499:
337:
1064:
1076:
34:
449:
It is able to perform simple and sophisticated operations on multivariate polynomials and on various data related to them (ideals, modules, matrices, rational functions). For example, it can readily compute
728:
589:
1102:
820:
474:. The capabilities of CoCoA and the flexibility of its use are further enhanced by the dedicated high-level programming language.
756:
1112:
1107:
813:
467:
564:
477:
Its mathematical core, CoCoALib, has been designed as an open source C++ library, focussing on ease of use and flexibility.
504:
870:
459:
405:
on x86. CoCoA is mainly used by researchers (see citations at and), but can be useful even for "simple" computations.
1068:
806:
1080:
1019:
905:
860:
512:
295:
156:
958:
845:
630:
463:
259:
95:
875:
998:
481:
455:
421:
237:
73:
850:
394:
378:
173:
793:
517:
1014:
336:
829:
362:
161:
606:
940:
837:
366:
462:, intersection, division, the radical of an ideal, the ideal of zero-dimensional schemes,
8:
973:
915:
300:
948:
890:
760:
583:
402:
963:
307:
168:
131:
451:
432:
993:
953:
417:
540:
471:
442:
700:
662:
1096:
988:
798:
20:
1039:
427:
374:
205:
41:
638:
885:
714:
382:
1029:
910:
895:
413:
1034:
968:
900:
312:
136:
1049:
1044:
1024:
982:
865:
33:
786:
323:
184:
978:
930:
920:
880:
686:
438:
398:
386:
370:
288:
148:
140:
124:
381:. CoCoA has been ported to many operating systems including
925:
390:
144:
742:
494:
377:. The CoCoA Library (CoCoALib) is available under
1094:
601:
599:
588:: CS1 maint: bot: original URL status unknown (
487:CoCoALib is used by ApCoCoA and NmzIntegrate
46:Abbott, J. and Bigatti, A. M. and Robbiano, L.
814:
657:
655:
596:
828:
623:
557:
1103:Computer algebra system software for Linux
1075:
821:
807:
652:
571:. Archived from the original on 1998-01-09
335:
715:"CoCoA - Mathematical software - swMATH"
1095:
535:
533:
802:
505:Free and open-source software portal
470:, factorization of polynomials, and
530:
373:, used to compute with numbers and
13:
265:0.99718 / 14 February 2022
14:
1124:
778:
101:5.4.1j / 21 February 2023
1074:
1063:
1062:
513:List of computer algebra systems
497:
32:
749:
735:
243:0.99800 / 28 April 2022
794:ApCoCoA, an extension of CoCoA
721:
707:
693:
679:
1:
1113:Science software that uses Qt
1108:Free computer algebra systems
523:
210:Abbott, J. and Bigatti, A. M.
79:5.4.0 / 11 April 2022
7:
999:Engineering Equation Solver
490:
482:GNU Multi-Precision Library
422:GNU Multi-Precision Library
56:; 36 years ago
10:
1129:
408:CoCoA's features include:
379:GNU General Public License
18:
1058:
1007:
939:
836:
518:Standard Template Library
318:
306:
294:
284:
280:
258:
236:
232:
214:
204:
179:
167:
155:
130:
120:
116:
94:
72:
68:
50:
40:
31:
830:Computer algebra systems
729:"CoCoA in GoogleScholar"
460:minimal free resolutions
19:Not to be confused with
631:"CoCoALib Beta Archive"
607:"CoCoA 5 Release Notes"
437:User interfaces: text;
363:computer algebra system
162:Computer algebra system
103:; 18 months ago
16:Computer algebra system
985:symbolic math toolbox)
220:; 17 years ago
480:CoCoALib is based on
267:; 2 years ago
245:; 2 years ago
81:; 2 years ago
701:"CoCoALib home page"
367:University of Genova
667:cocoa.dima.unige.it
635:cocoa.dima.unige.it
611:cocoa.dima.unige.it
569:cocoa.dima.unige.it
545:cocoa.dima.unige.it
201:
28:
757:"Normaliz website"
393:x86-64 & PPC,
361:lgebra) is a free
206:Original author(s)
199:
42:Original author(s)
26:
1090:
1089:
743:"ApCoCoA website"
468:Hilbert functions
365:developed by the
344:
343:
218:9 March 2007
197:
196:
1120:
1078:
1077:
1066:
1065:
949:ClassPad Manager
823:
816:
809:
800:
799:
790:
789:
787:Official website
772:
771:
769:
768:
759:. Archived from
753:
747:
746:
739:
733:
732:
725:
719:
718:
711:
705:
704:
697:
691:
690:
683:
677:
676:
674:
673:
659:
650:
649:
647:
646:
637:. Archived from
627:
621:
620:
618:
617:
603:
594:
593:
587:
579:
577:
576:
561:
555:
554:
552:
551:
537:
507:
502:
501:
500:
418:rational numbers
385:on PPC and x86,
340:
339:
332:
329:
327:
325:
275:
273:
268:
253:
251:
246:
228:
226:
221:
202:
198:
193:
190:
188:
186:
132:Operating system
111:
109:
104:
89:
87:
82:
64:
62:
57:
36:
29:
25:
1128:
1127:
1123:
1122:
1121:
1119:
1118:
1117:
1093:
1092:
1091:
1086:
1054:
1003:
994:TI InterActive!
935:
832:
827:
785:
784:
781:
776:
775:
766:
764:
755:
754:
750:
741:
740:
736:
727:
726:
722:
713:
712:
708:
699:
698:
694:
687:"CoCoA website"
685:
684:
680:
671:
669:
661:
660:
653:
644:
642:
629:
628:
624:
615:
613:
605:
604:
597:
581:
580:
574:
572:
565:"CoCoA History"
563:
562:
558:
549:
547:
539:
538:
531:
526:
503:
498:
496:
493:
464:Poincaré series
334:
322:
276:
271:
269:
266:
260:Preview release
254:
249:
247:
244:
224:
222:
219:
215:Initial release
183:
112:
107:
105:
102:
96:Preview release
90:
85:
83:
80:
60:
58:
55:
51:Initial release
24:
17:
12:
11:
5:
1126:
1116:
1115:
1110:
1105:
1088:
1087:
1085:
1084:
1072:
1059:
1056:
1055:
1053:
1052:
1047:
1042:
1037:
1032:
1027:
1022:
1017:
1011:
1009:
1005:
1004:
1002:
1001:
996:
991:
986:
976:
971:
966:
961:
956:
951:
945:
943:
937:
936:
934:
933:
928:
923:
918:
913:
908:
903:
898:
893:
888:
883:
878:
873:
868:
863:
858:
853:
848:
842:
840:
834:
833:
826:
825:
818:
811:
803:
797:
796:
791:
780:
779:External links
777:
774:
773:
748:
734:
720:
706:
692:
678:
651:
622:
595:
556:
541:"Citing CoCoA"
528:
527:
525:
522:
521:
520:
515:
509:
508:
492:
489:
447:
446:
435:
430:
424:
353:mputations in
342:
341:
320:
316:
315:
310:
304:
303:
298:
292:
291:
286:
282:
281:
278:
277:
264:
262:
256:
255:
242:
240:
238:Stable release
234:
233:
230:
229:
216:
212:
211:
208:
195:
194:
181:
177:
176:
171:
165:
164:
159:
153:
152:
134:
128:
127:
122:
118:
117:
114:
113:
100:
98:
92:
91:
78:
76:
74:Stable release
70:
69:
66:
65:
52:
48:
47:
44:
38:
37:
15:
9:
6:
4:
3:
2:
1125:
1114:
1111:
1109:
1106:
1104:
1101:
1100:
1098:
1083:
1082:
1073:
1071:
1070:
1061:
1060:
1057:
1051:
1048:
1046:
1043:
1041:
1038:
1036:
1033:
1031:
1028:
1026:
1023:
1021:
1018:
1016:
1013:
1012:
1010:
1006:
1000:
997:
995:
992:
990:
987:
984:
980:
977:
975:
972:
970:
967:
965:
962:
960:
957:
955:
952:
950:
947:
946:
944:
942:
938:
932:
929:
927:
924:
922:
919:
917:
914:
912:
909:
907:
904:
902:
899:
897:
894:
892:
889:
887:
884:
882:
879:
877:
874:
872:
869:
867:
864:
862:
859:
857:
854:
852:
849:
847:
844:
843:
841:
839:
835:
831:
824:
819:
817:
812:
810:
805:
804:
801:
795:
792:
788:
783:
782:
763:on 2015-12-08
762:
758:
752:
744:
738:
730:
724:
716:
710:
702:
696:
688:
682:
668:
664:
658:
656:
641:on 2007-04-26
640:
636:
632:
626:
612:
608:
602:
600:
591:
585:
570:
566:
560:
546:
542:
536:
534:
529:
519:
516:
514:
511:
510:
506:
495:
488:
485:
483:
478:
475:
473:
469:
465:
461:
457:
453:
452:Gröbner basis
444:
440:
436:
434:
433:Gröbner basis
431:
429:
426:Multivariate
425:
423:
419:
415:
411:
410:
409:
406:
404:
400:
396:
392:
388:
384:
380:
376:
372:
368:
364:
360:
356:
352:
348:
338:
331:
321:
317:
314:
311:
309:
305:
302:
299:
297:
293:
290:
287:
283:
279:
263:
261:
257:
241:
239:
235:
231:
217:
213:
209:
207:
203:
192:
182:
178:
175:
172:
170:
166:
163:
160:
158:
154:
150:
146:
142:
138:
135:
133:
129:
126:
123:
119:
115:
99:
97:
93:
77:
75:
71:
67:
53:
49:
45:
43:
39:
35:
30:
22:
1079:
1067:
1008:Discontinued
989:SMath Studio
855:
765:. Retrieved
761:the original
751:
737:
723:
709:
695:
681:
670:. Retrieved
666:
643:. Retrieved
639:the original
634:
625:
614:. Retrieved
610:
573:. Retrieved
568:
559:
548:. Retrieved
544:
486:
479:
476:
472:toric ideals
448:
407:
358:
354:
350:
346:
345:
974:Mathematica
941:Proprietary
838:Open-source
428:Polynomials
375:polynomials
21:Cocoa (API)
1097:Categories
1040:Mathomatic
767:2014-05-22
672:2022-07-06
663:"CoCoALib"
645:2023-03-09
616:2022-07-06
575:2023-03-09
550:2022-07-06
524:References
420:using the
357:mmutative
285:Written in
272:2022-02-14
250:2022-04-28
225:2007-03-09
121:Written in
108:2023-02-21
86:2022-04-11
926:Xcas/Giac
886:Macaulay2
412:Very big
383:Macintosh
1069:Category
1030:LiveMath
916:Singular
911:SageMath
896:Normaliz
584:cite web
491:See also
456:syzygies
441:-based;
414:integers
389:on x86,
200:CoCoALib
1035:Macsyma
969:Mathcad
901:PARI/GP
851:Cadabra
403:Windows
395:Solaris
319:Website
313:GNU GPL
308:License
301:Library
270: (
248: (
223: (
180:Website
174:GNU GPL
169:License
137:Windows
106: (
84: (
59: (
1050:ALTRAN
1045:muMATH
1025:Erable
1020:Derive
983:MATLAB
906:Reduce
891:Maxima
866:FriCAS
861:Fermat
445:-based
333:
328:.unige
189:.unige
1015:CAMAL
979:muPAD
964:Maple
959:Magma
931:Yacas
921:SymPy
881:GiNaC
856:CoCoA
846:Axiom
439:Emacs
399:SPARC
387:Linux
371:Italy
347:CoCoA
326:.dima
324:cocoa
187:.dima
185:cocoa
149:macOS
141:Linux
27:CoCoA
1081:List
954:KANT
871:FORM
590:link
466:and
458:and
416:and
401:and
391:Unix
296:Type
157:Type
145:Unix
61:1988
54:1988
876:GAP
397:on
330:.it
289:C++
191:.it
125:C++
1099::
665:.
654:^
633:.
609:.
598:^
586:}}
582:{{
567:.
543:.
532:^
484:.
454:,
443:Qt
369:,
355:Co
351:Co
147:,
139:,
981:(
822:e
815:t
808:v
770:.
745:.
731:.
717:.
703:.
689:.
675:.
648:.
619:.
592:)
578:.
553:.
359:A
349:(
274:)
252:)
227:)
151:,
143:/
110:)
88:)
63:)
23:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
