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236:(IBM Research and University of Waterloo), Josh Cohen (Yale University), Michael Rothstein (Kent State University), Manuel Bronstein (IBM Research), Michael Monagan (Simon Fraser University), Jonathan Steinbach (IBM Research), William Burge (IBM Research), Jim Wen (IBM Research), William Sit (City College of New York), and Clifton Williamson (IBM Research)
730:
for elementary integration, which was done by Manuel
Bronstein and Barry Trager. While this implementation can find most elementary antiderivatives and whether they exist, it does have some non-implemented branches, and raises an error when such cases are encountered during integration.
640:
It features 'HyperDoc', an interactive browser-like help system, and can display two and three dimensional graphics, also providing interactive features like rotation and lighting. It also has a specialized interaction mode for
505:
The Axiom project focuses on the “30 Year
Horizon”. The primary philosophy is that Axiom needs to develop several fundamental features in order to be useful to the next generation of computational mathematicians. Knuth's
1068:
James H. Griesmer; Richard D. Jenks (1971). "SCRATCHPAD/1: An interactive facility for symbolic mathematics | Proceedings of the second ACM symposium on
Symbolic and algebraic manipulation (SYMSAC '71)":
1487:
1397:
Buchberger's algorithm and staggered linear bases | Proceedings of the fifth ACM symposium on
Symbolic and algebraic computation (International Symposium on Symbolic and Algebraic Computation '86)
1304:
James H. Davenport; P. Gianni; Richard D. Jenks; V. Miller; Scott
Morrison; M. Rothstein; C. Sundaresan; Robert S. Sutor; Barry Trager (1984). "Scratchpad". Mathematical Sciences Department, IBM
228:(IBM Research). Implementation included Robert Sutor (IBM Research), Scott C. Morrison (University of California, Berkeley), Christine J. Sundaresan (IBM Research), Timothy Daly (IBM Research),
1666:
Manuel
Bronstein (1989). "Simplification of real elementary functions | Proceedings of the International Symposium on Symbolic and Algebraic Computation (SIGSAM '89)". ACM: 207–211.
1369:
Robert S. Sutor (1985). "The
Scratchpad II Computer Algebra Language and System | Proceedings of International Symposium on Symbolic and Algebraic Computation '85". Springer: 32–33.
1692:
Claire
Dicrescenzo; Dominique Duval (1989). P. Gianni (ed.). "Algebraic extensions and algebraic closure in Scratchpad II | Symbolic and Algebraic Computation". Springer: 440–446.
493:
The Axiom project has a major focus on providing documentation. Recently the project announced the first in a series of instructional videos, which are also available on the
625:
Axiom comes with an extension language called SPAD. All the mathematical knowledge of Axiom is written in this language. The interpreter accepts roughly the same language.
597:
1343:
Richard D. Jenks (1984). "A primer: 11 keys to New
Scratchpad | Proceedings of International Symposium on Symbolic and Algebraic Computation '84". Springer: 123–147.
2115:
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618:
Several operations can have the same name, and the types of both the arguments and the result are used to determine which operation is applied (cf.
1231:
Richard D. Jenks (1976). "A pattern compiler | Proceedings of the third ACM symposium on
Symbolic and algebraic manipulation (SYMSAC '76)": 60–65.
1108:
James H. Griesmer; Richard D. Jenks (1972). "Experience with an online symbolic mathematics system | Proceedings of the ONLINE72 Conference".
1039:
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technique is used throughout the source code. Axiom plans to use proof technology to prove the correctness of the algorithms (such as
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1194:
655:
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Containers as part of a continuous release process. The latest image is available on any platform using docker and the commands:
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1826:
1618:"Using Gröbner bases to determine algebra membership, split surjective algebra homomorphisms determine birational equivalence"
1516:
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1436:
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1448:
Applications of a software interconnection system in mathematical problem solving environments | Proceedings of SYMSAC '86
1883:
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Robert S. Sutor; Richard D. Jenks (1987). "The type inference and coercion facilities in the scratchpad II interpreter".
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125:
205:. The development of this software was stopped before any public release. The second Scratchpad, originally named
1971:
1622:
1576:
272:, following "serious disagreement about project goals". The Axiom project continued to be developed by Tim Daly.
65:
1888:
1015:
1609:
Programming with abstract data types: the symmetry package (SPDE) in Scratchpad | Trends in Computer Algebra
715:
224:(IBM Research). Early consultants on the project were David Barton (University of California, Berkeley) and
91:
2011:
1536:
Application of SCRATCHPAD to problems in special functions and combinatorics | Trends in Computer Algebra
691:
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220:(University of Bath), Barry M. Trager (IBM Research), David Y.Y. Yun (Southern Methodist University) and
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as argument, and returns the field of fractions of its argument. As another example, the ring of
243:
when IBM decided, circa 1990, to make it a commercial product. A few years later, it was sold to
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A function can take a type as argument, and its return value can also be a type. For example,
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In Axiom, each object has a type. Examples of types are mathematical structures (such as
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447:
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396:
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1776:
1334:
Richard D. Jenks (1984). "The New SCRATCHPAD Language and System for Computer Algebra".
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177:. It consists of an interpreter environment, a compiler and a library, which defines a
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291:. The source code is becoming available in a set of volumes which are available on the
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Timothy Daly "Axiom" Invited Talk, Free Software Conference, Lyon, France, May, 2002
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1040:"integration - Does there exist a complete implementation of the Risch algorithm?"
2006:
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Papers of the Symposium on Interpreters and interpretive techniques - SIGPLAN '87
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and a heuristic algorithm to make explicit type annotations mostly unnecessary.
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1413:
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George E. Andrews (1984). "Ramanujan and SCRATCHPAD | Proceedings of the 1984
996:
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A fast implementation of polynomial factorization | Proceedings of SYMSAC '86
1215:
170:
1645:
Hans-J. Boehm (1989). "Type inference in the presence of type abstraction".
1546:
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website. The first video provides details on the Axiom information sources.
2001:
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197:. The first one was started in 1965 by James Griesmer at the request of
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Scratchpad II: an abstract datatype system for mathematical computation
547:
25:
247:. In 2001, it was withdrawn from the market and re-released under the
232:(University of Pisa), Albrecht Fortenbacher (Universitaet Karlsruhe),
1898:
295:
website. These volumes contain the actual source code of the system.
1777:
Jenks, R.D. and Sutor, R. "Axiom, The Scientific Computation System"
2042:
1923:
1908:
1549:
Computer Algebra: Systems and Algorithms for Algebraic Computation
1259:
Ueberlegungen zur Implementierung eines Formelmanipulationssystems
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216:
The design is principally due to Richard D. Jenks (IBM Research),
2047:
1981:
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Scratchpad II: Présentation d'un nouveau langage de calcul formel
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1611:. Lecture Notes in Computer Science. Springer. pp. 167–176.
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2037:
1995:
1878:
1740:
1498:
1464:
1192:
Arthur C. Norman (1975). "Computing with Formal Power Series".
268:
852:
251:. Since then, the project's lead developer has been Tim Daly.
1991:
1943:
1933:
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1868:
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1478:
Pascale Sénéchaud; Françoise Siebert; Gilles Villard (1987).
963:
906:
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1938:
1414:
Richard D. Jenks; Robert S. Sutor; Stephen M. Watt (1986).
515:
1615:
1547:
James H. Davenport; Yvon Siret; Evelyne Tournier (1993) .
1426:
1142:
James H. Griesmer; Richard D. Jenks (1972). "Scratchpad".
925:"FriCAS 18a5ef5d99c796a89efeac06df40043a85b3d44d — FriCAS"
550:) as well as data structures from computer science (e.g.,
360:—Source code and explanation of X11 Hyperdoc help browser
1263:
Technischen Universitat Carolo-Wilhelmina zu Braunschweig
661:
HyperDoc displaying the available operations for a domain
529:
docker pull daly/axiom docker run -i -t daly/axiom axiom
353:—Source code for system commands and scripts (incomplete)
194:
1097:
META/PLUS - The Syntax Extension Facility for SCRATCHPAD
599:
matrices with rational entries would be constructed as
339:—Short essays on developer-specific topics (incomplete)
1016:"Manuel Bronstein on Axiom's Integration Capabilities"
907:"OpenAxiom: The Open Scientific Computation Platform"
579:
450:—Source code for Axiom Crystal front end (incomplete)
1163:
Richard D. Jenks (1974). "The SCRATCHPAD language".
738:
279:, that is, logical, rational, judicious, and sound.
997:"Axiom Computer Algebra System Information Sources"
591:
1533:
1336:Proceedings of the 1984 MACSYMA Users' Conference
1269:
443:—Source pages for Axiom Firefox browser front end
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332:—Guided examples of program writing (incomplete)
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633:Within the interpreter environment, Axiom uses
346:—Source code for Axiom interpreter (incomplete)
213:, under the direction of Richard Dimick Jenks.
1572:"On an installation of Buchberger's algorithm"
399:—Essays on implementation issues (incomplete)
1827:
1644:
1606:
325:—Detailed examples of domain use (incomplete)
71:Sourceforge master / February 6, 2022
1841:
1534:George E. Andrews (1988). R. Janssen (ed.).
2116:Common Lisp (programming language) software
1570:Rüdiger Gebauer; H. Michael Möller (1988).
1395:Rüdiger Gebauer; H. Michael Möller (1986).
871:"Richard D. Jenks Biographical Information"
392:—Source code for Spad compiler (incomplete)
2121:Computer algebra system software for Linux
2088:
1834:
1820:
1465:William H. Burge; Stephen M. Watt (1987).
1445:
607:is interpreted as the identity matrix and
603:. Of course, when working in this domain,
1635:
1589:
1256:
1195:ACM Transactions on Mathematical Software
1013:
828:
1607:Fritz Schwarz (1988). R. Janssen (ed.).
991:
989:
376:—Source code for X11 Graphics subsystem
1261:(Masters thesis) (in German). Germany:
1014:Bronstein, Manuel (September 5, 2003).
298:The currently available documents are:
2108:
817:ACM Communications in Computer Algebra
1815:
1616:David Shannon; Moss Sweedler (1988).
1427:Michael Lucks; Bruce W. Char (1986).
986:
810:
611:would give the inverse of the matrix
97:https://sourceforge.net/p/axiom/code/
749:Free and open-source software portal
406:—Essays containing background theory
1782:Daly, T. "Axiom Volume 1: Tutorial"
1726:Timothy Daly "Axiom" Invited Talk,
1467:Infinite Structure in SCRATCHPAD II
726:Axiom has an implementation of the
189:Two computer algebra systems named
49:release / November 13, 2015
13:
1061:
275:The current research direction is
14:
2142:
1746:Axiom (computer algebra software)
1734:
1540:Lecture Notes in Computer Science
1274:Users' Conference". Schenectady:
889:"EUROCAL '85 | SpringerLink"
697:Axiom simplifying a heat equation
601:SquareMatrix(4, Fraction Integer)
457:—Prove Axiom Algebra (incomplete)
413:—Source code for Axiom categories
258:twice, originating two different
209:, was developed from 1977 on, at
2131:Free software programmed in Lisp
2087:
2076:
2075:
1739:
1492:Grenoble Institute of Technology
1471:Thomas J. Watson Research Center
1420:Thomas J. Watson Research Center
1306:Thomas J. Watson Research Center
1101:Thomas J. Watson Research Center
767:List of computer algebra systems
741:
721:Axiom computing a Risch integral
714:
702:
690:
678:
666:
654:
282:
211:Thomas J. Watson Research Center
1730:, Metz, France, July 9–12, 2003
1719:"Axiom -- Thirty Years of Lisp"
1623:Journal of Symbolic Computation
1577:Journal of Symbolic Computation
1486:(Research report) (in French).
1032:
1007:
976:"Axiom Computer Algebra System"
968:
853:"Axiom Computer Algebra System"
685:Axiom Firefox Browser Interface
434:—Source code for Axiom numerics
427:—Source code for Axiom packages
367:—Source code for Hyperdoc pages
953:
935:
917:
899:
881:
863:
845:
804:
779:
645:, as well as a plugin for the
420:—Source code for Axiom domains
1:
2126:Free computer algebra systems
1637:10.1016/s0747-7171(88)80047-6
1591:10.1016/s0747-7171(88)80048-8
1542:. Springer. pp. 159–166.
811:Fitch, John (July 23, 2012).
772:
569:is a function, that takes an
500:
397:Axiom Algebra Implementation
7:
2012:Engineering Equation Solver
1758:Online sandbox to try Axiom
964:axiom-developer.org website
813:"James Griesmer 1929--2011"
734:
628:
30:Independent group of people
10:
2147:
1762:Source code repositories:
762:Aldor programming language
673:Axiom displaying a surface
383:—A Gallery of Axiom images
303:Combined Table of Contents
239:Scratchpad II was renamed
184:
2071:
2020:
1952:
1849:
1431:. ACM. pp. 228–232.
1399:. ACM. pp. 218–221.
1095:Richard D. Jenks (1971).
960:Why Literate Programming?
709:Axiom matrix manipulation
592:{\displaystyle 4\times 4}
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1843:Computer algebra systems
527:
484:—Useful function summary
411:Axiom Algebra Categories
1469:(Research report). IBM
1450:. ACM. pp. 16–23.
1418:(Research report). IBM
1177:10.1145/1086830.1086834
1099:(Research report). IBM
980:www.axiom-developer.org
830:10.1145/2338496.2338499
757:A# programming language
462:The Axiom SANE Compiler
330:Axiom Programmers Guide
175:computer algebra system
131:Computer algebra system
16:Computer algebra system
1998:symbolic math toolbox)
1728:Libre Software Meeting
1705:Cite journal requires
1679:Cite journal requires
1382:Cite journal requires
1356:Cite journal requires
1321:Cite journal requires
1291:Cite journal requires
1244:Cite journal requires
1129:Cite journal requires
1082:Cite journal requires
593:
470:—Literature references
432:Axiom Algebra Numerics
425:Axiom Algebra Packages
337:Axiom Developers Guide
318:—A simple introduction
1748:at Wikimedia Commons
1208:10.1145/355656.355660
1156:10.1145/942576.807019
594:
455:Proving Axiom Correct
418:Axiom Algebra Domains
309:Axiom Jenks and Sutor
73:; 2 years ago
51:; 8 years ago
1003:. November 30, 2008.
620:function overloading
577:
508:literate programming
482:Axiom Reference Card
404:Axiom Algebra Theory
365:Axiom Hyperdoc Pages
277:"Proving Axiom Sane"
249:Modified BSD License
143:Modified BSD License
1659:10.1145/74818.74835
1647:ACM SIGPLAN Notices
1509:10.1145/29650.29656
1446:J. Purtilo (1986).
1165:ACM SIGSAM Bulletin
1144:ACM SIGPLAN Notices
857:axiom-developer.org
495:axiom-developer.org
293:axiom-developer.org
254:In 2007, Axiom was
21:
1503:. pp. 56–63.
1257:E. Lueken (1977).
943:"History — FriCAS"
911:www.open-axiom.org
875:www.eecis.udel.edu
589:
468:Axiom Bibliography
311:—The main textbook
218:James H. Davenport
193:were developed by
173:, general-purpose
19:
2103:
2102:
1744:Media related to
1518:978-0-89791-235-8
1457:978-0-89791-199-3
1438:978-0-89791-199-3
1406:978-0-89791-199-3
1114:Brunel University
1020:groups.google.com
787:"daly/axiom Tags"
344:Axiom Interpreter
323:Axiom Users Guide
226:James W. Thatcher
201:, and written in
164:
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1962:ClassPad Manager
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1630:(2–3): 267–273.
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480:Reference Card:
294:
289:literate program
222:Victor S. Miller
160:
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156:.axiom-developer
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114:Operating system
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1062:Further reading
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230:Patrizia Gianni
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1753:Axiom Homepage
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1735:External links
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1715:
1707:|journal=
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1681:|journal=
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1653:(7): 192–206.
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1562:978-0122042300
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1553:Academic Press
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448:Axiom Crystal
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441:Axiom Browser
438:
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430:Volume 10.5:
429:
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423:Volume 10.4:
422:
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416:Volume 10.3:
415:
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409:Volume 10.2:
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402:Volume 10.1:
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381:Axiom Gallery
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351:Axiom Command
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1284:cite journal
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1199:
1193:
1171:(2): 20–30.
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1122:cite journal
1109:
1096:
1075:cite journal
1048:. Retrieved
1044:MathOverflow
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1023:. Retrieved
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794:. Retrieved
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199:Ralph Gomory
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26:Developer(s)
1987:Mathematica
1954:Proprietary
1851:Open-source
1806:SourceForge
1796:SourceForge
1768:SourceForge
1473:. RC 12794.
1422:. RC 12327.
560:hash tables
548:polynomials
521:Axiom uses
460:Volume 15:
453:Volume 13:
446:Volume 12:
439:Volume 11:
395:Volume 10:
379:Volume 8.1
363:Volume 7.1
287:Axiom is a
260:open-source
181:hierarchy.
2110:Categories
2053:Mathomatic
1338:: 409–416.
1278:: 383–408.
1116:: 457–476.
1103:. RC 3259.
1050:2023-02-10
1025:2023-02-10
791:Docker Hub
773:References
501:Philosophy
473:Bug List:
388:Volume 9:
372:Volume 8:
356:Volume 7:
349:Volume 6:
342:Volume 5:
335:Volume 4:
328:Volume 3:
321:Volume 2:
314:Volume 1:
307:Volume 0:
262:projects:
191:Scratchpad
103:Written in
92:Repository
78:2022-02-06
56:2015-11-13
1939:Xcas/Giac
1899:Macaulay2
1792:OpenAxiom
1600:0747-7171
1216:0098-3500
584:×
477:-Bug List
264:OpenAxiom
2082:Category
2043:LiveMath
1929:Singular
1924:SageMath
1909:Normaliz
1527:17700911
1494:. 640-M.
1224:18321863
1185:14537956
839:36788754
796:25 March
735:See also
649:editor.
629:Features
567:Fraction
2048:Macsyma
1982:Mathcad
1914:PARI/GP
1864:Cadabra
1272:MACSYMA
1001:YouTube
647:TeXmacs
203:Fortran
185:History
149:Website
138:License
76: (
54: (
45:Latest
2063:ALTRAN
2058:muMATH
2038:Erable
2033:Derive
1996:MATLAB
1919:Reduce
1904:Maxima
1879:FriCAS
1874:Fermat
1802:FriCAS
1764:Github
1598:
1559:
1525:
1515:
1454:
1435:
1403:
1222:
1214:
1183:
1069:42–58.
837:
544:fields
534:Design
523:Docker
489:Videos
269:FriCAS
256:forked
47:Docker
2028:CAMAL
1992:muPAD
1977:Maple
1972:Magma
1944:Yacas
1934:SymPy
1894:GiNaC
1869:CoCoA
1859:Axiom
1523:S2CID
1220:S2CID
1181:S2CID
835:S2CID
643:Emacs
556:trees
552:lists
540:rings
241:Axiom
169:is a
167:Axiom
20:Axiom
2094:List
1967:KANT
1884:FORM
1711:help
1685:help
1596:ISSN
1557:ISBN
1513:ISBN
1488:IMAG
1452:ISBN
1433:ISBN
1401:ISBN
1388:help
1362:help
1327:help
1297:help
1250:help
1212:ISSN
1135:help
1088:help
798:2022
609:A^-1
516:ACL2
514:and
266:and
171:free
158:.org
126:Type
107:Lisp
1889:GAP
1655:doi
1632:doi
1586:doi
1505:doi
1484:TIM
1204:doi
1173:doi
1152:doi
962:at
825:doi
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512:Coq
245:NAG
195:IBM
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