File: fmpz_poly.h

package info (click to toggle)
flint 2.5.2-19
  • links: PTS, VCS
  • area: main
  • in suites: buster
  • size: 30,308 kB
  • sloc: ansic: 289,367; cpp: 11,210; python: 1,280; sh: 649; makefile: 283
file content (1236 lines) | stat: -rw-r--r-- 48,411 bytes parent folder | download | duplicates (4)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
1001
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
1022
1023
1024
1025
1026
1027
1028
1029
1030
1031
1032
1033
1034
1035
1036
1037
1038
1039
1040
1041
1042
1043
1044
1045
1046
1047
1048
1049
1050
1051
1052
1053
1054
1055
1056
1057
1058
1059
1060
1061
1062
1063
1064
1065
1066
1067
1068
1069
1070
1071
1072
1073
1074
1075
1076
1077
1078
1079
1080
1081
1082
1083
1084
1085
1086
1087
1088
1089
1090
1091
1092
1093
1094
1095
1096
1097
1098
1099
1100
1101
1102
1103
1104
1105
1106
1107
1108
1109
1110
1111
1112
1113
1114
1115
1116
1117
1118
1119
1120
1121
1122
1123
1124
1125
1126
1127
1128
1129
1130
1131
1132
1133
1134
1135
1136
1137
1138
1139
1140
1141
1142
1143
1144
1145
1146
1147
1148
1149
1150
1151
1152
1153
1154
1155
1156
1157
1158
1159
1160
1161
1162
1163
1164
1165
1166
1167
1168
1169
1170
1171
1172
1173
1174
1175
1176
1177
1178
1179
1180
1181
1182
1183
1184
1185
1186
1187
1188
1189
1190
1191
1192
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1211
1212
1213
1214
1215
1216
1217
1218
1219
1220
1221
1222
1223
1224
1225
1226
1227
1228
1229
1230
1231
1232
1233
1234
1235
1236
/*=============================================================================

    This file is part of FLINT.

    FLINT is free software; you can redistribute it and/or modify
    it under the terms of the GNU General Public License as published by
    the Free Software Foundation; either version 2 of the License, or
    (at your option) any later version.

    FLINT is distributed in the hope that it will be useful,
    but WITHOUT ANY WARRANTY; without even the implied warranty of
    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
    GNU General Public License for more details.

    You should have received a copy of the GNU General Public License
    along with FLINT; if not, write to the Free Software
    Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA  02110-1301 USA

=============================================================================*/
/******************************************************************************

    Copyright (C) 2006, 2007, 2008, 2009, 2010, 2013 William Hart
    Copyright (C) 2009, 2011 Andy Novocin
    Copyright (C) 2010 Sebastian Pancratz
    Copyright (C) 2011 Fredrik Johansson

******************************************************************************/

#ifndef FMPZ_POLY_H
#define FMPZ_POLY_H

#ifdef FMPZ_POLY_INLINES_C
#define FMPZ_POLY_INLINE FLINT_DLL
#else
#define FMPZ_POLY_INLINE static __inline__
#endif

#undef ulong
#define ulong ulongxx /* interferes with system includes */
#include <stdio.h>
#undef ulong

#include <gmp.h>
#define ulong mp_limb_t

#include "flint.h"
#include "fmpz.h"
#include "fmpz_vec.h"
#include "nmod_poly.h"
#include "fmpq.h"

#ifdef __cplusplus
 extern "C" {
#endif

#define FMPZ_POLY_INV_NEWTON_CUTOFF 32

/*  Type definitions *********************************************************/

typedef struct
{
    fmpz * coeffs;
    slong alloc;
    slong length;
} fmpz_poly_struct;

typedef fmpz_poly_struct fmpz_poly_t[1];

typedef struct
{
   fmpz ** powers;
   slong len;
} fmpz_poly_powers_precomp_struct;

typedef fmpz_poly_powers_precomp_struct fmpz_poly_powers_precomp_t[1];

typedef struct {
    fmpz c;
    fmpz_poly_struct *p;
    slong *exp;
    slong num;
    slong alloc;
} fmpz_poly_factor_struct;

typedef fmpz_poly_factor_struct fmpz_poly_factor_t[1];

/*  Memory management ********************************************************/

FLINT_DLL void fmpz_poly_init(fmpz_poly_t poly);

FLINT_DLL void fmpz_poly_init2(fmpz_poly_t poly, slong alloc);

FLINT_DLL void fmpz_poly_realloc(fmpz_poly_t poly, slong alloc);

FLINT_DLL void fmpz_poly_fit_length(fmpz_poly_t poly, slong len);

FLINT_DLL void fmpz_poly_clear(fmpz_poly_t poly);

FLINT_DLL void _fmpz_poly_normalise(fmpz_poly_t poly);

FMPZ_POLY_INLINE
void _fmpz_poly_set_length(fmpz_poly_t poly, slong newlen)
{
    if (poly->length > newlen)
    {
        slong i;
        for (i = newlen; i < poly->length; i++)
            _fmpz_demote(poly->coeffs + i); 
    }
    poly->length = newlen;
}

/*  Polynomial parameters  ***************************************************/

FMPZ_POLY_INLINE
slong fmpz_poly_length(const fmpz_poly_t poly)
{
    return poly->length;
}

FMPZ_POLY_INLINE
slong fmpz_poly_degree(const fmpz_poly_t poly)
{
    return poly->length - 1;
}

/*  Assignment and basic manipulation  ***************************************/

FLINT_DLL void fmpz_poly_set(fmpz_poly_t poly1, const fmpz_poly_t poly2);

FLINT_DLL void fmpz_poly_set_ui(fmpz_poly_t poly, ulong c);

FLINT_DLL void fmpz_poly_set_si(fmpz_poly_t poly, slong c);

FLINT_DLL void fmpz_poly_set_fmpz(fmpz_poly_t poly, const fmpz_t c);

FLINT_DLL void fmpz_poly_set_mpz(fmpz_poly_t poly, const mpz_t c);

FLINT_DLL int _fmpz_poly_set_str(fmpz * poly, const char * str);

FLINT_DLL int fmpz_poly_set_str(fmpz_poly_t poly, const char * str);

FLINT_DLL char * _fmpz_poly_get_str(const fmpz * poly, slong len);

FLINT_DLL char * fmpz_poly_get_str(const fmpz_poly_t poly);

FLINT_DLL char * _fmpz_poly_get_str_pretty(const fmpz * poly, slong len, const char * x);

FLINT_DLL char * fmpz_poly_get_str_pretty(const fmpz_poly_t poly, const char * x);

FMPZ_POLY_INLINE
void fmpz_poly_zero(fmpz_poly_t poly)
{
   _fmpz_poly_set_length(poly, 0);
}

FMPZ_POLY_INLINE
void fmpz_poly_one(fmpz_poly_t poly)
{
    fmpz_poly_set_ui(poly, UWORD(1));
}

FLINT_DLL void fmpz_poly_zero_coeffs(fmpz_poly_t poly, slong i, slong j);

FLINT_DLL void fmpz_poly_swap(fmpz_poly_t poly1, fmpz_poly_t poly2);

FLINT_DLL void _fmpz_poly_reverse(fmpz * res, const fmpz * poly, slong len, slong n);

FLINT_DLL void fmpz_poly_reverse(fmpz_poly_t res, const fmpz_poly_t poly, slong n);

FMPZ_POLY_INLINE
void fmpz_poly_truncate(fmpz_poly_t poly, slong newlen)
{
    if (poly->length > newlen)
    {
        slong i;
        for (i = newlen; i < poly->length; i++)
            _fmpz_demote(poly->coeffs + i);
        poly->length = newlen;
        _fmpz_poly_normalise(poly);
    }  
}

FLINT_DLL void fmpz_poly_set_trunc(fmpz_poly_t res, const fmpz_poly_t poly, slong n);

/*  Randomisation  ***********************************************************/

FLINT_DLL void fmpz_poly_randtest(fmpz_poly_t f, flint_rand_t state, 
                                                slong len, mp_bitcnt_t bits);

FLINT_DLL void fmpz_poly_randtest_unsigned(fmpz_poly_t f, flint_rand_t state, 
                                                slong len, mp_bitcnt_t bits);

FLINT_DLL void fmpz_poly_randtest_not_zero(fmpz_poly_t f, flint_rand_t state,
                                                slong len, mp_bitcnt_t bits);

/*  Getting and setting coefficients  ****************************************/

FLINT_DLL slong fmpz_poly_get_coeff_si(const fmpz_poly_t poly, slong n);

FLINT_DLL void fmpz_poly_set_coeff_si(fmpz_poly_t poly, slong n, slong x);

FLINT_DLL ulong fmpz_poly_get_coeff_ui(const fmpz_poly_t poly, slong n);

FLINT_DLL void fmpz_poly_set_coeff_ui(fmpz_poly_t poly, slong n, ulong x);

FLINT_DLL void fmpz_poly_set_coeff_fmpz(fmpz_poly_t poly, slong n, const fmpz_t x);

FLINT_DLL void fmpz_poly_get_coeff_fmpz(fmpz_t x, const fmpz_poly_t poly, slong n);

#define fmpz_poly_get_coeff_ptr(poly, n) \
    ((n) < (poly)->length ? (poly)->coeffs + (n) : NULL)

#define fmpz_poly_lead(poly) \
    ((poly)->length ? (poly)->coeffs + (poly)->length - 1 : NULL)

/*  Comparison  **************************************************************/

FLINT_DLL int fmpz_poly_equal(const fmpz_poly_t poly1, const fmpz_poly_t poly2);

FLINT_DLL int fmpz_poly_equal_trunc(const fmpz_poly_t poly1, 
                                             const fmpz_poly_t poly2, slong n);

#define fmpz_poly_is_zero(poly) \
    ((poly)->length == 0)

FMPZ_POLY_INLINE
int _fmpz_poly_is_one(const fmpz *poly, slong len)
{
    return (len > 0 && fmpz_is_one(poly) 
                    && _fmpz_vec_is_zero(poly + 1, len - 1));
}

FMPZ_POLY_INLINE
int fmpz_poly_is_one(const fmpz_poly_t op)
{
    return (op->length) == 1 && (*(op->coeffs) == WORD(1));
}

FMPZ_POLY_INLINE
int fmpz_poly_is_unit(const fmpz_poly_t op)
{
    return (op->length == 1) && (*(op->coeffs) == WORD(1) || *(op->coeffs) == WORD(-1));
}

FMPZ_POLY_INLINE
int fmpz_poly_is_x(const fmpz_poly_t op)
{
    return (op->length) == 2 && (*(op->coeffs + 1) == WORD(1)) && (*(op->coeffs + 0) == WORD(0));
}

FMPZ_POLY_INLINE
int fmpz_poly_equal_fmpz(const fmpz_poly_t poly, const fmpz_t c)
{
	return ((poly->length == 0) && fmpz_is_zero(c)) ||
        ((poly->length == 1) && fmpz_equal(poly->coeffs, c));
}

/*  Addition and subtraction  ************************************************/

FLINT_DLL void _fmpz_poly_add(fmpz * res, const fmpz * poly1, slong len1, 
                                               const fmpz * poly2, slong len2);

FLINT_DLL void fmpz_poly_add(fmpz_poly_t res, const fmpz_poly_t poly1, 
                                                      const fmpz_poly_t poly2);

FLINT_DLL void fmpz_poly_add_series(fmpz_poly_t res, const fmpz_poly_t poly1,
                                             const fmpz_poly_t poly2, slong n);

FLINT_DLL void _fmpz_poly_sub(fmpz * res, const fmpz * poly1, slong len1, 
                                               const fmpz * poly2, slong len2);

FLINT_DLL void fmpz_poly_sub(fmpz_poly_t res, const fmpz_poly_t poly1, 
                                                      const fmpz_poly_t poly2);

FLINT_DLL void fmpz_poly_sub_series(fmpz_poly_t res, const fmpz_poly_t poly1,
                                             const fmpz_poly_t poly2, slong n);

FLINT_DLL void fmpz_poly_neg(fmpz_poly_t res, const fmpz_poly_t poly);

/*  Scalar multiplication and division  **************************************/

FLINT_DLL void fmpz_poly_scalar_mul_ui(fmpz_poly_t poly1, 
                             const fmpz_poly_t poly2, ulong x);

FLINT_DLL void fmpz_poly_scalar_mul_si(fmpz_poly_t poly1, 
                             const fmpz_poly_t poly2, slong x);

FLINT_DLL void fmpz_poly_scalar_mul_fmpz(fmpz_poly_t poly1, 
                               const fmpz_poly_t poly2, const fmpz_t x);

FLINT_DLL void fmpz_poly_scalar_addmul_fmpz(fmpz_poly_t poly1, 
                                   const fmpz_poly_t poly2, const fmpz_t x);

FLINT_DLL void fmpz_poly_scalar_submul_fmpz(fmpz_poly_t poly1, 
                                   const fmpz_poly_t poly2, const fmpz_t x);

FLINT_DLL void fmpz_poly_scalar_fdiv_ui(fmpz_poly_t poly1, 
                              const fmpz_poly_t poly2, ulong x);

FLINT_DLL void fmpz_poly_scalar_fdiv_si(fmpz_poly_t poly1, 
                              const fmpz_poly_t poly2, slong x);

FLINT_DLL void fmpz_poly_scalar_fdiv_fmpz(fmpz_poly_t poly1, 
                                const fmpz_poly_t poly2, const fmpz_t x);

FLINT_DLL void fmpz_poly_scalar_tdiv_ui(fmpz_poly_t poly1, 
                              const fmpz_poly_t poly2, ulong x);

FLINT_DLL void fmpz_poly_scalar_tdiv_si(fmpz_poly_t poly1, 
                              const fmpz_poly_t poly2, slong x);

FLINT_DLL void fmpz_poly_scalar_tdiv_fmpz(fmpz_poly_t poly1, 
                                const fmpz_poly_t poly2, const fmpz_t x);

FLINT_DLL void fmpz_poly_scalar_divexact_ui(fmpz_poly_t poly1, 
                                  const fmpz_poly_t poly2, ulong x);

FLINT_DLL void fmpz_poly_scalar_divexact_si(fmpz_poly_t poly1, 
                                  const fmpz_poly_t poly2, slong x);

FLINT_DLL void fmpz_poly_scalar_divexact_fmpz(fmpz_poly_t poly1, 
                                    const fmpz_poly_t poly2, const fmpz_t x);

FLINT_DLL void fmpz_poly_scalar_fdiv_2exp(fmpz_poly_t poly1, const fmpz_poly_t poly2,
                           ulong exp);

FLINT_DLL void fmpz_poly_scalar_tdiv_2exp(fmpz_poly_t poly1, const fmpz_poly_t poly2,
                           ulong exp);

FLINT_DLL void fmpz_poly_scalar_mul_2exp(fmpz_poly_t poly1, const fmpz_poly_t poly2,
                           ulong exp);

FMPZ_POLY_INLINE
void fmpz_poly_scalar_mod_fmpz(fmpz_poly_t poly1, 
                               const fmpz_poly_t poly2, const fmpz_t x)
{
    if (poly2->length == 0)
    {
        fmpz_poly_zero(poly1);
    }
    else
    {
        fmpz_poly_fit_length(poly1, poly2->length);
        _fmpz_vec_scalar_mod_fmpz(poly1->coeffs, poly2->coeffs, poly2->length, x);
        _fmpz_poly_set_length(poly1, poly2->length);
        _fmpz_poly_normalise(poly1);
    }
}

FMPZ_POLY_INLINE
void fmpz_poly_scalar_smod_fmpz(fmpz_poly_t poly1, 
                                const fmpz_poly_t poly2, const fmpz_t x)
{
    if (poly2->length == 0)
    {
        fmpz_poly_zero(poly1);
    }
    else
    {
        fmpz_poly_fit_length(poly1, poly2->length);
        _fmpz_vec_scalar_smod_fmpz(poly1->coeffs, poly2->coeffs, poly2->length, x);
        _fmpz_poly_set_length(poly1, poly2->length);
        _fmpz_poly_normalise(poly1);

    }
}

/*  Bit packing  *************************************************************/

FLINT_DLL void _fmpz_poly_bit_pack(mp_ptr arr, const fmpz * poly,
                                slong len, mp_bitcnt_t bit_size, int negate);

FLINT_DLL int _fmpz_poly_bit_unpack(fmpz * poly, slong len, 
                           mp_srcptr arr, mp_bitcnt_t bit_size, int negate);

FLINT_DLL void _fmpz_poly_bit_unpack_unsigned(fmpz * poly, slong len, 
                                       mp_srcptr arr, mp_bitcnt_t bit_size);

FLINT_DLL void fmpz_poly_bit_pack(fmpz_t f, const fmpz_poly_t poly,
        mp_bitcnt_t bit_size);

FLINT_DLL void fmpz_poly_bit_unpack(fmpz_poly_t poly, const fmpz_t f,
        mp_bitcnt_t bit_size);

FLINT_DLL void fmpz_poly_bit_unpack_unsigned(fmpz_poly_t poly, const fmpz_t f,
        mp_bitcnt_t bit_size);


/*  Multiplication  **********************************************************/

FLINT_DLL void _fmpz_poly_mul_classical(fmpz * res, const fmpz * poly1, slong len1, 
                                             const fmpz * poly2, slong len2);

FLINT_DLL void fmpz_poly_mul_classical(fmpz_poly_t res, 
                          const fmpz_poly_t poly1, const fmpz_poly_t poly2);

FLINT_DLL void _fmpz_poly_mullow_classical(fmpz * res, const fmpz * poly1, slong len1, 
                                     const fmpz * poly2, slong len2, slong n);

FLINT_DLL void fmpz_poly_mullow_classical(fmpz_poly_t res, const fmpz_poly_t poly1, 
                                           const fmpz_poly_t poly2, slong n);

FLINT_DLL void _fmpz_poly_mulhigh_classical(fmpz * res, const fmpz * poly1, 
                      slong len1, const fmpz * poly2, slong len2, slong start);

FLINT_DLL void fmpz_poly_mulhigh_classical(fmpz_poly_t res, 
              const fmpz_poly_t poly1, const fmpz_poly_t poly2, slong start);

FLINT_DLL void _fmpz_poly_mulmid_classical(fmpz * res, const fmpz * poly1, 
                                  slong len1, const fmpz * poly2, slong len2);

FLINT_DLL void fmpz_poly_mulmid_classical(fmpz_poly_t res, 
                          const fmpz_poly_t poly1, const fmpz_poly_t poly2);

FLINT_DLL void fmpz_poly_mul_karatsuba(fmpz_poly_t res, 
                          const fmpz_poly_t poly1, const fmpz_poly_t poly2);

FLINT_DLL void _fmpz_poly_mul_karatsuba(fmpz * res, const fmpz * poly1, 
                                  slong len1, const fmpz * poly2, slong len2);

FLINT_DLL void _fmpz_poly_mullow_karatsuba_n(fmpz * res, const fmpz * poly1, 
                                                const fmpz * poly2, slong n);

FLINT_DLL void fmpz_poly_mullow_karatsuba_n(fmpz_poly_t res, 
                  const fmpz_poly_t poly1, const fmpz_poly_t poly2, slong n);

FLINT_DLL void _fmpz_poly_mulhigh_karatsuba_n(fmpz * res, const fmpz * poly1, 
                                              const fmpz * poly2, slong len);

FLINT_DLL void fmpz_poly_mulhigh_karatsuba_n(fmpz_poly_t res, 
             const fmpz_poly_t poly1, const fmpz_poly_t poly2, slong length);

FLINT_DLL void _fmpz_poly_mul_KS(fmpz * res, const fmpz * poly1, slong len1, 
                                             const fmpz * poly2, slong len2);

FLINT_DLL void fmpz_poly_mul_KS(fmpz_poly_t res, 
                          const fmpz_poly_t poly1, const fmpz_poly_t poly2);

FLINT_DLL void _fmpz_poly_mullow_KS(fmpz * res, const fmpz * poly1, slong len1, 
                                     const fmpz * poly2, slong len2, slong n);

FLINT_DLL void fmpz_poly_mullow_KS(fmpz_poly_t res, const fmpz_poly_t poly1, 
                                           const fmpz_poly_t poly2, slong n);

FLINT_DLL void _fmpz_poly_mul_SS(fmpz * output, const fmpz * input1, slong length1, 
                                         const fmpz * input2, slong length2);

FLINT_DLL void fmpz_poly_mul_SS(fmpz_poly_t res,
                          const fmpz_poly_t poly1, const fmpz_poly_t poly2);

FLINT_DLL void _fmpz_poly_mullow_SS(fmpz * output, const fmpz * input1, slong length1, 
                                 const fmpz * input2, slong length2, slong n);

FLINT_DLL void fmpz_poly_mullow_SS(fmpz_poly_t res,
                  const fmpz_poly_t poly1, const fmpz_poly_t poly2, slong n);

FLINT_DLL void _fmpz_poly_mul(fmpz * res, const fmpz * poly1, 
                                  slong len1, const fmpz * poly2, slong len2);

FLINT_DLL void fmpz_poly_mul(fmpz_poly_t res, 
                          const fmpz_poly_t poly1, const fmpz_poly_t poly2);

FLINT_DLL void _fmpz_poly_mullow(fmpz * res, const fmpz * poly1, slong len1, 
                                     const fmpz * poly2, slong len2, slong n);

FLINT_DLL void fmpz_poly_mullow(fmpz_poly_t res, 
                  const fmpz_poly_t poly1, const fmpz_poly_t poly2, slong n);

FLINT_DLL void fmpz_poly_mulhigh_n(fmpz_poly_t res, 
                  const fmpz_poly_t poly1, const fmpz_poly_t poly2, slong n);

/* Squaring ******************************************************************/

FLINT_DLL void _fmpz_poly_sqr_KS(fmpz * rop, const fmpz * op, slong len);

FLINT_DLL void fmpz_poly_sqr_KS(fmpz_poly_t rop, const fmpz_poly_t op);

FLINT_DLL void fmpz_poly_sqr_karatsuba(fmpz_poly_t rop, const fmpz_poly_t op);

FLINT_DLL void _fmpz_poly_sqr_karatsuba(fmpz * rop, const fmpz * op, slong len);

FLINT_DLL void _fmpz_poly_sqr_classical(fmpz * rop, const fmpz * op, slong len);

FLINT_DLL void fmpz_poly_sqr_classical(fmpz_poly_t rop, const fmpz_poly_t op);

FLINT_DLL void _fmpz_poly_sqr(fmpz * rop, const fmpz * op, slong len);

FLINT_DLL void fmpz_poly_sqr(fmpz_poly_t rop, const fmpz_poly_t op);

FLINT_DLL void _fmpz_poly_sqrlow_KS(fmpz * res, const fmpz * poly, slong len, slong n);

FLINT_DLL void fmpz_poly_sqrlow_KS(fmpz_poly_t res, const fmpz_poly_t poly, slong n);

FLINT_DLL void _fmpz_poly_sqrlow_karatsuba_n(fmpz * res, const fmpz * poly, slong n);

FLINT_DLL void fmpz_poly_sqrlow_karatsuba_n(fmpz_poly_t res, const fmpz_poly_t poly, slong n);

FLINT_DLL void _fmpz_poly_sqrlow_classical(fmpz * res, const fmpz * poly, slong len, slong n);

FLINT_DLL void fmpz_poly_sqrlow_classical(fmpz_poly_t res, const fmpz_poly_t poly, slong n);

FLINT_DLL void _fmpz_poly_sqrlow(fmpz * res, const fmpz * poly, slong len, slong n);

FLINT_DLL void fmpz_poly_sqrlow(fmpz_poly_t res, const fmpz_poly_t poly, slong n);

/*  Powering  ****************************************************************/

FLINT_DLL void _fmpz_poly_pow_multinomial(fmpz * res, const fmpz * poly, slong len, ulong e);

FLINT_DLL void fmpz_poly_pow_multinomial(fmpz_poly_t res, const fmpz_poly_t poly, ulong e);

FLINT_DLL void _fmpz_poly_pow_binomial(fmpz * res, const fmpz * poly, ulong e);

FLINT_DLL void fmpz_poly_pow_binomial(fmpz_poly_t res, const fmpz_poly_t poly, ulong e);

FLINT_DLL void _fmpz_poly_pow_binexp(fmpz * res, const fmpz * poly, slong len, ulong e);

FLINT_DLL void fmpz_poly_pow_binexp(fmpz_poly_t res, const fmpz_poly_t poly, ulong e);

FLINT_DLL void _fmpz_poly_pow_addchains(fmpz * res, const fmpz * poly, slong len, const int * a, int n);

FLINT_DLL void fmpz_poly_pow_addchains(fmpz_poly_t res, const fmpz_poly_t poly, ulong e);

FLINT_DLL void _fmpz_poly_pow_small(fmpz * res, const fmpz * poly, slong len, ulong e);

FLINT_DLL void _fmpz_poly_pow(fmpz * res, const fmpz * poly, slong len, ulong e);

FLINT_DLL void fmpz_poly_pow(fmpz_poly_t res, const fmpz_poly_t poly, ulong e);

FLINT_DLL void _fmpz_poly_pow_trunc(fmpz * res, const fmpz * poly, ulong e, slong n);

void 
FLINT_DLL fmpz_poly_pow_trunc(fmpz_poly_t res, const fmpz_poly_t poly, ulong e, slong n);

/*  Shifting  ****************************************************************/

FLINT_DLL void _fmpz_poly_shift_left(fmpz * res, const fmpz * poly, slong len, slong n);

FLINT_DLL void _fmpz_poly_shift_right(fmpz * res, const fmpz * poly, slong len, slong n);

FLINT_DLL void fmpz_poly_shift_left(fmpz_poly_t res, const fmpz_poly_t poly, slong n);

FLINT_DLL void fmpz_poly_shift_right(fmpz_poly_t res, const fmpz_poly_t poly, slong n);

/*  Norms  *******************************************************************/

FLINT_DLL void _fmpz_poly_2norm(fmpz_t res, const fmpz * poly, slong len);

FLINT_DLL void fmpz_poly_2norm(fmpz_t res, const fmpz_poly_t poly);

FLINT_DLL mp_bitcnt_t _fmpz_poly_2norm_normalised_bits(const fmpz * poly, slong len);

FMPZ_POLY_INLINE
ulong fmpz_poly_max_limbs(const fmpz_poly_t poly)
{
    return _fmpz_vec_max_limbs(poly->coeffs, poly->length);
}

FMPZ_POLY_INLINE
slong fmpz_poly_max_bits(const fmpz_poly_t poly)
{
    return _fmpz_vec_max_bits(poly->coeffs, poly->length);
}

FMPZ_POLY_INLINE
void fmpz_poly_height(fmpz_t res, const fmpz_poly_t poly)
{
    _fmpz_vec_height(res, poly->coeffs, poly->length);
}

/*  Greatest common divisor  *************************************************/

FLINT_DLL void _fmpz_poly_gcd_subresultant(fmpz * res, const fmpz * poly1, slong len1, 
                                              const fmpz * poly2, slong len2);

FLINT_DLL void fmpz_poly_gcd_subresultant(fmpz_poly_t res, const fmpz_poly_t poly1, 
                                                    const fmpz_poly_t poly2);

FLINT_DLL int _fmpz_poly_gcd_heuristic(fmpz * res, const fmpz * poly1, slong len1, 
                                              const fmpz * poly2, slong len2);

FLINT_DLL int fmpz_poly_gcd_heuristic(fmpz_poly_t res,
                           const fmpz_poly_t poly1, const fmpz_poly_t poly2);

FLINT_DLL void _fmpz_poly_gcd_modular(fmpz * res, const fmpz * poly1, slong len1, 
                                              const fmpz * poly2, slong len2);

FLINT_DLL void fmpz_poly_gcd_modular(fmpz_poly_t res,
                           const fmpz_poly_t poly1, const fmpz_poly_t poly2);

FLINT_DLL void _fmpz_poly_gcd(fmpz * res, const fmpz * poly1, slong len1, 
                                               const fmpz * poly2, slong len2);

FLINT_DLL void fmpz_poly_gcd(fmpz_poly_t res, const fmpz_poly_t poly1, 
                                                      const fmpz_poly_t poly2);

FLINT_DLL void _fmpz_poly_lcm(fmpz * res, const fmpz * poly1, slong len1, 
                                               const fmpz * poly2, slong len2);

FLINT_DLL void fmpz_poly_lcm(fmpz_poly_t res, const fmpz_poly_t poly1, 
                                                      const fmpz_poly_t poly2);

FLINT_DLL void _fmpz_poly_resultant_euclidean(fmpz_t res, const fmpz * poly1, slong len1, 
                                               const fmpz * poly2, slong len2);

FLINT_DLL void fmpz_poly_resultant_euclidean(fmpz_t res, const fmpz_poly_t poly1, 
                                                      const fmpz_poly_t poly2);

FLINT_DLL void _fmpz_poly_resultant_modular(fmpz_t res, const fmpz * poly1, slong len1, 
                                               const fmpz * poly2, slong len2);

FLINT_DLL void fmpz_poly_resultant_modular(fmpz_t res, const fmpz_poly_t poly1,
                                                      const fmpz_poly_t poly2);

FLINT_DLL void _fmpz_poly_resultant(fmpz_t res, const fmpz * poly1, slong len1, 
                                               const fmpz * poly2, slong len2);

FLINT_DLL void fmpz_poly_resultant(fmpz_t res, const fmpz_poly_t poly1,
                                                      const fmpz_poly_t poly2);

FLINT_DLL void _fmpz_poly_xgcd_modular(fmpz_t r, fmpz * s, fmpz * t, 
               const fmpz * poly1, slong len1, const fmpz * poly2, slong len2);

FLINT_DLL void fmpz_poly_xgcd_modular(fmpz_t r, fmpz_poly_t s, fmpz_poly_t t,
                             const fmpz_poly_t poly1, const fmpz_poly_t poly2);

FMPZ_POLY_INLINE
void _fmpz_poly_xgcd(fmpz_t r, fmpz * s, fmpz * t, 
                const fmpz * poly1, slong len1, const fmpz * poly2, slong len2)
{
    _fmpz_poly_xgcd_modular(r, s, t, poly1, len1, poly2, len2);
}

FMPZ_POLY_INLINE
void fmpz_poly_xgcd(fmpz_t r, fmpz_poly_t s, fmpz_poly_t t,
                            const fmpz_poly_t poly1, const fmpz_poly_t poly2)
{
    fmpz_poly_xgcd_modular(r, s, t, poly1, poly2);
}

/*  Discriminant  ********************************************************/

FLINT_DLL void _fmpz_poly_discriminant(fmpz_t res, const fmpz * poly, slong len);

FLINT_DLL void fmpz_poly_discriminant(fmpz_t res, const fmpz_poly_t poly);

/*  Gaussian content  ********************************************************/

FLINT_DLL void _fmpz_poly_content(fmpz_t res, const fmpz * poly, slong len);

FLINT_DLL void fmpz_poly_content(fmpz_t res, const fmpz_poly_t poly);

FLINT_DLL void _fmpz_poly_primitive_part(fmpz * res, const fmpz * poly, slong len);

FLINT_DLL void fmpz_poly_primitive_part(fmpz_poly_t res, const fmpz_poly_t poly);

/*  Square-free  *************************************************************/

FLINT_DLL int _fmpz_poly_is_squarefree(const fmpz * poly, slong len);

FLINT_DLL int fmpz_poly_is_squarefree(const fmpz_poly_t poly);

/*  Euclidean division  ******************************************************/

FLINT_DLL void _fmpz_poly_divrem_basecase(fmpz * Q, fmpz * R, const fmpz * A, 
                                       slong lenA, const fmpz * B, slong lenB);

FLINT_DLL void fmpz_poly_divrem_basecase(fmpz_poly_t Q, fmpz_poly_t R, 
                                   const fmpz_poly_t A, const fmpz_poly_t B);

FLINT_DLL void _fmpz_poly_divrem_divconquer_recursive(fmpz * Q, fmpz * BQ, fmpz * W, 
                                 const fmpz * A, const fmpz * B, slong lenB);

FLINT_DLL void _fmpz_poly_divrem_divconquer(fmpz * Q, fmpz * R, 
                     const fmpz * A, slong lenA, const fmpz * B, slong lenB);

FLINT_DLL void fmpz_poly_divrem_divconquer(fmpz_poly_t Q, fmpz_poly_t R, 
                                   const fmpz_poly_t A, const fmpz_poly_t B);

FLINT_DLL void _fmpz_poly_divrem(fmpz * Q, fmpz * R, const fmpz * A, slong lenA, 
                                           const fmpz * B, slong lenB);

FLINT_DLL void fmpz_poly_divrem(fmpz_poly_t Q, fmpz_poly_t R, const fmpz_poly_t A, 
                                                          const fmpz_poly_t B);

FLINT_DLL void _fmpz_poly_div_basecase(fmpz * Q, fmpz * R, const fmpz * A, slong lenA,
                                                   const fmpz * B, slong lenB);

FLINT_DLL void fmpz_poly_div_basecase(fmpz_poly_t Q, 
                                     const fmpz_poly_t A, const fmpz_poly_t B);

FLINT_DLL void _fmpz_poly_divremlow_divconquer_recursive(fmpz * Q, fmpz * QB, 
                                   const fmpz * A, const fmpz * B, slong lenB);

FLINT_DLL void _fmpz_poly_div_divconquer_recursive(fmpz * Q, fmpz * temp, 
                                   const fmpz * A, const fmpz * B, slong lenB);

FLINT_DLL void _fmpz_poly_div_divconquer(fmpz * Q, const fmpz * A, slong lenA, 
                                                   const fmpz * B, slong lenB);

FLINT_DLL void fmpz_poly_div_divconquer(fmpz_poly_t Q, 
                                     const fmpz_poly_t A, const fmpz_poly_t B);

FLINT_DLL void _fmpz_poly_div(fmpz * Q, const fmpz * A, slong lenA, 
                                                   const fmpz * B, slong lenB);

FLINT_DLL void fmpz_poly_div(fmpz_poly_t Q, const fmpz_poly_t A, const fmpz_poly_t B);

FLINT_DLL void _fmpz_poly_preinvert(fmpz * B_inv, const fmpz * B, slong n);

FLINT_DLL void fmpz_poly_preinvert(fmpz_poly_t B_inv, const fmpz_poly_t B);

FLINT_DLL void _fmpz_poly_div_preinv(fmpz * Q, const fmpz * A, slong len1, 
                               const fmpz * B, const fmpz * B_inv, slong len2);

FLINT_DLL void fmpz_poly_div_preinv(fmpz_poly_t Q, const fmpz_poly_t A, 
                                 const fmpz_poly_t B, const fmpz_poly_t B_inv);

FLINT_DLL void _fmpz_poly_divrem_preinv(fmpz * Q, fmpz * A, slong len1, 
                               const fmpz * B, const fmpz * B_inv, slong len2);

FLINT_DLL void fmpz_poly_divrem_preinv(fmpz_poly_t Q, fmpz_poly_t R, 
            const fmpz_poly_t A, const fmpz_poly_t B, const fmpz_poly_t B_inv);

FLINT_DLL fmpz ** _fmpz_poly_powers_precompute(const fmpz * B, slong len);

FLINT_DLL void fmpz_poly_powers_precompute(fmpz_poly_powers_precomp_t pinv, 
                                                             fmpz_poly_t poly);

FLINT_DLL void _fmpz_poly_powers_clear(fmpz ** powers, slong len);

FLINT_DLL void fmpz_poly_powers_clear(fmpz_poly_powers_precomp_t pinv);

FLINT_DLL void _fmpz_poly_rem_powers_precomp(fmpz * A, slong m, 
                                const fmpz * B, slong n, fmpz ** const powers);

FLINT_DLL void fmpz_poly_rem_powers_precomp(fmpz_poly_t R, 
                             const fmpz_poly_t A, const fmpz_poly_t B, 
                                       const fmpz_poly_powers_precomp_t B_inv);

FLINT_DLL void _fmpz_poly_rem_basecase(fmpz * Q, const fmpz * A, slong lenA,
                                                   const fmpz * B, slong lenB);

FLINT_DLL void fmpz_poly_rem_basecase(fmpz_poly_t R, 
                                     const fmpz_poly_t A, const fmpz_poly_t B);

FLINT_DLL void _fmpz_poly_rem(fmpz * R, const fmpz * A, slong lenA, 
                              const fmpz * B, slong lenB);

FLINT_DLL void fmpz_poly_rem(fmpz_poly_t R, const fmpz_poly_t A, const fmpz_poly_t B);

FLINT_DLL void fmpz_poly_div_root(fmpz_poly_t Q, const fmpz_poly_t A, const fmpz_t c);

FLINT_DLL void _fmpz_poly_div_root(fmpz * Q, const fmpz * A, slong len, const fmpz_t c);

/*  Power series division  ***************************************************/

FLINT_DLL void _fmpz_poly_inv_series_basecase(fmpz * Qinv, const fmpz * Q, slong Qlen, slong n);

FLINT_DLL void fmpz_poly_inv_series_basecase(fmpz_poly_t Qinv, const fmpz_poly_t Q, slong n);

FLINT_DLL void _fmpz_poly_inv_series_newton(fmpz * Qinv, const fmpz * Q, slong Qlen, slong n);

FLINT_DLL void fmpz_poly_inv_series_newton(fmpz_poly_t Qinv, const fmpz_poly_t Q, slong n);

FLINT_DLL void _fmpz_poly_inv_series(fmpz * Qinv, const fmpz * Q, slong Qlen, slong n);

FLINT_DLL void fmpz_poly_inv_series(fmpz_poly_t Qinv, const fmpz_poly_t Q, slong n);

FLINT_DLL void _fmpz_poly_div_series(fmpz * Q, const fmpz * A, slong Alen,
    const fmpz * B, slong Blen, slong n);

FLINT_DLL void fmpz_poly_div_series(fmpz_poly_t Q, const fmpz_poly_t A, 
                                         const fmpz_poly_t B, slong n);

/*  Divisibility testing  ***************************************************/

FLINT_DLL int _fmpz_poly_divides(fmpz * q, const fmpz * a, 
                                         slong len1, const fmpz * b, slong len2);

FLINT_DLL int fmpz_poly_divides(fmpz_poly_t q, const fmpz_poly_t a, const fmpz_poly_t b);


/*  Pseudo division  *********************************************************/

FLINT_DLL void _fmpz_poly_pseudo_divrem_basecase(fmpz * Q, fmpz * R, 
                   ulong * d, const fmpz * A, slong A_len, 
                        const fmpz * B, slong B_len, const fmpz_preinvn_t inv);

FLINT_DLL void fmpz_poly_pseudo_divrem_basecase(fmpz_poly_t Q, fmpz_poly_t R, 
                          ulong * d, const fmpz_poly_t A, const fmpz_poly_t B);

FLINT_DLL void _fmpz_poly_pseudo_divrem_divconquer(fmpz * Q, fmpz * R, 
                    ulong * d, const fmpz * A, slong lenA, 
                         const fmpz * B, slong lenB, const fmpz_preinvn_t inv);

FLINT_DLL void fmpz_poly_pseudo_divrem_divconquer(fmpz_poly_t Q, fmpz_poly_t R, 
                          ulong * d, const fmpz_poly_t A, const fmpz_poly_t B);

FLINT_DLL void _fmpz_poly_pseudo_divrem_cohen(fmpz * Q, fmpz * R, const fmpz * A, 
                                       slong lenA, const fmpz * B, slong lenB);

FLINT_DLL void fmpz_poly_pseudo_divrem_cohen(fmpz_poly_t Q, fmpz_poly_t R, 
                                     const fmpz_poly_t A, const fmpz_poly_t B);

FLINT_DLL void _fmpz_poly_pseudo_rem_cohen(fmpz * R, const fmpz * A, slong lenA, 
                                                   const fmpz * B, slong lenB);

FLINT_DLL void fmpz_poly_pseudo_rem_cohen(fmpz_poly_t R, const fmpz_poly_t A, 
                                                          const fmpz_poly_t B);

FMPZ_POLY_INLINE
void _fmpz_poly_pseudo_divrem(fmpz * Q, fmpz * R, 
                    ulong * d, const fmpz * A, slong A_len, 
                         const fmpz * B, slong B_len, const fmpz_preinvn_t inv)
{
    _fmpz_poly_pseudo_divrem_divconquer(Q, R, d, A, A_len, B, B_len, inv);
}

FMPZ_POLY_INLINE
void fmpz_poly_pseudo_divrem(fmpz_poly_t Q, fmpz_poly_t R, 
                           ulong * d, const fmpz_poly_t A, const fmpz_poly_t B)
{
    fmpz_poly_pseudo_divrem_divconquer(Q, R, d, A, B);
}

FLINT_DLL void _fmpz_poly_pseudo_div(fmpz * Q, ulong * d, const fmpz * A, slong lenA, 
                         const fmpz * B, slong lenB, const fmpz_preinvn_t inv);

FLINT_DLL void fmpz_poly_pseudo_div(fmpz_poly_t Q, ulong * d, const fmpz_poly_t A, 
                                                          const fmpz_poly_t B);

FLINT_DLL void _fmpz_poly_pseudo_rem(fmpz * R, ulong * d, const fmpz * A, slong lenA, 
                         const fmpz * B, slong lenB, const fmpz_preinvn_t inv);

FLINT_DLL void fmpz_poly_pseudo_rem(fmpz_poly_t R, ulong * d, const fmpz_poly_t A, 
                                                          const fmpz_poly_t B);

/*  Derivative  **************************************************************/

FLINT_DLL void _fmpz_poly_derivative(fmpz * rpoly, const fmpz * poly, slong len);
 
FLINT_DLL void fmpz_poly_derivative(fmpz_poly_t res, const fmpz_poly_t poly);

/*  Evaluation  **************************************************************/

void 
FLINT_DLL _fmpz_poly_evaluate_divconquer_fmpz(fmpz_t res, const fmpz * poly, slong len, 
                                                const fmpz_t a);

FLINT_DLL void fmpz_poly_evaluate_divconquer_fmpz(fmpz_t res, const fmpz_poly_t poly, 
                                        const fmpz_t a);

FLINT_DLL void _fmpz_poly_evaluate_horner_fmpz(fmpz_t res, const fmpz * f, slong len, 
                                                               const fmpz_t a);

FLINT_DLL void fmpz_poly_evaluate_horner_fmpz(fmpz_t res, const fmpz_poly_t f, 
                                                               const fmpz_t a);

FLINT_DLL void _fmpz_poly_evaluate_fmpz(fmpz_t res, const fmpz * f, slong len, const fmpz_t a);

FLINT_DLL void fmpz_poly_evaluate_fmpz(fmpz_t res, const fmpz_poly_t f, const fmpz_t a);

FLINT_DLL void _fmpz_poly_evaluate_horner_fmpq(fmpz_t rnum, fmpz_t rden, 
                                    const fmpz * f, slong len, 
                                    const fmpz_t anum, const fmpz_t aden);

FLINT_DLL void fmpz_poly_evaluate_horner_fmpq(fmpq_t res, const fmpz_poly_t f, 
                                                                const fmpq_t a);

FLINT_DLL void _fmpz_poly_evaluate_divconquer_fmpq(fmpz_t rnum, fmpz_t rden, 
                                    const fmpz * f, slong len, 
                                    const fmpz_t anum, const fmpz_t aden);

FLINT_DLL void fmpz_poly_evaluate_divconquer_fmpq(fmpq_t res, const fmpz_poly_t f, 
                                                                const fmpq_t a);

FLINT_DLL void _fmpz_poly_evaluate_fmpq(fmpz_t rnum, fmpz_t rden, 
                                    const fmpz * f, slong len, 
                                    const fmpz_t anum, const fmpz_t aden);

FLINT_DLL void fmpz_poly_evaluate_fmpq(fmpq_t res, const fmpz_poly_t f, const fmpq_t a);


FLINT_DLL void fmpz_poly_evaluate_mpq(mpq_t res, const fmpz_poly_t f, const mpq_t a);

FLINT_DLL mp_limb_t _fmpz_poly_evaluate_mod(const fmpz * poly, slong len, mp_limb_t a, 
                                  mp_limb_t n, mp_limb_t ninv);

FLINT_DLL mp_limb_t fmpz_poly_evaluate_mod(const fmpz_poly_t poly, mp_limb_t a, 
                                 mp_limb_t n);

/*  Composition  *************************************************************/

FLINT_DLL void _fmpz_poly_compose_horner(fmpz * res, const fmpz * poly1, slong len1, 
                                                const fmpz * poly2, slong len2);

FLINT_DLL void fmpz_poly_compose_horner(fmpz_poly_t res, const fmpz_poly_t poly1, 
                                                      const fmpz_poly_t poly2);

FLINT_DLL void _fmpz_poly_compose_divconquer(fmpz * res, const fmpz * poly1, slong len1, 
                                                const fmpz * poly2, slong len2);

FLINT_DLL void fmpz_poly_compose_divconquer(fmpz_poly_t res, const fmpz_poly_t poly1, 
                                                      const fmpz_poly_t poly2);

FLINT_DLL void _fmpz_poly_compose(fmpz * res, const fmpz * poly1, slong len1, 
                                                const fmpz * poly2, slong len2);

FLINT_DLL void fmpz_poly_compose(fmpz_poly_t res, const fmpz_poly_t poly1, 
                                                      const fmpz_poly_t poly2);

/*  Taylor shift  ************************************************************/

FLINT_DLL void _fmpz_poly_taylor_shift_horner(fmpz * poly, const fmpz_t c, slong n);

FLINT_DLL void fmpz_poly_taylor_shift_horner(fmpz_poly_t g, const fmpz_poly_t f,
    const fmpz_t c);

FLINT_DLL void _fmpz_poly_taylor_shift_divconquer(fmpz * poly, const fmpz_t c, slong n);

FLINT_DLL void fmpz_poly_taylor_shift_divconquer(fmpz_poly_t g, const fmpz_poly_t f,
    const fmpz_t c);

FLINT_DLL void _fmpz_poly_taylor_shift_multi_mod(fmpz * poly, const fmpz_t c, slong n);

FLINT_DLL void fmpz_poly_taylor_shift_multi_mod(fmpz_poly_t g, const fmpz_poly_t f, const fmpz_t c);

FLINT_DLL void _fmpz_poly_taylor_shift(fmpz * poly, const fmpz_t c, slong n);

FLINT_DLL void fmpz_poly_taylor_shift(fmpz_poly_t g, const fmpz_poly_t f, const fmpz_t c);

/*  Power series composition and compositional inverse  **********************/

FLINT_DLL void _fmpz_poly_compose_series_brent_kung(fmpz * res, const fmpz * poly1, slong len1, 
                                      const fmpz * poly2, slong len2, slong n);

FLINT_DLL void fmpz_poly_compose_series_brent_kung(fmpz_poly_t res, 
                    const fmpz_poly_t poly1, const fmpz_poly_t poly2, slong n);

FLINT_DLL void _fmpz_poly_compose_series_horner(fmpz * res, const fmpz * poly1, slong len1, 
                                      const fmpz * poly2, slong len2, slong n);

FLINT_DLL void fmpz_poly_compose_series_horner(fmpz_poly_t res, 
                    const fmpz_poly_t poly1, const fmpz_poly_t poly2, slong n);

FLINT_DLL void _fmpz_poly_compose_series(fmpz * res, const fmpz * poly1, slong len1, 
                                      const fmpz * poly2, slong len2, slong n);

FLINT_DLL void fmpz_poly_compose_series(fmpz_poly_t res, 
                    const fmpz_poly_t poly1, const fmpz_poly_t poly2, slong n);

FLINT_DLL void _fmpz_poly_revert_series_lagrange(fmpz * Qinv, const fmpz * Q, slong Qlen, slong n);

FLINT_DLL void fmpz_poly_revert_series_lagrange(fmpz_poly_t Qinv, const fmpz_poly_t Q, slong n);

FLINT_DLL void _fmpz_poly_revert_series_lagrange_fast(fmpz * Qinv, const fmpz * Q, slong Qlen, slong n);

FLINT_DLL void fmpz_poly_revert_series_lagrange_fast(fmpz_poly_t Qinv,
    const fmpz_poly_t Q, slong n);

FLINT_DLL void _fmpz_poly_revert_series_newton(fmpz * Qinv, const fmpz * Q, slong Qlen, slong n);

FLINT_DLL void fmpz_poly_revert_series_newton(fmpz_poly_t Qinv, const fmpz_poly_t Q, slong n);

FLINT_DLL void _fmpz_poly_revert_series(fmpz * Qinv, const fmpz * Q, slong Qlen, slong n);

FLINT_DLL void fmpz_poly_revert_series(fmpz_poly_t Qinv, const fmpz_poly_t Q, slong n);

/*  Square root  *************************************************************/

FLINT_DLL int _fmpz_poly_sqrt_classical(fmpz * res, const fmpz * poly, slong len);

FLINT_DLL int fmpz_poly_sqrt_classical(fmpz_poly_t b, const fmpz_poly_t a);

FLINT_DLL int _fmpz_poly_sqrt(fmpz * res, const fmpz * poly, slong len);

FLINT_DLL int fmpz_poly_sqrt(fmpz_poly_t b, const fmpz_poly_t a);


/*  Signature  ***************************************************************/

FLINT_DLL void _fmpz_poly_signature(slong * r1, slong * r2, const fmpz * poly, slong len);

FLINT_DLL void fmpz_poly_signature(slong * r1, slong * r2, const fmpz_poly_t poly);

/*  Input and output  ********************************************************/

FLINT_DLL int fmpz_poly_fprint(FILE * file, const fmpz_poly_t poly);

FLINT_DLL int _fmpz_poly_fprint_pretty(FILE * file, 
                             const fmpz * poly, slong len, const char * x);

FLINT_DLL int fmpz_poly_fprint_pretty(FILE * file, 
                                       const fmpz_poly_t poly, const char * x);

FMPZ_POLY_INLINE
int fmpz_poly_print(const fmpz_poly_t poly)
{
    return fmpz_poly_fprint(stdout, poly);
}

FMPZ_POLY_INLINE
int fmpz_poly_print_pretty(const fmpz_poly_t poly, const char * x)
{
    return fmpz_poly_fprint_pretty(stdout, poly, x);
}

FLINT_DLL int fmpz_poly_fread(FILE * file, fmpz_poly_t poly);

FLINT_DLL int fmpz_poly_fread_pretty(FILE *file, fmpz_poly_t poly, char **x);

FMPZ_POLY_INLINE
int fmpz_poly_read(fmpz_poly_t poly)
{
    return fmpz_poly_fread(stdin, poly);
}

FMPZ_POLY_INLINE
int fmpz_poly_read_pretty(fmpz_poly_t poly, char **x)
{
    return fmpz_poly_fread_pretty(stdin, poly, x);
}

FMPZ_POLY_INLINE
void fmpz_poly_debug(const fmpz_poly_t poly)
{
    flint_printf("(alloc = %wd, length = %wd, vec = ", poly->alloc, poly->length);
    if (poly->coeffs)
    {
        flint_printf("{");
        _fmpz_vec_print(poly->coeffs, poly->alloc);
        flint_printf("}");
    }
    else
    {
        flint_printf("NULL");
    }
    flint_printf(")");
    fflush(stdout);
}

/*  CRT  ********************************************************************/

FLINT_DLL void fmpz_poly_get_nmod_poly(nmod_poly_t res, const fmpz_poly_t poly);

FLINT_DLL void fmpz_poly_set_nmod_poly(fmpz_poly_t res, const nmod_poly_t poly);

FLINT_DLL void fmpz_poly_set_nmod_poly_unsigned(fmpz_poly_t res, const nmod_poly_t poly);

void
FLINT_DLL _fmpz_poly_CRT_ui_precomp(fmpz * res, const fmpz * poly1, slong len1,
               const fmpz_t m1, mp_srcptr poly2, slong len2, mp_limb_t m2,
                mp_limb_t m2inv, fmpz_t m1m2, mp_limb_t c, int sign);

FLINT_DLL void _fmpz_poly_CRT_ui(fmpz * res, const fmpz * poly1, slong len1,
               const fmpz_t m1, mp_srcptr poly2, slong len2, mp_limb_t m2,
                                                    mp_limb_t m2inv, int sign);

FLINT_DLL void fmpz_poly_CRT_ui(fmpz_poly_t res, const fmpz_poly_t poly1,
                                     const fmpz_t m1, const nmod_poly_t poly2,
                                        int sign);


/* Products *****************************************************************/

FLINT_DLL void _fmpz_poly_product_roots_fmpz_vec(fmpz * poly,
                                        const fmpz * xs, slong n);

FLINT_DLL void fmpz_poly_product_roots_fmpz_vec(fmpz_poly_t poly,
                                        const fmpz * xs, slong n);

/* Newton basis *************************************************************/

FLINT_DLL void _fmpz_poly_monomial_to_newton(fmpz * poly, const fmpz * roots, slong n);

FLINT_DLL void _fmpz_poly_newton_to_monomial(fmpz * poly, const fmpz * roots, slong n);


/* Multipoint evaluation and interpolation *********************************/

FLINT_DLL void fmpz_poly_evaluate_fmpz_vec(fmpz * res, const fmpz_poly_t f,
                                const fmpz * a, slong n);

FLINT_DLL void fmpz_poly_interpolate_fmpz_vec(fmpz_poly_t poly,
                                    const fmpz * xs, const fmpz * ys, slong n);

/* Hensel lifting ************************************************************/

FLINT_DLL void fmpz_poly_hensel_build_tree(slong * link, fmpz_poly_t *v, fmpz_poly_t *w, 
                                 const nmod_poly_factor_t fac);

void fmpz_poly_hensel_lift(fmpz_poly_t Gout, fmpz_poly_t Hout, 
    fmpz_poly_t Aout, fmpz_poly_t Bout, 
    const fmpz_poly_t f, 
    const fmpz_poly_t g, const fmpz_poly_t h, 
    const fmpz_poly_t a, const fmpz_poly_t b, 
    const fmpz_t p, const fmpz_t p1);

FLINT_DLL void _fmpz_poly_hensel_lift_without_inverse(fmpz *G, fmpz *H, 
    const fmpz *f, slong lenF, 
    const fmpz *g, slong lenG, const fmpz *h, slong lenH, 
    const fmpz *a, slong lenA, const fmpz *b, slong lenB, 
    const fmpz_t p, const fmpz_t p1);

FLINT_DLL void fmpz_poly_hensel_lift_without_inverse(fmpz_poly_t Gout, fmpz_poly_t Hout, 
    const fmpz_poly_t f, const fmpz_poly_t g, const fmpz_poly_t h, 
    const fmpz_poly_t a, const fmpz_poly_t b, 
    const fmpz_t p, const fmpz_t p1);

FLINT_DLL void _fmpz_poly_hensel_lift_only_inverse(fmpz *A, fmpz *B, 
    const fmpz *G, slong lenG, const fmpz *H, slong lenH, 
    const fmpz *a, slong lenA, const fmpz *b, slong lenB, 
    const fmpz_t p, const fmpz_t p1);

FLINT_DLL void fmpz_poly_hensel_lift_only_inverse(fmpz_poly_t Aout, fmpz_poly_t Bout, 
    const fmpz_poly_t G, const fmpz_poly_t H, 
    const fmpz_poly_t a, const fmpz_poly_t b, 
    const fmpz_t p, const fmpz_t p1);

FLINT_DLL void fmpz_poly_hensel_lift_tree_recursive(slong *link, 
    fmpz_poly_t *v, fmpz_poly_t *w, fmpz_poly_t f, slong j, slong inv, 
    const fmpz_t p0, const fmpz_t p1);

FLINT_DLL void fmpz_poly_hensel_lift_tree(slong *link, fmpz_poly_t *v, fmpz_poly_t *w, 
    fmpz_poly_t f, slong r, const fmpz_t p, slong e0, slong e1, slong inv);

FLINT_DLL slong _fmpz_poly_hensel_start_lift(fmpz_poly_factor_t lifted_fac, slong *link, 
    fmpz_poly_t *v, fmpz_poly_t *w, const fmpz_poly_t f, 
    const nmod_poly_factor_t local_fac, slong target_exp);

FLINT_DLL slong _fmpz_poly_hensel_continue_lift(fmpz_poly_factor_t lifted_fac, 
    slong *link, fmpz_poly_t *v, fmpz_poly_t *w, const fmpz_poly_t f, 
    slong prev, slong curr, slong N, const fmpz_t p);

FLINT_DLL void fmpz_poly_hensel_lift_once(fmpz_poly_factor_t lifted_fac, 
                                const fmpz_poly_t f, 
                                const nmod_poly_factor_t local_fac, slong N);

/* Some functions for backwards compatibility */

FMPZ_POLY_INLINE
void fmpz_poly_scalar_mul_mpz(fmpz_poly_t poly1,
                               const fmpz_poly_t poly2, const mpz_t x)
{
    fmpz_t t;
    fmpz_init_set_readonly(t, x);
    fmpz_poly_scalar_mul_fmpz(poly1, poly2, t);
    fmpz_clear_readonly(t);
}

FMPZ_POLY_INLINE
void fmpz_poly_scalar_divexact_mpz(fmpz_poly_t poly1,
                               const fmpz_poly_t poly2, const mpz_t x)
{
    fmpz_t t;
    fmpz_init_set_readonly(t, x);
    fmpz_poly_scalar_divexact_fmpz(poly1, poly2, t);
    fmpz_clear_readonly(t);
}

FMPZ_POLY_INLINE
void fmpz_poly_scalar_fdiv_mpz(fmpz_poly_t poly1,
                               const fmpz_poly_t poly2, const mpz_t x)
{
    fmpz_t t;
    fmpz_init_set_readonly(t, x);
    fmpz_poly_scalar_fdiv_fmpz(poly1, poly2, t);
    fmpz_clear_readonly(t);
}

FMPZ_POLY_INLINE
void fmpz_poly_set_coeff_mpz(fmpz_poly_t poly, slong n,
    const mpz_t x)
{
    fmpz_t t;
    fmpz_init_set_readonly(t, x);
    fmpz_poly_set_coeff_fmpz(poly, n, t);
    fmpz_clear_readonly(t);
}

FMPZ_POLY_INLINE
void fmpz_poly_get_coeff_mpz(mpz_t x, const fmpz_poly_t poly, slong n)
{
    fmpz_t t;
    fmpz_init(t);
    fmpz_poly_get_coeff_fmpz(t, poly, n);
    fmpz_get_mpz(x, t);
    fmpz_clear(t);
}

/* Roots */

FLINT_DLL void _fmpz_poly_bound_roots(fmpz_t bound, const fmpz * poly, slong len);

FLINT_DLL void fmpz_poly_bound_roots(fmpz_t bound, const fmpz_poly_t poly);

/* Special polynomials */

FLINT_DLL void _fmpz_poly_cyclotomic(fmpz * a, ulong n, mp_ptr factors,
                                        slong num_factors, ulong phi);
FLINT_DLL void fmpz_poly_cyclotomic(fmpz_poly_t poly, ulong n);

FLINT_DLL void _fmpz_poly_cos_minpoly(fmpz * f, ulong n);

FLINT_DLL void fmpz_poly_cos_minpoly(fmpz_poly_t f, ulong n);

FLINT_DLL void _fmpz_poly_swinnerton_dyer(fmpz * T, ulong n);

FLINT_DLL void fmpz_poly_swinnerton_dyer(fmpz_poly_t poly, ulong n);

FLINT_DLL void _fmpz_poly_chebyshev_t(fmpz * coeffs, ulong n);

FLINT_DLL void fmpz_poly_chebyshev_t(fmpz_poly_t poly, ulong n);

FLINT_DLL void _fmpz_poly_chebyshev_u(fmpz * coeffs, ulong n);

FLINT_DLL void fmpz_poly_chebyshev_u(fmpz_poly_t poly, ulong n);

FLINT_DLL void _fmpz_poly_eta_qexp(fmpz * f, slong e, slong n);

FLINT_DLL void fmpz_poly_eta_qexp(fmpz_poly_t f, slong e, slong n);

FLINT_DLL void _fmpz_poly_theta_qexp(fmpz * f, slong e, slong n);

FLINT_DLL void fmpz_poly_theta_qexp(fmpz_poly_t f, slong e, slong n);

#ifdef __cplusplus
}
#endif

#include "fmpz_poly_factor.h"

#endif