%%% -*-BibTeX-*- %%% ==================================================================== %%% BibTeX-file{ %%% author = "Nelson H. F. Beebe", %%% version = "1.05", %%% date = "14 October 2017", %%% time = "10:24:02 MDT", %%% filename = "magma.bib", %%% address = "University of Utah %%% Department of Mathematics, 110 LCB %%% 155 S 1400 E RM 233 %%% Salt Lake City, UT 84112-0090 %%% USA", %%% telephone = "+1 801 581 5254", %%% FAX = "+1 801 581 4148", %%% URL = "http://www.math.utah.edu/~beebe", %%% checksum = "35106 2997 13002 138497", %%% email = "beebe at math.utah.edu, beebe at acm.org, %%% beebe at computer.org (Internet)", %%% codetable = "ISO/ASCII", %%% keywords = "bibliography; BibTeX; Cayley computer algebra %%% system; Magma computational computer algebra %%% system; symbolic algebra", %%% license = "public domain", %%% supported = "yes", %%% docstring = "This is a bibliography of publications about %%% the Magma computational algebra system, %%% developed at the University of Sydney, %%% Sydney, New South Wales, Australia. %%% %%% Magma replaces an earlier algebra system, %%% Cayley (1982--1993), and this bibliography %%% therefore also includes entries for %%% publications about Cayley. %%% %%% According to the history in the closing %%% remarks section of entry Bosma:1997:MAS, %%% Magma Version 1 was released at the end of %%% 1993, and Version 2 in 1996. In 2014, the %%% current version is 2.20. %%% %%% The developer Web site is at %%% %%% http://magma.maths.usyd.edu.au/magma/ %%% %%% At version 1.05, the year coverage looked %%% like this: %%% %%% 1984 ( 2) 1995 ( 3) 2006 ( 17) %%% 1985 ( 0) 1996 ( 3) 2007 ( 4) %%% 1986 ( 0) 1997 ( 3) 2008 ( 7) %%% 1987 ( 0) 1998 ( 0) 2009 ( 2) %%% 1988 ( 0) 1999 ( 2) 2010 ( 5) %%% 1989 ( 1) 2000 ( 1) 2011 ( 1) %%% 1990 ( 1) 2001 ( 3) 2012 ( 0) %%% 1991 ( 18) 2002 ( 1) 2013 ( 2) %%% 1992 ( 1) 2003 ( 4) 2014 ( 4) %%% 1993 ( 0) 2004 ( 0) 2015 ( 2) %%% 1994 ( 4) 2005 ( 1) %%% %%% Article: 41 %%% Book: 10 %%% InCollection: 22 %%% InProceedings: 7 %%% Manual: 3 %%% Misc: 2 %%% PhdThesis: 1 %%% Proceedings: 6 %%% %%% Total entries: 92 %%% %%% The Magma programming language is described %%% in entries Bosma:1997:MAS and %%% Bailey:2006:AML. %%% %%% Some indications of the broad scope of Magma %%% are given at links from %%% %%% http://magma.maths.usyd.edu.au/magma/citations/ %%% %%% That site says that about 4000 publications %%% have resulted from the use of Magma, but most %%% of those articles are not linked to Magma in %%% journal databases, making them hard to locate %%% and identify for possible future inclusion in %%% this bibliography. %%% %%% For acknowledging use of Magma in %%% publications, the developers request that you %%% cite either entry Bosma:1997:MAS or entry %%% Cannon:2014:HMF (or a similar entry for the %%% particular edition that you used). %%% %%% There is an online encyclopedia entry for %%% Magma at %%% %%% https://en.wikipedia.org/wiki/Magma_(computer_algebra_system) %%% %%% There is an important news story about it %%% here: %%% %%% http://www.simonsfoundation.org/features/foundation-news/foundation-supports-access-to-mathematical-software-package/ %%% %%% BibTeX citation tags are uniformly chosen %%% as name:year:abbrev, where name is the %%% family name of the first author or editor, %%% year is a 4-digit number, and abbrev is a %%% 3-letter condensation of important title %%% words. Citation tags were automatically %%% generated by software developed for the %%% BibNet Project. %%% %%% This bibliography is sorted by year, and %%% within each year, by author and title key, %%% with ``bibsort -byyear''. Cross-referenced %%% proceedings entries appear at the end, %%% because of a restriction in the current %%% BibTeX. %%% %%% Data for this bibliography have been %%% collected, and merged into BibTeX entries, %%% from numerous sources, including at least %%% these: %%% %%% * the University of Utah Mathematics %%% Department bibliography archives %%% %%% * the TeX User Group bibliography %%% archives %%% %%% * the Karlsruhe Computer Science %%% bibliography archives %%% %%% * the Karlsruhe virtual catalog at %%% http://www.ubka.uni-karlsruhe.de/kvk_en.html %%% %%% * the US Library of Congress catalog at %%% http://catalog.loc.gov/ %%% %%% * the author's cattobib utility, which %%% provides Z39.50 interfaces to many %%% large libraries around the world, at %%% http://www.math.utah.edu/pub/cattobib/ %%% %%% * the European Mathematical Society %%% Zentralblatt fuer Mathematik database %%% at http://zb.msri.org/ZMATH/zmath/en/ %%% %%% * the American Mathematical Society %%% MathSciNet database at %%% http://ams.rice.edu/mathscinet/search.html %%% %%% * the American Institute of Physics %%% Scitation database at %%% http://scitation.aip.org/search_scitation %%% %%% * the American Physical Society PROLA %%% database at %%% http://publish.aps.org/search %%% %%% * the Canadian Journal of Physics %%% database at %%% http://www.nrcresearchpress.com/search/advanced %%% %%% * the Europhysics journal archive at %%% http://www.europhysicsnews.org %%% %%% * the Nature journal archive at %%% http://www.nature.com/search/ %%% %%% * the Science journal archive at %%% http://www.sciencemag.org/search %%% %%% * the Springer journal database at %%% http://www.springer.com/?SGWID=0-102-13-0-0 %%% %%% * the Wiley journal database at %%% http://onlinelibrary.wiley.com/ %%% %%% * the JSTOR database at %%% http://www.jstor.org/, and %%% %%% * many online library catalogs, including %%% those of the British Library, the %%% Karlsruhe Virtual Library catalog, the %%% Cambridge University Library, the %%% Oxford University Library, the %%% University of California library %%% system, and the US Library of Congress. %%% %%% The checksum field above contains a CRC-16 %%% checksum as the first value, followed by the %%% equivalent of the standard UNIX wc (word %%% count) utility output of lines, words, and %%% characters. This is produced by Robert %%% Solovay's checksum utility.", %%% } %%% ====================================================================

@Preamble{"\input bibnames.sty " # "\input path.sty " # "\hyphenation{ }" }

%%% ==================================================================== %%% Acknowledgement abbreviations:

@String{ack-nhfb= "Nelson H. F. Beebe, University of Utah, Department of Mathematics, 110 LCB, 155 S 1400 E RM 233, Salt Lake City, UT 84112-0090, USA, Tel: +1 801 581 5254, FAX: +1 801 581 4148, e-mail: \path|beebe@math.utah.edu|, \path|beebe@acm.org|, \path|beebe@computer.org| (Internet), URL: \path|http://www.math.utah.edu/~beebe/|"}

%%% ==================================================================== %%% Institution abbreviations:

%%% ==================================================================== %%% Journal abbreviations:

@String{j-ACM-COMM-COMP-ALGEBRA= "ACM Communications in Computer Algebra"} @String{j-ARS-COMB= "Ars Combinatoria. The Canadian Journal of Combinatorics"} @String{j-COMMUN-ALGEBRA= "Communications in Algebra"} @String{j-EUROMATH-BULL= "Euromath Bulletin"} @String{j-ITAL-J-PURE-APPL-MATH= "Ital. J. Pure Appl. Math."} @String{j-J-SYMBOLIC-COMP= "Journal of Symbolic Computation"} @String{j-LECT-NOTES-COMP-SCI= "Lecture Notes in Computer Science"} @String{j-LMS-J-COMPUT-MATH= "LMS Journal of Computation and Mathematics"} @String{j-SIGSAM= "SIGSAM Bulletin (ACM Special Interest Group on Symbolic and Algebraic Manipulation)"}

%%% ==================================================================== %%% Publisher abbreviations:

@String{pub-ACM= "ACM Press"} @String{pub-ACM:adr= "New York, NY 10036, USA"} @String{pub-BIRKHAUSER= "Birkh{\"{a}}user"} @String{pub-BIRKHAUSER:adr= "Cambridge, MA, USA; Berlin, Germany; Basel, Switzerland"} @String{pub-CAMBRIDGE= "Cambridge University Press"} @String{pub-CAMBRIDGE:adr= "Cambridge, UK"} @String{pub-IEEE= "IEEE Computer Society Press"} @String{pub-IEEE:adr= "1109 Spring Street, Suite 300, Silver Spring, MD 20910, USA"} @String{pub-JOHNS-HOPKINS= "The Johns Hopkins University Press"} @String{pub-JOHNS-HOPKINS:adr= "Baltimore, MD, USA"} @String{pub-KLUWER= "Kluwer Academic Publishers Group"} @String{pub-KLUWER:adr= "Norwell, MA, USA, and Dordrecht, The Netherlands"} @String{pub-SV= "Springer-Verlag"} @String{pub-SV:adr= "Berlin, Germany~/ Heidelberg, Germany~/ London, UK~/ etc."} @String{pub-WILEY= "John Wiley"} @String{pub-WILEY:adr= "New York, NY, USA"}

%%% ==================================================================== %%% Series abbreviations:

@String{ser-LNCS= "Lecture Notes in Computer Science"}

%%% ==================================================================== %%% Bibliography entries, sorted by ascending year, and then by citation %%% label:

@Article{Anonymous:1984:PSM, author = "Anonymous", title = "Papers from {Symbolic Mathematical Systems and Their Effects on the Curriculum --- International Congress on Mathematical Education}", journal = j-SIGSAM, volume = "18", number = "4", pages = "1--62", month = nov # "\slash " # feb, year = "1984", CODEN = "SIGSBZ", ISSN = "0163-5824 (print), 1557-9492 (electronic)", ISSN-L = "0163-5824", bibdate = "Tue Jan 6 12:34:09 MST 1998", bibsource = "http://www.math.utah.edu/pub/tex/bib/magma.bib; http://www.math.utah.edu/pub/tex/bib/sigsam.bib", note = "Issue labeled vol. 18, no. 4, November 1984 (issue \#72) and vol. 19, no. 1, February 1985 (issue \#73).", acknowledgement = ack-nhfb, classification = "C0220 (Computing education and training); C7310 (Mathematics computing); C7810C (Computer-aided instruction)", conflocation = "Adelaide, SA, Australia; 24-30 Aug. 1984", conftitle = "Papers from Symbolic Mathematical Systems and Their Effects on the Curriculum --- International Congress on Mathematical Education", fjournal = "SIGSAM Bulletin (ACM Special Interest Group on Symbolic and Algebraic Manipulation)", issue = "72/73", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1000", keywords = "algebraic; algebraic algorithms; algorithms; Austrian schools; CAMP; Cayley; classroom experiences; complexity issues; computation; computer aided instruction; computer aided vector algebra; computer aided vector algebra system; computer algebra; computer-based-tools; congruent number; education; high schools; interactive formula; interactive formula manipulation; manipulation; maths education; muMath; self explanatory symbolic; self explanatory symbolic computation; symbol manipulation; symbolic computation; symbolic mathematics; system; teaching; teaching group theory; teaching project; undergraduate studies; University of Linz", } @Article{Cannon:1984:CTG, author = "John J. Cannon and Jim Richardson", title = "{Cayley}: teaching group theory by computer", journal = j-SIGSAM, volume = "18--19", number = "4--1", pages = "15--18", month = nov # "\slash " # feb, year = "1984", CODEN = "SIGSBZ", ISSN = "0163-5824 (print), 1557-9492 (electronic)", ISSN-L = "0163-5824", bibdate = "Wed Oct 5 08:31:59 MDT 2005", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/magma.bib; http://www.math.utah.edu/pub/tex/bib/sigsam.bib", acknowledgement = ack-nhfb, classcodes = "C1110 (Algebra); C1160 (Combinatorial mathematics); C7310 (Mathematics computing); C7810C (Computer-aided instruction)", classification = "C1110 (Algebra); C1160 (Combinatorial mathematics); C7310 (Mathematics computing); C7810C (Computer-aided instruction)", conflocation = "Adelaide, SA, Australia; 24-30 Aug. 1984", conftitle = "Papers from Symbolic Mathematical Systems and Their Effects on the Curriculum --- International Congress on Mathematical Education", corpsource = "Dept of Pure Math., Sydney Univ., NSW, Australia", fjournal = "SIGSAM Bulletin (ACM Special Interest Group on Symbolic and Algebraic Manipulation)", issue = "72/73", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1000", keywords = "CAI; calculator; computer aided instruction; courseware; design; group theory; manipulation; mathematical objects; problem library; problems file; Pure Mathematics; routine calculation; symbol; symbol manipulation; teaching; theory; tutorial computer programs", pubcountry = "USA A04", remark = "Issue labeled vol. 18, no. 4, November 1984 (issue \#72) and vol. 19, no. 1, February 1985 (issue \#73).", subject = "G.2 Mathematics of Computing, DISCRETE MATHEMATICS, Miscellaneous \\ J.2 Computer Applications, PHYSICAL SCIENCES AND ENGINEERING, Mathematics and statistics \\ K.3.2 Computing Milieux, COMPUTERS AND EDUCATION, Computer and Information Science Education, Curriculum", treatment = "G General Review", } @Article{Havel:1989:PGA, author = "T. F. Havel and B. Sturmfels and N. White", title = "Proposal for a geometric algebra software package", journal = j-SIGSAM, volume = "23", number = "1", pages = "13--15", month = jan, year = "1989", CODEN = "SIGSBZ", ISSN = "0163-5824 (print), 1557-9492 (electronic)", ISSN-L = "0163-5824", bibdate = "Fri Feb 8 18:27:00 MST 2002", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/magma.bib; http://www.math.utah.edu/pub/tex/bib/sigsam.bib", acknowledgement = ack-nhfb, classcodes = "C4130 (Interpolation and function approximation); C7310 (Mathematics)", corpsource = "Dept. of Molecular Biol., Res. Inst. of Scripps Clinic, La Jolla, CA, USA", fjournal = "SIGSAM Bulletin (ACM Special Interest Group on Symbolic and Algebraic Manipulation)", issue = "87", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1000", keywords = "algebra; bracket; Cayley algebra; Cayley-Grassmann algebra; computational geometry; computing; coordinate-free algebra; design; geometric algebra software package; linear algebra; mathematics; theory", subject = "D.3.3 Software, PROGRAMMING LANGUAGES, Language Constructs, Modules, packages \\ F.2.2 Theory of Computation, ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY, Nonnumerical Algorithms and Problems, Geometrical problems and computations", treatment = "P Practical", } @Article{Schneider:1990:CER, author = "Gerhard J. A. Schneider", title = "Computing with Endomorphism Rings of Modular Representations", journal = j-J-SYMBOLIC-COMP, volume = "9", number = "5--6", pages = "607--636", month = may # "--" # jun, year = "1990", CODEN = "JSYCEH", ISSN = "0747-7171 (print), 1095-855X (electronic)", ISSN-L = "0747-7171", MRclass = "20C40 (20C05 20C20)", MRnumber = "92a:20015", MRreviewer = "Shigeo Koshitani", bibdate = "Sat May 10 15:54:09 MDT 1997", bibsource = "http://www.math.utah.edu/pub/tex/bib/jsymcomp.bib; http://www.math.utah.edu/pub/tex/bib/magma.bib", note = "Computational group theory, Part I.", acknowledgement = ack-nhfb, classcodes = "C6130 (Data handling techniques); C7310 (Mathematics)", corpsource = "Inst. fur Exp. Math., Essen Univ., West Germany", fjournal = "Journal of Symbolic Computation", journal-URL = "http://www.sciencedirect.com/science/journal/07477171/", keywords = "algorithms; CAYLEY; endomorphism rings; indecomposability; mathematics computing; modular representations; properties; sources; symbol manipulation; system; vertices", treatment = "P Practical", } @Article{Anonymous:1991:PTC, author = "Anonymous", title = "Proceedings of the {Third CAYLEY Users Conference, November 17--19, 1988, Universit{\"a}t Essen}", journal = j-SIGSAM, volume = "25", number = "1", pages = "25--81", month = jan, year = "1991", CODEN = "SIGSBZ", ISSN = "0163-5824 (print), 1557-9492 (electronic)", ISSN-L = "0163-5824", bibdate = "Thu Mar 20 16:02:15 MST 1997", bibsource = "http://www.math.utah.edu/pub/tex/bib/magma.bib; http://www.math.utah.edu/pub/tex/bib/sigsam.bib", acknowledgement = ack-nhfb, classcodes = "C7310 (Mathematics); C1110 (Algebra); C4140 (Linear algebra)", conflocation = "Essen, West Germany; 17-19 Nov. 1988", conftitle = "Third CAYLEY Users Conference", fjournal = "SIGSAM Bulletin (ACM Special Interest Group on Symbolic and Algebraic Manipulation)", issue = "95", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1000", keywords = "2-modular representations; algebra; CAYLEY; character degrees; character tables; common data; commutativity; computer algebra system; conjugacy classes; descriptions; group; group ring package; group theory; high level language; mathematics computing; matrix; maximal; normal subgroups; p-groups; permutations; power-commutator; presentations; representation theory; simple groups; structures; subgroups; Sylow subgroups; symbol manipulation; symplectic groups; vertex-transitive graphs; Wielandt length", treatment = "P Practical; T Theoretical or Mathematical; X Experimental", } @Article{Cannon:1991:BCC, author = "John Cannon", title = "A bibliography of {Cayley} citations", journal = j-SIGSAM, volume = "25", number = "1", pages = "75--81", month = jan, year = "1991", CODEN = "SIGSBZ", ISSN = "0163-5824 (print), 1557-9492 (electronic)", ISSN-L = "0163-5824", bibdate = "Fri Feb 8 18:27:01 MST 2002", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/magma.bib; http://www.math.utah.edu/pub/tex/bib/sigsam.bib", acknowledgement = ack-nhfb, classcodes = "C1110 (Algebra); C7310 (Mathematics); C4140 (Linear algebra)", conflocation = "Essen, West Germany; 17-19 Nov. 1988", conftitle = "Third CAYLEY Users Conference", fjournal = "SIGSAM Bulletin (ACM Special Interest Group on Symbolic and Algebraic Manipulation)", issue = "95", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1000", keywords = "algebra; CAYLEY; computational; computer algebra system; group theory; mathematical research; mathematics computing; matrix; symbol manipulation", treatment = "B Bibliography", } @Article{Dockx:1991:CTC, author = "Kris Dockx and Paul Igodt", title = "Character tables and commutativity of normal subgroups", journal = j-SIGSAM, volume = "25", number = "1", pages = "28--31", month = jan, year = "1991", CODEN = "SIGSBZ", ISSN = "0163-5824 (print), 1557-9492 (electronic)", ISSN-L = "0163-5824", bibdate = "Fri Feb 8 18:27:01 MST 2002", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/magma.bib; http://www.math.utah.edu/pub/tex/bib/sigsam.bib", acknowledgement = ack-nhfb, classcodes = "C1110 (Algebra); C7310 (Mathematics)", conflocation = "Essen, West Germany; 17-19 Nov. 1988", conftitle = "Third CAYLEY Users Conference", corpsource = "Katholieke Univ. Leuven, Kortrijk, Belgium", fjournal = "SIGSAM Bulletin (ACM Special Interest Group on Symbolic and Algebraic Manipulation)", issue = "95", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1000", keywords = "abelian; CAYLEY; character table; conjugate classes; finite groups; group theory; mathematics computing; normal subgroup; permutation characters; symbol manipulation", treatment = "T Theoretical or Mathematical; X Experimental", } @Article{Glasby:1991:EGD, author = "S. P. Glasby", title = "Extensions of groups defined by power-commutator presentations", journal = j-SIGSAM, volume = "25", number = "1", pages = "32--35", month = jan, year = "1991", CODEN = "SIGSBZ", ISSN = "0163-5824 (print), 1557-9492 (electronic)", ISSN-L = "0163-5824", bibdate = "Fri Feb 8 18:27:01 MST 2002", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/magma.bib; http://www.math.utah.edu/pub/tex/bib/sigsam.bib", acknowledgement = ack-nhfb, classcodes = "C7310 (Mathematics); C1110 (Algebra)", conflocation = "Essen, West Germany; 17-19 Nov. 1988", conftitle = "Third CAYLEY Users Conference", corpsource = "Dept. of Math., Victoria Univ. of Wellington, New Zealand", fjournal = "SIGSAM Bulletin (ACM Special Interest Group on Symbolic and Algebraic Manipulation)", issue = "95", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1000", keywords = "AG-; algebra; Auflosbare Gruppen; CAYLEY; divisor; finite soluble group; group theory; group-theory language; manipulation; mathematics computing; pc-presentation group; power-commutator presentations; symbol; system", treatment = "P Practical; T Theoretical or Mathematical", } @Article{Gollan:1991:MRP, author = "Holger W. Gollan", title = "The $2$-modular representation of {$ J_1$} in the principal block", journal = j-SIGSAM, volume = "25", number = "1", pages = "36--39", month = jan, year = "1991", CODEN = "SIGSBZ", ISSN = "0163-5824 (print), 1557-9492 (electronic)", ISSN-L = "0163-5824", bibdate = "Fri Feb 8 18:27:01 MST 2002", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/magma.bib; http://www.math.utah.edu/pub/tex/bib/sigsam.bib", acknowledgement = ack-nhfb, classcodes = "C7310 (Mathematics); C1110 (Algebra); C4140 (Linear algebra)", conflocation = "Essen, West Germany; 17-19 Nov. 1988", conftitle = "Third CAYLEY Users Conference", corpsource = "Inst. for Exp. Math., Essen Univ., West Germany", fjournal = "SIGSAM Bulletin (ACM Special Interest Group on Symbolic and Algebraic Manipulation)", issue = "95", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1000", keywords = "algebra; CAYLEY-procedures; finite group; Green-correspondents; group theory; mathematics computing; matrix; modular irreducible modules; modular representation theory; p-; prime; sources; symbol manipulation; vertices", treatment = "T Theoretical or Mathematical", } @Article{Grams:1991:SGR, author = "Gerhard Grams", title = "Special generators and relations for some orthogonal and symplectic groups over {GF(2)}", journal = j-SIGSAM, volume = "25", number = "1", pages = "39--45", month = jan, year = "1991", CODEN = "SIGSBZ", ISSN = "0163-5824 (print), 1557-9492 (electronic)", ISSN-L = "0163-5824", bibdate = "Fri Feb 8 18:27:01 MST 2002", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/magma.bib; http://www.math.utah.edu/pub/tex/bib/sigsam.bib", acknowledgement = ack-nhfb, classcodes = "C7310 (Mathematics); C1110 (Algebra); C4140 (Linear algebra)", conflocation = "Essen, West Germany; 17-19 Nov. 1988", conftitle = "Third CAYLEY Users Conference", corpsource = "Math. Inst., Giessen, Germany", fjournal = "SIGSAM Bulletin (ACM Special Interest Group on Symbolic and Algebraic Manipulation)", issue = "95", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1000", keywords = "algebra; CAYLEY; Coxeter graph; Coxeter groups; epimorphic images; group theory; infinite; isomorphism classes; manipulation; mathematics computing; special finite quotients; symbol; symplectic groups; Todd--Coxeter-algorithm", treatment = "P Practical; T Theoretical or Mathematical", } @InProceedings{Havas:1991:CES, author = "George Havas", title = "Coset enumeration strategies", crossref = "Watt:1991:IPI", pages = "191--199", year = "1991", bibdate = "Thu Mar 12 08:38:03 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib; http://www.math.utah.edu/pub/tex/bib/magma.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/120694/p191-havas/", abstract = "A primary reference on computer implementation of coset enumeration procedures is a 1973 paper of Cannon, Dimino, Havas and Watson. Programs and techniques described there are updated in this paper. Improved coset definition strategies, space saving techniques and advice for obtaining improved performance are included. New coset definition strategies for Felsch-type methods give substantial reductions in total cosets defined for some pathological enumerations. Significant time savings are achieved for coset enumeration procedures in general. Statistics on performance are presented, both in terms of time and in terms of maximum and total cosets defined for selected enumerations.", acknowledgement = ack-nhfb, affiliation = "Dept. of Comput. Sci., Queensland Univ., St. Lucia, Qld., Australia", classification = "C1160 (Combinatorial mathematics); C7310 (Mathematics)", keywords = "Coset definition strategies; Coset enumeration procedures; Felsch-type methods; Pathological enumerations; performance; Subgroups", subject = "{\bf I.1.0} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, General. {\bf G.2.m} Mathematics of Computing, DISCRETE MATHEMATICS, Miscellaneous. {\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, CAYLEY.", thesaurus = "Mathematics computing; Set theory", } @Article{Jamali:1991:LSG, author = "A. R. Jamali and E. F. Robertson", title = "A library of simple groups: permutations, presentations, conjugacy classes, maximal subgroups and {Sylow} subgroups", journal = j-SIGSAM, volume = "25", number = "1", pages = "46--49", month = jan, year = "1991", CODEN = "SIGSBZ", ISSN = "0163-5824 (print), 1557-9492 (electronic)", ISSN-L = "0163-5824", bibdate = "Fri Feb 8 18:27:01 MST 2002", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/magma.bib; http://www.math.utah.edu/pub/tex/bib/sigsam.bib", acknowledgement = ack-nhfb, classcodes = "C7310 (Mathematics); C1110 (Algebra); C4140 (Linear algebra)", conflocation = "Essen, West Germany; 17-19 Nov. 1988", conftitle = "Third CAYLEY Users Conference", corpsource = "Math. Inst., St. Andrews Univ., UK", fjournal = "SIGSAM Bulletin (ACM Special Interest Group on Symbolic and Algebraic Manipulation)", issue = "95", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1000", keywords = "conjugacy classes; group theory; mathematics computing; maximal subgroups; Sylow subgroups; symbol manipulation", treatment = "P Practical", } @Article{McMillan:1991:DSA, author = "Tim McMillan and Neil L. White", title = "The Dotted Straightening Algorithm", journal = j-J-SYMBOLIC-COMP, volume = "11", number = "5--6", pages = "471--482", month = may # "--" # jun, year = "1991", CODEN = "JSYCEH", ISSN = "0747-7171 (print), 1095-855X (electronic)", ISSN-L = "0747-7171", MRclass = "68Q40", MRnumber = "92e:68087", bibdate = "Sat May 10 15:54:09 MDT 1997", bibsource = "http://www.math.utah.edu/pub/tex/bib/jsymcomp.bib; http://www.math.utah.edu/pub/tex/bib/magma.bib", note = "Invariant-theoretic algorithms in geometry (Minneapolis, MN, 1987).", acknowledgement = ack-nhfb, classcodes = "C4130 (Interpolation and function approximation)", corpsource = "Dept. of Math., Florida Univ., Gainesville, FL, USA", fjournal = "Journal of Symbolic Computation", journal-URL = "http://www.sciencedirect.com/science/journal/07477171/", keywords = "bracket polynomial; Cayley algebra; dotted bracket expression; dotted straightening algorithm; homogeneous; polynomials; symbol manipulation", treatment = "T Theoretical or Mathematical", } @Article{Newman:1991:WLS, author = "M. F. Newman and E. A. O'Brien", title = "The {Wielandt} length of some $3$-groups", journal = j-SIGSAM, volume = "25", number = "1", pages = "50--51", month = jan, year = "1991", CODEN = "SIGSBZ", ISSN = "0163-5824 (print), 1557-9492 (electronic)", ISSN-L = "0163-5824", bibdate = "Fri Feb 8 18:27:01 MST 2002", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/magma.bib; http://www.math.utah.edu/pub/tex/bib/sigsam.bib", acknowledgement = ack-nhfb, classcodes = "C7310 (Mathematics); C1110 (Algebra); C4140 (Linear algebra)", conflocation = "Essen, West Germany; 17-19 Nov. 1988", conftitle = "Third CAYLEY Users Conference", corpsource = "Sch. of Math. Sci., Australian Nat. Univ., Canberra, ACT, Australia", fjournal = "SIGSAM Bulletin (ACM Special Interest Group on Symbolic and Algebraic Manipulation)", issue = "95", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1000", keywords = "CAYLEY; group theory; machine-aided computation; mathematics computing; Nilpotent Quotient Program; symbol manipulation; Wielandt length", treatment = "P Practical; T Theoretical or Mathematical", } @Article{OBrien:1991:PEA, author = "E. A. O'Brien", title = "Providing electronic access to group descriptions", journal = j-SIGSAM, volume = "25", number = "1", pages = "52--56", month = jan, year = "1991", CODEN = "SIGSBZ", ISSN = "0163-5824 (print), 1557-9492 (electronic)", ISSN-L = "0163-5824", bibdate = "Fri Feb 8 18:27:01 MST 2002", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/magma.bib; http://www.math.utah.edu/pub/tex/bib/sigsam.bib", acknowledgement = ack-nhfb, classcodes = "C7310 (Mathematics); C1110 (Algebra); C4140 (Linear algebra)", conflocation = "Essen, West Germany; 17-19 Nov. 1988", conftitle = "Third CAYLEY Users Conference", corpsource = "Marquette Univ., Milwaukee, WI, USA", fjournal = "SIGSAM Bulletin (ACM Special Interest Group on Symbolic and Algebraic Manipulation)", issue = "95", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1000", keywords = "CAYLEY; GPS256; group descriptions; group theory; manipulation; mathematics computing; matrix algebra; p-group generation algorithm; symbol; TWOGPS", treatment = "P Practical; T Theoretical or Mathematical", } @Article{Royle:1991:CVT, author = "Gordon F. Royle", title = "Constructing the vertex-transitive graphs on 24 vertices", journal = j-SIGSAM, volume = "25", number = "1", pages = "56--59", month = jan, year = "1991", CODEN = "SIGSBZ", ISSN = "0163-5824 (print), 1557-9492 (electronic)", ISSN-L = "0163-5824", bibdate = "Fri Feb 8 18:27:01 MST 2002", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/magma.bib; http://www.math.utah.edu/pub/tex/bib/sigsam.bib", acknowledgement = ack-nhfb, classcodes = "C7310 (Mathematics); C1110 (Algebra); C4140 (Linear algebra); C1160 (Combinatorial mathematics)", conflocation = "Essen, West Germany; 17-19 Nov. 1988", conftitle = "Third CAYLEY Users Conference", corpsource = "Dept. of Math., Univ. of Western Australia, Nedlands, WA, Australia", fjournal = "SIGSAM Bulletin (ACM Special Interest Group on Symbolic and Algebraic Manipulation)", issue = "95", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1000", keywords = "doubly; graph theory; group theory; manipulation; mathematics computing; smallest non-trivial block system; symbol; transitive; twenty-four vertices; vertex-transitive graphs", treatment = "T Theoretical or Mathematical; X Experimental", } @Article{Sandling:1991:GRP, author = "Robert Sandling", title = "A group ring package for {Cayley}", journal = j-SIGSAM, volume = "25", number = "1", pages = "60--64", month = jan, year = "1991", CODEN = "SIGSBZ", ISSN = "0163-5824 (print), 1557-9492 (electronic)", ISSN-L = "0163-5824", bibdate = "Fri Feb 8 18:27:01 MST 2002", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/magma.bib; http://www.math.utah.edu/pub/tex/bib/sigsam.bib", acknowledgement = ack-nhfb, classcodes = "C7310 (Mathematics); C1110 (Algebra); C4140 (Linear algebra)", conflocation = "Essen, West Germany; 17-19 Nov. 1988", conftitle = "Third CAYLEY Users Conference", corpsource = "Dept. of Math., Manchester Univ., UK", fjournal = "SIGSAM Bulletin (ACM Special Interest Group on Symbolic and Algebraic Manipulation)", issue = "95", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1000", keywords = "arithmetic operations; CAYLEY; group ring facility; group theory; mathematics computing; structural investigations; symbol manipulation", treatment = "T Theoretical or Mathematical", } @Article{Schneider:1991:RTC, author = "Gerhard J. A. Schneider", title = "Representation theory in {CAYLEY}: tools and algorithms", journal = j-SIGSAM, volume = "25", number = "1", pages = "64--70", month = jan, year = "1991", CODEN = "SIGSBZ", ISSN = "0163-5824 (print), 1557-9492 (electronic)", ISSN-L = "0163-5824", bibdate = "Fri Feb 8 18:27:01 MST 2002", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/magma.bib; http://www.math.utah.edu/pub/tex/bib/sigsam.bib", acknowledgement = ack-nhfb, classcodes = "C7310 (Mathematics); C1110 (Algebra); C4140 (Linear algebra)", conflocation = "Essen, West Germany; 17-19 Nov. 1988", conftitle = "Third CAYLEY Users Conference", corpsource = "Inst. fur Experimentelle Math., Essen Univ., Germany", fjournal = "SIGSAM Bulletin (ACM Special Interest Group on Symbolic and Algebraic Manipulation)", issue = "95", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1000", keywords = "abstract; CAYLEY; computer algebra; field; group; group theory; manipulation; mathematics computing; matrix algebra; matrix group; representation theory; symbol; vector space", treatment = "P Practical; T Theoretical or Mathematical", } @Article{Slattery:1991:CDG, author = "Michael C. Slattery", title = "Character degrees of $p$-groups: a case study", journal = j-SIGSAM, volume = "25", number = "1", pages = "71--74", month = jan, year = "1991", CODEN = "SIGSBZ", ISSN = "0163-5824 (print), 1557-9492 (electronic)", ISSN-L = "0163-5824", bibdate = "Fri Feb 8 18:27:01 MST 2002", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/magma.bib; http://www.math.utah.edu/pub/tex/bib/sigsam.bib", acknowledgement = ack-nhfb, classcodes = "C1110 (Algebra); C7310 (Mathematics); C4140 (Linear algebra)", conflocation = "Essen, West Germany; 17-19 Nov. 1988", conftitle = "Third CAYLEY Users Conference", corpsource = "Marquette Univ., Milwaukee, WI, USA", fjournal = "SIGSAM Bulletin (ACM Special Interest Group on Symbolic and Algebraic Manipulation)", issue = "95", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1000", keywords = "algebra; derived; finite p-group; group theory; irreducible character degrees; length; mathematics computing; matrix; symbol manipulation", treatment = "P Practical; T Theoretical or Mathematical", } @Article{Sturmfels:1991:SFP, author = "Bernd Sturmfels and Walter Whiteley", title = "On the Synthetic Factorization of Projectively Invariant Polynomials", journal = j-J-SYMBOLIC-COMP, volume = "11", number = "5--6", pages = "439--454 (or 439--453??)", month = may # "--" # jun, year = "1991", CODEN = "JSYCEH", ISSN = "0747-7171 (print), 1095-855X (electronic)", ISSN-L = "0747-7171", MRclass = "68Q40", MRnumber = "92i:68075", MRreviewer = "Timothy Stokes", bibdate = "Sat May 10 15:54:09 MDT 1997", bibsource = "http://www.math.utah.edu/pub/tex/bib/jsymcomp.bib; http://www.math.utah.edu/pub/tex/bib/magma.bib", note = "Invariant-theoretic algorithms in geometry (Minneapolis, MN, 1987).", acknowledgement = ack-nhfb, classcodes = "C4130 (Interpolation and function approximation); C4290 (Other computer theory); C1230 (Artificial intelligence)", corpsource = "Dept. of Math., Cornell Univ., Ithaca, NY, USA", fjournal = "Journal of Symbolic Computation", journal-URL = "http://www.sciencedirect.com/science/journal/07477171/", keywords = "algorithm; automated geometry theorem proving; Cayley algebra; computational geometry; explicit; homogeneous bracket polynomial; polynomial functions; polynomials; projective geometry; projectively invariant polynomials; spatial reasoning; symbol manipulation; synthetic constructions; synthetic factorization; theorem proving", treatment = "T Theoretical or Mathematical", } @Article{White:1991:MCF, author = "Neil L. White", title = "Multilinear {Cayley} factorization", journal = j-J-SYMBOLIC-COMP, volume = "11", number = "5--6", pages = "421--438", month = may # "--" # jun, year = "1991", CODEN = "JSYCEH", ISSN = "0747-7171 (print), 1095-855X (electronic)", ISSN-L = "0747-7171", MRclass = "68Q40 (03B35 68U05)", MRnumber = "92i:68074", MRreviewer = "Timothy Stokes", bibdate = "Sat May 10 15:54:09 MDT 1997", bibsource = "http://www.math.utah.edu/pub/tex/bib/jsymcomp.bib; http://www.math.utah.edu/pub/tex/bib/magma.bib", note = "Invariant-theoretic algorithms in geometry (Minneapolis, MN, 1987).", acknowledgement = ack-nhfb, classcodes = "C4130 (Interpolation and function approximation); C4290 (Other computer theory); C1230 (Artificial intelligence)", corpsource = "Dept. of Math., Florida Univ., Gainesville, FL, USA", fjournal = "Journal of Symbolic Computation", journal-URL = "http://www.sciencedirect.com/science/journal/07477171/", keywords = "algebraic expressions; bracket algebra; Cayley algebra; Cayley factorization problem; computational geometry; computer-aided geometric reasoning; geometric; homogeneous bracket; interpretations; polynomial; polynomials; projective geometry; spatial reasoning; symbol manipulation", treatment = "T Theoretical or Mathematical", } @Article{Richardson:1992:BBP, author = "J. Richardson", title = "The {Blockhandler} and the {Bitfield} package", journal = j-J-SYMBOLIC-COMP, volume = "14", number = "1", pages = "93--102 (or 93--101??)", month = jul, year = "1992", CODEN = "JSYCEH", ISSN = "0747-7171 (print), 1095-855X (electronic)", ISSN-L = "0747-7171", bibdate = "Wed Mar 19 13:51:24 MST 1997", bibsource = "http://www.math.utah.edu/pub/tex/bib/jsymcomp.bib; http://www.math.utah.edu/pub/tex/bib/magma.bib", acknowledgement = ack-nhfb, classcodes = "C6120 (File organisation); C7310 (Mathematics)", corpsource = "Sch. of Math. and Stat., Sydney Univ., NSW, Australia", fjournal = "Journal of Symbolic Computation", journal-URL = "http://www.sciencedirect.com/science/journal/07477171/", keywords = "Bitfield package; Blockhandler; C; Cayley; computer algebra system; data access; garbage collection; implementation; indirect; memory management; programming interface; reference; storage management; symbol manipulation", treatment = "P Practical", } @InProceedings{Bosma:1994:PAS, author = "Wieb Bosma and John Cannon and Graham Matthews", title = "Programming with algebraic structures: design of the {Magma} language", crossref = "ACM:1994:IPI", pages = "52--57", year = "1994", bibdate = "Thu Mar 12 08:41:19 MST 1998", bibsource = "http://www.acm.org/pubs/toc/; http://www.math.utah.edu/pub/tex/bib/issac.bib; http://www.math.utah.edu/pub/tex/bib/magma.bib", URL = "http://www.acm.org:80/pubs/citations/proceedings/issac/190347/p52-bosma/", abstract = "MAGMA is a new software system for computational algebra, number theory and geometry whose design is centred on the concept of algebraic structure (magma). The use of algebraic structure as a design paradigm provides a natural strong typing mechanism. Further, structures and their morphisms appear in the language as first class objects. Standard mathematical notions are used for the basic data types. The result is a powerful, clean language which deals with objects in a mathematically rigorous manner. The conceptual and implementation ideas behind MAGMA will be examined in this paper. This conceptual base differs significantly from those underlying other computer algebra systems.", acknowledgement = ack-nhfb, affiliation = "Sch. of Math., Sydney Univ., NSW, Australia", classification = "C1160 (Combinatorial mathematics); C6110 (Systems analysis and programming); C6130 (Data handling techniques); C7310 (Mathematics computing)", keywords = "Algebraic structures; algorithms; Computational algebra; Computer algebra systems; Data types; design; Magma language; Mathematical notions; Number theory; Software system; Strong typing mechanism", subject = "{\bf I.1.3} Computing Methodologies, SYMBOLIC AND ALGEBRAIC MANIPULATION, Languages and Systems, Special-purpose algebraic systems. {\bf D.3.3} Software, PROGRAMMING LANGUAGES, Language Constructs and Features, Data types and structures. {\bf F.3.3} Theory of Computation, LOGICS AND MEANINGS OF PROGRAMS, Studies of Program Constructs, Type structure. {\bf D.3.2} Software, PROGRAMMING LANGUAGES, Language Classifications, C.", thesaurus = "Number theory; Programming; Symbol manipulation", } @Article{Dehon:1994:CGC, author = "Michel Dehon", title = "Classifying Geometries with {Cayley}", journal = j-J-SYMBOLIC-COMP, volume = "17", number = "3", pages = "259--276", month = mar, year = "1994", CODEN = "JSYCEH", ISSN = "0747-7171 (print), 1095-855X (electronic)", ISSN-L = "0747-7171", MRclass = "51E24 (51-04)", MRnumber = "95f:51007", MRreviewer = "Gernot Stroth", bibdate = "Sat May 10 15:54:09 MDT 1997", bibsource = "http://www.math.utah.edu/pub/tex/bib/jsymcomp.bib; http://www.math.utah.edu/pub/tex/bib/magma.bib", acknowledgement = ack-nhfb, classcodes = "C4260 (Computational geometry)", corpsource = "Dept. de Math., Univ. Libre de Bruxelles, Belgium", fjournal = "Journal of Symbolic Computation", journal-URL = "http://www.sciencedirect.com/science/journal/07477171/", keywords = "computational geometry; geometrical objects; geometries classification; group; Hall-Janko", treatment = "T Theoretical or Mathematical", } @Article{Lucchini:1994:CSG, author = "Andrea Lucchini and Federico Menegazzo", title = "Computing a Set of Generators of Minimal Cardinality in a Solvable Group", journal = j-J-SYMBOLIC-COMP, volume = "17", number = "5", pages = "409--420", month = may, year = "1994", CODEN = "JSYCEH", ISSN = "0747-7171 (print), 1095-855X (electronic)", ISSN-L = "0747-7171", MRclass = "20D10 (20-04 68Q40)", MRnumber = "95e:20030", bibdate = "Sat May 10 15:54:09 MDT 1997", bibsource = "http://www.math.utah.edu/pub/tex/bib/jsymcomp.bib; http://www.math.utah.edu/pub/tex/bib/magma.bib", acknowledgement = ack-nhfb, classcodes = "C7310 (Mathematics); C6130 (Data handling techniques)", corpsource = "Dipartimento di Matematica Pura e Applicata, Padova Univ., Italy", fjournal = "Journal of Symbolic Computation", journal-URL = "http://www.sciencedirect.com/science/journal/07477171/", keywords = "CAYLEY V.3.7.2; chief series; minimal cardinality; polycyclic presentation; procedures; set of generators; solvable group; symbol manipulation", treatment = "P Practical; T Theoretical or Mathematical", } @InCollection{Bosma:1995:CCP, author = "Wieb Bosma", booktitle = "Computational algebra and number theory ({Sydney}, 1992)", title = "Computation of cyclotomic polynomials with {Magma}", volume = "325", publisher = pub-KLUWER, address = pub-KLUWER:adr, pages = "213--225", year = "1995", MRclass = "11R18 (11T06 11Y40)", MRnumber = "1344932 (96j:11142)", MRreviewer = "Aleksander Grytczuk", bibdate = "Sat Aug 9 16:07:25 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/magma.bib", series = "Math. Appl.", acknowledgement = ack-nhfb, } @Manual{Bosma:1995:SPM, author = "W. Bosma and J. J. Cannon and C. Playoust and A. Steel", title = "Solving Problems with {Magma}", organization = "School of Mathematics and Statistics, University of Sydney", address = "Sydney, NSW, Australia", year = "1995", bibdate = "Tue Aug 12 08:39:49 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/magma.bib", acknowledgement = ack-nhfb, } @InProceedings{Waki:1995:IM, author = "Katsushi Waki", editor = "Matu-Tarow Noda", booktitle = "Research on the theory and applications of computer algebra. Proceedings of a symposium held at the Research Institute for Mathematical Sciences, Kyoto University, Kyoto, Japan, November 16--18, 1994", title = "An introduction to {Magma}", volume = "920", publisher = "Kyoto University", address = "Kyoto, Japan", pages = "173--179", year = "1995", bibdate = "Tue Aug 12 09:45:51 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/magma.bib", series = "RIMS Kokyuroku", acknowledgement = ack-nhfb, language = "Japanese", } @Manual{Bosma:1996:HMF, author = "W. Bosma and J. J. Cannon", title = "Handbook of {Magma} Functions", organization = "School of Mathematics and Statistics, University of Sydney", address = "Sydney, NSW, Australia", year = "1996", bibdate = "Tue Aug 12 08:36:49 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/magma.bib", acknowledgement = ack-nhfb, } @Article{Buekenhout:1996:LFP, author = "Francis Buekenhout and Dimitri Leemans", title = "On the List of Finite Primitive Permutation Groups of Degree {$ \leq 50 $}", journal = j-J-SYMBOLIC-COMP, volume = "22", number = "2", pages = "215--226 (or 215--225??)", month = aug, year = "1996", CODEN = "JSYCEH", ISSN = "0747-7171 (print), 1095-855X (electronic)", ISSN-L = "0747-7171", MRclass = "20Bxx", MRnumber = "1 422 147", bibdate = "Sat May 10 15:54:09 MDT 1997", bibsource = "http://www.math.utah.edu/pub/tex/bib/jsymcomp.bib; http://www.math.utah.edu/pub/tex/bib/magma.bib", acknowledgement = ack-nhfb, classcodes = "C7310 (Mathematics computing); C1110 (Algebra)", corpsource = "Dept. de Math., Univ. Libre de Bruxelles, Belgium", fjournal = "Journal of Symbolic Computation", journal-URL = "http://www.sciencedirect.com/science/journal/07477171/", keywords = "CAYLEY library; finite primitive permutation groups; group theory; permutation groups; primitive; Sims' list; symbol manipulation", treatment = "T Theoretical or Mathematical", } @Article{Cannon:1996:MNC, author = "John Cannon and Catherine Playoust", title = "{MAGMA}: a new computer algebra system", journal = j-EUROMATH-BULL, volume = "2", number = "1", pages = "113--144", year = "1996", ISSN = "1359-4346", ISSN-L = "1359-4346", MRclass = "68Q40", MRnumber = "1413180", bibdate = "Sat Aug 9 16:03:22 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/magma.bib", acknowledgement = ack-nhfb, fjournal = "Euromath Bulletin", } @Article{Bosma:1997:MAS, author = "Wieb Bosma and John J. Cannon and Catherine Playoust", title = "The {Magma} algebra system. {I}. {The} user language", journal = j-J-SYMBOLIC-COMP, volume = "24", number = "3--4", pages = "235--265", month = sep # "--" # oct, year = "1997", CODEN = "JSYCEH", DOI = "https://doi.org/10.1006/jsco.1996.0125", ISSN = "0747-7171 (print), 1095-855X (electronic)", ISSN-L = "0747-7171", MRclass = "68Q40; 68W30 (symbolic computation and algebraic computation)", MRnumber = "1 484 478", bibdate = "Tue Nov 10 06:53:22 MST 1998", bibsource = "http://www.math.utah.edu/pub/tex/bib/jsymcomp.bib; http://www.math.utah.edu/pub/tex/bib/magma.bib", note = "Computational algebra and number theory (London, 1993).", ZMnumber = "0898.68039", accepted = "7 November 1996", acknowledgement = ack-nhfb, fjournal = "Journal of Symbolic Computation", journal-URL = "http://www.sciencedirect.com/science/journal/07477171/", received = "10 January 1996", } @Article{Cannon:1997:UMC, author = "J. Cannon and C. Playoust", title = "Using the {Magma} Computer Algebra System in Abstract Algebra Courses", journal = j-J-SYMBOLIC-COMP, volume = "23", number = "5--6", pages = "459--484", month = may # "--" # jun, year = "1997", CODEN = "JSYCEH", ISSN = "0747-7171 (print), 1095-855X (electronic)", ISSN-L = "0747-7171", bibdate = "Thu Jul 30 07:11:32 MDT 1998", bibsource = "Compendex database; http://www.math.utah.edu/pub/tex/bib/jsymcomp.bib; http://www.math.utah.edu/pub/tex/bib/magma.bib", acknowledgement = ack-nhfb, fjournal = "Journal of Symbolic Computation", journal-URL = "http://www.sciencedirect.com/science/journal/07477171/", journalabr = "J Symb Comput", } @Misc{Kemper:1997:CIM, author = "Gregor Kemper", title = "Calculating invariants of modular reflection groups with {Magma}", howpublished = "Where was this published??", year = "1997", bibdate = "Tue Aug 12 09:44:36 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/magma.bib", acknowledgement = ack-nhfb, } @Article{Lewis:1999:CPO, author = "Robert H. Lewis and Michael Wester", title = "Comparison of polynomial-oriented computer algebra systems", journal = j-SIGSAM, volume = "33", number = "4", pages = "5--13", month = dec, year = "1999", CODEN = "SIGSBZ", DOI = "https://doi.org/10.1145/500457.500459", ISSN = "0163-5824 (print), 1557-9492 (electronic)", ISSN-L = "0163-5824", bibdate = "Tue Oct 18 05:08:13 2005", bibsource = "http://www.math.utah.edu/pub/tex/bib/magma.bib; http://www.math.utah.edu/pub/tex/bib/sigsam.bib", abstract = "Exact symbolic computation with polynomials and matrices over polynomial rings has wide applicability to many fields [Hereman96, Lewis99]. By ``exact symbolic'', we mean computation with polynomials whose coefficients are integers (of any size), rational numbers, or from finite fields, as opposed to coefficients that are ``floats'' of a certain precision. Such computation is part of most computer algebra (CA) systems. Over the last dozen years, several large CA systems have become widely available, such as Axiom, Derive, Macsyma, Maple, Mathematica and Reduce. They tend to have great breadth, be produced by profit-making companies, and be relatively expensive, at least for a full blown non-student version. However, most if not all of these systems have difficulty computing with the polynomials and matrices that arise in actual research. Real problems tend to produce large polynomials and large matrices that the general CA systems cannot handle [Lewis99].In the last few years, several smaller CA systems focused on polynomials have been produced at universities by individual researchers or small teams. They run on Macs, PCs and workstations. They are freeware or shareware. Several claim to be much more efficient than the large systems at exact polynomial computations. The list of these systems includes CoCoA, Fermat, MuPAD, Pari-GP and Singular [CoCoA, Fermat, MuPAD, Pari-GP, Singular].In this paper, we compare these small systems to each other and to two of the large systems (Magma and Maple) on a set of problems involving exact symbolic computation with polynomials and matrices. The problems here involve: (*) the ground rings Z, Q, Z/p and other finite fields (*) basic arithmetic of polynomials over the ground ring (*) basic arithmetic of rational functions over the ground ring (*) polynomial evaluation (substitution) (*) matrix normal forms (*) determinants and characteristic polynomials (*) GCDs of multivariate polynomials (*) resultants.", acknowledgement = ack-nhfb, fjournal = "SIGSAM Bulletin (ACM Special Interest Group on Symbolic and Algebraic Manipulation)", issue = "130", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1000", } @Book{Wester:1999:CAS, editor = "Michael J. Wester", title = "Computer algebra systems: a practical guide", publisher = pub-WILEY, address = pub-WILEY:adr, pages = "xvi + 436", year = "1999", ISBN = "0-471-98353-5", ISBN-13 = "978-0-471-98353-8", LCCN = "QA155.7.E4 W48 1999", bibdate = "Tue Aug 12 10:30:42 MDT 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib; http://www.math.utah.edu/pub/tex/bib/macsyma.bib; http://www.math.utah.edu/pub/tex/bib/magma.bib; http://www.math.utah.edu/pub/tex/bib/maple-extract.bib; http://www.math.utah.edu/pub/tex/bib/mathematica.bib; z3950.loc.gov:7090/Voyager", URL = "http://www.loc.gov/catdir/description/wiley033/99021149.html; http://www.loc.gov/catdir/toc/onix03/99021149.html", acknowledgement = ack-nhfb, keywords = "Magma", subject = "Algebra; Data processing", tableofcontents = "Symbolic Math Powerhouses Revisited \\ Quite a Year \\ Besides the Big Three \\ Axiom \\ Interface and Language \\ The Problems Suite \\ Derive \\ Interface and Capabilities \\ The Test Suite \\ Macsyma \\ Interface and Capabilities \\ Test Suite Results \\ Maple \\ Interface and Features \\ Test Suite Results \\ Mathematica 3.0 \\ Interface and Capabilities \\ The Test Suite \\ Symbolic Alternatives \\ MuPAD \\ Test Suite Results \\ The Test Suite \\ Company Information \\ Symbolic Magic \\ Macsyma 2.3 \\ Maple V Release 5 \\ A Critique of the Mathematical Abilities of CA Systems \\ The Summary Table \\ Selection of Problems \\ Point of View \\ Observations \\ Documentation \\ Language \\ Simplification \\ The Complex Domain \\ General Remarks \\ Simplifying Square Roots of Square Roots by Denesting \\ Why Denest Square Roots? \\ Where Do Nested Radicals Arise? \\ Developing Algorithms \\ The Algorithms \\ Square Root of a Three-Term Sum \\ Square Root of Square Roots \\ Types of Implementation \\ A Measure of the Degree of Nesting of a Radical \\ If x is a Number \\ If x is an nth Root of Something \\ If x is a Product \\ If x is a Sum \\ Recursive Simplification \\ Testing \\ Can Your Computer Do Complex Analysis? \\ Basic Problems of Multiple-Valued Complex Functions \\ Computer Tests \\ Efficient Computation of Chebyshev Polynomials in Computer Algebra \\ The Chebyshev Polynomials \\ Determinants \\ Generating Functions \\ Rodrigues Formulas \\ Matrix Powers \\ Recurrence Equations", } @Article{Giulietti:2000:ACF, author = "Massimo Giulietti", title = "Algebraic curves over finite fields and {MAGMA}", journal = j-ITAL-J-PURE-APPL-MATH, volume = "8", pages = "19--32", year = "2000", ISSN = "1126-8042 (print), 2239-0227 (electronic)", ISSN-L = "1126-8042", MRclass = "14Q05 (14G15 51E21)", MRnumber = "1793739 (2001i:14082)", bibdate = "Sat Aug 9 16:07:25 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/magma.bib", acknowledgement = ack-nhfb, ajournal = "Ital. J. Pure Appl. Math.", fjournal = "Italian Journal of Pure and Applied Mathematics", journal-URL = "http://ijpam.uniud.it/journal/", } @Article{Bosma:2001:SIC, author = "Wieb Bosma", title = "Special Issue on Computational Algebra and Number Theory: Proceedings of the {Second Magma Conference}: Foreword of the {Guest Editor}", journal = j-J-SYMBOLIC-COMP, volume = "31", number = "1--2", pages = "1--1", month = jan # "/" # feb, year = "2001", CODEN = "JSYCEH", DOI = "https://doi.org/10.1006/jsco.2000.0435", ISSN = "0747-7171 (print), 1095-855X (electronic)", ISSN-L = "0747-7171", bibdate = "Tue Jul 17 09:13:33 MDT 2001", bibsource = "http://www.idealibrary.com/cgi-bin/links/toc/sy; http://www.math.utah.edu/pub/tex/bib/jsymcomp.bib; http://www.math.utah.edu/pub/tex/bib/magma.bib", URL = "http://www.idealibrary.com/links/doi/10.1006/jsco.2000.0435; http://www.idealibrary.com/links/doi/10.1006/jsco.2000.0435/pdf", acknowledgement = ack-nhfb, fjournal = "Journal of Symbolic Computation", journal-URL = "http://www.sciencedirect.com/science/journal/07477171/", } @Article{Faina:2001:DGC, author = "Giorgio Faina and Massimo Giulietti", title = "Decoding {Goppa} codes with {MAGMA}", journal = j-ARS-COMB, volume = "61", pages = "221--232", year = "2001", CODEN = "ACOMDN", ISSN = "0381-7032", ISSN-L = "0381-7032", MRclass = "94B35 (94B27)", MRnumber = "1863382", bibdate = "Sat Aug 9 16:07:25 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/magma.bib", acknowledgement = ack-nhfb, ajournal = "Ars Combin.", fjournal = "Ars Combinatoria", journal-URL = "http://www.combinatorialmath.ca/arscombinatoria/", } @Article{Key:2001:SAM, author = "J. D. Key", title = "Some Applications of {Magma} in Designs and Codes: Oval Designs, {Hermitian} Unitals and Generalized {Reed--Muller} Codes", journal = j-J-SYMBOLIC-COMP, volume = "31", number = "1--2", pages = "37--53", month = jan # "/" # feb, year = "2001", CODEN = "JSYCEH", DOI = "https://doi.org/10.1006/jsco.1999.1007", ISSN = "0747-7171 (print), 1095-855X (electronic)", ISSN-L = "0747-7171", MRnumber = "MR1806205 (2002d:94064)", bibdate = "Tue Jul 17 09:13:33 MDT 2001", bibsource = "http://www.idealibrary.com/cgi-bin/links/toc/sy; http://www.math.utah.edu/pub/tex/bib/jsymcomp.bib; http://www.math.utah.edu/pub/tex/bib/magma.bib", URL = "http://www.idealibrary.com/links/doi/10.1006/jsco.1999.1007; http://www.idealibrary.com/links/doi/10.1006/jsco.1999.1007/pdf; http://www.idealibrary.com/links/doi/10.1006/jsco.1999.1007/ref", acknowledgement = ack-nhfb, fjournal = "Journal of Symbolic Computation", journal-URL = "http://www.sciencedirect.com/science/journal/07477171/", } @Article{Dehon:2002:CCG, author = "Michel Dehon and Dimitri Leemans", title = "Constructing coset geometries with {MAGMA}: an application to the sporadic groups {$ M_{12} $} and {$ J_1 $}", journal = "Atti del Seminario Matematico e Fisico dell'Universit\`a di Modena", volume = "50", number = "2", pages = "415--427", year = "2002", CODEN = "ASMMAK", ISSN = "0041-8986", ISSN-L = "0041-8986", MRclass = "51E24 (20D08)", MRnumber = "1958289 (2003m:51016)", bibdate = "Sat Aug 9 16:07:25 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/magma.bib", acknowledgement = ack-nhfb, ajournal = "Atti Sem. Mat. Fis. Univ. Modena", fjournal = "Atti del Seminario Matematico e Fisico dell'Universit\`a di Modena", } @InCollection{Dewar:2003:CAS, author = "Michael Dewar and Johannes Grabmeier and Stephen Watt and Bernhard Kutzler and John Cannon and Bill Unger and Wolfgang Windsteiger and J{\"u}rgen Gerhard and Andreas Sorgatz and Herbert Melenk and Sebastien Veigneau and David P. Jacobs and David Ford and Wolfgang Thomas and J{\"o}rgen Backelin and Svetlana Cojocaru and Victor Ufnarovski and Oliver Gloor and J{\"u}rgen Opgenorth and Wilhelm Plesken and Tilman Schulz and Ralf Hemmecke and Erik Hillgarter and Franz Winkler and Meinolf Geck and Frank L{\"u}beck and Klaus Lux and Peter Dr{\"a}xler and Rainer N{\"o}renberg and Claire Di Crrescenzo and Fran{\c{c}}oise Jung and Eckhard Pfl{\"u}gel and Anton Betten and Reinhard Laue and Alfred Wassermann and Joachim Apel and Uwe Klaus and Robert H. Lewis and Erich Kaltofen and Thomas Breuer and Alexander Hulpke and Christian Bauer and Alexander Frink and Richard Kreckel and Nobuki Takayama and Johannes Buchmann and Thomas Pfahler and Marc A. A. van Leeuwen and Alan Head and Daniel R. Grayson and Michael E. Stillman and Kredel Heinz and Michael Pesch and Wendelin Degen and Gerhard Hiss and Karim Belabas and Wolfgang Kuechlin and Sarah Rees and Reinhard B{\"u}ndgen and Olaf Delgado Friedrichs and Andreas W. M. Dress and Daniel H. Huson and Elaine Kant and Stan Steinberg and Curt Randall and Larry Akers and Bob Young and Robert L. Young and Minaz Punjani and Marc Conrad and Susanne Schmitt and Gert-Martin Greuel and Gerahrd Pfister and Hans Sch{\"o}nemann and Weiguang Huang and Adalbert Kerber and Axel Kohnert and Bruno Buchberger and Tudor Jebelean and Allan Bonadio and M. F. Newman and Werner Nickel and Alice C. Niemeyer and E. A. O. Brien and Sebastian Egner and Markus P{\"u}schel and Thomas Beth and Hans-Gert Gr{\"a}be and Bruno Haible and Thomas Wolf and G. E. Prince and M. Jerie and Sergei Klioner and Thomas Hahn and Hagen Eck and Sepp K{\"u}blbeck and Leonard H. Soicher and Adalbert Kerber and Pierre Lescanne and Bogdan Popov and Oksana Laushnyk and A. Balfag{\'o}n and X. Ja{\'e}n", title = "Computer Algebra Systems", crossref = "Grabmeier:2003:CAH", pages = "261--483", year = "2003", bibdate = "Tue Aug 12 10:26:39 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/magma.bib", acknowledgement = ack-nhfb, keywords = "Magma", } @Article{Li:2003:ASPa, author = "Hongbo Li and Yihong Wu", title = "Automated short proof generation for projective geometric theorems with {Cayley} and bracket algebras: {I}. {Incidence} geometry", journal = j-J-SYMBOLIC-COMP, volume = "36", number = "5", pages = "717--762", month = nov, year = "2003", CODEN = "JSYCEH", ISSN = "0747-7171 (print), 1095-855X (electronic)", ISSN-L = "0747-7171", bibdate = "Tue Dec 16 09:13:39 MST 2003", bibsource = "http://www.math.utah.edu/pub/tex/bib/jsymcomp.bib; http://www.math.utah.edu/pub/tex/bib/magma.bib", acknowledgement = ack-nhfb, fjournal = "Journal of Symbolic Computation", journal-URL = "http://www.sciencedirect.com/science/journal/07477171/", } @Article{Li:2003:ASPb, author = "Hongbo Li and Yihong Wu", title = "Automated short proof generation for projective geometric theorems with {Cayley} and bracket algebras: {II}. {Conic} geometry", journal = j-J-SYMBOLIC-COMP, volume = "36", number = "5", pages = "763--809", month = nov, year = "2003", CODEN = "JSYCEH", ISSN = "0747-7171 (print), 1095-855X (electronic)", ISSN-L = "0747-7171", bibdate = "Tue Dec 16 09:13:39 MST 2003", bibsource = "http://www.math.utah.edu/pub/tex/bib/jsymcomp.bib; http://www.math.utah.edu/pub/tex/bib/magma.bib", acknowledgement = ack-nhfb, fjournal = "Journal of Symbolic Computation", journal-URL = "http://www.sciencedirect.com/science/journal/07477171/", } @InCollection{Bailey:2006:AML, author = "Geoff Bailey", title = "Appendix: The {Magma} language", crossref = "Bosma:2006:DMM", pages = "331--356", year = "2006", DOI = "https://doi.org/10.1007/978-3-540-37634-7_15", bibdate = "Tue Aug 12 09:24:34 MDT 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/magma.bib", URL = "http://link.springer.com/content/pdf/10.1007/978-3-540-37634-7_15.pdf", acknowledgement = ack-nhfb, book-DOI = "https://doi.org/10.1007/978-3-540-37634-7", book-URL = "http://www.springerlink.com/content/978-3-540-37634-7", } @InCollection{Bosma:2006:SCE, author = "Wieb Bosma", title = "Some computational experiments in number theory", crossref = "Bosma:2006:DMM", pages = "1--30", year = "2006", DOI = "https://doi.org/10.1007/978-3-540-37634-7_1", bibdate = "Tue Aug 12 09:24:34 MDT 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/magma.bib", URL = "http://link.springer.com/content/pdf/10.1007/978-3-540-37634-7_1.pdf; http://link.springer.com/content/pdf/bfm:978-3-540-37634-7/1.pdf", acknowledgement = ack-nhfb, book-DOI = "https://doi.org/10.1007/978-3-540-37634-7", book-URL = "http://www.springerlink.com/content/978-3-540-37634-7", } @InCollection{Brown:2006:GRS, author = "Gavin Brown", title = "Graded rings and special {K3} surfaces", crossref = "Bosma:2006:DMM", pages = "137--159", year = "2006", DOI = "https://doi.org/10.1007/978-3-540-37634-7_6", bibdate = "Tue Aug 12 09:24:34 MDT 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/magma.bib", URL = "http://link.springer.com/content/pdf/10.1007/978-3-540-37634-7_6.pdf", acknowledgement = ack-nhfb, book-DOI = "https://doi.org/10.1007/978-3-540-37634-7", book-URL = "http://www.springerlink.com/content/978-3-540-37634-7", } @InCollection{Bruin:2006:STD, author = "Nils Bruin", title = "Some ternary {Diophantine} equations of signature $ (n, n, 2) $", crossref = "Bosma:2006:DMM", pages = "63--91", year = "2006", DOI = "https://doi.org/10.1007/978-3-540-37634-7_3", bibdate = "Tue Aug 12 09:24:34 MDT 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/magma.bib", URL = "http://link.springer.com/content/pdf/10.1007/978-3-540-37634-7_3.pdf", acknowledgement = ack-nhfb, book-DOI = "https://doi.org/10.1007/978-3-540-37634-7", book-URL = "http://www.springerlink.com/content/978-3-540-37634-7", } @InCollection{Carlson:2006:SVM, author = "Jon F. Carlson", title = "Support varieties for modules", crossref = "Bosma:2006:DMM", pages = "187--204", year = "2006", DOI = "https://doi.org/10.1007/978-3-540-37634-7_8", bibdate = "Tue Aug 12 09:24:34 MDT 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/magma.bib", URL = "http://link.springer.com/content/pdf/10.1007/978-3-540-37634-7_8.pdf", acknowledgement = ack-nhfb, book-DOI = "https://doi.org/10.1007/978-3-540-37634-7", book-URL = "http://www.springerlink.com/content/978-3-540-37634-7", } @InCollection{Carlson:2006:WPD, author = "Jon F. Carlson", title = "When is projectivity detected on subalgebras?", crossref = "Bosma:2006:DMM", pages = "205--220", year = "2006", DOI = "https://doi.org/10.1007/978-3-540-37634-7_9", bibdate = "Tue Aug 12 09:24:34 MDT 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/magma.bib", URL = "http://link.springer.com/content/pdf/10.1007/978-3-540-37634-7_9.pdf", acknowledgement = ack-nhfb, book-DOI = "https://doi.org/10.1007/978-3-540-37634-7", book-URL = "http://www.springerlink.com/content/978-3-540-37634-7", } @Book{Crilly:2006:ACM, author = "A. J. Crilly", title = "{Arthur Cayley}: mathematician laureate of the {Victorian} age", publisher = pub-JOHNS-HOPKINS, address = pub-JOHNS-HOPKINS:adr, pages = "xxi + 609", year = "2006", ISBN = "0-8018-8011-4", ISBN-13 = "978-0-8018-8011-7", LCCN = "QA29 .C39 C75 2006", bibdate = "Thu Jun 27 08:59:04 MDT 2013", bibsource = "http://www.math.utah.edu/pub/tex/bib/histmath.bib; http://www.math.utah.edu/pub/tex/bib/magma.bib; z3950.loc.gov:7090/Voyager", URL = "http://www.loc.gov/catdir/bios/jhu052/2004005682.html; http://www.loc.gov/catdir/description/jhu051/2004005682.html; http://www.loc.gov/catdir/toc/fy0612/2004005682.html", acknowledgement = ack-nhfb, subject = "Cayley, Arthur; Mathematicians; Great Britain; Biography", subject-dates = "1821--1895", } @InCollection{Fieker:2006:ACF, author = "Claus Fieker", title = "Applications of the class field theory of global fields", crossref = "Bosma:2006:DMM", pages = "31--62", year = "2006", DOI = "https://doi.org/10.1007/978-3-540-37634-7_2", bibdate = "Tue Aug 12 09:24:34 MDT 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/magma.bib", URL = "http://link.springer.com/content/pdf/10.1007/978-3-540-37634-7_2.pdf", acknowledgement = ack-nhfb, book-DOI = "https://doi.org/10.1007/978-3-540-37634-7", book-URL = "http://www.springerlink.com/content/978-3-540-37634-7", } @InCollection{Gebhardt:2006:CAD, author = "Volker Gebhardt", title = "Computer aided discovery of a fast algorithm for testing conjugacy in braid groups", crossref = "Bosma:2006:DMM", pages = "261--285", year = "2006", DOI = "https://doi.org/10.1007/978-3-540-37634-7_12", bibdate = "Tue Aug 12 09:24:34 MDT 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/magma.bib", URL = "http://link.springer.com/content/pdf/10.1007/978-3-540-37634-7_12.pdf", acknowledgement = ack-nhfb, book-DOI = "https://doi.org/10.1007/978-3-540-37634-7", book-URL = "http://www.springerlink.com/content/978-3-540-37634-7", } @InCollection{Grassl:2006:SLC, author = "Markus Grassl", title = "Searching for linear codes with large minimum distance", crossref = "Bosma:2006:DMM", pages = "287--313", year = "2006", DOI = "https://doi.org/10.1007/978-3-540-37634-7_13", bibdate = "Tue Aug 12 09:24:34 MDT 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/magma.bib", URL = "http://link.springer.com/content/pdf/10.1007/978-3-540-37634-7_13.pdf", acknowledgement = ack-nhfb, book-DOI = "https://doi.org/10.1007/978-3-540-37634-7", book-URL = "http://www.springerlink.com/content/978-3-540-37634-7", } @InCollection{Holt:2006:CGE, author = "Derek F. Holt", title = "Cohomology and group extensions in {Magma}", crossref = "Bosma:2006:DMM", pages = "221--241", year = "2006", DOI = "https://doi.org/10.1007/978-3-540-37634-7_10", bibdate = "Tue Aug 12 09:24:34 MDT 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/magma.bib", URL = "http://link.springer.com/content/pdf/10.1007/978-3-540-37634-7_10.pdf", acknowledgement = ack-nhfb, book-DOI = "https://doi.org/10.1007/978-3-540-37634-7", book-URL = "http://www.springerlink.com/content/978-3-540-37634-7", } @InCollection{Lieby:2006:CPG, author = "Paulette Lieby", title = "Colouring planar graphs", crossref = "Bosma:2006:DMM", pages = "315--330", year = "2006", DOI = "https://doi.org/10.1007/978-3-540-37634-7_14", bibdate = "Tue Aug 12 09:24:34 MDT 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/magma.bib", URL = "http://link.springer.com/content/pdf/10.1007/978-3-540-37634-7_14.pdf", acknowledgement = ack-nhfb, book-DOI = "https://doi.org/10.1007/978-3-540-37634-7", book-URL = "http://www.springerlink.com/content/978-3-540-37634-7", } @InCollection{Roney-Dougal:2006:CPP, author = "Colva M. Roney-Dougal and William R. Unger", title = "Computing the primitive permutation groups of degree less than $ 1000 $", crossref = "Bosma:2006:DMM", pages = "243--260", year = "2006", DOI = "https://doi.org/10.1007/978-3-540-37634-7_11", bibdate = "Tue Aug 12 09:24:34 MDT 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/magma.bib", URL = "http://link.springer.com/content/pdf/10.1007/978-3-540-37634-7_11.pdf", acknowledgement = ack-nhfb, book-DOI = "https://doi.org/10.1007/978-3-540-37634-7", book-URL = "http://www.springerlink.com/content/978-3-540-37634-7", } @InCollection{Stein:2006:SBS, author = "William Stein", title = "Studying the {Birch} and {Swinnerton-Dyer} conjecture for modular abelian varieties using {Magma}", crossref = "Bosma:2006:DMM", pages = "93--116", year = "2006", DOI = "https://doi.org/10.1007/978-3-540-37634-7_4", bibdate = "Tue Aug 12 09:24:34 MDT 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/magma.bib", URL = "http://link.springer.com/content/pdf/10.1007/978-3-540-37634-7_4.pdf", acknowledgement = ack-nhfb, book-DOI = "https://doi.org/10.1007/978-3-540-37634-7", book-URL = "http://www.springerlink.com/content/978-3-540-37634-7", } @InCollection{Taylor:2006:CSO, author = "Donald E. Taylor", title = "Constructing the split octonions", crossref = "Bosma:2006:DMM", pages = "161--185", year = "2006", DOI = "https://doi.org/10.1007/978-3-540-37634-7_7", bibdate = "Tue Aug 12 09:24:34 MDT 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/magma.bib", URL = "http://link.springer.com/content/pdf/10.1007/978-3-540-37634-7_7.pdf", acknowledgement = ack-nhfb, book-DOI = "https://doi.org/10.1007/978-3-540-37634-7", book-URL = "http://www.springerlink.com/content/978-3-540-37634-7", } @InCollection{vanWamelen:2006:CAJ, author = "Paul B. van Wamelen", title = "Computing with the analytic {Jacobian} of a genus $2$ curve", crossref = "Bosma:2006:DMM", pages = "117--135", year = "2006", DOI = "https://doi.org/10.1007/978-3-540-37634-7_5", bibdate = "Tue Aug 12 09:24:34 MDT 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/magma.bib", URL = "http://link.springer.com/content/pdf/10.1007/978-3-540-37634-7_5.pdf", acknowledgement = ack-nhfb, book-DOI = "https://doi.org/10.1007/978-3-540-37634-7", book-URL = "http://www.springerlink.com/content/978-3-540-37634-7", } @Book{Cox:2007:IVA, author = "David A. Cox and John B. Little and Donal O'Shea", title = "Ideals, varieties, and algorithms: an introduction to computational algebraic geometry and commutative algebra", publisher = pub-SV, address = pub-SV:adr, edition = "Third", pages = "xv + 551", year = "2007", DOI = "https://doi.org/10.1007/978-0-387-35651-8", ISBN = "0-387-35650-9, 0-387-35651-7 (e-book)", ISBN-13 = "978-0-387-35650-1, 978-0-387-35651-8 (e-book)", LCCN = "QA564 .C688 2007", bibdate = "Sat Aug 9 14:06:32 MDT 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/magma.bib; z3950.loc.gov:7090/Voyager", series = "Undergraduate texts in mathematics", URL = "http://www.loc.gov/catdir/enhancements/fy0814/2006930875-d.html; http://www.loc.gov/catdir/enhancements/fy0814/2006930875-t.html; http://www.springerlink.com/openurl.asp?genre=book&isbn=978-0-387-35650-1", abstract = "The solutions of a system of polynomial equations form a geometric object called a variety; the corresponding algebraic object is an ideal. There is a close relationship between ideals and varieties which reveals the intimate link between algebra and geometry. Written at a level appropriate to undergraduates, this book covers such topics as the Hilbert Basis Theorem, the Nullstellensatz, invariant theory, projective geometry, and dimension theory.", acknowledgement = ack-nhfb, keywords = "Algorithme; Alg{\'e}brique; Alg{\`e}bre; Application; Appliqu{\'e}; Automatique; Axiom; Base; Cocoa; Commutatif 653; Dimension; Elimination; Equation; Extension; Fini; Fonction; Groupe; Gr{\=o}bner; G{\'e}om{\'e}trie; Hilbert 653; Ideal; Informatique; Macaulay; Magma; Maple; Mathematica; Math{\'e}matique; Nullstellensatz; Polynomial; Preuve; Programme 653; Projectif; Rationnel; Robotique; Singular; Syst{\`e}me; Th{\'e}orie; Th{\'e}or{\`e}me; Vari{\'e}t{\'e}", subject = "Geometry, Algebraic; Data processing; Commutative algebra", tableofcontents = "Preface to the First Edition \\ Preface to the Second Edition \\ Preface to the Third Edition \\ Geometry, Algebra, and Algorithms \\ Gr{\"o}bner Bases \\ Elimination Theory \\ The Algebra-Geometry Dictionary \\ Polynomial and Rational Functions on a Variety \\ Robotics and Automatic Geometric Theorem Proving \\ Invariant Theory of Finite Groups \\ Projective Algebraic Geometry \\ The Dimension of a Variety \\ Appendix A. Some Concepts from Algebra \\ Appendix B. Pseudocode \\ Appendix C. Computer Algebra Systems \\ Appendix D. Independent Projects \\ References \\ Index", } @InProceedings{Li:2007:VGP, author = "Xin Li and Marc Moreno Maza and {\'E}ric Schost", title = "On the Virtues of Generic Programming for Symbolic Computation", crossref = "Shi:2007:CSIb", pages = "251--258", year = "2007", DOI = "https://doi.org/10.1007/978-3-540-72586-2_35", bibdate = "Tue Aug 12 10:36:21 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib; http://www.math.utah.edu/pub/tex/bib/magma.bib; http://www.math.utah.edu/pub/tex/bib/maple-extract.bib", acknowledgement = ack-nhfb, keywords = "Axiom; Magma; Maple", } @Book{OShea:2007:IVA, author = "Donal O'Shea and John B. Mathematiker Little and David Archibald Math{\'e}maticien {Cox, fre} and David Archibald Mathematiker {Cox, ger} and David Archibald Mathematician {Cox, eng}", title = "Ideals, varieties, and algorithms: an introduction to computational algebraic geometry and commutative algebra", publisher = pub-SV, address = pub-SV:adr, edition = "Third", pages = "xv + 552", year = "2007", DOI = "https://doi.org/10.1007/978-0-387-35651-8", ISBN = "0-387-35650-9, 0-387-35651-7 (e-book)", ISBN-13 = "978-0-387-35650-1, 978-0-387-35651-8 (e-book)", LCCN = "????", bibdate = "Sat Aug 9 14:28:19 MDT 2014", bibsource = "fsz3950.oclc.org:210/WorldCat; http://www.math.utah.edu/pub/tex/bib/magma.bib", series = "Undergraduate texts in mathematics", URL = "http://sfx.ethz.ch/sfx\_locater?sid=ALEPH:EBI01&genre=book&isbn=978-0-387-35650-1&id=doi:10.1007/978-0-387-35651-8", abstract = "The solutions of a system of polynomial equations form a geometric object called a variety; the corresponding algebraic object is an ideal. There is a close relationship between ideals and varieties which reveals the intimate link between algebra and geometry. Written at a level appropriate to undergraduates, this book covers such topics as the Hilbert Basis Theorem, the Nullstellensatz, invariant theory, projective geometry, and dimension theory.--P. 4 of cover.", acknowledgement = ack-nhfb, remark = "Corrected reprint. Originally published: 2007.", subject = "Geometry, Algebraic; Data processing; Commutative algebra; Data processing.; Algebraische Geometrie; Kommutative Algebra; Algebra; Computer software; Geometry, Algebraic; Logic, Symbolic and mathematical; Algebraic Geometry; Commutative Rings and Algebras; Mathematical Logic and Foundations; Mathematical Software; Mathematics; Algebra; Computer software; Geometry, Algebraic; Logic, Symbolic and mathematical.", tableofcontents = "1: Geometry, algebra, and algorithms \\ 2: Gr{\"o}bner bases \\ 3: Elimination theory \\ 4: algebra-geometry dictionary \\ 5: Polynomial and rational functions on a variety \\ 6: Robotics and automatic geometric theorem proving \\ 7: Invariant theory of finite groups \\ 8: Projective algebraic geometry \\ 9: dimension of a variety \\ Appendix A: Some concepts from algebra \\ Appendix B: Pseudocode \\ Appendix C: Computer algebra systems \\ Appendix D: Independent projects", } @Book{Cannon:2008:APMa, author = "John Cannon and Wieb Bosma and Catherine Playoust", title = "Algebraic programming with {Magma}: an introduction to the Magma {language}", volume = "1", publisher = pub-SV, address = pub-SV:adr, year = "2008", ISBN = "3-540-62746-4", ISBN-13 = "978-3-540-62746-3", LCCN = "????", bibdate = "Tue Aug 12 08:44:23 MDT 2014", bibsource = "fsz3950.oclc.org:210/WorldCat; http://www.math.utah.edu/pub/tex/bib/magma.bib", acknowledgement = ack-nhfb, } @Book{Cannon:2008:APMb, author = "John Cannon and Wieb Bosma and Catherine Playoust", title = "Algebraic programming with {Magma}: an introduction to the {Magma} language", volume = "2", publisher = pub-SV, address = pub-SV:adr, year = "2008", ISBN = "3-540-62747-2", ISBN-13 = "978-3-540-62747-0", LCCN = "????", bibdate = "Tue Aug 12 08:44:24 MDT 2014", bibsource = "fsz3950.oclc.org:210/WorldCat; http://www.math.utah.edu/pub/tex/bib/magma.bib", acknowledgement = ack-nhfb, } @InCollection{Gaston:2008:DAM, author = "B. Gast{\'o}n and J. Pujol and M. Villanueva", booktitle = "Sixth {Conference} on {Discrete} {Mathematics} and {Computer} {Science} ({Spanish})", title = "Development of algorithmic methods for binary non-linear codes in {MAGMA}", publisher = "Univ. Lleida, Lleida", pages = "345--351", year = "2008", MRclass = "94B05", MRnumber = "2522006", bibdate = "Sat Aug 9 16:07:25 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/magma.bib", acknowledgement = ack-nhfb, } @Article{Joyner:2008:SCT, author = "David Joyner and Robert Miller", title = "{SAGE} and coding theory (abstract only)", journal = j-ACM-COMM-COMP-ALGEBRA, volume = "42", number = "1--2", pages = "74--78", month = mar # "/" # jun, year = "2008", CODEN = "????", DOI = "https://doi.org/10.1145/1394042.1394085", ISSN = "1932-2232 (print), 1932-2240 (electronic)", ISSN-L = "1932-2232", bibdate = "Tue Aug 12 17:30:40 MDT 2008", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/magma.bib; http://www.math.utah.edu/pub/tex/bib/sigsam.bib", abstract = "This is a very brief survey of recent work in SAGE on implementing algorithms to compute with linear block codes. \url{http://www.sagemath.org}.\par SAGE is a mathematical software package similar to the `big M's' (Maple, Mathematica, Magma, and Matlab) but free and open source. Download information and manuals are available at \url{http://www.sagemath.org/}. Included in SAGE is the group theory package GAP and GUAVA, GAP's coding theory package. All of GUAVA's functions can be accessed within SAGE.", acknowledgement = ack-nhfb, fjournal = "ACM Communications in Computer Algebra", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1000", } @InProceedings{Li:2008:HPS, author = "Xin Li and M. M. Maza and R. Rasheed and E. Schost", booktitle = "{ICCSA '08. International Conference on Computational Sciences and Its Applications, 2008}", title = "High-Performance Symbolic Computation in a Hybrid Compiled-Interpreted Programming Environment", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "331--341", month = jun, year = "2008", DOI = "https://doi.org/10.1109/ICCSA.2008.68", bibdate = "Sat Aug 9 16:36:38 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/magma.bib; http://www.math.utah.edu/pub/tex/bib/maple-extract.bib", acknowledgement = ack-nhfb, keywords = "Algebra; Application software; arithmetic; C implementation; C language; Data conversion; Digital arithmetic; fast arithmetic operations; fast polynomial arithmetic; High performance computing; High-performance; high-performance symbolic computation; hybrid compiled-interpreted programming environment; Kernel; Libraries; MAGMA; MAPLE; mathematics computing; Modpn library; Packaging; Polynomials; program compilers; program interpreters; Programming environments; symbol manipulation; symbolic computation; triangular decompositions", } @InProceedings{Stein:2008:CWC, author = "William A. Stein", title = "Can we create a viable free open source alternative to {Magma}, {Maple}, {Mathematica} and {Matlab}?", crossref = "Jeffrey:2008:PAM", pages = "5--6", year = "2008", DOI = "https://doi.org/10.1145/1390768.1390771", bibdate = "Tue Aug 5 18:10:09 MDT 2008", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/gnu.bib; http://www.math.utah.edu/pub/tex/bib/issac.bib; http://www.math.utah.edu/pub/tex/bib/magma.bib; http://www.math.utah.edu/pub/tex/bib/maple-extract.bib; http://www.math.utah.edu/pub/tex/bib/mathematica.bib; http://www.math.utah.edu/pub/tex/bib/matlab.bib", abstract = "The goal of the Sage project ({\tt http://sagemath.org}) is to create a truly viable free open source alternative to Magma, Maple, Mathematica and Matlab. Is this possible?", acknowledgement = ack-nhfb, keywords = "free; Magma; Maple; Mathematica; Matlab; open source", } @Misc{DominguezPerez:2009:ICP, author = "Luis J. {Dominguez Perez} and Ezekiel J. Kachisa and Michael Scott", title = "Implementing cryptographic pairings: A {Magma} tutorial", howpublished = "IACR Cryptology ePrint Archive", pages = "30", year = "2009", bibdate = "Tue Aug 12 09:50:23 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/magma.bib", URL = "http:eprint.iacr.org/2009/072.pdf", acknowledgement = ack-nhfb, } @Article{Cannon:2010:MTN, author = "John Cannon and Steve Donnelly and Claus Fieker and Mark Watkins", title = "{Magma} --- a Tool for Number Theory", journal = j-LECT-NOTES-COMP-SCI, volume = "6327", pages = "253--255", year = "2010", CODEN = "LNCSD9", DOI = "https://doi.org/10.1007/978-3-642-15582-6_43", ISSN = "0302-9743 (print), 1611-3349 (electronic)", ISSN-L = "0302-9743", bibdate = "Sat Aug 9 15:34:26 MDT 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/magma.bib", URL = "http://link.springer.com/content/pdf/10.1007/978-3-642-15582-6_43.pdf", acknowledgement = ack-nhfb, book-DOI = "https://doi.org/10.1007/978-3-642-15582-6", book-URL = "http://www.springerlink.com/content/978-3-642-15582-6", fjournal = "Lecture Notes in Computer Science", } @Article{Erocal:2010:SPU, author = "Bur{\c{c}}in Er{\"o}cal and William Stein", title = "The {Sage Project}: Unifying Free Mathematical Software to Create a Viable Alternative to {Magma}, {Maple}, {Mathematica} and {MATLAB}", journal = j-LECT-NOTES-COMP-SCI, volume = "6327", pages = "12--27", year = "2010", CODEN = "LNCSD9", DOI = "https://doi.org/10.1007/978-3-642-15582-6_4", ISSN = "0302-9743 (print), 1611-3349 (electronic)", ISSN-L = "0302-9743", bibdate = "Sat Aug 9 15:34:11 MDT 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/lncs2010a.bib; http://www.math.utah.edu/pub/tex/bib/magma.bib; http://www.math.utah.edu/pub/tex/bib/maple-extract.bib; http://www.math.utah.edu/pub/tex/bib/mathematica.bib; http://www.math.utah.edu/pub/tex/bib/matlab.bib", URL = "http://link.springer.com/content/pdf/10.1007/978-3-642-15582-6_4.pdf", acknowledgement = ack-nhfb, book-DOI = "https://doi.org/10.1007/978-3-642-15582-6", book-URL = "http://www.springerlink.com/content/978-3-642-15582-6", fjournal = "Lecture Notes in Computer Science", } @InCollection{Kida:2010:CAS, author = "Masanari Kida", booktitle = "Algebraic number theory and related topics 2008", title = "Computing algebraic structures with {Magma}", publisher = "Res. Inst. Math. Sci. (RIMS), Kyoto", pages = "107--116", year = "2010", MRclass = "11-01 (11-04)", MRnumber = "2757559 (2012b:11001)", bibdate = "Sat Aug 9 16:07:25 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/magma.bib", series = "RIMS K\^oky\^uroku Bessatsu, B19", acknowledgement = ack-nhfb, } @Article{Monagan:2010:SPM, author = "Michael Monagan and Roman Pearce", title = "Sparse polynomial multiplication and division in {Maple 14}", journal = j-ACM-COMM-COMP-ALGEBRA, volume = "44", number = "4", pages = "205--209", month = dec, year = "2010", CODEN = "????", DOI = "https://doi.org/10.1145/1940475.1940521", ISSN = "1932-2232 (print), 1932-2240 (electronic)", ISSN-L = "1932-2232", bibdate = "Thu Mar 31 10:24:16 MDT 2011", bibsource = "http://portal.acm.org/; http://www.math.utah.edu/pub/tex/bib/magma.bib; http://www.math.utah.edu/pub/tex/bib/maple-extract.bib; http://www.math.utah.edu/pub/tex/bib/sigsam.bib", abstract = "We demonstrate new routines for sparse multivariate polynomial multiplication and division over the integers that we have integrated into Maple 14 through the expand and divide commands. These routines are currently the fastest available, and the multiplication routine is parallelized with superlinear speedup. The performance of Maple is significantly improved. We describe our polynomial data structure and compare it with Maple's. Then we present benchmarks comparing Maple 14 with Maple 13, Magma, Mathematica, Singular, Pari, and Trip.", acknowledgement = ack-nhfb, fjournal = "ACM Communications in Computer Algebra", issue = "174", journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1000", } @InProceedings{Cai:2011:ADB, author = "Ying Cai and Tiefeng Wang", booktitle = "2011 International Conference on Electrical and Control Engineering (ICECE)", title = "Analysis and design of binary pseudorandom sequences based on the {Magma} package", publisher = pub-IEEE, address = pub-IEEE:adr, pages = "5759--5762", month = sep, year = "2011", DOI = "https://doi.org/10.1109/ICECENG.2011.6057331", bibdate = "Sat Aug 9 16:38:45 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/magma.bib; http://www.math.utah.edu/pub/tex/bib/prng.bib", acknowledgement = ack-nhfb, keywords = "autocorrelation; Balance; binary pseudorandom sequence; Binary sequences; binary sequences; C; C++ language; code division multiple access communication system; Complexity theory; Correlation; Data conversion; Data mining; Magma; Magma software package; mathematics computing; Multiaccess communication; multiterminal system identification; Presses; raging system; random sequences; software packages; spread spectrum communication system; SQL; SQL database system; stream cipher; Telecommunications", } @Book{Parrochia:2013:TGT, author = "Daniel Parrochia and Pierre Neuville", title = "Towards a general theory of classifications", publisher = pub-BIRKHAUSER, address = pub-BIRKHAUSER:adr, pages = "xxiii + 304", year = "2013", DOI = "https://doi.org/10.1007/978-3-0348-0609-1", ISBN = "3-0348-0608-6 (softcover), 3-0348-0609-4 (e-book)", ISBN-13 = "978-3-0348-0608-4 (softcover), 978-3-0348-0609-1 (e-book)", LCCN = "????", MRclass = "03-xx, 03Axx, 06-xx, 62H30, 91C20", bibdate = "Sat Aug 9 14:06:42 MDT 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/magma.bib; z3950.loc.gov:7090/Voyager", series = "Studies in universal logic", abstract = "This book is an essay on the epistemology of classifications. Its main purpose is not to provide an exposition of an actual mathematical theory of classifications, that is, a general theory which would be available to any kind of them: hierarchical or non-hierarchical, ordinary or fuzzy, overlapping or non-overlapping, finite or infinite, and so on, establishing a basis for all possible divisions of the real world. For the moment, such a theory remains nothing but a dream. Instead, the authors essentially put forward a number of key questions. Their aim is rather to reveal the ``state of art'' of this dynamic field and the philosophy one may eventually adopt to go further. To this end they present some advances made in the course of the last century, discuss a few tricky problems that remain to be solved, and show the avenues open to those who no longer wish to stay on the wrong track. Researchers and professionals interested in the epistemology and philosophy of science, library science, logic and set theory, order theory or cluster analysis will find this book a comprehensive, original and progressive introduction to the main questions in this field.", acknowledgement = ack-nhfb, tableofcontents = "Philosophical problems \\ Information data structures \\ Empirical clustering and classic hierarchies \\ Algebra of trees \\ Generalized classifications \\ Topology of generalized classifications \\ Metaclassification \\ For an axiomatic theory of classifications \\ Alternative theories and higher infinite \\ Postscript", } @InCollection{Stein:2013:SCV, author = "William Stein", editor = "Felipe Cucker and Teresa Krick and Allan Pinkus and Agnes Szanto", booktitle = "Foundations of computational mathematics, {Budapest} 2011", title = "{Sage}: creating a viable free open source alternative to {Magma}, {Maple}, {Mathematica}, and {MATLAB}", volume = "403", publisher = pub-CAMBRIDGE, address = pub-CAMBRIDGE:adr, bookpages = "x + 238", pages = "230--238", year = "2013", DOI = "https://doi.org/10.1017/CBO9781139095402.011", ISBN = "1-107-60407-9 (paperback), 1-139-09540-4 (e-book), 1-139-61690-0", ISBN-13 = "978-1-107-60407-0 (paperback), 978-1-139-09540-2 (e-book), 978-1-139-61690-4", LCCN = "QA297 .F635 2011", MRclass = "65Y15", MRnumber = "3137640", bibdate = "Sat Aug 9 16:07:25 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/magma.bib; http://www.math.utah.edu/pub/tex/bib/maple-extract.bib; http://www.math.utah.edu/pub/tex/bib/mathematica.bib; http://www.math.utah.edu/pub/tex/bib/matlab.bib; z3950.loc.gov:7090/Voyager", series = "London Mathematical Society lecture note series", acknowledgement = ack-nhfb, book-DOI = "https://doi.org/10.1017/CBO9781139095402", tableofcontents = "The state of the art in Smale's 7th problem / C. Beltr{\'a}n \\ The shape of data / G. Carlsson \\ Upwinding in finite element systems of differential forms / S. H. Christiansen \\ On the complexity of computing quadrature formulas for SDEs / S. Dereich, T. M{\"u}ller-Gronbach and K. Ritter \\ The quantum walk of F. Riesz / F. A. Gr{\"u}nbaum and L. Vel{\'a}zquez \\ Modulated Fourier expansions for continuous and discrete oscillatory systems / E. Hairer and Ch. Lubich \\ The dual role of convection in 3D Navier--Stokes equations / T. Y. Hou, Z. Shi and S. Wang \\ Algebraic and differential invariants / E. Hubert \\ Through the kaleidoscope: symmetries, groups and Chebyshev-approximations from a computational point of view / H. Munthe-Kaas, M. Nome and B. N. Ryland \\ Sage: creating a viable free open source alternative to Magma, Maple, Mathematica, and MATLAB / W. Stein", } @Manual{Cannon:2014:HMF, author = "John Cannon and Wieb Bosma and Claus Fieker and Allan Steel", title = "Handbook of {Magma} Functions", organization = "University of Sydney", address = "Sydney, NSW, Australia", pages = "cxxxv + 5383 + lxiv", day = "30", month = jan, year = "2014", bibdate = "Sat Aug 09 16:47:09 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/magma.bib", acknowledgement = ack-nhfb, } @InCollection{Lee:2014:MID, author = "Kwankyu Lee", booktitle = "Mathematical software---{ICMS 2014}", title = "{Magma} implementation of decoding algorithms for general algebraic geometry codes", volume = "8592", publisher = pub-SV, address = pub-SV:adr, pages = "119--123", year = "2014", DOI = "https://doi.org/10.1007/978-3-662-44199-2_21", MRclass = "94B27 (14G50 68W30)", MRnumber = "3334755", bibdate = "Fri Nov 25 17:41:52 2016", bibsource = "http://www.math.utah.edu/pub/tex/bib/magma.bib", series = "Lecture Notes in Comput. Sci.", acknowledgement = ack-nhfb, } @Article{Lundstrom:2014:GMG, author = "Patrik Lundstr{\"o}m", title = "Good {Magma} gradings on rings", journal = j-COMMUN-ALGEBRA, volume = "42", number = "12", pages = "5357--5373", year = "2014", CODEN = "COALDM", DOI = "https://doi.org/10.1080/00927872.2011.616563", ISSN = "0092-7872 (print), 1532-4125 (electronic)", ISSN-L = "0092-7872", MRclass = "16S34 (16W50)", MRnumber = "3223644", MRreviewer = "Maria J. Asensio", bibdate = "Fri Nov 25 17:42:32 2016", bibsource = "http://www.math.utah.edu/pub/tex/bib/magma.bib", acknowledgement = ack-nhfb, fjournal = "Communications in Algebra", } @PhdThesis{Smertnig:2014:FTM, author = "Daniel Smertnig", title = "Factorization Theory in Maximal Orders", type = "{Ph.D.} thesis", school = "Institut f{\"u}r Mathematik und Wissenschaftliches Rechnen, Naturwissenschaftliche Fakult{\"a}t, Universit{\"a}t Graz", address = "Graz, Austria", month = feb, year = "2014", bibdate = "Sat Aug 09 14:29:21 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/magma.bib", URL = "http://permalink.obvsg.at/AC11698360", abstract = "In a noetherian ring, any element that is not a zero-divisor can be expressed as a product of finitely many atoms (irreducible elements), but usually such a representation is not unique.Factorization theory concerns itself with investigating such phenomena of non-unique factorizations, often by studying suitable arithmetical invariants. This publication-based thesis presents a foray into the study of factorizations in noncommutative settings. It extends the well-understood machinery from commutative Krull monoids, with the main application being to classical maximal orders in central simple algebras over global fields. However, the necessary tools are developed in much greater generality by means of the divisorial one-sided ideal theory of arithmetical maximal orders?a class of semigroups that generalizes the setting of commutative Krull monoids. Under an additional hypothesis, a transfer homomorphism to a monoid of zero-sum sequences over a subset of an abelian group is obtained. In this way, many questions about factorizations in arithmetical maximal orders can be reduced to well-studied problems in combinatorial number theory, completely analogous to the way it is done in Krull monoids. The study of classical maximal orders in central simple algebras over global fields splits into two cases: In the main case, when every stably free left ideal is free, the already mentioned additional hypothesis is satisfied and the transfer results apply. The system of sets of lengths and various catenary degrees are determined by those of a monoid of zero-sum sequences over a ray class group. In the second case the transfer results do not apply. For classical maximal orders over a ring of algebraic integers, we show that in the second case it is impossible to construct a transfer homomorphism to any monoid of zero-sum sequences, and that the values of some central arithmetical invariants are substantially different from those in the main case.", acknowledgement = ack-nhfb, } @InCollection{Chi:2015:ABG, author = "Jes{\'u}s-Javier Chi and Thomaz Oliveira", booktitle = "Progress in cryptology---{LATINCRYPT} 2015", title = "Attacking a binary {GLS} elliptic curve with {Magma}", volume = "9230", publisher = pub-SV, address = pub-SV:adr, pages = "308--326", year = "2015", DOI = "https://doi.org/10.1007/978-3-319-22174-8_17", MRclass = "94A60", MRnumber = "3447381", bibdate = "Fri Nov 25 17:44:30 2016", bibsource = "http://www.math.utah.edu/pub/tex/bib/magma.bib", series = "Lecture Notes in Comput. Sci.", acknowledgement = ack-nhfb, } @Article{Thiel:2015:CCA, author = "U. Thiel", title = "{Champ}: a {Cherednik} algebra {Magma} package", journal = j-LMS-J-COMPUT-MATH, volume = "18", number = "1", pages = "266--307", year = "2015", CODEN = "????", DOI = "https://doi.org/10.1112/S1461157015000054", ISSN = "1461-1570", MRclass = "16Z05 (16-04 16S99 20F55)", MRnumber = "3361642", bibdate = "Wed Aug 19 09:40:26 MDT 2015", bibsource = "http://journals.cambridge.org/action/displayJournal?jid=JCM; http://www.math.utah.edu/pub/tex/bib/lms-j-comput-math.bib; http://www.math.utah.edu/pub/tex/bib/magma.bib", acknowledgement = ack-nhfb, ajournal = "LMS J. Comput. Math.", fjournal = "LMS Journal of Computation and Mathematics", onlinedate = "22 April 2015", }

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@Proceedings{ACM:1994:IPI, editor = "{ACM}", booktitle = "{ISSAC '94: Proceedings of the 1994 International Symposium on Symbolic and Algebraic Computation: July 20--22, 1994, Oxford, England, United Kingdom}", title = "{ISSAC '94: Proceedings of the 1994 International Symposium on Symbolic and Algebraic Computation: July 20--22, 1994, Oxford, England, United Kingdom}", publisher = pub-ACM, address = pub-ACM:adr, pages = "ix + 359", year = "1994", ISBN = "0-89791-638-7", ISBN-13 = "978-0-89791-638-7", LCCN = "QA76.95.I59 1994", bibdate = "Thu Sep 26 05:45:15 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib; http://www.math.utah.edu/pub/tex/bib/magma.bib", acknowledgement = ack-nhfb, confdate = "20--22 July 1994", conflocation = "Oxford, UK", confsponsor = "ACM", pubcountry = "USA", } @Book{Grabmeier:2003:CAH, editor = "Johannes Grabmeier and Erich Kaltofen and Volker Weispfenning", booktitle = "Computer algebra handbook: foundations, applications, systems", title = "Computer algebra handbook: foundations, applications, systems", publisher = pub-SV, address = pub-SV:adr, pages = "xx + 637", year = "2003", DOI = "https://doi.org/10.1007/978-3-642-55826-9", ISBN = "3-540-65466-6, 3-642-55826-7 (e-book)", ISBN-13 = "978-3-540-65466-7, 978-3-642-55826-9 (e-book)", LCCN = "QA155.7.E4 C64954 2003eb", bibdate = "Sat Aug 9 14:28:33 MDT 2014", bibsource = "fsz3950.oclc.org:210/WorldCat; http://www.math.utah.edu/pub/tex/bib/magma.bib; z3950.loc.gov:7090/Voyager", URL = "http://www.loc.gov/catdir/enhancements/fy0817/2002190828-d.html; http://www.loc.gov/catdir/enhancements/fy0817/2002190828-t.html", abstract = "This Computer Algebra Handbook gives a comprehensive snapshot of this field at the intersection of mathematics and computer science with applications in physics, engineering and education. It contains both theory, systems and practice of the discipline of symbolic computation and computer algebra. With the wide angle of a ``lense'' of about 200 contributors it shows the state of computer algebra research and applications in the last decade of the twentieth century. Aside from discussing the foundations of computer algebra, the handbook describes 67 software systems and packages that perform tasks in symbolic computation. In addition, the handbook offers 100 pages on applications in physics, mathematics, computer science, engineering chemistry and education. This book will be very useful as a reference to graduate students and researchers in symbolic computation and computer algebra.", acknowledgement = ack-nhfb, subject = "Algebra; Data processing; Data processing; Computerwiskunde; Algebra; Getaltheorie; Groepentheorie; {\'A}lgebra computacional; Teoria dos grupos; Teoria dos conjuntos; {\'A}lgebra linear; Application; Logiciel; Calcul formel; Alg{\`e}bre; Traitement des donn{\'e}es; Computeralgebraa", tableofcontents = "List of Contributing Authors \\ Foreword \\ Editorial Remarks \\ 1. Development, Characterization, Prospects \\ 2. Topics of Computer Algebra \\ 3. Applications of Computer Algebra \\ 4. Computer Algebra Systems \\ 5. Meetings and Publications \\ Cited References \\ Subject Index \\ Index for Authors' Contributions", } @Proceedings{Ganzha:2005:CAS, editor = "Victor G. Ganzha and Ernst W. Mayr and Evgenii V. Vorozhtsov", booktitle = "{Computer algebra in scientific computing: 8th international workshop, CASC 2005, Kalamata, Greece, September 12--16, 2005: proceedings}", title = "{Computer algebra in scientific computing: 8th international workshop, CASC 2005, Kalamata, Greece, September 12--16, 2005: proceedings}", volume = "3718", publisher = pub-SV, address = pub-SV:adr, pages = "500", year = "2005", CODEN = "LNCSD9", DOI = "https://doi.org/10.1007/11555964", ISBN = "3-540-28966-6", ISBN-13 = "978-3-540-28966-1", ISSN = "0302-9743 (print), 1611-3349 (electronic)", ISSN-L = "0302-9743", LCCN = "????", bibdate = "Thu Sep 29 06:46:02 MDT 2005", bibsource = "http://www.math.utah.edu/pub/tex/bib/lncs.bib; http://www.math.utah.edu/pub/tex/bib/magma.bib", series = ser-LNCS, URL = "http://www.springerlink.com/content/978-3-540-28966-1; http://www.springerlink.com/openurl.asp?genre=issue&issn=0302-9743&volume=3718", acknowledgement = ack-nhfb, } @Book{Bosma:2006:DMM, author = "Wieb Bosma and John Cannon", booktitle = "Discovering mathematics with {Magma}: reducing the abstract to the concrete", title = "Discovering mathematics with {Magma}: reducing the abstract to the concrete", volume = "19", publisher = pub-SV, address = pub-SV:adr, pages = "xxiv + 374", year = "2006", DOI = "https://doi.org/10.1007/978-3-540-37634-7", ISBN = "3-540-37632-1 (hardcover), 3-540-37634-8 (e-book)", ISBN-13 = "978-3-540-37632-3 (hardcover), 978-3-540-37634-7 (e-book)", ISSN = "1431-1550", LCCN = "QA155.7.E4 D57 2006", MRclass = "00B15 (11-06 14-06 20-06)", MRnumber = "2265375 (2007h:00016)", bibdate = "Sat Aug 9 14:06:25 MDT 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/magma.bib; http://www.math.utah.edu/pub/tex/bib/master.bib; z3950.loc.gov:7090/Voyager", series = "Algorithms and computation in mathematics", URL = "http://www.loc.gov/catdir/enhancements/fy0824/2006931477-b.html; http://www.loc.gov/catdir/enhancements/fy0824/2006931477-d.html; http://www.loc.gov/catdir/toc/fy0707/2006931477.html; http://www.springerlink.com/content/978-3-642-01960-9; http://www.springerlink.com/openurl.asp?genre=book&isbn=978-3-540-37632-3", abstract = "With a design based on the ontology and semantics of algebra, Magma enables users to rapidly formulate and perform calculations in the more abstract parts of mathematics. This book introduces the role Magma plays in advanced mathematical research through 14 case studies which, in most cases, describe computations underpinning theoretical results.", acknowledgement = ack-nhfb, libnote = "Not in my library.", subject = "Algebra; Data processing; Alg{\`e}bre; Informatique; MATHEMATICS; Abstract; Algebra; Data processing; algebra; data processing; symbolic algebra", tableofcontents = "Cover \\ Contents \\ Preface \\ Magma: The project \\ Discovering mathematics: About this volume \\ How to read the Magma code? \\ Some computational experiments in number theory \\ Applications of the class field theory of global fields \\ Some ternary Diophantine equations of signature $(n, n, 2)$ \\ Studying the Birch and Swinnerton-Dyer conjecture for modular abelian varieties using Magma \\ Computing with the analytic Jacobian of a genus $2$ curve \\ Graded rings and special $K_3$ surfaces \\ Constructing the split octonions \\ Support varieties for modules \\ When is projectivity detected on subalgebras? \\ Cohomology and group extensions in Magma \\ Computing the primitive permutation groups of degree less than $1000$ \\ Computer aided discovery of a fast algorithm for testing conjugacy in braid groups \\ Searching for linear codes with large minimum distance \\ Colouring planar graphs \\ Appendix: The Magma language \\ Index \\ Last Page", } @Proceedings{Shi:2007:CSIb, editor = "Yong Shi and Geert Dick van Albada and Jack Dongarra and Peter M. A. Sloot", booktitle = "{Computational Science --- ICCS 2007: 7th International Conference, Beijing, China, May 27 --- 30, 2007, Proceedings, Part II}", title = "{Computational Science --- ICCS 2007: 7th International Conference, Beijing, China, May 27 --- 30, 2007, Proceedings, Part II}", volume = "4488", publisher = pub-SV, address = pub-SV:adr, pages = "153 (est.)", year = "2007", CODEN = "LNCSD9", DOI = "https://doi.org/10.1007/978-3-540-72586-2", ISBN = "3-540-72585-7 (print), 3-540-72586-5 (e-book)", ISBN-13 = "978-3-540-72585-5 (print), 978-3-540-72586-2 (e-book)", ISSN = "0302-9743 (print), 1611-3349 (electronic)", ISSN-L = "0302-9743", LCCN = "????", bibdate = "Wed Dec 19 15:19:26 MST 2012", bibsource = "http://www.math.utah.edu/pub/tex/bib/axiom.bib; http://www.math.utah.edu/pub/tex/bib/lncs.bib; http://www.math.utah.edu/pub/tex/bib/magma.bib; http://www.math.utah.edu/pub/tex/bib/maple-extract.bib", series = ser-LNCS, URL = "http://www.springerlink.com/content/978-3-540-72586-2", acknowledgement = ack-nhfb, } @Proceedings{Jeffrey:2008:PAM, editor = "David Jeffrey", booktitle = "{Proceedings of the 21st annual meeting of the International Symposium on Symbolic Computation, ISSAC 2008, July 20--23, 2008, Hagenberg, Austria}", title = "{Proceedings of the 21st annual meeting of the International Symposium on Symbolic Computation, ISSAC 2008, July 20--23, 2008, Hagenberg, Austria}", publisher = pub-ACM, address = pub-ACM:adr, pages = "x + 338", year = "2008", ISBN = "1-59593-904-0", ISBN-13 = "978-1-59593-904-3", LCCN = "????", bibdate = "Fri Jun 20 08:53:37 2008", bibsource = "http://www.math.utah.edu/pub/tex/bib/magma.bib; http://www.math.utah.edu/pub/tex/bib/maple-extract.bib", acknowledgement = ack-nhfb, } @Book{Klin:2009:AAC, editor = "Mikhail Klin and Gareth Aneurin Jones and Aleksandar Juri{\v{s}}i{\'c} and Mikhail Muzychuk and Ilia Ponomarenko", booktitle = "Algorithmic algebraic combinatorics and {Gr{\"o}bner} bases", title = "Algorithmic algebraic combinatorics and {Gr{\"o}bner} bases", publisher = pub-SV, address = pub-SV:adr, pages = "xii + 311", year = "2009", DOI = "https://doi.org/10.1007/978-3-642-01960-9", ISBN = "3-642-01959-5, 3-642-01960-9 (e)", ISBN-13 = "978-3-642-01959-3, 978-3-642-01960-9 (eISBN)", LCCN = "QA164 .A427 2009", MRclass = "05E30, 13P10, 20B25, 68-04", bibdate = "Sat Aug 9 14:06:26 MDT 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/magma.bib; z3950.loc.gov:7090/Voyager", URL = "http://www.loc.gov/catdir/enhancements/fy1203/2009927505-b.html; http://www.loc.gov/catdir/enhancements/fy1203/2009927505-d.html; http://www.loc.gov/catdir/enhancements/fy1402/2009927505-t.html", abstract = "This collection of tutorial and research papers introduces readers to diverse areas of modern pure and applied algebraic combinatorics and finite geometries with a special emphasis on algorithmic aspects and the use of the theory of Grobner bases. Topics covered include coherent configurations, association schemes, permutation groups, Latin squares, the Jacobian conjecture, mathematical chemistry, extremal combinatorics, coding theory, designs, etc. Special attention is paid to the description of innovative practical algorithms and their implementation in software packages such as GAP and MAGMA. Readers will benefit from the exceptional combination of instructive training goals with the presentation of significant new scientific results of an interdisciplinary nature.", acknowledgement = ack-nhfb, subject = "Combinatorial analysis", } @Proceedings{Fukuda:2010:MSI, editor = "Komei Fukuda and Joris van der Hoeven and Michael Joswig and Nobuki Takayama", booktitle = "{Mathematical software --- ICMS 2010: third International Congress on Mathematical Software, K{\=o}be, Japan, September 13--17, 2010: proceedings}", title = "{Mathematical software --- ICMS 2010: third International Congress on Mathematical Software, K{\=o}be, Japan, September 13--17, 2010: proceedings}", volume = "6327", publisher = pub-SV, address = pub-SV:adr, pages = "xvi + 368", year = "2010", DOI = "https://doi.org/10.1007/978-3-642-15582-6", ISBN = "3-642-15581-2 (paperback), 3-642-15582-0 (e-book)", ISBN-13 = "978-3-642-15581-9 (paperback), 978-3-642-15582-6 (e-book)", LCCN = "QA76.95 .I5654 2010", bibdate = "Sat Aug 9 14:06:27 MDT 2014", bibsource = "http://www.math.utah.edu/pub/tex/bib/fparith.bib; http://www.math.utah.edu/pub/tex/bib/lncs.bib; http://www.math.utah.edu/pub/tex/bib/lncs2010a.bib; http://www.math.utah.edu/pub/tex/bib/magma.bib; z3950.loc.gov:7090/Voyager", series = ser-LNCS, URL = "http://www.springerlink.com/content/978-3-642-15581-9", acknowledgement = ack-nhfb, subject = "Mathematics; Data processing; Congresses; Computer software", } @Proceedings{Watt:1991:IPI, editor = "Stephen M. Watt", booktitle = "{ISSAC '91: proceedings of the 1991 International Symposium on Symbolic and Algebraic Computation, July 15--17, 1991, Bonn, Germany}", title = "{ISSAC '91: proceedings of the 1991 International Symposium on Symbolic and Algebraic Computation, July 15--17, 1991, Bonn, Germany}", publisher = pub-ACM, address = pub-ACM:adr, pages = "xiii + 468", year = "1991", ISBN = "0-89791-437-6", ISBN-13 = "978-0-89791-437-6", LCCN = "QA 76.95 I59 1991", bibdate = "Thu Sep 26 06:00:06 MDT 1996", bibsource = "http://www.math.utah.edu/pub/tex/bib/issac.bib; http://www.math.utah.edu/pub/tex/bib/magma.bib", abstract = "The following topics were dealt with: algorithms for symbolic mathematical computation; languages, systems and packages; computational geometry, group theory and number theory; automatic theorem proving and programming; interface of symbolics, numerics and graphics; applications in mathematics, science and engineering; and symbolic and algebraic computation in education.", acknowledgement = ack-nhfb, classification = "C1160 (Combinatorial mathematics); C4130 (Interpolation and function approximation); C4210 (Formal logic); C4240 (Programming and algorithm theory); C7310 (Mathematics)", confdate = "15--17 July 1991", conflocation = "Bonn, Germany", confsponsor = "ACM", keywords = "algebra --- data processing --- congresses; Algebraic computation; Algorithms; Automatic theorem proving; Computational geometry; Education; Engineering; Graphics; Group theory; Languages; Mathematics; mathematics --- data processing --- congresses; Number theory; Programming; Science; Symbolic mathematical computation; Symbolics", pubcountry = "USA", thesaurus = "Computational complexity; Formal languages; Interpolation; Number theory; Polynomials; Symbol manipulation", }

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