-
Notifications
You must be signed in to change notification settings - Fork 2
/
usual.h
968 lines (812 loc) · 37.1 KB
/
usual.h
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
// -*- mode:C++ ; compile-command: "g++ -I.. -g -c usual.cc" -*-
/*
* Copyright (C) 2000,2014 B. Parisse, Institut Fourier, 38402 St Martin d'Heres
*
* This program 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 3 of the License, or
* (at your option) any later version.
*
* This program 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 this program. If not, see <http://www.gnu.org/licenses/>.
*/
#ifndef _GIAC_USUAL_H
#define _GIAC_USUAL_H
#include "first.h"
#include <string>
#ifndef NO_NAMESPACE_GIAC
namespace giac {
#endif // ndef NO_NAMESPACE_GIAC
bool check_vect_38(const std::string & s); // check if s is a string identifier of a vector, matrix or list
// Global vectors of tractable functions and equivalents
std::vector<const unary_function_ptr *> & limit_tractable_functions();
typedef gen ( * gen_op ) (const gen & arg);
std::vector<gen_op_context> & limit_tractable_replace();
#ifdef HAVE_SIGNAL_H_OLD
extern std::string messages_to_print ;
#endif
// declare here pointers to rational operators
// These are global variables but that's normal for functional obj
class gen;
struct unary_function_ptr;
class unary_function_eval;
gen frac_neg_out(const gen & g,GIAC_CONTEXT);
gen _constant_one(const gen & args,GIAC_CONTEXT);
gen _constant_zero(const gen & args,GIAC_CONTEXT);
gen _rm_a_z(const gen & args,GIAC_CONTEXT);
gen _rm_all_vars(const gen & args,const context * contextptr);
bool is_equal(const gen & g);
gen apply_to_equal(const gen & g,const gen_op & f);
gen apply_to_equal(const gen & g,gen (* f) (const gen &, GIAC_CONTEXT),GIAC_CONTEXT);
gen apply_unit(const gen & args,const gen_op_context & f,GIAC_CONTEXT);
gen _id(const gen & args,GIAC_CONTEXT);
gen _not(const gen & args,GIAC_CONTEXT);
gen _neg(const gen & args,GIAC_CONTEXT);
gen _inv(const gen & args,GIAC_CONTEXT);
gen ln(const gen & e,GIAC_CONTEXT);
gen log(const gen & e,GIAC_CONTEXT);
gen log10(const gen & e,GIAC_CONTEXT);
gen alog10(const gen & e,GIAC_CONTEXT);
gen atan(const gen & e0,GIAC_CONTEXT);
gen exp(const gen & e0,GIAC_CONTEXT);
// convert a gen to a string, format=0 (normal), 1 (tex)
std::string gen2string(const gen & g,int format,GIAC_CONTEXT);
// Demodularize
gen unmod(const gen & g);
gen unmodunprod(const gen & g);
gen double2gen(double d);
bool is_equal(const gen & g);
gen apply_to_equal(const gen & g,const gen_op & f);
gen apply_to_equal(const gen & g,gen (* f) (const gen &, GIAC_CONTEXT),GIAC_CONTEXT);
std::string print_with_parenthesis_if_required(const gen & g,int format,GIAC_CONTEXT);
// usual zero args
extern const unary_function_ptr * const at_zero;
extern const unary_function_ptr * const at_one;
extern const unary_function_ptr * const at_id;
extern const unary_function_ptr * const at_rm_a_z;
extern const unary_function_ptr * const at_rm_all_vars;
// usual unary function related declarations (extended unary)
extern const unary_function_ptr * const at_neg ;
extern const unary_function_ptr * const at_inv ;
extern const unary_function_ptr * const at_not;
extern const unary_function_ptr * const at_exp ;
extern const unary_function_ptr * const at_ln ;
extern const unary_function_ptr * const at_log10 ;
extern const unary_function_ptr * const at_alog10 ;
extern const unary_function_ptr * const at_atan ;
// e = +/- simpl*doubl^d
void zint2simpldoublpos(const gen & e,gen & simpl,gen & doubl,bool & pos,int d,GIAC_CONTEXT);
gen sqrt_noabs(const gen & e,GIAC_CONTEXT);
gen sqrt(const gen & e,GIAC_CONTEXT);
gen sqrt_mod(const gen & a,const gen & b,bool isprime,GIAC_CONTEXT); // set isprime to true if b is prime
extern const unary_function_ptr * const at_sqrt ;
gen _sq(const gen & e);
extern const unary_function_ptr * const at_sq ;
gen sin(const gen & e,GIAC_CONTEXT);
extern const unary_function_ptr * const at_sin ;
gen cos(const gen & e,GIAC_CONTEXT);
extern const unary_function_ptr * const at_cos ;
gen tan(const gen & e,GIAC_CONTEXT);
extern const unary_function_ptr * const at_tan ;
gen asin(const gen & e,GIAC_CONTEXT);
extern const unary_function_ptr * const at_asin ;
gen acos(const gen & e,GIAC_CONTEXT);
extern const unary_function_ptr * const at_acos ;
gen sinh(const gen & e,GIAC_CONTEXT);
extern const unary_function_ptr * const at_sinh ;
gen cosh(const gen & e,GIAC_CONTEXT);
extern const unary_function_ptr * const at_cosh ;
gen tanh(const gen & e,GIAC_CONTEXT);
extern const unary_function_ptr * const at_tanh ;
gen asinh(const gen & e,GIAC_CONTEXT);
extern const unary_function_ptr * const at_asinh ;
gen acosh(const gen & e,GIAC_CONTEXT);
extern const unary_function_ptr * const at_acosh ;
gen atanh(const gen & e,GIAC_CONTEXT);
extern const unary_function_ptr * const at_atanh ;
symbolic symb_inv(const gen & e);
symbolic symb_exp(const gen & e);
symbolic symb_ln(const gen & e);
symbolic symb_cos(const gen & e);
symbolic symb_sin(const gen & e);
symbolic symb_cosh(const gen & e);
symbolic symb_sinh(const gen & e);
symbolic symb_tan(const gen & e);
symbolic symb_atan(const gen & e);
symbolic symb_not(const gen & e);
symbolic symb_asin(const gen & e);
symbolic symb_quote(const gen & arg);
gen quote(const gen & e,GIAC_CONTEXT);
extern const unary_function_ptr * const at_quote ;
gen unquote(const gen & e,GIAC_CONTEXT);
extern const unary_function_ptr * const at_unquote ;
gen re(const gen & a,GIAC_CONTEXT);
gen im(const gen & a,GIAC_CONTEXT);
gen conj(const gen & a,GIAC_CONTEXT);
gen _sign(const gen & g,GIAC_CONTEXT);
gen order_size(const gen & e,GIAC_CONTEXT);
extern const unary_function_ptr * const at_order_size ;
symbolic symb_and(const gen & a,const gen & b);
gen _and(const gen & args,GIAC_CONTEXT);
extern const unary_function_ptr * const at_and;
gen and2(const gen & a,const gen & b);
symbolic symb_ou(const gen & a,const gen & b);
gen _ou(const gen & args,GIAC_CONTEXT);
gen ou2(const gen & a,const gen & b);
extern const unary_function_ptr * const at_ou;
gen _xor(const gen & args,GIAC_CONTEXT);
gen xor2(const gen & a,const gen & b,GIAC_CONTEXT);
extern const unary_function_ptr * const at_xor;
symbolic symb_min(const gen & a,const gen & b);
gen _min(const gen & args,GIAC_CONTEXT);
extern const unary_function_ptr * const at_min;
symbolic symb_max(const gen & a,const gen & b);
gen _max(const gen & args,GIAC_CONTEXT);
extern const unary_function_ptr * const at_max;
gen _gcd(const gen & args,GIAC_CONTEXT);
extern const unary_function_ptr * const at_gcd;
gen _lcm(const gen & args,GIAC_CONTEXT);
extern const unary_function_ptr * const at_lcm;
gen _egcd(const gen & args,GIAC_CONTEXT);
extern const unary_function_ptr * const at_egcd;
gen _iegcd(const gen & args,GIAC_CONTEXT);
extern const unary_function_ptr * const at_iegcd;
// check that indice is integral, if required convert float/double to int
bool is_integral(gen & indice);
gen Iquo(const gen & a,const gen & b);
gen _iquo(const gen & args,GIAC_CONTEXT);
extern const unary_function_ptr * const at_iquo;
gen _irem(const gen & args,GIAC_CONTEXT);
extern const unary_function_ptr * const at_irem;
gen _mods(const gen & args,GIAC_CONTEXT);
extern const unary_function_ptr * const at_mods;
gen _quote_pow(const gen & args,GIAC_CONTEXT);
extern const unary_function_ptr * const at_quote_pow;
gen _iquorem(const gen & args,GIAC_CONTEXT);
extern const unary_function_ptr * const at_iquorem;
gen _smod(const gen & args,GIAC_CONTEXT);
extern const unary_function_ptr * const at_smod;
gen _rdiv(const gen & args,GIAC_CONTEXT);
extern const unary_function_ptr * const at_rdiv;
gen _is_prime(const gen & args,GIAC_CONTEXT);
extern const unary_function_ptr * const at_is_prime;
gen _is_pseudoprime(const gen & args,GIAC_CONTEXT);
gen nextprime1(const gen & a,GIAC_CONTEXT);
gen prevprime1(const gen & a,GIAC_CONTEXT);
gen _nextprime(const gen & args,GIAC_CONTEXT);
extern const unary_function_ptr * const at_nextprime;
gen _prevprime(const gen & args,GIAC_CONTEXT);
extern const unary_function_ptr * const at_prevprime;
gen _jacobi_symbol(const gen & args,GIAC_CONTEXT);
gen _legendre_symbol(const gen & args,GIAC_CONTEXT);
gen _floor(const gen & args,GIAC_CONTEXT);
extern const unary_function_ptr * const at_floor;
gen _ceil(const gen & args,GIAC_CONTEXT);
extern const unary_function_ptr * const at_ceil;
gen ceil2floor(const gen & g,GIAC_CONTEXT,bool quotesubst=false);
gen _round(const gen & args,GIAC_CONTEXT);
extern const unary_function_ptr * const at_round;
gen _print(const gen & args,GIAC_CONTEXT);
extern const unary_function_ptr * const at_print;
#if !defined RTOS_THREADX && !defined NSPIRE && !defined FXCG
extern const unary_function_eval __print;
#endif
extern const unary_function_ptr * const at_jacobi_symbol;
extern const unary_function_ptr * const at_legendre_symbol;
gen ichinrem2(const gen & a_orig,const gen & b_orig);
gen _ichinrem(const gen & args,GIAC_CONTEXT);
extern const unary_function_ptr * const at_ichinrem;
gen double_is_int(const gen & g,GIAC_CONTEXT);
gen _fracmod(const gen & args,GIAC_CONTEXT);
extern const unary_function_ptr * const at_fracmod;
gen _factorial(const gen & args,GIAC_CONTEXT);
extern const unary_function_ptr * const at_factorial;
gen _perm(const gen & args,GIAC_CONTEXT);
extern const unary_function_ptr * const at_perm;
gen comb(const gen & n,const gen &k,GIAC_CONTEXT);
gen _comb(const gen & args,GIAC_CONTEXT);
extern const unary_function_ptr * const at_comb;
gen _chinrem(const gen & args,GIAC_CONTEXT);
extern const unary_function_ptr * const at_chinrem;
extern const unary_function_ptr * const at_re;
extern const unary_function_ptr * const at_im;
symbolic symb_conj(const gen & e);
extern const unary_function_ptr * const at_conj ;
gen _abs(const gen & args,GIAC_CONTEXT);
symbolic symb_abs(const gen & e);
extern const unary_function_ptr * const at_abs ;
symbolic symb_arg(const gen & e);
extern const unary_function_ptr * const at_arg ;
extern const unary_function_ptr * const at_sign;
gen _cyclotomic(const gen & a,GIAC_CONTEXT);
extern const unary_function_ptr * const at_cyclotomic ;
gen _calc_mode(const gen & args,GIAC_CONTEXT);
extern const unary_function_ptr * const at_quo ;
extern const unary_function_ptr * const at_rem ;
gen _quorem(const gen & args,GIAC_CONTEXT);
gen quorem(const gen & a,const gen & b);
gen _quo(const gen & args,GIAC_CONTEXT);
gen _rem(const gen & args,GIAC_CONTEXT);
extern const unary_function_ptr * const at_quorem ;
extern const unary_function_ptr * const at_normalmod;
symbolic symb_sto(const gen & a,gen & b,bool in_place=false);
symbolic parser_symb_sto(const gen & a_,gen & b,bool in_place=false);
// same as symb_sto but check if a is a vector, if so make a copy
symbolic symb_sto(const gen & e);
extern const unary_function_ptr * const at_sto ;
extern const unary_function_ptr * const at_array_sto ;
extern const unary_function_ptr * const at_increment;
extern const unary_function_ptr * const at_decrement;
extern const unary_function_ptr * const at_multcrement;
extern const unary_function_ptr * const at_divcrement;
extern const unary_function_ptr * const at_iquosto;
extern const unary_function_ptr * const at_iremsto;
extern const unary_function_ptr * const at_andsto;
extern const unary_function_ptr * const at_orsto;
extern const unary_function_ptr * const at_xorsto;
extern const unary_function_ptr * const at_shiftsto;
extern const unary_function_ptr * const at_powsto;
gen _shiftsto(const gen & a,const context * contextptr);
extern const unary_function_ptr * const at_rotatesto;
gen _rotatesto(const gen & a,const context * contextptr);
gen sto(const gen & a,const gen & b,GIAC_CONTEXT);
gen sto(const gen & a,const gen & b,bool in_place,GIAC_CONTEXT);
gen _sto(const gen & g,const context * contextptr);
gen _array_sto(const gen & a,const context * contextptr);
bool is_assumed_real(const gen & g,GIAC_CONTEXT);
bool is_assumed_integer(const gen & g,GIAC_CONTEXT);
bool is_numericv(const vecteur & v, int withfracint = 0);
bool is_numericm(const vecteur & v, int withfracint = 0);
bool check_vect_38(const std::string & s);
// check value type for storing value in s using 38 compatibility mode
bool check_sto_38(gen & value,const char * s);
extern bool (*storcl_38)(gen & value,const char * name_space,const char * idname,gen indice,bool at_of,GIAC_CONTEXT, gen const *sto,bool OnlyLocal);
extern int (*is_known_name_38)(const char * name_space,const char * idname);
extern gen (*of_pointer_38)(const void * appptr,const void * varptr,const gen & args);
extern gen_op_context * interactive_op_tab;
// if this pointer is non NULL, it should point to a table of gen_op_context replacing
// { _input,_inputform,_interactive,_click,_getKey,
// _current_sheet,_Row,_Col,_xyztrange,_widget_size}
// leave an individual pointer to 0 if you don't want to redefine it's action
gen _increment(const gen & a,const context * contextptr);
gen _decrement(const gen & a,const context * contextptr);
gen _multcrement(const gen & a,const context * contextptr);
gen _divcrement(const gen & a,const context * contextptr);
// assume format _VECT of subtype _ASSUME__VECT
// [ _DOUBLE_ , list of intervals, excluded ]
// [ _INT_, ]
extern const unary_function_ptr * const at_assume ;
gen giac_assume(const gen & a,GIAC_CONTEXT);
extern const unary_function_ptr * const at_additionally ;
gen giac_additionally(const gen & a,GIAC_CONTEXT);
// returns the assumed idnt name
// used if assumptions are in OR conjonction
gen assumesymbolic(const gen & a,gen idnt_must_be,GIAC_CONTEXT);
// v = previous assumptions, a=the real value, direction
// is positive for [a,+inf[, negative for ]-inf,a]
// |direction| = 1 (large) or 2 (strict)
gen doubleassume_and(const vecteur & v,const gen & a,int direction,bool or_assumption,GIAC_CONTEXT);
gen _equal(const gen & args,GIAC_CONTEXT);
gen symb_equal(const gen & a,const gen & b);
extern const unary_function_ptr * const at_equal;
extern const unary_function_ptr * const at_equal2;
gen symb_same(const gen & a);
symbolic symb_same(const gen & a,const gen & b);
gen _same(const gen & args,GIAC_CONTEXT);
extern const unary_function_ptr * const at_same;
symbolic symb_inferieur_strict(const gen & a);
symbolic symb_inferieur_strict(const gen & a,const gen & b);
gen _inferieur_strict(const gen & args,GIAC_CONTEXT);
extern const unary_function_ptr * const at_inferieur_strict;
symbolic symb_inferieur_egal(const gen & a);
symbolic symb_inferieur_egal(const gen & a,const gen & b);
gen _inferieur_egal(const gen & args,GIAC_CONTEXT);
extern const unary_function_ptr * const at_inferieur_egal;
symbolic symb_superieur_strict(const gen & a);
symbolic symb_superieur_strict(const gen & a,const gen & b);
gen _superieur_strict(const gen & args,GIAC_CONTEXT);
extern const unary_function_ptr * const at_superieur_strict;
symbolic symb_superieur_egal(const gen & a);
symbolic symb_superieur_egal(const gen & a,const gen & b);
gen _superieur_egal(const gen & args,GIAC_CONTEXT);
extern const unary_function_ptr * const at_superieur_egal;
int is_inequality(const gen & g);
gen _different(const gen & args,GIAC_CONTEXT);
extern const unary_function_ptr * const at_different;
symbolic symb_of(const gen & a);
symbolic symb_of(const gen & a,const gen & b);
gen check_symb_of(const gen & a,const gen & b,GIAC_CONTEXT);
gen _of(const gen & args,GIAC_CONTEXT);
extern const unary_function_ptr * const at_of;
symbolic symb_at(const gen & a);
symbolic symb_at(const gen & a,const gen & b,GIAC_CONTEXT);
gen _at(const gen & args,GIAC_CONTEXT);
extern const unary_function_ptr * const at_at;
gen _table(const gen & args,GIAC_CONTEXT);
extern const unary_function_ptr * const at_table;
// usual multiargs
// for multiargs we use _name for the corresponding "unary" function
// to avoid confusion of pointers since name is used
symbolic symb_plus(const gen & a,const gen & b);
gen _plus(const gen & args,GIAC_CONTEXT);
extern const unary_function_ptr * const at_plus ;
extern const unary_function_ptr * const at_pointplus ;
extern const unary_function_ptr * const at_pointminus ;
gen symb_prod(const gen & a,const gen & b);
gen _prod(const gen & args,GIAC_CONTEXT);
extern const unary_function_ptr * const at_prod ;
std::string printasand(const gen & feuille,const char * sommetstr,GIAC_CONTEXT);
std::string texprintasand(const gen & g,const char * s,GIAC_CONTEXT);
std::string printasor(const gen & feuille,const char * sommetstr,GIAC_CONTEXT);
std::string texprintasor(const gen & g,const char * s,GIAC_CONTEXT);
symbolic symb_pow(const gen & a,const gen & b);
std::string cprintaspow(const gen & feuille,const char * sommetstr_orig,GIAC_CONTEXT);
#ifndef GIAC_HAS_STO_38
#if defined NSPIRE || defined FXCG
extern const alias_unary_function_eval __pow;
#else
extern unary_function_eval __pow;
#endif
#endif
gen _pow(const gen & args,GIAC_CONTEXT);
extern const unary_function_ptr * const at_pow ;
extern const char _pow_s[];
gen _powmod(const gen & args,GIAC_CONTEXT);
extern const unary_function_ptr * const at_powmod ;
symbolic symb_tran(const gen & a);
symbolic symb_trace(const gen & a);
symbolic symb_rref(const gen & a);
symbolic symb_idn(const gen & e);
symbolic symb_ranm(const gen & e);
symbolic symb_det(const gen & a);
symbolic symb_pcar(const gen & a);
symbolic symb_ker(const gen & a);
symbolic symb_image(const gen & a);
symbolic symb_moyal(const gen & a,const gen & b, const gen &vars,const gen & order);
extern const unary_function_ptr * const at_evalf;
gen _eval(const gen & a,GIAC_CONTEXT);
gen _evalf(const gen &,GIAC_CONTEXT);
extern const unary_function_ptr * const at_eval;
extern const unary_function_ptr * const at_evalm;
symbolic symb_eval(const gen & a);
symbolic symb_evalf(const gen & a);
symbolic symb_subst(const gen & e);
gen _subst(const gen & args,GIAC_CONTEXT);
extern const unary_function_ptr * const at_subst;
gen _subs(const gen & args,GIAC_CONTEXT);
extern const unary_function_ptr * const at_subs;
gen _maple_subs(const gen & args,GIAC_CONTEXT);
extern const unary_function_ptr * const at_maple_subs;
gen _ampersand_times(const gen & g,GIAC_CONTEXT);
extern const unary_function_ptr * const at_ampersand_times;
extern const unary_function_ptr * const at_version;
std::string version();
gen _version(const gen & a,GIAC_CONTEXT);
gen Gamma(const gen & x,GIAC_CONTEXT);
gen _Gamma(const gen & args,GIAC_CONTEXT);
gen _lower_incomplete_gamma(const gen & args,GIAC_CONTEXT);
extern const unary_function_ptr * const at_lower_incomplete_gamma ;
extern const unary_function_ptr * const at_igamma_exp ;
double lngamma(double x);
gen lngamma(const gen & x,GIAC_CONTEXT);
extern const unary_function_ptr * const at_Gamma;
extern const unary_function_ptr * const at_lnGamma_minus;
extern const unary_function_ptr * const at_erfs;
extern const unary_function_ptr * const at_SiCi_f ;
extern const unary_function_ptr * const at_SiCi_g ;
extern const unary_function_ptr * const at_Si;
extern const unary_function_ptr * const at_Ei ;
extern const unary_function_ptr * const at_Ei_f ;
extern const unary_function_ptr * const at_LambertW;
extern const unary_function_ptr * const at_LambertWs;
gen _LambertW(const gen & args,GIAC_CONTEXT);
gen Psi(const gen & x,GIAC_CONTEXT);
gen Psi(const gen & x,int n,GIAC_CONTEXT);
gen _Psi(const gen & args,GIAC_CONTEXT);
extern const unary_function_ptr * const at_Psi;
gen Zeta(const gen & x,GIAC_CONTEXT);
gen _Zeta(const gen & args,GIAC_CONTEXT);
extern const unary_function_ptr * const at_Zeta;
extern const unary_function_ptr * const at_Eta;
gen _erf(const gen & args,GIAC_CONTEXT);
gen erf(const gen & args,GIAC_CONTEXT);
extern const unary_function_ptr * const at_erf ;
gen _erfc(const gen & args,GIAC_CONTEXT);
gen erfc(const gen & args,GIAC_CONTEXT);
extern const unary_function_ptr * const at_erfc ;
extern const unary_function_ptr * const at_Si;
extern const unary_function_ptr * const at_Ci;
extern const unary_function_ptr * const at_Ci0;
gen _Ci(const gen & g,GIAC_CONTEXT);
gen _Si(const gen & g,GIAC_CONTEXT);
gen _Ei(const gen & g,GIAC_CONTEXT);
extern const unary_function_ptr * const at_Ei;
extern const unary_function_ptr * const at_Ei0;
extern const unary_function_ptr * const at_Heaviside ;
extern const unary_function_ptr * const at_Dirac ;
gen _Heaviside(const gen & args,GIAC_CONTEXT);
gen _Dirac(const gen & args,GIAC_CONTEXT);
#if defined(EMCC) || defined(EMCC2)
#define gen_zero gen(0)
#else
#define gen_zero zero
#endif
#if defined(GIAC_GENERIC_CONSTANTS) // || (defined(VISUALC) && !defined(RTOS_THREADX)) || defined(x86_64)
extern const gen zero;
extern const gen plus_one;
extern const gen minus_one;
extern const gen plus_two;
extern const gen plus_three;
#if defined(EMCC) || defined(EMCC2)
#define cst_i gen(0,1)
#else
extern const gen cst_i;
#endif
#else
extern const alias_gen alias_zero;
extern const gen & zero;
extern const alias_gen alias_plus_one;
extern const gen & plus_one;
extern const alias_gen alias_plus_two;
extern const gen & plus_two;
extern const alias_gen alias_plus_three;
extern const gen & plus_three;
extern const alias_gen alias_minus_one;
extern const gen & minus_one;
extern const int cst_i_refcount;
extern const int cst_i_display;
extern const alias_gen alias_cst_i;
extern const gen & cst_i;
#endif
extern const vecteur null_vetor;
extern const double rad2deg_d;
extern const double deg2rad_d;
extern const gen & rad2deg_g;
extern const gen & deg2rad_g;
//grad
extern const double rad2grad_d;
extern const double grad2rad_d;
extern const gen & rad2grad_g;
extern const gen & grad2rad_g;
#if defined(GIAC_GENERIC_CONSTANTS) // || (defined(VISUALC) && !defined(RTOS_THREADX)) || defined(x86_64)
extern gen cst_two_pi;
extern gen cst_pi_over_2;
extern gen plus_inf;
extern gen minus_inf;
extern gen plus_one_half;
extern gen minus_one_half;
extern gen plus_sqrt3;
extern gen plus_sqrt2;
extern gen plus_sqrt6;
extern gen minus_sqrt3;
extern gen minus_sqrt2;
extern gen minus_sqrt6;
extern gen minus_sqrt3_2;
extern gen minus_sqrt2_2;
extern gen minus_sqrt3_3;
extern gen plus_sqrt2_2;
extern gen plus_sqrt3_2;
extern gen plus_sqrt3_3;
extern gen cos_pi_12;
extern gen sin_pi_12;
extern gen minus_cos_pi_12;
extern gen minus_sin_pi_12;
extern gen tan_pi_12;
extern gen minus_tan_pi_12;
extern gen tan_5pi_12;
extern gen minus_tan_5pi_12;
extern gen rad2deg_e;
extern gen deg2rad_e;
//grad
extern gen rad2grad_e;
extern gen grad2rad_e;
extern const gen * const table_cos[];
extern const gen * const table_tan[];
#else
extern const alias_gen alias_cst_two_pi_tab[];
extern const alias_ref_vecteur cst_two_pi_refv;
extern const alias_ref_symbolic cst_two_pi_symb;
extern const gen & cst_two_pi;
extern const alias_gen alias_cst_pi_over_2_tab[];
extern const gen & cst_pi_over_2;
extern const alias_ref_symbolic inv_2_symb;
extern const alias_gen alias_inv_2;
extern const alias_ref_symbolic inv_3_symb;
extern const alias_gen alias_inv_3;
extern const alias_ref_symbolic inv_4_symb;
extern const alias_gen alias_inv_4;
extern const alias_gen alias_cst_pi_over_2_tab[];
extern const alias_ref_vecteur cst_pi_over_2_refv;
extern const alias_ref_symbolic cst_pi_over_2_symb ;
extern const alias_gen alias_cst_pi_over_2;
extern const gen & cst_pi_over_2 ;
extern const alias_ref_symbolic plus_inf_symb ;
extern const alias_gen alias_plus_inf;
extern const gen & plus_inf ;
extern const alias_ref_symbolic minus_inf_symb ;
extern const alias_gen alias_minus_inf;
extern const gen & minus_inf ;
extern const alias_ref_fraction plus_one_half_ref;
extern const alias_gen alias_plus_one_half1;
extern const alias_gen alias_plus_one_half2;
// extern const alias_ref_fraction plus_one_half_ref;
extern const alias_gen alias_plus_one_half;
extern const gen & plus_one_half ;
extern const alias_ref_symbolic minus_one_half_symb ;
extern const alias_gen alias_minus_one_half;
extern const gen & minus_one_half ;
extern const alias_gen alias_plus_sqrt3_tab[];
extern const alias_ref_vecteur plus_sqrt3_refv;
extern const alias_ref_symbolic plus_sqrt3_symb ;
extern const alias_gen alias_plus_sqrt3;
extern const gen & plus_sqrt3 ;
extern const alias_gen alias_plus_sqrt2_tab[];
extern const alias_ref_vecteur plus_sqrt2_refv;
extern const alias_ref_symbolic plus_sqrt2_symb ;
extern const alias_gen alias_plus_sqrt2;
extern const gen & plus_sqrt2 ;
extern const alias_gen alias_plus_sqrt6_tab[];
extern const alias_ref_vecteur plus_sqrt6_refv;
extern const alias_ref_symbolic plus_sqrt6_symb ;
extern const alias_gen alias_plus_sqrt6;
extern const gen & plus_sqrt6 ;
extern const alias_ref_symbolic minus_sqrt2_symb ;
extern const alias_gen alias_minus_sqrt2;
extern const gen & minus_sqrt2 ;
extern const alias_ref_symbolic minus_sqrt3_symb ;
extern const alias_gen alias_minus_sqrt3;
extern const gen & minus_sqrt3 ;
extern const alias_ref_symbolic minus_sqrt6_symb ;
extern const alias_gen alias_minus_sqrt6;
extern const gen & minus_sqrt6 ;
extern const alias_gen alias_minus_sqrt3_2_tab[];
extern const alias_ref_vecteur minus_sqrt3_2_refv;
extern const alias_ref_symbolic minus_sqrt3_2_symb ;
extern const alias_gen alias_minus_sqrt3_2;
extern const gen & minus_sqrt3_2 ;
extern const alias_gen alias_minus_sqrt2_2_tab[];
extern const alias_ref_vecteur minus_sqrt2_2_refv;
extern const alias_ref_symbolic minus_sqrt2_2_symb ;
extern const alias_gen alias_minus_sqrt2_2;
extern const gen & minus_sqrt2_2 ;
extern const alias_gen alias_minus_sqrt3_3_tab[];
extern const alias_ref_vecteur minus_sqrt3_3_refv;
extern const alias_ref_symbolic minus_sqrt3_3_symb ;
extern const alias_gen alias_minus_sqrt3_3;
extern const gen & minus_sqrt3_3 ;
extern const alias_gen alias_plus_sqrt3_2_tab[];
extern const alias_ref_vecteur plus_sqrt3_2_refv;
extern const alias_ref_symbolic plus_sqrt3_2_symb ;
extern const alias_gen alias_plus_sqrt3_2;
extern const gen & plus_sqrt3_2 ;
extern const alias_gen alias_plus_sqrt2_2_tab[];
extern const alias_ref_vecteur plus_sqrt2_2_refv;
extern const alias_ref_symbolic plus_sqrt2_2_symb ;
extern const alias_gen alias_plus_sqrt2_2;
extern const gen & plus_sqrt2_2 ;
extern const alias_gen alias_plus_sqrt3_3_tab[];
extern const alias_ref_vecteur plus_sqrt3_3_refv;
extern const alias_ref_symbolic plus_sqrt3_3_symb ;
extern const alias_gen alias_plus_sqrt3_3;
extern const gen & plus_sqrt3_3 ;
extern const alias_gen alias_cos_pi_12_4_tab[];
extern const alias_ref_vecteur cos_pi_12_4_refv;
extern const alias_ref_symbolic cos_pi_12_4_symb ;
extern const alias_gen alias_cos_pi_12_4;
extern const alias_gen alias_cos_pi_12_tab1;
extern const alias_ref_vecteur cos_pi_12_refv;
extern const alias_ref_symbolic cos_pi_12_symb ;
extern const alias_gen alias_cos_pi_12;
extern const gen & cos_pi_12 ;
extern const alias_gen alias_minus_cos_pi_12_4_tab[];
extern const alias_ref_vecteur minus_cos_pi_12_4_refv;
extern const alias_ref_symbolic minus_cos_pi_12_4_symb ;
extern const alias_gen alias_minus_cos_pi_12_4;
extern const alias_gen alias_minus_cos_pi_12_tab1;
extern const alias_ref_vecteur minus_cos_pi_12_refv;
extern const alias_ref_symbolic minus_cos_pi_12_symb ;
extern const alias_gen alias_minus_cos_pi_12;
extern const gen & minus_cos_pi_12 ;
extern const alias_gen alias_sin_pi_12_4_tab[];
extern const alias_ref_vecteur sin_pi_12_4_refv;
extern const alias_ref_symbolic sin_pi_12_4_symb ;
extern const alias_gen alias_sin_pi_12_4;
extern const alias_gen alias_sin_pi_12_tab1;
extern const alias_ref_vecteur sin_pi_12_refv;
extern const alias_ref_symbolic sin_pi_12_symb ;
extern const alias_gen alias_sin_pi_12;
extern const gen & sin_pi_12 ;
extern const alias_gen alias_minus_sin_pi_12_4_tab[];
extern const alias_ref_vecteur minus_sin_pi_12_4_refv;
extern const alias_ref_symbolic minus_sin_pi_12_4_symb ;
extern const alias_gen alias_minus_sin_pi_12_4;
extern const alias_gen alias_minus_sin_pi_12_tab1;
extern const alias_ref_vecteur minus_sin_pi_12_refv;
extern const alias_ref_symbolic minus_sin_pi_12_symb ;
extern const alias_gen alias_minus_sin_pi_12;
extern const gen & minus_sin_pi_12 ;
extern const alias_gen alias_tan_pi_12_tab[];
extern const alias_ref_vecteur tan_pi_12_refv;
extern const alias_ref_symbolic tan_pi_12_symb ;
extern const alias_gen alias_tan_pi_12;
extern const gen & tan_pi_12 ;
extern const alias_gen alias_tan_5pi_12_tab[];
extern const alias_ref_vecteur tan_5pi_12_refv;
extern const alias_ref_symbolic tan_5pi_12_symb ;
extern const alias_gen alias_tan_5pi_12;
extern const gen & tan_5pi_12 ;
extern const alias_ref_symbolic minus_tan_pi_12_symb ;
extern const alias_gen alias_minus_tan_pi_12;
extern const gen & minus_tan_pi_12 ;
extern const alias_ref_symbolic minus_tan_5pi_12_symb ;
extern const alias_gen alias_minus_tan_5pi_12;
extern const gen & minus_tan_5pi_12 ;
extern const alias_ref_symbolic inv_pi_symb;
extern const alias_gen alias_inv_pi;
extern const gen & cst_inv_pi;
extern const alias_ref_symbolic inv_180_symb;
extern const alias_gen alias_inv_180;
extern const gen & cst_inv_180;
extern const alias_gen alias_rad2deg_e_tab[];
extern const alias_ref_vecteur rad2deg_e_refv;
extern const alias_ref_symbolic rad2deg_e_symb ;
extern const alias_gen alias_rad2deg_e;
extern const gen & rad2deg_e ;
extern const alias_gen alias_deg2rad_e_tab[];
extern const alias_ref_vecteur deg2rad_e_refv;
extern const alias_ref_symbolic deg2rad_e_symb ;
extern const alias_gen alias_deg2rad_e;
extern const gen & deg2rad_e ;
//grad
extern const alias_gen alias_rad2grad_e_tab[];
extern const alias_ref_vecteur rad2grad_e_refv;
extern const alias_ref_symbolic rad2grad_e_symb;
extern const alias_gen alias_rad2grad_e;
extern const gen & rad2grad_e;
extern const alias_gen alias_grad2rad_e_tab[];
extern const alias_ref_vecteur grad2rad_e_refv;
extern const alias_ref_symbolic grad2rad_e_symb;
extern const alias_gen alias_grad2rad_e;
extern const gen & grad2rad_e;
extern const gen * const * table_cos;
extern const gen * const * table_tan;
#endif
// for subst.cc
// extern std::vector<unary_function_ptr> sincostan_v;
// extern std::vector<unary_function_ptr> asinacosatan_v,sinhcoshtanh_v,sincostansinhcoshtanh_v;
extern const unary_function_ptr * const exp_tab;
extern const unary_function_ptr * const tan_tab;
extern const unary_function_ptr * const asin_tab;
extern const unary_function_ptr * const acos_tab;
extern const unary_function_ptr * const atan_tab;
extern const unary_function_ptr * const pow_tab;
extern const unary_function_ptr * const Heaviside_tab;
extern const unary_function_ptr * const invpowtan_tab;
extern const gen_op_context halftan_tab[];
extern const gen_op_context hyp2exp_tab[];
extern const gen_op_context hypinv2exp_tab[];
extern const gen_op_context trig2exp_tab[];
extern const gen_op_context atrig2ln_tab[];
// extern std::vector< gen_op_context > halftan_v;
// extern std::vector< gen_op_context > hyp2exp_v;
// extern std::vector< gen_op_context > trig2exp_v;
extern const gen_op_context halftan_hyp2exp_tab[];
extern const gen_op_context exp2sincos_tab[];
extern const gen_op_context tan2sincos_tab[];
extern const gen_op_context tan2sincos2_tab[];
extern const gen_op_context tan2cossin2_tab[];
extern const gen_op_context asin2acos_tab[];
extern const gen_op_context asin2atan_tab[];
extern const gen_op_context acos2asin_tab[];
extern const gen_op_context acos2atan_tab[];
extern const gen_op_context atan2asin_tab[];
extern const gen_op_context atan2acos_tab[];
extern const gen_op_context atrig2ln_tab[];
extern const gen_op_context trigcos_tab[];
extern const gen_op_context trigsin_tab[];
extern const gen_op_context trigtan_tab[];
extern const gen_op_context powexpand_tab[];
extern const gen_op_context powneg2invpow_tab[];
extern const gen_op_context exp2power_tab[];
extern const unary_function_ptr * const gamma_tab;
extern const gen_op_context gamma2factorial_tab[];
extern const unary_function_ptr * const factorial_tab;
extern const gen_op_context factorial2gamma_tab[];
// extern std::vector<unary_function_ptr> sign_floor_ceil_round_tab;
extern const unary_function_ptr * const analytic_sommets;
extern const unary_function_ptr * const primitive_tab_op;
extern const unary_function_ptr * const inverse_tab_op;
extern const unary_function_ptr * const inequality_tab;
extern const unary_function_ptr * const solve_fcns_tab;
extern const unary_function_ptr * const sincostan_tab;
extern const unary_function_ptr * const sincostansinhcoshtanh_tab;
extern const unary_function_ptr * const asinacosatan_tab;
extern const unary_function_ptr * const sinhcoshtanh_tab;
extern const unary_function_ptr * const sinhcoshtanhinv_tab;
extern const unary_function_ptr * const sign_floor_ceil_round_tab;
extern const unary_function_ptr * const reim_op;
extern const unary_function_ptr * const limit_tab;
extern const gen_op_context limit_replace[];
bool need_parenthesis(const gen & g);
void prod2frac(const gen & g,vecteur & num,vecteur & den);
gen vecteur2prod(const vecteur & num);
gen _multistring(const gen & args,GIAC_CONTEXT);
extern const unary_function_ptr * const at_multistring;
std::string unquote(const std::string & s);
gen Gamma(const gen & x,GIAC_CONTEXT);
gen _Gamma(const gen & args,GIAC_CONTEXT) ;
extern const unary_function_ptr * const at_Psi_minus_ln;
gen Psi(const gen & x,GIAC_CONTEXT);
gen Psi(const gen & x,int n,GIAC_CONTEXT);
gen _Psi(const gen & args,GIAC_CONTEXT) ;
gen _normalmod(const gen & g,GIAC_CONTEXT);
// a=expression, x variable, n=number of terms,
// compute an approx value of sum((-1)^k*a(k),k,0,+infinity)
// using Chebychev polynomials
gen alternate_series(const gen & a,const gen & x,int n,GIAC_CONTEXT);
gen Eta(const gen & s,int ndiff,GIAC_CONTEXT);
gen Eta(const gen & s0,GIAC_CONTEXT);
gen Zeta(const gen & x,int ndiff,GIAC_CONTEXT);
gen Zeta(const gen & x,GIAC_CONTEXT);
gen _Zeta(const gen & args,GIAC_CONTEXT) ;
gen _Eta(const gen & args,GIAC_CONTEXT) ;
gen _erfs(const gen & g,GIAC_CONTEXT);
gen erf(const gen & x,GIAC_CONTEXT);
gen _erf(const gen & args,GIAC_CONTEXT);
gen erfc(const gen & x,GIAC_CONTEXT);
gen _erfc(const gen & args,GIAC_CONTEXT);
gen _SiCi_f(const gen & args,GIAC_CONTEXT);
gen _SiCi_g(const gen & args,GIAC_CONTEXT);
gen _Si(const gen & args,GIAC_CONTEXT);
gen _Ci(const gen & args,GIAC_CONTEXT);
gen _Ci0(const gen & args,GIAC_CONTEXT);
gen _Ei_f(const gen & args,GIAC_CONTEXT);
gen Ei(const gen & args,GIAC_CONTEXT);
gen Ei(const gen & args,int n,GIAC_CONTEXT);
gen _Ei(const gen & args,GIAC_CONTEXT);
gen _Ei0(const gen & args,GIAC_CONTEXT);
gen Ci_replace0(const gen & g,GIAC_CONTEXT);
gen Ei_replace0(const gen & g,GIAC_CONTEXT);
gen _Dirac(const gen & args,GIAC_CONTEXT);
gen _Heaviside(const gen & args,GIAC_CONTEXT);
std::string printasexp(const gen & g,const char * s,GIAC_CONTEXT);
std::string printassubs(const gen & feuille,const char * sommetstr,GIAC_CONTEXT);
std::string printasmaple_subs(const gen & feuille,const char * sommetstr,GIAC_CONTEXT);
void fonction_bidon();
std::string printassto(const gen & feuille,const char * sommetstr,GIAC_CONTEXT);
gen fast_icontent(const gen & g); // fast compute integer content of g
gen fast_divide_by_icontent(const gen & g,const gen & z);
#ifdef NO_UNARY_FUNCTION_COMPOSE // STATIC_BUILTIN_LEXER_FUNCTIONS
extern const alias_unary_function_eval __sto;
#else
extern const unary_function_eval __sto;
#endif
extern const unary_function_ptr * const at_step_infolevel;
#ifndef VISUALC
gen * normal_sin_pi_12_ptr_();
gen * normal_cos_pi_12_ptr_();
#endif
// additions by L. Marohnić:
std::string to_unix_path(const std::string &path);
std::string temp_file_name(const char *fallback_name,const char *ext=NULL);
bool ckfileexists(const char *fname);
class temp_file {
// TEMPORARY FILE CLASS
// This is a temporary file object that is accessed through the 'handle' member.
// The file is created and opened by constructor and automatically deleted by destructor.
std::string _fname;
public:
FILE *handle;
temp_file(const char *fallback_name,const char *ext=NULL);
~temp_file();
bool fail() const { return handle==NULL; }
};
#ifndef NO_NAMESPACE_GIAC
} // namespace giac
#endif // ndef NO_NAMESPACE_GIAC
#endif // _GIAC_USUAL_H