_odd(dx, dy))
1760 0 : res = Flx_neg(res, p);
1761 0 : x = y; y = r;
1762 : }
1763 0 : (void) FlxqX_halfres(x, y, T, p, pi, &x, &y, &res);
1764 0 : if (gc_needed(av,2))
1765 : {
1766 0 : if (DEBUGMEM>1) pari_warn(warnmem,"FlxqX_resultant (y = %ld)",degpol(y));
1767 0 : (void)gc_all(av,3,&x,&y,&res);
1768 : }
1769 : }
1770 56 : res = Flxq_mul_pre(res, FlxqX_resultant_basecase(x, y, T, p, pi), T, p, pi);
1771 56 : return gc_upto(av, res);
1772 : }
1773 : GEN
1774 56 : FlxqX_resultant(GEN x, GEN y, GEN T, ulong p)
1775 56 : { return FlxqX_resultant_pre(x, y, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
1776 :
1777 : /* disc P = (-1)^(n(n-1)/2) lc(P)^(n - deg P' - 2) Res(P,P'), n = deg P */
1778 : GEN
1779 14 : FlxqX_disc(GEN P, GEN T, ulong p)
1780 : {
1781 14 : pari_sp av = avma;
1782 14 : GEN L, dP = FlxX_deriv(P, p), D = FlxqX_resultant(P, dP, T, p);
1783 : long dd;
1784 14 : if (!lgpol(D)) return pol0_Flx(get_Flx_var(T));
1785 14 : dd = degpol(P) - 2 - degpol(dP); /* >= -1; > -1 iff p | deg(P) */
1786 14 : L = leading_coeff(P);
1787 14 : if (dd && !Flx_equal1(L))
1788 : {
1789 0 : ulong pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
1790 0 : D = (dd == -1)? Flxq_div_pre(D,L,T,p,pi)
1791 0 : : Flxq_mul_pre(D, Flxq_powu_pre(L, dd, T,p,pi), T,p,pi); }
1792 14 : if (degpol(P) & 2) D = Flx_neg(D, p);
1793 14 : return gc_upto(av, D);
1794 : }
1795 :
1796 : INLINE GEN
1797 6080 : FlxXn_recip(GEN x, long n, long v)
1798 6080 : { return FlxX_recipspec(x+2, minss(lgpol(x), n), n, v); }
1799 :
1800 : GEN
1801 2432 : FlxqX_Newton_pre(GEN P, long n, GEN T, ulong p, ulong pi)
1802 : {
1803 2432 : pari_sp av = avma;
1804 2432 : long d = degpol(P), vT = get_Flx_var(T);
1805 2432 : GEN dP = FlxXn_recip(FlxX_deriv(P, p), d, vT);
1806 2432 : GEN Q = FlxqXn_mul_pre(FlxqXn_inv_pre(FlxXn_recip(P, d+1, vT), n, T,p,pi),
1807 : dP, n, T, p, pi);
1808 2432 : return gc_GEN(av, Q);
1809 : }
1810 : GEN
1811 0 : FlxqX_Newton(GEN P, long n, GEN T, ulong p)
1812 0 : { return FlxqX_Newton_pre(P, n, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
1813 :
1814 : GEN
1815 1216 : FlxqX_fromNewton_pre(GEN P, GEN T, ulong p, ulong pi)
1816 : {
1817 1216 : pari_sp av = avma;
1818 1216 : long vT = get_Flx_var(T);
1819 1216 : long n = Flx_constant(constant_coeff(P))+1;
1820 1216 : GEN z = FlxX_neg(FlxX_shift(P, -1, vT), p);
1821 1216 : GEN Q = FlxXn_recip(FlxqXn_expint_pre(z, n, T, p, pi), n, vT);
1822 1216 : return gc_GEN(av, Q);
1823 : }
1824 : GEN
1825 0 : FlxqX_fromNewton(GEN P, GEN T, ulong p)
1826 0 : { return FlxqX_fromNewton_pre(P, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
1827 :
1828 : GEN
1829 1216 : FlxqX_composedsum(GEN P, GEN Q, GEN T, ulong p)
1830 : {
1831 1216 : pari_sp av = avma;
1832 1216 : ulong pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
1833 1216 : long n = 1+ degpol(P)*degpol(Q);
1834 1216 : GEN Pl = FlxX_invLaplace(FlxqX_Newton_pre(P,n, T,p,pi), p);
1835 1216 : GEN Ql = FlxX_invLaplace(FlxqX_Newton_pre(Q,n, T,p,pi), p);
1836 1216 : GEN L = FlxX_Laplace(FlxqXn_mul_pre(Pl, Ql, n, T,p,pi), p);
1837 1216 : GEN R = FlxqX_fromNewton_pre(L, T, p, pi);
1838 1216 : GEN lead = Flxq_mul_pre(Flxq_powu_pre(leading_coeff(P),degpol(Q), T,p,pi),
1839 1216 : Flxq_powu_pre(leading_coeff(Q),degpol(P), T,p,pi),
1840 : T, p, pi);
1841 1216 : return gc_upto(av, FlxqX_Flxq_mul_pre(R, lead, T, p, pi));
1842 : }
1843 :
1844 : GEN
1845 223093 : FlxqXV_prod(GEN V, GEN T, ulong p)
1846 : {
1847 223093 : struct _FlxqXQ d; d.p=p; d.T=T; d.pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
1848 223093 : return gen_product(V, (void*)&d, &_FlxqX_mul);
1849 : }
1850 :
1851 : static GEN
1852 32151 : FlxqV_roots_to_deg1(GEN x, GEN T, ulong p, long v)
1853 : {
1854 32151 : long sv = get_Flx_var(T);
1855 124249 : pari_APPLY_same(deg1pol_shallow(pol1_Flx(sv),Flx_neg(gel(x,i),p),v))
1856 : }
1857 :
1858 : GEN
1859 32151 : FlxqV_roots_to_pol(GEN V, GEN T, ulong p, long v)
1860 : {
1861 32151 : pari_sp ltop = avma;
1862 32151 : GEN W = FlxqV_roots_to_deg1(V, T, p, v);
1863 32151 : return gc_upto(ltop, FlxqXV_prod(W, T, p));
1864 : }
1865 :
1866 : /*******************************************************************/
1867 : /* */
1868 : /* (Fl[X]/T(X))[Y] / S(Y) */
1869 : /* */
1870 : /*******************************************************************/
1871 :
1872 : GEN
1873 470985 : FlxqXQ_mul_pre(GEN x, GEN y, GEN S, GEN T, ulong p, ulong pi)
1874 470985 : { return FlxqX_rem_pre(FlxqX_mul_pre(x,y,T,p,pi),S,T,p,pi); }
1875 : GEN
1876 1947 : FlxqXQ_mul(GEN x, GEN y, GEN S, GEN T, ulong p)
1877 1947 : { return FlxqXQ_mul_pre(x, y, S, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
1878 :
1879 : GEN
1880 261973 : FlxqXQ_sqr_pre(GEN x, GEN S, GEN T, ulong p, ulong pi)
1881 261973 : { return FlxqX_rem_pre(FlxqX_sqr_pre(x,T,p,pi),S,T,p,pi); }
1882 : GEN
1883 0 : FlxqXQ_sqr(GEN x, GEN S, GEN T, ulong p)
1884 0 : { return FlxqXQ_sqr_pre(x, S, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
1885 :
1886 : GEN
1887 14 : FlxqXQ_invsafe_pre(GEN x, GEN S, GEN T, ulong p, ulong pi)
1888 : {
1889 14 : GEN V, z = FlxqX_extgcd_pre(get_FlxqX_mod(S), x, T, p, pi, NULL, &V);
1890 14 : if (degpol(z)) return NULL;
1891 14 : z = Flxq_invsafe_pre(gel(z,2),T,p,pi);
1892 14 : if (!z) return NULL;
1893 14 : return FlxqX_Flxq_mul_pre(V, z, T, p, pi);
1894 : }
1895 : GEN
1896 0 : FlxqXQ_invsafe(GEN x, GEN S, GEN T, ulong p)
1897 0 : { return FlxqXQ_invsafe_pre(x, S, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
1898 :
1899 : GEN
1900 14 : FlxqXQ_inv_pre(GEN x, GEN S, GEN T, ulong p, ulong pi)
1901 : {
1902 14 : pari_sp av = avma;
1903 14 : GEN U = FlxqXQ_invsafe_pre(x, S, T, p, pi);
1904 14 : if (!U) pari_err_INV("FlxqXQ_inv",x);
1905 14 : return gc_upto(av, U);
1906 : }
1907 : GEN
1908 14 : FlxqXQ_inv(GEN x, GEN S, GEN T,ulong p)
1909 14 : { return FlxqXQ_inv_pre(x, S, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
1910 :
1911 : GEN
1912 0 : FlxqXQ_div_pre(GEN x, GEN y, GEN S, GEN T, ulong p, ulong pi)
1913 0 : { return FlxqXQ_mul_pre(x, FlxqXQ_inv_pre(y,S,T,p,pi),S,T,p,pi); }
1914 : GEN
1915 0 : FlxqXQ_div(GEN x, GEN y, GEN S, GEN T, ulong p)
1916 0 : { return FlxqXQ_div_pre(x, y, S, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
1917 :
1918 : static GEN
1919 0 : _FlxqX_add(void *data, GEN x, GEN y) {
1920 0 : struct _FlxqXQ *d = (struct _FlxqXQ*) data;
1921 0 : return FlxX_add(x,y, d->p);
1922 : }
1923 : static GEN
1924 5526 : _FlxqX_sub(void *data, GEN x, GEN y) {
1925 5526 : struct _FlxqXQ *d = (struct _FlxqXQ*) data;
1926 5526 : return FlxX_sub(x,y, d->p);
1927 : }
1928 : #if 0
1929 : static GEN
1930 : _FlxqXQ_cmul(void *data, GEN P, long a, GEN x) {
1931 : struct _FlxqXQ *d = (struct _FlxqXQ*) data;
1932 : return FlxX_Flx_mul(x,gel(P,a+2), d->p);
1933 : }
1934 : #endif
1935 : static GEN
1936 6044 : _FlxqXQ_red(void *data, GEN x) {
1937 6044 : struct _FlxqXQ *d = (struct _FlxqXQ*) data;
1938 6044 : return FlxqX_red_pre(x, d->T, d->p, d->pi);
1939 : }
1940 : static GEN
1941 179118 : _FlxqXQ_mul(void *data, GEN x, GEN y) {
1942 179118 : struct _FlxqXQ *d = (struct _FlxqXQ*) data;
1943 179118 : return FlxqXQ_mul_pre(x,y, d->S,d->T, d->p, d->pi);
1944 : }
1945 : static GEN
1946 261525 : _FlxqXQ_sqr(void *data, GEN x) {
1947 261525 : struct _FlxqXQ *d = (struct _FlxqXQ*) data;
1948 261525 : return FlxqXQ_sqr_pre(x, d->S,d->T, d->p, d->pi);
1949 : }
1950 :
1951 : static GEN
1952 111276 : _FlxqXQ_one(void *data) {
1953 111276 : struct _FlxqXQ *d = (struct _FlxqXQ*) data;
1954 111276 : return pol1_FlxX(get_FlxqX_var(d->S),get_Flx_var(d->T));
1955 : }
1956 :
1957 : static GEN
1958 316 : _FlxqXQ_zero(void *data) {
1959 316 : struct _FlxqXQ *d = (struct _FlxqXQ*) data;
1960 316 : return pol_0(get_FlxqX_var(d->S));
1961 : }
1962 :
1963 : static struct bb_algebra FlxqXQ_algebra = { _FlxqXQ_red, _FlxqX_add,
1964 : _FlxqX_sub, _FlxqXQ_mul, _FlxqXQ_sqr, _FlxqXQ_one, _FlxqXQ_zero };
1965 :
1966 : const struct bb_algebra *
1967 761 : get_FlxqXQ_algebra(void **E, GEN S, GEN T, ulong p)
1968 : {
1969 761 : ulong pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
1970 761 : GEN z = new_chunk(sizeof(struct _FlxqXQ));
1971 761 : struct _FlxqXQ *e = (struct _FlxqXQ *) z;
1972 761 : e->T = Flx_get_red_pre(T, p, pi);
1973 761 : e->S = FlxqX_get_red_pre(S, e->T, p, pi);
1974 761 : e->p = p;
1975 761 : e->pi= pi; *E = (void*)e;
1976 761 : return &FlxqXQ_algebra;
1977 : }
1978 :
1979 : static struct bb_algebra FlxqX_algebra = { _FlxqXQ_red, _FlxqX_add,
1980 : _FlxqX_sub, _FlxqX_mul, _FlxqX_sqr, _FlxqXQ_one, _FlxqXQ_zero };
1981 :
1982 : const struct bb_algebra *
1983 0 : get_FlxqX_algebra(void **E, GEN T, ulong p, long v)
1984 : {
1985 0 : ulong pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
1986 0 : GEN z = new_chunk(sizeof(struct _FlxqXQ));
1987 0 : struct _FlxqXQ *e = (struct _FlxqXQ *) z;
1988 0 : e->T = Flx_get_red(T, p);
1989 0 : e->S = pol_x(v);
1990 0 : e->p = p;
1991 0 : e->pi= pi; *E = (void*)e;
1992 0 : return &FlxqX_algebra;
1993 : }
1994 :
1995 : /* x over Fq, return lift(x^n) mod S */
1996 : GEN
1997 91 : FlxqXQ_pow_pre(GEN x, GEN n, GEN S, GEN T, ulong p, ulong pi)
1998 : {
1999 91 : pari_sp av = avma;
2000 : struct _FlxqXQ D;
2001 91 : long s = signe(n);
2002 91 : if (!s) return pol1_FlxX(get_FlxqX_var(S),get_Flx_var(T));
2003 91 : if (s < 0) x = FlxqXQ_inv_pre(x,S,T,p,pi);
2004 91 : if (is_pm1(n)) return s < 0 ? x : gcopy(x);
2005 91 : if (degpol(x) >= get_FlxqX_degree(S)) x = FlxqX_rem_pre(x,S,T,p,pi);
2006 91 : T = Flx_get_red_pre(T, p, pi);
2007 91 : S = FlxqX_get_red_pre(S, T, p, pi);
2008 91 : D.S = S; D.T = T; D.p = p; D.pi = pi;
2009 91 : x = gen_pow_i(x, n, (void*)&D, &_FlxqXQ_sqr, &_FlxqXQ_mul);
2010 91 : return gc_GEN(av, x);
2011 : }
2012 : GEN
2013 35 : FlxqXQ_pow(GEN x, GEN n, GEN S, GEN T, ulong p)
2014 35 : { return FlxqXQ_pow_pre(x, n, S, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
2015 :
2016 : /* x over Fq, return lift(x^n) mod S */
2017 : GEN
2018 82058 : FlxqXQ_powu_pre(GEN x, ulong n, GEN S, GEN T, ulong p, ulong pi)
2019 : {
2020 82058 : pari_sp av = avma;
2021 : struct _FlxqXQ D;
2022 82058 : switch(n)
2023 : {
2024 0 : case 0: return pol1_FlxX(get_FlxqX_var(S),get_Flx_var(T));
2025 7690 : case 1: return gcopy(x);
2026 448 : case 2: return FlxqXQ_sqr_pre(x, S, T, p, pi);
2027 : }
2028 73920 : T = Flx_get_red_pre(T, p, pi);
2029 73920 : S = FlxqX_get_red_pre(S, T, p, pi);
2030 73920 : D.S = S; D.T = T; D.p = p; D.pi = pi;
2031 73920 : x = gen_powu_i(x, n, (void*)&D, &_FlxqXQ_sqr, &_FlxqXQ_mul);
2032 73920 : return gc_GEN(av, x);
2033 : }
2034 : GEN
2035 0 : FlxqXQ_powu(GEN x, ulong n, GEN S, GEN T, ulong p)
2036 0 : { return FlxqXQ_powu_pre(x, n, S, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
2037 :
2038 : GEN
2039 108241 : FlxqXQ_powers_pre(GEN x, long l, GEN S, GEN T, ulong p, ulong pi)
2040 : {
2041 : struct _FlxqXQ D;
2042 108241 : int use_sqr = 2*degpol(x) >= get_FlxqX_degree(S);
2043 108241 : T = Flx_get_red_pre(T, p, pi);
2044 108241 : S = FlxqX_get_red_pre(S, T, p, pi);
2045 108241 : D.S = S; D.T = T; D.p = p; D.pi = pi;
2046 108241 : return gen_powers(x, l, use_sqr, (void*)&D, &_FlxqXQ_sqr, &_FlxqXQ_mul,&_FlxqXQ_one);
2047 : }
2048 : GEN
2049 0 : FlxqXQ_powers(GEN x, long l, GEN S, GEN T, ulong p)
2050 0 : { return FlxqXQ_powers_pre(x, l, S, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
2051 :
2052 : /* Let v a linear form, return the linear form z->v(tau*z)
2053 : that is, v*(M_tau) */
2054 : static GEN
2055 506 : FlxqXQ_transmul_init(GEN tau, GEN S, GEN T, ulong p, ulong pi)
2056 : {
2057 : GEN bht;
2058 506 : GEN h, Sp = get_FlxqX_red(S, &h);
2059 506 : long n = degpol(Sp), vS = varn(Sp), vT = get_Flx_var(T);
2060 506 : GEN ft = FlxX_recipspec(Sp+2, n+1, n+1, vT);
2061 506 : GEN bt = FlxX_recipspec(tau+2, lgpol(tau), n, vT);
2062 506 : setvarn(ft, vS); setvarn(bt, vS);
2063 506 : if (h)
2064 0 : bht = FlxqXn_mul_pre(bt, h, n-1, T, p, pi);
2065 : else
2066 : {
2067 506 : GEN bh = FlxqX_div_pre(FlxX_shift(tau, n-1, vT), S, T, p, pi);
2068 506 : bht = FlxX_recipspec(bh+2, lgpol(bh), n-1, vT);
2069 506 : setvarn(bht, vS);
2070 : }
2071 506 : return mkvec3(bt, bht, ft);
2072 : }
2073 :
2074 : static GEN
2075 1071 : FlxqXQ_transmul(GEN tau, GEN a, long n, GEN T, ulong p, ulong pi)
2076 : {
2077 1071 : pari_sp ltop = avma;
2078 : GEN t1, t2, t3, vec;
2079 1071 : GEN bt = gel(tau, 1), bht = gel(tau, 2), ft = gel(tau, 3);
2080 1071 : long vT = get_Flx_var(T);
2081 1071 : if (signe(a)==0) return pol_0(varn(a));
2082 1061 : t2 = FlxX_shift(FlxqX_mul_pre(bt, a, T, p, pi),1-n,vT);
2083 1061 : if (signe(bht)==0) return gc_GEN(ltop, t2);
2084 767 : t1 = FlxX_shift(FlxqX_mul_pre(ft, a, T, p, pi),-n,vT);
2085 767 : t3 = FlxqXn_mul_pre(t1, bht, n-1, T, p, pi);
2086 767 : vec = FlxX_sub(t2, FlxX_shift(t3, 1, vT), p);
2087 767 : return gc_upto(ltop, vec);
2088 : }
2089 :
2090 : static GEN
2091 253 : polxn_FlxX(long n, long v, long vT)
2092 : {
2093 253 : long i, a = n+2;
2094 253 : GEN p = cgetg(a+1, t_POL);
2095 253 : p[1] = evalsigne(1)|evalvarn(v);
2096 2171 : for (i = 2; i < a; i++) gel(p,i) = pol0_Flx(vT);
2097 253 : gel(p,a) = pol1_Flx(vT); return p;
2098 : }
2099 :
2100 : GEN
2101 224 : FlxqXQ_minpoly_pre(GEN x, GEN S, GEN T, ulong p, ulong pi)
2102 : {
2103 224 : pari_sp ltop = avma;
2104 : long vS, vT, n;
2105 : GEN v_x, g, tau;
2106 224 : vS = get_FlxqX_var(S);
2107 224 : vT = get_Flx_var(T);
2108 224 : n = get_FlxqX_degree(S);
2109 224 : g = pol1_FlxX(vS,vT);
2110 224 : tau = pol1_FlxX(vS,vT);
2111 224 : S = FlxqX_get_red_pre(S, T, p, pi);
2112 224 : v_x = FlxqXQ_powers_pre(x, usqrt(2*n), S, T, p, pi);
2113 477 : while(signe(tau) != 0)
2114 : {
2115 : long i, j, m, k1;
2116 : GEN M, v, tr;
2117 : GEN g_prime, c;
2118 253 : if (degpol(g) == n) { tau = pol1_FlxX(vS, vT); g = pol1_FlxX(vS, vT); }
2119 253 : v = random_FlxqX(n, vS, T, p);
2120 253 : tr = FlxqXQ_transmul_init(tau, S, T, p, pi);
2121 253 : v = FlxqXQ_transmul(tr, v, n, T, p, pi);
2122 253 : m = 2*(n-degpol(g));
2123 253 : k1 = usqrt(m);
2124 253 : tr = FlxqXQ_transmul_init(gel(v_x,k1+1), S, T, p, pi);
2125 253 : c = cgetg(m+2,t_POL);
2126 253 : c[1] = evalsigne(1)|evalvarn(vS);
2127 1071 : for (i=0; i<m; i+=k1)
2128 : {
2129 818 : long mj = minss(m-i, k1);
2130 2736 : for (j=0; j<mj; j++)
2131 1918 : gel(c,m+1-(i+j)) = FlxqX_dotproduct(v, gel(v_x,j+1), T, p);
2132 818 : v = FlxqXQ_transmul(tr, v, n, T, p, pi);
2133 : }
2134 253 : c = FlxX_renormalize(c, m+2);
2135 : /* now c contains <v,x^i> , i = 0..m-1 */
2136 253 : M = FlxqX_halfgcd_pre(polxn_FlxX(m, vS, vT), c, T, p, pi);
2137 253 : g_prime = gmael(M, 2, 2);
2138 253 : if (degpol(g_prime) < 1) continue;
2139 252 : g = FlxqX_mul_pre(g, g_prime, T, p, pi);
2140 252 : tau = FlxqXQ_mul_pre(tau, FlxqX_FlxqXQV_eval_pre(g_prime, v_x, S, T,p,pi),
2141 : S, T, p,pi);
2142 : }
2143 224 : g = FlxqX_normalize_pre(g,T,p,pi);
2144 224 : return gc_GEN(ltop,g);
2145 : }
2146 : GEN
2147 62 : FlxqXQ_minpoly(GEN x, GEN S, GEN T, ulong p)
2148 62 : { return FlxqXQ_minpoly_pre(x, S, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
2149 :
2150 : GEN
2151 0 : FlxqXQ_matrix_pow(GEN y, long n, long m, GEN S, GEN T, ulong p)
2152 0 : { return FlxXV_to_FlxM(FlxqXQ_powers(y,m-1,S,T,p), n, get_Flx_var(T)); }
2153 :
2154 : static GEN
2155 138362 : FlxX_blocks_FlxM(GEN P, long n, long m, long v)
2156 : {
2157 138362 : GEN z = cgetg(m+1,t_MAT);
2158 138362 : long i,j, k=2, l = lg(P);
2159 536339 : for(i=1; i<=m; i++)
2160 : {
2161 397977 : GEN zi = cgetg(n+1,t_COL);
2162 397977 : gel(z,i) = zi;
2163 1274305 : for(j=1; j<=n; j++)
2164 876328 : gel(zi, j) = k==l ? pol0_Flx(v) : gel(P,k++);
2165 : }
2166 138362 : return z;
2167 : }
2168 :
2169 : GEN
2170 138362 : FlxqX_FlxqXQV_eval_pre(GEN Q, GEN x, GEN S, GEN T, ulong p, ulong pi)
2171 : {
2172 138362 : pari_sp btop, av = avma;
2173 138362 : long v = get_FlxqX_var(S), m = get_FlxqX_degree(S);
2174 138362 : long vT = get_Flx_var(T);
2175 138362 : long i, l = lg(x)-1, lQ = lgpol(Q), n, d;
2176 : GEN A, B, C, R, g;
2177 138362 : if (lQ == 0) return pol_0(v);
2178 138362 : if (lQ <= l)
2179 : {
2180 43859 : n = l;
2181 43859 : d = 1;
2182 : }
2183 : else
2184 : {
2185 94503 : n = l-1;
2186 94503 : d = (lQ+n-1)/n;
2187 : }
2188 138362 : A = FlxXV_to_FlxM_lg(x, m, n, vT);
2189 138362 : B = FlxX_blocks_FlxM(Q, n, d, vT);
2190 138362 : C = gc_upto(av, FlxqM_mul(A, B, T, p));
2191 138362 : g = gel(x, l);
2192 138362 : T = Flx_get_red_pre(T, p, pi);
2193 138362 : S = FlxqX_get_red_pre(S, T, p, pi);
2194 138362 : btop = avma;
2195 138362 : R = FlxV_to_FlxX(gel(C, d), v);
2196 397977 : for (i = d-1; i>0; i--)
2197 : {
2198 259615 : R = FlxX_add(FlxqXQ_mul_pre(R, g, S, T,p,pi), FlxV_to_FlxX(gel(C,i), v), p);
2199 259615 : if (gc_needed(btop,1))
2200 6 : R = gc_upto(btop, R);
2201 : }
2202 138362 : return gc_GEN(av, R);
2203 : }
2204 : GEN
2205 0 : FlxqX_FlxqXQV_eval(GEN Q, GEN x, GEN S, GEN T, ulong p)
2206 0 : { return FlxqX_FlxqXQV_eval_pre(Q,x,S,T,p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
2207 :
2208 : GEN
2209 76758 : FlxqX_FlxqXQ_eval_pre(GEN Q, GEN x, GEN S, GEN T, ulong p, ulong pi)
2210 : {
2211 76758 : pari_sp av = avma;
2212 : GEN z, V;
2213 76758 : long d = degpol(Q), rtd;
2214 76758 : if (d < 0) return pol_0(get_FlxqX_var(S));
2215 76758 : rtd = (long) sqrt((double)d);
2216 76758 : T = Flx_get_red_pre(T, p, pi);
2217 76758 : S = FlxqX_get_red_pre(S, T, p, pi);
2218 76758 : V = FlxqXQ_powers_pre(x, rtd, S, T, p, pi);
2219 76758 : z = FlxqX_FlxqXQV_eval_pre(Q, V, S, T, p, pi);
2220 76758 : return gc_upto(av, z);
2221 : }
2222 : GEN
2223 0 : FlxqX_FlxqXQ_eval(GEN Q, GEN x, GEN S, GEN T, ulong p)
2224 0 : { return FlxqX_FlxqXQ_eval_pre(Q, x, S, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
2225 :
2226 : GEN
2227 0 : FlxqXC_FlxqXQV_eval_pre(GEN x, GEN v, GEN S, GEN T, ulong p, ulong pi)
2228 0 : { pari_APPLY_type(t_COL, FlxqX_FlxqXQV_eval_pre(gel(x,i), v, S, T, p, pi)) }
2229 : GEN
2230 0 : FlxqXC_FlxqXQV_eval(GEN x, GEN v, GEN S, GEN T, ulong p)
2231 0 : { return FlxqXC_FlxqXQV_eval_pre(x, v, S, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
2232 :
2233 : GEN
2234 0 : FlxqXC_FlxqXQ_eval(GEN x, GEN F, GEN S, GEN T, ulong p)
2235 : {
2236 0 : long d = brent_kung_optpow(get_FlxqX_degree(S)-1,lg(x)-1,1);
2237 0 : ulong pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
2238 0 : GEN Fp = FlxqXQ_powers_pre(F, d, S, T, p, pi);
2239 0 : return FlxqXC_FlxqXQV_eval_pre(x, Fp, S, T, p, pi);
2240 : }
2241 :
2242 : static GEN
2243 72682 : FlxqXQ_autpow_sqr(void * E, GEN x)
2244 : {
2245 72682 : struct _FlxqXQ *D = (struct _FlxqXQ *)E;
2246 72682 : GEN S = D->S, T = D->T;
2247 72682 : ulong p = D->p, pi = D->pi;
2248 72682 : GEN phi = gel(x,1), S1 = gel(x,2);
2249 72682 : long n = brent_kung_optpow(get_Flx_degree(T)-1,lgpol(S1)+1,1);
2250 72682 : GEN V = Flxq_powers_pre(phi, n, T, p, pi);
2251 72682 : GEN phi2 = Flx_FlxqV_eval_pre(phi, V, T, p, pi);
2252 72682 : GEN Sphi = FlxY_FlxqV_evalx_pre(S1, V, T, p, pi);
2253 72682 : GEN S2 = FlxqX_FlxqXQ_eval_pre(Sphi, S1, S, T, p, pi);
2254 72682 : return mkvec2(phi2, S2);
2255 : }
2256 :
2257 : static GEN
2258 3714 : FlxqXQ_autpow_mul(void * E, GEN x, GEN y)
2259 : {
2260 3714 : struct _FlxqXQ *D = (struct _FlxqXQ *)E;
2261 3714 : GEN S = D->S, T = D->T;
2262 3714 : ulong p = D->p, pi = D->pi;
2263 3714 : GEN phi1 = gel(x,1), S1 = gel(x,2);
2264 3714 : GEN phi2 = gel(y,1), S2 = gel(y,2);
2265 3714 : long n = brent_kung_optpow(get_Flx_degree(T)-1,lgpol(S1)+1,1);
2266 3714 : GEN V = Flxq_powers_pre(phi2, n, T, p, pi);
2267 3714 : GEN phi3 = Flx_FlxqV_eval_pre(phi1, V, T, p, pi);
2268 3714 : GEN Sphi = FlxY_FlxqV_evalx_pre(S1, V, T, p, pi);
2269 3714 : GEN S3 = FlxqX_FlxqXQ_eval_pre(Sphi, S2, S, T, p, pi);
2270 3714 : return mkvec2(phi3, S3);
2271 : }
2272 :
2273 : GEN
2274 69275 : FlxqXQ_autpow_pre(GEN aut, long n, GEN S, GEN T, ulong p, ulong pi)
2275 : {
2276 69275 : pari_sp av = avma;
2277 : struct _FlxqXQ D;
2278 69275 : T = Flx_get_red_pre(T, p, pi);
2279 69275 : S = FlxqX_get_red_pre(S, T, p, pi);
2280 69275 : D.S = S; D.T = T; D.p = p; D.pi = pi;
2281 69275 : aut = gen_powu_i(aut,n,&D,FlxqXQ_autpow_sqr,FlxqXQ_autpow_mul);
2282 69275 : return gc_GEN(av, aut);
2283 : }
2284 : GEN
2285 0 : FlxqXQ_autpow(GEN aut, long n, GEN S, GEN T, ulong p)
2286 0 : { return FlxqXQ_autpow_pre(aut, n, S, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
2287 :
2288 : static GEN
2289 29983 : FlxqXQ_autsum_mul(void *E, GEN x, GEN y)
2290 : {
2291 29983 : struct _FlxqXQ *D = (struct _FlxqXQ *)E;
2292 29983 : GEN S = D->S, T = D->T;
2293 29983 : ulong p = D->p, pi = D->pi;
2294 29983 : GEN phi1 = gel(x,1), S1 = gel(x,2), a1 = gel(x,3);
2295 29983 : GEN phi2 = gel(y,1), S2 = gel(y,2), a2 = gel(y,3);
2296 29983 : long n2 = brent_kung_optpow(get_Flx_degree(T)-1, lgpol(S1)+lgpol(a1)+1,1);
2297 29983 : GEN V2 = Flxq_powers_pre(phi2, n2, T, p, pi);
2298 29983 : GEN phi3 = Flx_FlxqV_eval_pre(phi1, V2, T, p, pi);
2299 29983 : GEN Sphi = FlxY_FlxqV_evalx_pre(S1, V2, T, p, pi);
2300 29983 : GEN aphi = FlxY_FlxqV_evalx_pre(a1, V2, T, p, pi);
2301 29983 : long n = brent_kung_optpow(maxss(degpol(Sphi),degpol(aphi)),2,1);
2302 29983 : GEN V = FlxqXQ_powers_pre(S2, n, S, T, p, pi);
2303 29983 : GEN S3 = FlxqX_FlxqXQV_eval_pre(Sphi, V, S, T, p, pi);
2304 29983 : GEN aS = FlxqX_FlxqXQV_eval_pre(aphi, V, S, T, p, pi);
2305 29983 : GEN a3 = FlxqXQ_mul_pre(aS, a2, S, T, p, pi);
2306 29983 : return mkvec3(phi3, S3, a3);
2307 : }
2308 :
2309 : static GEN
2310 18582 : FlxqXQ_autsum_sqr(void * T, GEN x)
2311 18582 : { return FlxqXQ_autsum_mul(T, x, x); }
2312 :
2313 : GEN
2314 12125 : FlxqXQ_autsum_pre(GEN aut, long n, GEN S, GEN T, ulong p, ulong pi)
2315 : {
2316 12125 : pari_sp av = avma;
2317 : struct _FlxqXQ D;
2318 12125 : T = Flx_get_red_pre(T, p, pi);
2319 12125 : S = FlxqX_get_red_pre(S, T, p, pi);
2320 12125 : D.S=S; D.T=T; D.p=p; D.pi=pi;
2321 12125 : aut = gen_powu_i(aut,n,&D,FlxqXQ_autsum_sqr,FlxqXQ_autsum_mul);
2322 12125 : return gc_GEN(av, aut);
2323 : }
2324 : GEN
2325 0 : FlxqXQ_autsum(GEN aut, long n, GEN S, GEN T, ulong p)
2326 0 : { return FlxqXQ_autsum_pre(aut, n, S, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
2327 :
2328 : static GEN
2329 27 : FlxqXQ_auttrace_mul(void *E, GEN x, GEN y)
2330 : {
2331 27 : struct _FlxqXQ *D = (struct _FlxqXQ *)E;
2332 27 : GEN S = D->S, T = D->T;
2333 27 : ulong p = D->p, pi = D->pi;
2334 27 : GEN S1 = gel(x,1), a1 = gel(x,2);
2335 27 : GEN S2 = gel(y,1), a2 = gel(y,2);
2336 27 : long n = brent_kung_optpow(maxss(degpol(S1),degpol(a1)),2,1);
2337 27 : GEN V = FlxqXQ_powers_pre(S2, n, S, T, p, pi);
2338 27 : GEN S3 = FlxqX_FlxqXQV_eval_pre(S1, V, S, T, p, pi);
2339 27 : GEN aS = FlxqX_FlxqXQV_eval_pre(a1, V, S, T, p, pi);
2340 27 : GEN a3 = FlxX_add(aS, a2, p);
2341 27 : return mkvec2(S3, a3);
2342 : }
2343 :
2344 : static GEN
2345 20 : FlxqXQ_auttrace_sqr(void *E, GEN x)
2346 20 : { return FlxqXQ_auttrace_mul(E, x, x); }
2347 :
2348 : GEN
2349 337 : FlxqXQ_auttrace_pre(GEN x, ulong n, GEN S, GEN T, ulong p, ulong pi)
2350 : {
2351 337 : pari_sp av = avma;
2352 : struct _FlxqXQ D;
2353 337 : T = Flx_get_red_pre(T, p, pi);
2354 337 : S = FlxqX_get_red_pre(S, T, p, pi);
2355 337 : D.S=S; D.T=T; D.p=p; D.pi = pi;
2356 337 : x = gen_powu_i(x,n,(void*)&D,FlxqXQ_auttrace_sqr,FlxqXQ_auttrace_mul);
2357 337 : return gc_GEN(av, x);
2358 : }
2359 : GEN
2360 0 : FlxqXQ_auttrace(GEN x, ulong n, GEN S, GEN T, ulong p)
2361 0 : { return FlxqXQ_auttrace_pre(x, n, S, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
2362 :
2363 : /*******************************************************************/
2364 : /* */
2365 : /* FlxYqQ */
2366 : /* */
2367 : /*******************************************************************/
2368 :
2369 : /*Preliminary implementation to speed up FpX_ffisom*/
2370 : typedef struct {
2371 : GEN S, T;
2372 : ulong p, pi;
2373 : } FlxYqq_muldata;
2374 :
2375 : /* reduce x in Fl[X, Y] in the algebra Fl[X, Y]/ (P(X),Q(Y)) */
2376 : static GEN
2377 90883 : FlxYqq_redswap(GEN x, GEN S, GEN T, ulong p, ulong pi)
2378 : {
2379 90883 : pari_sp ltop=avma;
2380 90883 : long n = get_Flx_degree(S);
2381 90882 : long m = get_Flx_degree(T);
2382 90882 : long w = get_Flx_var(T);
2383 90882 : GEN V = FlxX_swap(x,m,w);
2384 90882 : V = FlxqX_red_pre(V,S,p,pi);
2385 90877 : V = FlxX_swap(V,n,w);
2386 90883 : return gc_GEN(ltop,V);
2387 : }
2388 : static GEN
2389 80516 : FlxYqq_sqr(void *data, GEN x)
2390 : {
2391 80516 : FlxYqq_muldata *D = (FlxYqq_muldata*)data;
2392 80516 : return FlxYqq_redswap(FlxqX_sqr_pre(x,D->T,D->p,D->pi),D->S,D->T,D->p,D->pi);
2393 : }
2394 :
2395 : static GEN
2396 10368 : FlxYqq_mul(void *data, GEN x, GEN y)
2397 : {
2398 10368 : FlxYqq_muldata *D = (FlxYqq_muldata*)data;
2399 10368 : return FlxYqq_redswap(FlxqX_mul_pre(x,y, D->T,D->p,D->pi),D->S,D->T,D->p,D->pi);
2400 : }
2401 :
2402 : /* x in Z[X,Y], S in Z[X] over Fq = Z[Y]/(p,T); compute lift(x^n mod (S,T,p)) */
2403 : GEN
2404 39226 : FlxYqq_pow(GEN x, GEN n, GEN S, GEN T, ulong p)
2405 : {
2406 : FlxYqq_muldata D;
2407 39226 : D.S = S; D.T = T; D.p = p; D.pi = SMALL_ULONG(p)? 0: get_Fl_red(p);
2408 39226 : return gen_pow(x, n, (void*)&D, &FlxYqq_sqr, &FlxYqq_mul);
2409 : }
2410 :
2411 : /*******************************************************************/
2412 : /* */
2413 : /* FlxqXn */
2414 : /* */
2415 : /*******************************************************************/
2416 :
2417 : GEN
2418 66178 : FlxXn_red(GEN a, long n)
2419 : {
2420 66178 : long i, L = n+2, l = lg(a);
2421 : GEN b;
2422 66178 : if (L >= l) return a; /* deg(x) < n */
2423 36739 : b = cgetg(L, t_POL); b[1] = a[1];
2424 391759 : for (i=2; i<L; i++) gel(b,i) = gel(a,i);
2425 36739 : return FlxX_renormalize(b,L);
2426 : }
2427 :
2428 : GEN
2429 40415 : FlxqXn_mul_pre(GEN a, GEN b, long n, GEN T, ulong p, ulong pi)
2430 40415 : { return FlxXn_red(FlxqX_mul_pre(a, b, T, p, pi), n); }
2431 : GEN
2432 0 : FlxqXn_mul(GEN a, GEN b, long n, GEN T, ulong p)
2433 0 : { return FlxqXn_mul_pre(a, b, n, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
2434 :
2435 : GEN
2436 0 : FlxqXn_sqr_pre(GEN a, long n, GEN T, ulong p, ulong pi)
2437 0 : { return FlxXn_red(FlxqX_sqr_pre(a, T, p, pi), n); }
2438 : GEN
2439 0 : FlxqXn_sqr(GEN a, long n, GEN T, ulong p)
2440 0 : { return FlxqXn_sqr_pre(a, n, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
2441 :
2442 : /* (f*g) \/ x^n */
2443 : static GEN
2444 18000 : FlxqX_mulhigh_i(GEN f, GEN g, long n, GEN T, ulong p, ulong pi)
2445 18000 : { return FlxX_shift(FlxqX_mul_pre(f, g, T, p, pi), -n , get_Flx_var(T)); }
2446 :
2447 : static GEN
2448 13195 : FlxqXn_mulhigh(GEN f, GEN g, long n2, long n, GEN T, ulong p, ulong pi)
2449 : {
2450 13195 : long vT = get_Flx_var(T);
2451 13195 : GEN F = FlxX_blocks(f, n2, 2, vT), fl = gel(F,1), fh = gel(F,2);
2452 13196 : return FlxX_add(FlxqX_mulhigh_i(fl, g, n2, T, p, pi),
2453 : FlxqXn_mul_pre(fh, g, n - n2, T, p, pi), p);
2454 : }
2455 :
2456 : GEN
2457 2432 : FlxqXn_inv_pre(GEN f, long e, GEN T, ulong p, ulong pi)
2458 : {
2459 2432 : pari_sp av = avma, av2;
2460 : ulong mask;
2461 : GEN W, a;
2462 2432 : long v = varn(f), n = 1, vT = get_Flx_var(T);
2463 :
2464 2432 : if (!signe(f)) pari_err_INV("FlxqXn_inv",f);
2465 2432 : a = Flxq_inv_pre(gel(f,2), T, p, pi);
2466 2432 : if (e == 1) return scalarpol(a, v);
2467 2432 : else if (e == 2)
2468 : {
2469 : GEN b;
2470 0 : if (degpol(f) <= 0) return scalarpol(a, v);
2471 0 : b = Flx_neg(gel(f,3), p);
2472 0 : if (lgpol(b)==0) return scalarpol(a, v);
2473 0 : b = Flxq_mul_pre(b, Flxq_sqr_pre(a, T, p, pi), T, p, pi);
2474 0 : W = deg1pol_shallow(b, a, v);
2475 0 : return gc_GEN(av, W);
2476 : }
2477 2432 : W = scalarpol_shallow(Flxq_inv_pre(gel(f,2), T, p, pi), v);
2478 2432 : mask = quadratic_prec_mask(e);
2479 2432 : av2 = avma;
2480 12040 : for (;mask>1;)
2481 : {
2482 : GEN u, fr;
2483 9608 : long n2 = n;
2484 9608 : n<<=1; if (mask & 1) n--;
2485 9608 : mask >>= 1;
2486 9608 : fr = FlxXn_red(f, n);
2487 9607 : u = FlxqXn_mul_pre(W, FlxqXn_mulhigh(fr, W, n2, n, T,p,pi), n-n2, T,p,pi);
2488 9608 : W = FlxX_sub(W, FlxX_shift(u, n2, vT), p);
2489 9608 : if (gc_needed(av2,2))
2490 : {
2491 0 : if(DEBUGMEM>1) pari_warn(warnmem,"FlxqXn_inv, e = %ld", n);
2492 0 : W = gc_upto(av2, W);
2493 : }
2494 : }
2495 2432 : return gc_upto(av, W);
2496 : }
2497 : GEN
2498 0 : FlxqXn_inv(GEN f, long e, GEN T, ulong p)
2499 0 : { return FlxqXn_inv_pre(f, e, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
2500 :
2501 : /* Compute intformal(x^n*S)/x^(n+1) */
2502 : static GEN
2503 4804 : FlxX_integXn(GEN x, long n, ulong p)
2504 : {
2505 4804 : long i, lx = lg(x);
2506 : GEN y;
2507 4804 : if (lx == 2) return gcopy(x);
2508 3998 : y = cgetg(lx, t_POL); y[1] = x[1];
2509 26757 : for (i=2; i<lx; i++)
2510 : {
2511 22759 : GEN xi = gel(x,i);
2512 22759 : gel(y,i) = Flx_Fl_mul(xi, Fl_inv((n+i-1)%p, p), p);
2513 : }
2514 3998 : return FlxX_renormalize(y, lx);;
2515 : }
2516 :
2517 : GEN
2518 1216 : FlxqXn_expint_pre(GEN h, long e, GEN T, ulong p, ulong pi)
2519 : {
2520 1216 : pari_sp av = avma, av2;
2521 1216 : long v = varn(h), n = 1, vT = get_Flx_var(T);
2522 1216 : GEN f = pol1_FlxX(v, vT), g = pol1_FlxX(v, vT);
2523 1216 : ulong mask = quadratic_prec_mask(e);
2524 1216 : av2 = avma;
2525 4804 : for (;mask>1;)
2526 : {
2527 : GEN u, w;
2528 4804 : long n2 = n;
2529 4804 : n<<=1; if (mask & 1) n--;
2530 4804 : mask >>= 1;
2531 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);
2532 4804 : u = FlxX_add(u, FlxX_shift(FlxXn_red(h, n-1), 1-n2, vT), p);
2533 4804 : w = FlxqXn_mul_pre(f, FlxX_integXn(u, n2-1, p), n-n2, T, p, pi);
2534 4804 : f = FlxX_add(f, FlxX_shift(w, n2, vT), p);
2535 4804 : if (mask<=1) break;
2536 3588 : u = FlxqXn_mul_pre(g, FlxqXn_mulhigh(f, g, n2, n, T,p,pi), n-n2, T,p,pi);
2537 3588 : g = FlxX_sub(g, FlxX_shift(u, n2, vT), p);
2538 3588 : if (gc_needed(av2,2))
2539 : {
2540 0 : if (DEBUGMEM>1) pari_warn(warnmem,"FlxqXn_exp, e = %ld", n);
2541 0 : (void)gc_all(av2, 2, &f, &g);
2542 : }
2543 : }
2544 1216 : return gc_upto(av, f);
2545 : }
2546 : GEN
2547 0 : FlxqXn_expint(GEN h, long e, GEN T, ulong p)
2548 0 : { return FlxqXn_expint_pre(h, e, T, p, SMALL_ULONG(p)? 0: get_Fl_red(p)); }
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