@Preamble{"\input bibnames.sty "
# "\input path.sty "
# "\hyphenation{ }"
}
@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|https://www.math.utah.edu/~beebe/|"}
@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)"}
@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"}
@String{ser-LNCS = "Lecture Notes in Computer Science"}
@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 = "https://www.math.utah.edu/pub/tex/bib/magma.bib;
https://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/;
https://www.math.utah.edu/pub/tex/bib/magma.bib;
https://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/;
https://www.math.utah.edu/pub/tex/bib/magma.bib;
https://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 = "https://www.math.utah.edu/pub/tex/bib/jsymcomp.bib;
https://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 = "https://www.math.utah.edu/pub/tex/bib/magma.bib;
https://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/;
https://www.math.utah.edu/pub/tex/bib/magma.bib;
https://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/;
https://www.math.utah.edu/pub/tex/bib/magma.bib;
https://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/;
https://www.math.utah.edu/pub/tex/bib/magma.bib;
https://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/;
https://www.math.utah.edu/pub/tex/bib/magma.bib;
https://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/;
https://www.math.utah.edu/pub/tex/bib/magma.bib;
https://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/;
https://www.math.utah.edu/pub/tex/bib/issac.bib;
https://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/;
https://www.math.utah.edu/pub/tex/bib/magma.bib;
https://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 = "https://www.math.utah.edu/pub/tex/bib/jsymcomp.bib;
https://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/;
https://www.math.utah.edu/pub/tex/bib/magma.bib;
https://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/;
https://www.math.utah.edu/pub/tex/bib/magma.bib;
https://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/;
https://www.math.utah.edu/pub/tex/bib/magma.bib;
https://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/;
https://www.math.utah.edu/pub/tex/bib/magma.bib;
https://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/;
https://www.math.utah.edu/pub/tex/bib/magma.bib;
https://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/;
https://www.math.utah.edu/pub/tex/bib/magma.bib;
https://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 = "https://www.math.utah.edu/pub/tex/bib/jsymcomp.bib;
https://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 = "https://www.math.utah.edu/pub/tex/bib/jsymcomp.bib;
https://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 = "https://www.math.utah.edu/pub/tex/bib/jsymcomp.bib;
https://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/;
https://www.math.utah.edu/pub/tex/bib/issac.bib;
https://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 = "https://www.math.utah.edu/pub/tex/bib/jsymcomp.bib;
https://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 = "https://www.math.utah.edu/pub/tex/bib/jsymcomp.bib;
https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://www.math.utah.edu/pub/tex/bib/jsymcomp.bib;
https://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 = "https://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 = "https://www.math.utah.edu/pub/tex/bib/jsymcomp.bib;
https://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;
https://www.math.utah.edu/pub/tex/bib/jsymcomp.bib;
https://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 = "https://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 = "https://www.math.utah.edu/pub/tex/bib/magma.bib;
https://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 = "https://www.math.utah.edu/pub/tex/bib/axiom.bib;
https://www.math.utah.edu/pub/tex/bib/macsyma.bib;
https://www.math.utah.edu/pub/tex/bib/magma.bib;
https://www.math.utah.edu/pub/tex/bib/maple-extract.bib;
https://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 = "https://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;
https://www.math.utah.edu/pub/tex/bib/jsymcomp.bib;
https://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 = "https://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;
https://www.math.utah.edu/pub/tex/bib/jsymcomp.bib;
https://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 = "https://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 = "https://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 = "https://www.math.utah.edu/pub/tex/bib/jsymcomp.bib;
https://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 = "https://www.math.utah.edu/pub/tex/bib/jsymcomp.bib;
https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://www.math.utah.edu/pub/tex/bib/histmath.bib;
https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://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 = "https://www.math.utah.edu/pub/tex/bib/axiom.bib;
https://www.math.utah.edu/pub/tex/bib/magma.bib;
https://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;
https://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;
https://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;
https://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 = "https://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/;
https://www.math.utah.edu/pub/tex/bib/magma.bib;
https://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 = "https://www.math.utah.edu/pub/tex/bib/magma.bib;
https://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/;
https://www.math.utah.edu/pub/tex/bib/gnu.bib;
https://www.math.utah.edu/pub/tex/bib/issac.bib;
https://www.math.utah.edu/pub/tex/bib/magma.bib;
https://www.math.utah.edu/pub/tex/bib/maple-extract.bib;
https://www.math.utah.edu/pub/tex/bib/mathematica.bib;
https://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 = "https://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 = "https://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 = "https://www.math.utah.edu/pub/tex/bib/lncs2010a.bib;
https://www.math.utah.edu/pub/tex/bib/magma.bib;
https://www.math.utah.edu/pub/tex/bib/maple-extract.bib;
https://www.math.utah.edu/pub/tex/bib/mathematica.bib;
https://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 = "https://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/;
https://www.math.utah.edu/pub/tex/bib/magma.bib;
https://www.math.utah.edu/pub/tex/bib/maple-extract.bib;
https://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 = "https://www.math.utah.edu/pub/tex/bib/magma.bib;
https://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 = "https://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 = "https://www.math.utah.edu/pub/tex/bib/magma.bib;
https://www.math.utah.edu/pub/tex/bib/maple-extract.bib;
https://www.math.utah.edu/pub/tex/bib/mathematica.bib;
https://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 = "https://www.math.utah.edu/pub/tex/bib/magma.bib",
acknowledgement = ack-nhfb,
}
@InProceedings{Lee:2014:MID,
author = "Kwankyu Lee",
title = "{Magma} Implementation of Decoding Algorithms for
General Algebraic Geometry Codes",
crossref = "Hong:2014:MSI",
pages = "119--123",
year = "2014",
DOI = "https://doi.org/10.1007/978-3-662-44199-2_21",
MRclass = "94B27 (14G50 68W30)",
MRnumber = "3334755",
bibdate = "Tue Sep 26 10:39:16 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/magma.bib",
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 = "https://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 = "https://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 = "https://www.math.utah.edu/pub/tex/bib/magma.bib",
series = "Lecture Notes in Comput. Sci.",
acknowledgement = ack-nhfb,
}
@InCollection{Steel:2015:DSM,
author = "Allan Steel",
booktitle = "{PASCO'2015 --- Proceedings of the 2015 International
Workshop on Parallel Symbolic Computation}",
title = "Direct solution of the $ (11, 9, 8) $-{MinRank}
problem by the block {Wiedemann} algorithm in {Magma}
with a {Tesla GPU}",
publisher = pub-ACM,
address = pub-ACM:adr,
pages = "2--6",
year = "2015",
MRclass = "13P10 (13P15 68W30)",
MRnumber = "3612348",
bibdate = "Tue Jan 8 10:58:21 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/magma.bib",
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;
https://www.math.utah.edu/pub/tex/bib/lms-j-comput-math.bib;
https://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",
}
@InCollection{Elsenhans:2016:CGG,
author = "Andreas-Stephan Elsenhans",
booktitle = "Mathematical and computational approaches in advancing
modern science and engineering",
title = "Computation of {Galois} groups in {\tt magma}",
publisher = "Springer",
address = "Cham, Switzerland",
pages = "621--628",
year = "2016",
MRclass = "35K57 (34C40 35K40)",
MRnumber = "3838226",
bibdate = "Tue Jan 8 10:58:21 2019",
bibsource = "https://www.math.utah.edu/pub/tex/bib/magma.bib",
acknowledgement = ack-nhfb,
}
@Article{Sutherland:2017:DCG,
author = "Nicole Sutherland",
title = "A demonstration of computing {Galois} groups of
polynomials in {Magma}",
journal = j-ACM-COMM-COMP-ALGEBRA,
volume = "51",
number = "3",
pages = "81--82",
month = sep,
year = "2017",
CODEN = "????",
DOI = "https://doi.org/10.1145/3177795.3177796",
ISSN = "1932-2232 (print), 1932-2240 (electronic)",
ISSN-L = "1932-2232",
bibdate = "Fri Jan 5 06:22:51 MST 2018",
bibsource = "https://www.math.utah.edu/pub/tex/bib/magma.bib;
https://www.math.utah.edu/pub/tex/bib/sigsam.bib",
abstract = "We demonstrate some of the computations of Galois
groups which are possible in Magma [1].",
acknowledgement = ack-nhfb,
fjournal = "ACM Communications in Computer Algebra",
journal-URL = "http://portal.acm.org/browse_dl.cfm?idx=J1000",
}
@Article{Koprowski:2020:CMP,
author = "Przemys{\l}aw Koprowski",
title = "{CQF Magma} package",
journal = j-ACM-COMM-COMP-ALGEBRA,
volume = "54",
number = "2",
pages = "53--56",
month = sep,
year = "2020",
CODEN = "????",
DOI = "https://doi.org/10.1145/3427218.3427224",
ISSN = "1932-2232 (print), 1932-2240 (electronic)",
ISSN-L = "1932-2232",
bibdate = "Wed Sep 30 13:46:41 MDT 2020",
bibsource = "https://www.math.utah.edu/pub/tex/bib/gnu.bib;
https://www.math.utah.edu/pub/tex/bib/magma.bib;
https://www.math.utah.edu/pub/tex/bib/sigsam.bib",
URL = "https://dl.acm.org/doi/10.1145/3427218.3427224",
abstract = "CQF is a free, open-source Magma package for doing
computations in quadratic forms theory. We present some
selected ingredients of the package.",
acknowledgement = ack-nhfb,
fjournal = "ACM Communications in Computer Algebra",
journal-URL = "https://dl.acm.org/loi/sigsam-cca",
}
@Unpublished{Goel:2022:IIR,
author = "Kriti Goel and Jack Jeffries and Anurag K. Singh",
title = "The $a$-invariant of an invariant ring",
year = "2022",
bibdate = "Wed Jul 06 08:57:07 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/magma.bib",
note = "In preparation.",
acknowledgement = ack-nhfb,
}
@Article{Kao:2022:FTL,
author = "Chiu-Yen Kao and Braxton Osting and Jackson C.
Turner",
title = "Flat tori with large {Laplacian} eigenvalues in
dimensions up to eight",
journal = "arXiv.org",
volume = "??",
number = "??",
pages = "18",
day = "16",
month = feb,
year = "2022",
DOI = "https://doi.org/10.48550/arXiv.2202.08351",
MRclass = "35P15, 49K35, 58J50, 52C17",
bibdate = "Wed Jul 06 08:50:03 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/kepler.bib;
https://www.math.utah.edu/pub/tex/bib/magma.bib",
URL = "http://arxiv.org/abs/2202.08351",
abstract = "We consider the optimization problem of maximizing the
$k$-th Laplacian eigenvalue, $ \lambda k$, over flat
$d$-dimensional tori of fixed volume. For $ k = 1$,
this problem is equivalent to the densest lattice
sphere packing problem. For larger $k$, this is
equivalent to the NP-hard problem of finding the
$d$-dimensional (dual) lattice with longest $k$-th
shortest lattice vector. As a result of extensive
computations, for $ d \leq 8$, we obtain a sequence of
flat tori, $ T_{k, d}$, each of volume one, such that
the $k$-th Laplacian eigenvalue of $ T_{k, d}$ is very
large; for each (finite) $k$ the $k$-th eigenvalue
exceeds the value in (the $ k \to \infty $ asymptotic)
Weyl's law by a factor between 1.54 and 2.01, depending
on the dimension. Stationarity conditions are derived
and numerically verified for $ T_{k, d}$ and we
describe the degeneration of the tori as $ k \to \infty
$.",
acknowledgement = ack-nhfb,
}
@Unpublished{Hochster:2022:WNE,
author = "Melvin Hochster and Jack Jeffries and Vaibhav Pandey
and Anurag K. Singh",
title = "When are the natural embeddings of classical invariant
rings pure?",
year = "2022",
bibdate = "Wed Jul 06 08:55:22 2022",
bibsource = "https://www.math.utah.edu/pub/tex/bib/magma.bib",
note = "In preparation.",
acknowledgement = ack-nhfb,
}
@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 = "https://www.math.utah.edu/pub/tex/bib/issac.bib;
https://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;
https://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 = "https://www.math.utah.edu/pub/tex/bib/lncs.bib;
https://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,
editor = "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 = "https://www.math.utah.edu/pub/tex/bib/magma.bib;
https://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 = "Preface \\
Magma: the project \\
Discovering mathematics: about this volume \\
How to read the Magma code? \\
Some computational experiments in number theory / Wieb
Bosma \\
Applications of the class field theory of global fields
/ Claus Fieker \\
Some ternary Diophantine equations of signature (n, n,
2) / Nils Bruin \\
Studying the Birch and Swinnerton-Dyer conjecture for
modular abelian varieties using Magma / William Stein
\\
Computing with the analytic Jacobian of a genus 2 curve
/ Paul B. van Wamelen \\
Graded rings and special K3 surfaces / Gavin Brown
\\
Constructing the split octonions / Donald E. Taylor
\\
Support varieties for modules / Jon F. Carlson \\
When is projectivity detected on subalgebras? / Jon F.
Carlson \\
Cohomology and group extensions in Magma / Derek F.
Holt \\
Computing the primitive permutation groups of degree
less than 1000 / Colva M. Roney-Dougal and William R.
Unger \\
Computer aided discovery of a fast algorithm for
testing conjugacy in braid groups / Volker Gebhardt
\\
Searching for linear codes with large minimum distance
/ Markus Grassl \\
Colouring planar graphs / Paulette Lieby \\
Appendix: The Magma language / Geoff Bailey",
}
@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 = "https://www.math.utah.edu/pub/tex/bib/axiom.bib;
https://www.math.utah.edu/pub/tex/bib/lncs.bib;
https://www.math.utah.edu/pub/tex/bib/magma.bib;
https://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 = "https://www.math.utah.edu/pub/tex/bib/magma.bib;
https://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 = "https://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 = "https://www.math.utah.edu/pub/tex/bib/fparith.bib;
https://www.math.utah.edu/pub/tex/bib/lncs.bib;
https://www.math.utah.edu/pub/tex/bib/lncs2010a.bib;
https://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 = "https://www.math.utah.edu/pub/tex/bib/issac.bib;
https://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",
}
@Proceedings{Hong:2014:MSI,
editor = "Hoon Hong and Chee Yap",
booktitle = "Mathematical Software --- {ICMS 2014: 4th
International Conference, Seoul, South Korea, August
5--9, 2014, Proceedings}",
title = "Mathematical Software --- {ICMS 2014: 4th
International Conference, Seoul, South Korea, August
5--9, 2014, Proceedings}",
volume = "8592",
publisher = pub-SV,
address = pub-SV:adr,
pages = "xxxii + 735",
year = "2014",
DOI = "https://doi.org/10.1007/978-3-662-44199-2",
ISBN = "3-662-44198-5 (paperback), 3-662-44199-3 (e-book)",
ISBN-13 = "978-3-662-44198-5 (paperback), 978-3-662-44199-2
(e-book)",
LCCN = "QA76.9.M35",
bibdate = "Sat Sep 23 09:59:48 2023",
bibsource = "https://www.math.utah.edu/pub/tex/bib/elefunt.bib;
https://www.math.utah.edu/pub/tex/bib/gnu.bib;
https://www.math.utah.edu/pub/tex/bib/magma.bib;
https://www.math.utah.edu/pub/tex/bib/maple-extract.bib;
https://www.math.utah.edu/pub/tex/bib/mathematica.bib;
https://www.math.utah.edu/pub/tex/bib/texbook3.bib",
acknowledgement = ack-nhfb,
tableofcontents = "Front Matter \\
Invited Talks \\
Experimental Computation and Visual Theorems / Jonathan
M. Borwein / 1--8 \\
Soft Math Math Soft / Bruno Buchberger / 9--15 \\
Mathematical Theory Exploration \\
Flyspecking Flyspeck / Mark Adams / 16--20 \\
Symbolic Computing Package for Mathematica for
Versatile Manipulation of Mathematical Expressions /
Youngjoo Chung / 21--25 \\
Representing, Archiving, and Searching the Space of
Mathematical Knowledge / Mihnea Iancu, Michael
Kohlhase, Corneliu Prodescu / 26--30 \\
Early Examples of Software in Mathematical Knowledge
Management / Patrick Ion / 31--35 \\
Discourse-Level Parallel Markup and Meaning Adoption in
Flexiformal Theory Graphs / Michael Kohlhase, Mihnea
Iancu / 36--40 \\
Complexity Analysis of the Bivariate Buchberger
Algorithm in Theorema / Alexander Maletzky, Bruno
Buchberger / 41--48 \\
Theorema 2.0: A System for Mathematical Theory
Exploration / Wolfgang Windsteiger / 49--52 \\
Computational Group Theory \\
New Approaches in Black Box Group Theory / Alexandre
Borovik, {\c{S}}{\"u}kr{\"u} Yal{\c{c}}{\i}nkaya /
53--58 \\
A GAP Package for Computing with Real Semisimple Lie
Algebras / Heiko Dietrich, Paolo Faccin, Willem A. de
Graaf / 59--66 \\
Bacterial Genomics and Computational Group Theory: The
BioGAP Package for GAP / Attila Egri-Nagy, Andrew R.
Francis, Volker Gebhardt / 67--74 \\
SgpDec: Cascade (De)Compositions of Finite
Transformation Semigroups and Permutation Groups /
Attila Egri-Nagy, James D. Mitchell, Chrystopher L.
Nehaniv / 75--82 \\
Approximating Generators for Integral Arithmetic Groups
/ Bettina Eick / 83--86 \\
Software for Groups: Theory and Practice / Alexander
Hulpke / 87--91 \\
Computation of Genus 0 Belyi Functions / Mark van
Hoeij, Raimundas Vidunas / 92--98 \\
On Computation of the First Baues--Wirsching Cohomology
of a Freely-Generated Small Category / Yasuhiro Momose,
Yasuhide Numata / 99--105 \\
Coding Theory \\
Codes over a Non Chain Ring with Some Applications /
Aysegul Bayram, Elif Segah Oztas, Irfan Siap / 106--110
\\
On the Weight Enumerators of the Projections of the
2-adic Golay Code of Length 24 to $\mathbb{Z}_{2^e}$ /
Sunghyu Han / 111--114 \\
Coding Theory \\
Computer Based Reconstruction of Binary Extremal
Self-dual Codes of Length 32 / Jon-Lark Kim / 115--118
\\
Magma Implementation of Decoding Algorithms for General
Algebraic Geometry Codes / Kwankyu Lee / 119--123 \\
Reversible Codes and Applications to DNA / Elif Segah
Oztas, Irfan Siap, Bahattin Yildiz / 124--128 \\
Computational Topology \\
javaPlex: A Research Software Package for Persistent
(Co)Homology / Henry Adams, Andrew Tausz, Mikael
Vejdemo-Johansson / 129--136 \\
PHAT --- Persistent Homology Algorithms Toolbox /
Ulrich Bauer, Michael Kerber, Jan Reininghaus, Hubert
Wagner / 137--143 \\
Computing Persistence Modules on Commutative Ladders of
Finite Type / Emerson G. Escolar, Yasuaki Hiraoka /
144--151 \\
Heuristics for Sphere Recognition / Michael Joswig,
Frank H. Lutz, Mimi Tsuruga / 152--159 \\
CAPD::RedHom v2 --- Homology Software Based on
Reduction Algorithms / Mateusz Juda, Marian Mrozek /
160--166 \\
The Gudhi Library: Simplicial Complexes and Persistent
Homology / Cl{\'e}ment Maria, Jean-Daniel Boissonnat,
Marc Glisse, Mariette Yvinec / 167--174 \\
Numerical Algebraic Geometry \\
Bertini_real: Software for One- and Two-Dimensional
Real Algebraic Sets / Daniel A. Brake, Daniel J. Bates,
Wenrui Hao, Jonathan D. Hauenstein, Andrew J. Sommese,
CharlesW. Wampler / 175--182 \\
Hom4PS-3: A Parallel Numerical Solver for Systems of
Polynomial Equations Based on Polyhedral Homotopy
Continuation Methods / Tianran Chen, Tsung-Lin Lee,
Tien-Yien Li / 183--190 \\
Geometry \\
CGAL --- Reliable Geometric Computing for Academia and
Industry / Eric Berberich / 191--197 \\
Implementing the $L_\infty$ Segment Voronoi Diagram in
CGAL and Applying in VLSI Pattern Analysis / Panagiotis
Cheilaris, Sandeep Kumar Dey, Maria Gabrani, Evanthia
Papadopoulou / 198--205 \\
BULL! --- The Molecular Geometry Engine Based on
Voronoi Diagram, Quasi-Triangulation, and Beta-Complex
/ Deok-Soo Kim, Youngsong Cho, Jae-Kwan Kim, Joonghyun
Ryu, Mokwon Lee, Jehyun Cha et al. / 206--213 \\
Integrating Circumradius and Area Formulae for Cyclic
Pentagons / Shuichi Moritsugu / 214--221 \\
Computer Aided Geometry / Douglas Navarro Guevara,
Adrian Navarro Alvarez / 222--229 \\
The Sustainability of Digital Educational Resources /
Yongsheng Rao, Ying Wang, Yu Zou, Jingzhong Zhang /
230--234 \\
A Touch-Operation-Based Dynamic Geometry System: Design
and Implementation / Wei Su, Paul S. Wang, Chuan Cai,
Lian Li / 235--239 \\
OpenGeo: An Open Geometric Knowledge Base / Dongming
Wang, Xiaoyu Chen, Wenya An, Lei Jiang, Dan Song /
240--245 \\
Curves and Surfaces \\
On Computing a Cell Decomposition of a Real Surface
Containing Infinitely Many Singularities / Daniel J.
Bates, Daniel A. Brake, Jonathan D. Hauenstein, Andrew
J. Sommese, Charles W. Wampler / 246--252 \\
Robustly and Efficiently Computing Algebraic Curves and
Surfaces / Eric Berberich / 253--260 \\
Computing the Orthogonal Projection of Rational Curves
onto Rational Parameterized Surface by Symbolic Methods
/ Zhiwang Gan, Meng Zhou / 261--268 \\
Isotopic $\epsilon$-Approximation of Algebraic Curves /
Kai Jin / 269--276 \\
Isotopic Arrangement of Simple Curves: An Exact
Numerical Approach Based on Subdivision / Jyh-Ming
Lien, Vikram Sharma, Gert Vegter, Chee Yap / 277--282
\\
Quantified Reasoning \\
Real Quantifier Elimination in the RegularChains
Library / Changbo Chen, Marc Moreno Maza / 283--290 \\
Software for Quantifier Elimination in Propositional
Logic / Eugene Goldberg, Panagiotis Manolios / 291--294
\\
Quantifier Elimination for Linear Modular Constraints /
Ajith K. John, Supratik Chakraborty / 295--302 \\
Skolemization Modulo Theories / Konstantin Korovin,
Margus Veanes / 303--306 \\
Incremental QBF Solving by DepQBF / Florian Lonsing,
Uwe Egly / 307--314 \\
NLCertify: A Tool for Formal Nonlinear Optimization /
Victor Magron / 315--320 \\
Special Functions and Concrete Mathematics \\
Developing Linear Algebra Packages on Risa/Asir for
Eigenproblems / Katsuyoshi Ohara, Shinichi Tajima,
Akira Terui / 321--324 \\
Mathematical Software for Modified Bessel Functions /
Juri Rappoport / 325--332 \\
BetaSCP2: A Program for the Optimal Prediction of
Side-Chains in Proteins / Joonghyun Ryu, Mokwon Lee,
Jehyun Cha, Chanyoung Song, Deok-Soo Kim / 333--340 \\
Computation of an Improved Lower Bound to Giuga's
Primality Conjecture / Matthew Skerritt / 341--345 \\
An Extension and Efficient Calculation of the Horner's
Rule for Matrices / Shinichi Tajima, Katsuyoshi Ohara,
Akira Terui / 346--351 \\
Groebner Bases \\
What Is New in CoCoA? / John Abbott, Anna Maria Bigatti
/ 352--358 \\
Maximizing Likelihood Function for Parameter Estimation
in Point Clouds via Groebner Basis / Joseph Awange,
B{\'e}la Pal{\'a}ncz, Robert Lewis / 359--366 \\
Groebner Basis in Geodesy and Geoinformatics / Joseph
Awange, B{\'e}la Pal{\'a}ncz, Robert Lewis / 367--373
\\
Groebner Bases in Theorema / Bruno Buchberger,
Alexander Maletzky / 374--381 \\
Effective Computation of Radical of Ideals and Its
Application to Invariant Theory / Amir Hashemi /
382--389 \\
Generic and Parallel Groebner Bases in JAS / Heinz
Kredel / 390--397 \\
Application of Groebner Basis Methodology to Nonlinear
Mechanics Problems / Y. Jane Liu, John Peddieson /
398--405 \\
Software for Discussing Parametric Polynomial Systems:
The Gr{\"o}bner Cover / Antonio Montes, Michael Wibmer
/ 406--413 \\
An Algorithm for Computing Standard Bases by Change of
Ordering via Algebraic Local Cohomology / Katsusuke
Nabeshima, Shinichi Tajima / 414--418 \\
Verification of Gr{\"o}bner Basis Candidates / Masayuki
Noro, Kazuhiro Yokoyama / 419--424 \\
Triangular Decompositions of Polynomial Systems \\
Cylindrical Algebraic Decomposition in the
RegularChains Library / Changbo Chen, Marc Moreno Maza
/ 425--433 \\
Hierarchical Comprehensive Triangular Decomposition /
Zhenghong Chen, Xiaoxian Tang, Bican Xia / 434--441 \\
A Package for Parametric Matrix Computations / Robert
M. Corless, Steven E. Thornton / 442--449 \\
Choosing a Variable Ordering for Truth-Table Invariant
Cylindrical Algebraic Decomposition by Incremental
Triangular Decomposition / Matthew England, Russell
Bradford, James H. Davenport, David Wilson / 450--457
\\
Using the Regular Chains Library to Build Cylindrical
Algebraic Decompositions by Projecting and Lifting /
Matthew England, David Wilson, Russell Bradford, James
H. Davenport / 458--465 \\
An Improvement of Rosenfeld--Gr{\"o}bner Algorithm /
Amir Hashemi, Zahra Touraji / 466--471 \\
Doing Algebraic Geometry with the RegularChains Library
/ Parisa Alvandi, Changbo Chen, Steffen Marcus, Marc
Moreno Maza, {\'E}ric Schost, Paul Vrbik / 472--479 \\
On Multivariate Birkhoff Rational Interpolation / Peng
Xia, Bao-Xin Shang, Na Lei / 480--483 \\
Computing Moore--Penrose Inverses of Ore Polynomial
Matrices / Yang Zhang / 484--491 \\
Parametric Polynomial Systems \\
Software Using the Gr{\"o}bner Cover for Geometrical
Loci Computation and Classification / Miguel A.
Ab{\'a}nades, Francisco Botana, Antonio Montes,
Tom{\'a}s Recio / 492--499 \\
Using Maple's RegularChains Library to Automatically
Classify Plane Geometric Loci / Francisco Botana,
Tom{\'a}s Recio / 500--503 \\
Solving Parametric Polynomial Systems by
RealComprehensiveTriangularize / Changbo Chen, Marc
Moreno Maza / 504--511 \\
QE Software Based on Comprehensive Gr{\"o}bner Systems
/ Ryoya Fukasaku / 512--517 \\
SyNRAC: A Toolbox for Solving Real Algebraic
Constraints / Hidenao Iwane, Hitoshi Yanami, Hirokazu
Anai / 518--522 \\
An Algorithm for Computing Tjurina Stratifications of
$\mu$-Constant Deformations by Using Local Cohomology
Classes with Parameters / Katsusuke Nabeshima, Shinichi
Tajima / 523--530 \\
An Implementation Method of Boolean Gr{\"o}bner Bases
and Comprehensive Boolean Gr{\"o}bner Bases on General
Computer Algebra Systems / Akira Nagai, Shutaro Inoue /
531--536 \\
A Method to Determine if Two Parametric Polynomial
Systems Are Equal / Jie Zhou, Dingkang Wang / 537--544
\\
Mathematical Web/Mobile Interfaces and Visualization
\\
An Implementation Method of a CAS with a Handwriting
Interface on Tablet Devices / Mitsushi Fujimoto /
545--548 \\
New Way of Explanation of the Stochastic Interpretation
of Wave Functions and Its Teaching Materials Using
KETpic / Kenji Fukazawa / 549--553 \\
{IFSGen4\LaTeX}: Interactive Graphical User Interface
for Generation and Visualization of Iterated Function
Systems in {\LaTeX} / Akemi G{\'a}lvez, Kiyoshi
Kitahara, Masataka Kaneko / 554--561 \\
GNU {\TeX}MACS: towards a Scientific Office Suite /
Massimiliano Gubinelli, Joris van der Hoeven,
Fran{\c{c}}ois Poulain, Denis Raux / 562--569 \\
Computer Software Program for Representation and
Visualization of Free-Form Curves through Bio-inspired
Optimization Techniques / Andr{\'e}s Iglesias, Akemi
G{\'a}lvez / 570--577 \\
On Some Attempts to Verify the Effect of Using
High-Quality Graphics in Mathematics Education /
Kiyoshi Kitahara, Tadashi Takahashi, Masataka Kaneko /
578--585 \\
Math Web Search Interfaces and the Generation Gap of
Mathematicians / Andrea Kohlhase / 586--593 \\
Practice with Computer Algebra Systems in Mathematics
Education and Teacher Training Courses / Hideyo
Makishita / 594--600 \\
Development of Visual Aid Materials in Teaching the
Bivariate Normal Distributions / Toshifumi Nomachi,
Toshihiko Koshiba, Shunji Ouchi / 601--606 \\
Creating Interactive Graphics for Mathematics Education
Utilizing KETpic / Shunji Ouchi, Yoshifumi Maeda,
Kiyoshi Kitahara, Naoki Hamaguchi / 607--613 \\
A Tablet-Compatible Web-Interface for Mathematical
Collaboration / Marco Pollanen, Jeff Hooper, Bruce
Cater, Sohee Kang / 614--620 \\
Development and Evaluation of a Web-Based Drill System
to Master Basic Math Formulae Using a New Interactive
Math Input Method / Shizuka Shirai, Tetsuo Fukui /
621--628 \\
Generating Data of Mathematical Figures for 3D Printers
with KETpic and Educational Impact of the Printed
Models / Setsuo Takato, Naoki Hamaguchi, Haiduke
Sarafian / 629--634 \\
A Touch-Based Mathematical Expression Editor / Wei Su,
Paul S. Wang, Lian Li / 635--640 \\
Establishment of KETpic Programming Styles for Drawing
/ Satoshi Yamashita, Yoshifumi Maeda, Hisashi Usui,
Kiyoshi Kitahara, Hideyo Makishita, Kazushi Ahara /
641--646 \\
General Session \\
Integration of Libnormaliz in CoCoALib and CoCoA 5 /
John Abbott, Anna Maria Bigatti, Christof S{\"o}ger /
647--653 \\
Elements of Design for Containers and Solutions in the
LinBox Library / Brice Boyer, Jean-Guillaume Dumas,
Pascal Giorgi, Cl{\'e}ment Pernet, B. David Saunders /
654--662 \\
Recent Developments in Normaliz / Winfried Bruns,
Christof S{\"o}ger / 663--668 \\
The Basic Polynomial Algebra Subprograms / Changbo
Chen, Svyatoslav Covanov, Farnam Mansouri, Marc Moreno
Maza, Ning Xie, Yuzhen Xie / 669--676 \\
Function Interval Arithmetic / Jan Duracz, Amin
Farjudian, Michal Kone{\v{c}}n{\'y}, Walid Taha /
677--684 \\
Generating Optimized Sparse Matrix Vector Product over
Finite Fields / Pascal Giorgi, Bastien Vialla /
685--690 \\
swMATH --- An Information Service for Mathematical
Software / Gert-Martin Greuel, Wolfram Sperber /
691--701 \\
MathLibre: Modifiable Desktop Environment for
Mathematics / Tatsuyoshi Hamada / 702--705 \\
Software Packages for Holonomic Gradient Method / Tamio
Koyama, Hiromasa Nakayama, Katsuyoshi Ohara, Tomonari
Sei, Nobuki Takayama / 706--712 \\
Metalibm: A Mathematical Functions Code Generator /
Olga Kupriianova, Christoph Lauter / 713--717 \\
From Calculus to Algorithms without Errors / Norbert
M{\"u}ller, Martin Ziegler / 718--724 \\
Dense Arithmetic over Finite Fields with the CUMODP
Library / Sardar Anisul Haque, Xin Li, Farnam Mansouri,
Marc Moreno Maza, Wei Pan, Ning Xie / 725--732 \\
Back Matter / / 733--735",
}
