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247:(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)
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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.
651:
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
516:
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
1079:
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)":
1498:
1408:
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)
1315:
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
239:(IBM Research). Implementation included Robert Sutor (IBM Research), Scott C. Morrison (University of California, Berkeley), Christine J. Sundaresan (IBM Research), Timothy Daly (IBM Research),
1677:
Manuel
Bronstein (1989). "Simplification of real elementary functions | Proceedings of the International Symposium on Symbolic and Algebraic Computation (SIGSAM '89)". ACM: 207–211.
1380:
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.
1703:
Claire
Dicrescenzo; Dominique Duval (1989). P. Gianni (ed.). "Algebraic extensions and algebraic closure in Scratchpad II | Symbolic and Algebraic Computation". Springer: 440–446.
2126:
2131:
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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
636:
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.
1844:
608:
1354:
Richard D. Jenks (1984). "A primer: 11 keys to New
Scratchpad | Proceedings of International Symposium on Symbolic and Algebraic Computation '84". Springer: 123–147.
1756:
2141:
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629:
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.
1242:
Richard D. Jenks (1976). "A pattern compiler | Proceedings of the third ACM symposium on
Symbolic and algebraic manipulation (SYMSAC '76)": 60–65.
2136:
1837:
1119:
James H. Griesmer; Richard D. Jenks (1972). "Experience with an online symbolic mathematics system | Proceedings of the ONLINE72 Conference".
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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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Containers as part of a continuous release process. The latest image is available on any platform using docker and the commands:
221:
1982:
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1587:
1629:"Using Gröbner bases to determine algebra membership, split surjective algebra homomorphisms determine birational equivalence"
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1459:
Applications of a software interconnection system in mathematical problem solving environments | Proceedings of SYMSAC '86
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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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216:. The development of this software was stopped before any public release. The second Scratchpad, originally named
283:, following "serious disagreement about project goals". The Axiom project continued to be developed by Tim Daly.
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714:
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Programming with abstract data types: the symmetry package (SPDE) in Scratchpad | Trends in Computer Algebra
235:(IBM Research). Early consultants on the project were David Barton (University of California, Berkeley) and
185:
141:
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Application of SCRATCHPAD to problems in special functions and combinatorics | Trends in Computer Algebra
231:(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
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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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1345:
Richard D. Jenks (1984). "The New SCRATCHPAD Language and System for Computer Algebra".
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188:. It consists of an interpreter environment, a compiler and a library, which defines a
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302:. 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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2012:
313:
153:
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1051:"integration - Does there exist a complete implementation of the Risch algorithm?"
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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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George E. Andrews (1984). "Ramanujan and SCRATCHPAD | Proceedings of the 1984
1007:
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36:
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A fast implementation of polynomial factorization | Proceedings of SYMSAC '86
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Hans-J. Boehm (1989). "Type inference in the presence of type abstraction".
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website. The first video provides details on the Axiom information sources.
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208:. The first one was started in 1965 by James Griesmer at the request of
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1992:
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Scratchpad II: an abstract datatype system for mathematical computation
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213:
258:. In 2001, it was withdrawn from the market and re-released under the
243:(University of Pisa), Albrecht Fortenbacher (Universitaet Karlsruhe),
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2006:
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website. These volumes contain the actual source code of the system.
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Jenks, R.D. and Sutor, R. "Axiom, The Scientific Computation System"
2002:
1954:
1944:
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Computer Algebra: Systems and Algorithms for Algebraic Computation
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Ueberlegungen zur Implementierung eines Formelmanipulationssystems
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227:
The design is principally due to Richard D. Jenks (IBM Research),
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1491:
Scratchpad II: Présentation d'un nouveau langage de calcul formel
164:
1949:
1812:
1622:. Lecture Notes in Computer Science. Springer. pp. 167–176.
526:
1826:
1203:
Arthur C. Norman (1975). "Computing with Formal Power Series".
863:
262:. Since then, the project's lead developer has been Tim Daly.
205:
1763:
1489:
Pascale Sénéchaud; Françoise Siebert; Gilles Villard (1987).
974:
917:
1802:
935:
1425:
Richard D. Jenks; Robert S. Sutor; Stephen M. Watt (1986).
1558:
James H. Davenport; Yvon Siret; Evelyne Tournier (1993) .
1153:
James H. Griesmer; Richard D. Jenks (1972). "Scratchpad".
936:"FriCAS 18a5ef5d99c796a89efeac06df40043a85b3d44d — FriCAS"
561:) as well as data structures from computer science (e.g.,
371:—Source code and explanation of X11 Hyperdoc help browser
1274:
Technischen Universitat Carolo-Wilhelmina zu Braunschweig
672:
HyperDoc displaying the available operations for a domain
540:
docker pull daly/axiom docker run -i -t daly/axiom axiom
364:—Source code for system commands and scripts (incomplete)
1108:
META/PLUS - The Syntax Extension Facility for SCRATCHPAD
610:
matrices with rational entries would be constructed as
350:—Short essays on developer-specific topics (incomplete)
1027:"Manuel Bronstein on Axiom's Integration Capabilities"
918:"OpenAxiom: The Open Scientific Computation Platform"
590:
461:—Source code for Axiom Crystal front end (incomplete)
1174:
Richard D. Jenks (1974). "The SCRATCHPAD language".
290:, that is, logical, rational, judicious, and sound.
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1963:
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1008:"Axiom Computer Algebra System Information Sources"
159:
147:
135:
123:
113:
101:
75:
49:
35:
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1347:Proceedings of the 1984 MACSYMA Users' Conference
454:—Source pages for Axiom Firefox browser front end
343:—Guided examples of program writing (incomplete)
644:Within the interpreter environment, Axiom uses
357:—Source code for Axiom interpreter (incomplete)
224:, under the direction of Richard Dimick Jenks.
1583:"On an installation of Buchberger's algorithm"
410:—Essays on implementation issues (incomplete)
1838:
336:—Detailed examples of domain use (incomplete)
82:Sourceforge master / February 6, 2022
8:
1545:George E. Andrews (1988). R. Janssen (ed.).
30:
2127:Common Lisp (programming language) software
1581:Rüdiger Gebauer; H. Michael Möller (1988).
1406:Rüdiger Gebauer; H. Michael Möller (1986).
882:"Richard D. Jenks Biographical Information"
403:—Source code for Spad compiler (incomplete)
2132:Computer algebra system software for Linux
2099:
1845:
1831:
1823:
1476:William H. Burge; Stephen M. Watt (1987).
618:is interpreted as the identity matrix and
614:. Of course, when working in this domain,
29:
1646:
1600:
1206:ACM Transactions on Mathematical Software
839:
589:
1618:Fritz Schwarz (1988). R. Janssen (ed.).
1002:
1000:
387:—Source code for X11 Graphics subsystem
1272:(Masters thesis) (in German). Germany:
1025:Bronstein, Manuel (September 5, 2003).
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662:
309:The currently available documents are:
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828:ACM Communications in Computer Algebra
1627:David Shannon; Moss Sweedler (1988).
1438:Michael Lucks; Bruce W. Char (1986).
622:would give the inverse of the matrix
108:https://sourceforge.net/p/axiom/code/
7:
760:Free and open-source software portal
417:—Essays containing background theory
1793:Daly, T. "Axiom Volume 1: Tutorial"
1737:Timothy Daly "Axiom" Invited Talk,
1478:Infinite Structure in SCRATCHPAD II
737:Axiom has an implementation of the
200:Two computer algebra systems named
60:release / November 13, 2015
286:The current research direction is
25:
1757:Axiom (computer algebra software)
1551:Lecture Notes in Computer Science
1285:Users' Conference". Schenectady:
900:"EUROCAL '85 | SpringerLink"
708:Axiom simplifying a heat equation
612:SquareMatrix(4, Fraction Integer)
468:—Prove Axiom Algebra (incomplete)
424:—Source code for Axiom categories
269:twice, originating two different
220:, was developed from 1977 on, at
2142:Free software programmed in Lisp
2098:
2087:
2086:
1750:
1503:Grenoble Institute of Technology
1482:Thomas J. Watson Research Center
1431:Thomas J. Watson Research Center
1317:Thomas J. Watson Research Center
1112:Thomas J. Watson Research Center
778:List of computer algebra systems
752:
732:Axiom computing a Risch integral
725:
713:
701:
689:
677:
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222:Thomas J. Watson Research Center
1741:, Metz, France, July 9–12, 2003
1730:"Axiom -- Thirty Years of Lisp"
1634:Journal of Symbolic Computation
1588:Journal of Symbolic Computation
1497:(Research report) (in French).
987:"Axiom Computer Algebra System"
864:"Axiom Computer Algebra System"
696:Axiom Firefox Browser Interface
445:—Source code for Axiom numerics
438:—Source code for Axiom packages
378:—Source code for Hyperdoc pages
656:, as well as a plugin for the
431:—Source code for Axiom domains
1:
2137:Free computer algebra systems
1648:10.1016/s0747-7171(88)80047-6
1602:10.1016/s0747-7171(88)80048-8
1553:. Springer. pp. 159–166.
822:Fitch, John (July 23, 2012).
580:is a function, that takes an
18:Axiom computer algebra system
408:Axiom Algebra Implementation
2023:Engineering Equation Solver
1769:Online sandbox to try Axiom
975:axiom-developer.org website
824:"James Griesmer 1929--2011"
41:Independent group of people
2158:
1773:Source code repositories:
773:Aldor programming language
684:Axiom displaying a surface
394:—A Gallery of Axiom images
314:Combined Table of Contents
250:Scratchpad II was renamed
2082:
1442:. ACM. pp. 228–232.
1410:. ACM. pp. 218–221.
1106:Richard D. Jenks (1971).
971:Why Literate Programming?
720:Axiom matrix manipulation
603:{\displaystyle 4\times 4}
97:
45:
1854:Computer algebra systems
538:
495:—Useful function summary
422:Axiom Algebra Categories
1480:(Research report). IBM
1461:. ACM. pp. 16–23.
1429:(Research report). IBM
1188:10.1145/1086830.1086834
1110:(Research report). IBM
991:www.axiom-developer.org
841:10.1145/2338496.2338499
768:A# programming language
473:The Axiom SANE Compiler
341:Axiom Programmers Guide
186:computer algebra system
142:Computer algebra system
27:Computer algebra system
2009:symbolic math toolbox)
1739:Libre Software Meeting
1716:Cite journal requires
1690:Cite journal requires
1393:Cite journal requires
1367:Cite journal requires
1332:Cite journal requires
1302:Cite journal requires
1255:Cite journal requires
1140:Cite journal requires
1093:Cite journal requires
604:
481:—Literature references
443:Axiom Algebra Numerics
436:Axiom Algebra Packages
348:Axiom Developers Guide
329:—A simple introduction
1759:at Wikimedia Commons
1219:10.1145/355656.355660
1167:10.1145/942576.807019
605:
466:Proving Axiom Correct
429:Axiom Algebra Domains
320:Axiom Jenks and Sutor
84:; 2 years ago
62:; 8 years ago
1014:. November 30, 2008.
631:function overloading
588:
519:literate programming
493:Axiom Reference Card
415:Axiom Algebra Theory
376:Axiom Hyperdoc Pages
288:"Proving Axiom Sane"
260:Modified BSD License
154:Modified BSD License
1670:10.1145/74818.74835
1658:ACM SIGPLAN Notices
1520:10.1145/29650.29656
1457:J. Purtilo (1986).
1176:ACM SIGSAM Bulletin
1155:ACM SIGPLAN Notices
868:axiom-developer.org
506:axiom-developer.org
304:axiom-developer.org
265:In 2007, Axiom was
32:
1514:. pp. 56–63.
1268:E. Lueken (1977).
954:"History — FriCAS"
922:www.open-axiom.org
886:www.eecis.udel.edu
600:
479:Axiom Bibliography
322:—The main textbook
229:James H. Davenport
204:were developed by
184:, general-purpose
2114:
2113:
1755:Media related to
1529:978-0-89791-235-8
1468:978-0-89791-199-3
1449:978-0-89791-199-3
1417:978-0-89791-199-3
1125:Brunel University
1031:groups.google.com
798:"daly/axiom Tags"
355:Axiom Interpreter
334:Axiom Users Guide
237:James W. Thatcher
212:, and written in
175:
174:
16:(Redirected from
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1973:ClassPad Manager
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491:Reference Card:
305:
300:literate program
233:Victor S. Miller
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167:.axiom-developer
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125:Operating system
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1764:Axiom Homepage
1747:
1746:External links
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1718:|journal=
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1692:|journal=
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1664:(7): 192–206.
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459:Axiom Crystal
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452:Axiom Browser
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441:Volume 10.5:
440:
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434:Volume 10.4:
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427:Volume 10.3:
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420:Volume 10.2:
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413:Volume 10.1:
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392:Axiom Gallery
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362:Axiom Command
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1059:. Retrieved
1055:MathOverflow
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37:Developer(s)
1998:Mathematica
1965:Proprietary
1862:Open-source
1817:SourceForge
1807:SourceForge
1779:SourceForge
1484:. RC 12794.
1433:. RC 12327.
571:hash tables
559:polynomials
532:Axiom uses
471:Volume 15:
464:Volume 13:
457:Volume 12:
450:Volume 11:
406:Volume 10:
390:Volume 8.1
374:Volume 7.1
298:Axiom is a
271:open-source
192:hierarchy.
2121:Categories
2064:Mathomatic
1349:: 409–416.
1289:: 383–408.
1127:: 457–476.
1114:. RC 3259.
1061:2023-02-10
1036:2023-02-10
802:Docker Hub
784:References
512:Philosophy
484:Bug List:
399:Volume 9:
383:Volume 8:
367:Volume 7:
360:Volume 6:
353:Volume 5:
346:Volume 4:
339:Volume 3:
332:Volume 2:
325:Volume 1:
318:Volume 0:
273:projects:
202:Scratchpad
114:Written in
103:Repository
89:2022-02-06
67:2015-11-13
1950:Xcas/Giac
1910:Macaulay2
1803:OpenAxiom
1611:0747-7171
1227:0098-3500
595:×
488:-Bug List
275:OpenAxiom
2093:Category
2054:LiveMath
1940:Singular
1935:SageMath
1920:Normaliz
1538:17700911
1505:. 640-M.
1235:18321863
1196:14537956
850:36788754
807:25 March
746:See also
660:editor.
640:Features
578:Fraction
2059:Macsyma
1993:Mathcad
1925:PARI/GP
1875:Cadabra
1283:MACSYMA
1012:YouTube
658:TeXmacs
214:Fortran
196:History
160:Website
149:License
87: (
65: (
56:Latest
2074:ALTRAN
2069:muMATH
2049:Erable
2044:Derive
2007:MATLAB
1930:Reduce
1915:Maxima
1890:FriCAS
1885:Fermat
1813:FriCAS
1775:Github
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1570:
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1526:
1465:
1446:
1414:
1233:
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1080:42–58.
848:
555:fields
545:Design
534:Docker
500:Videos
280:FriCAS
267:forked
58:Docker
2039:CAMAL
2003:muPAD
1988:Maple
1983:Magma
1955:Yacas
1945:SymPy
1905:GiNaC
1880:CoCoA
1870:Axiom
1534:S2CID
1231:S2CID
1192:S2CID
846:S2CID
654:Emacs
567:trees
563:lists
551:rings
252:Axiom
180:is a
178:Axiom
31:Axiom
2105:List
1978:KANT
1895:FORM
1722:help
1696:help
1607:ISSN
1568:ISBN
1524:ISBN
1499:IMAG
1463:ISBN
1444:ISBN
1412:ISBN
1399:help
1373:help
1338:help
1308:help
1261:help
1223:ISSN
1146:help
1099:help
809:2022
620:A^-1
527:ACL2
525:and
277:and
182:free
169:.org
137:Type
118:Lisp
1900:GAP
1666:doi
1643:doi
1597:doi
1516:doi
1495:TIM
1215:doi
1184:doi
1163:doi
973:at
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256:NAG
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