Book Review
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MathSciNet review:
4119620
Full text of review:
PDF
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Book Information:
Authors:
Paul Zimmermann,
Alexandre Casamayou,
Nathann Cohen,
Guillaume Connan,
Thierry Dumont,
Laurent Fousse,
François Maltey,
Matthias Meulien,
Marc Mezzarobba,
Clément Pernet,
Nicolas M. Thiéry,
Erik Bray,
John Cremona,
Marcelo Forets,
Alexandru Ghitza and
Hugh Thomas
Title:
Computational Mathematics with
SageMath
Additional book information:
Society for Industrial and Applied Mathematics (SIAM),
Philadelphia, Pennsylvania,
2018,
xiv+464 pp.,
ISBN 978-1-611975-45-1,
US$69.00
J. Abbott, A. M. Bigatti, and L. Robbiano, CoCoA: A system for doing Computations in Commutative Algebra, available at http://cocoa.dima.unige.it
D. Bates, J. Hauenstein, A. Sommese, and C. Wampler, Bertini: Software for Numerical Algebraic Geometry, available at bertini.nd.edu with permanent doi: dx.doi.org/10.7274/R0H41PB5.
Mats Boij and Jonas Söderberg, Graded Betti numbers of Cohen-Macaulay modules and the multiplicity conjecture, J. Lond. Math. Soc. (2) 78 (2008), no. 1, 85–106. MR 2427053, DOI 10.1112/jlms/jdn013
Wieb Bosma, John Cannon, and Catherine Playoust, The Magma algebra system. I. The user language, J. Symbolic Comput. 24 (1997), no. 3-4, 235–265. Computational algebra and number theory (London, 1993). MR 1484478, DOI 10.1006/jsco.1996.0125
W. Decker, G.-M. Greuel, G. Pfister, and H. Schönemann, Singular 4-1-2—A computer algebra system for polynomial computations, 2019, available at http://www.singular.uni-kl.de.
David Eisenbud and Frank-Olaf Schreyer, Betti numbers of graded modules and cohomology of vector bundles, J. Amer. Math. Soc. 22 (2009), no. 3, 859–888. MR 2505303, DOI 10.1090/S0894-0347-08-00620-6
The GAP Group, GAP—Groups, Algorithms, and Programming, Version 4.10.2; 2019, available at https://www.gap-system.org.
Gert-Martin Greuel and Gerhard Pfister, A Singular introduction to commutative algebra, Second, extended edition, Springer, Berlin, 2008. With contributions by Olaf Bachmann, Christoph Lossen and Hans Schönemann; With 1 CD-ROM (Windows, Macintosh and UNIX). MR 2363237
D. Grayson and M. Stillman, Macaulay2, a software system for research in algebraic geometry, available at http://www.math.uiuc.edu/Macaulay2/.
David Hilbert, Ueber die Theorie der algebraischen Formen, Math. Ann. 36 (1890), no. 4, 473–534 (German). MR 1510634, DOI 10.1007/BF01208503
Maple 2019. Maplesoft, a division of Waterloo Maple Inc., Waterloo, Ontario.
MATLAB and Symbolic Mathematics Toolbox Release 2019b, The MathWorks, Inc., Natick, Massachusetts, United States.
The PARI Group, PARI/GP version 2.11.0, Univ. Bordeaux, 2018, available at http://pari.math.u-bordeaux.fr/.
W. A. Stein et al., SageMath Mathematics Software, The SageMath Development Team, 2019, available at https://www.sagemath.org.
Wolfram Research, Inc., Mathematica, Version 12.0, 2019, Champaign, IL.
References
- J. Abbott, A. M. Bigatti, and L. Robbiano, CoCoA: A system for doing Computations in Commutative Algebra, available at http://cocoa.dima.unige.it
- D. Bates, J. Hauenstein, A. Sommese, and C. Wampler, Bertini: Software for Numerical Algebraic Geometry, available at bertini.nd.edu with permanent doi: dx.doi.org/10.7274/R0H41PB5.
- Mats Boij and Jonas Söderberg, Graded Betti numbers of Cohen-Macaulay modules and the multiplicity conjecture, J. Lond. Math. Soc. (2) 78 (2008), no. 1, 85–106. MR 2427053, DOI 10.1112/jlms/jdn013
- Wieb Bosma, John Cannon, and Catherine Playoust, The Magma algebra system. I. The user language, J. Symbolic Comput. 24 (1997), no. 3-4, 235–265. Computational algebra and number theory (London, 1993). MR 1484478, DOI 10.1006/jsco.1996.0125
- W. Decker, G.-M. Greuel, G. Pfister, and H. Schönemann, Singular 4-1-2—A computer algebra system for polynomial computations, 2019, available at http://www.singular.uni-kl.de.
- David Eisenbud and Frank-Olaf Schreyer, Betti numbers of graded modules and cohomology of vector bundles, J. Amer. Math. Soc. 22 (2009), no. 3, 859–888. MR 2505303, DOI 10.1090/S0894-0347-08-00620-6
- The GAP Group, GAP—Groups, Algorithms, and Programming, Version 4.10.2; 2019, available at https://www.gap-system.org.
- Gert-Martin Greuel and Gerhard Pfister, A Singular introduction to commutative algebra, Second, extended edition, Springer, Berlin, 2008. With contributions by Olaf Bachmann, Christoph Lossen and Hans Schönemann; With 1 CD-ROM (Windows, Macintosh and UNIX). MR 2363237
- D. Grayson and M. Stillman, Macaulay2, a software system for research in algebraic geometry, available at http://www.math.uiuc.edu/Macaulay2/.
- David Hilbert, Ueber die Theorie der algebraischen Formen, Math. Ann. 36 (1890), no. 4, 473–534 (German). MR 1510634, DOI 10.1007/BF01208503
- Maple 2019. Maplesoft, a division of Waterloo Maple Inc., Waterloo, Ontario.
- MATLAB and Symbolic Mathematics Toolbox Release 2019b, The MathWorks, Inc., Natick, Massachusetts, United States.
- The PARI Group, PARI/GP version 2.11.0, Univ. Bordeaux, 2018, available at http://pari.math.u-bordeaux.fr/.
- W. A. Stein et al., SageMath Mathematics Software, The SageMath Development Team, 2019, available at https://www.sagemath.org.
- Wolfram Research, Inc., Mathematica, Version 12.0, 2019, Champaign, IL.
Review Information:
Reviewer:
John B. Little
Affiliation:
Department of Mathematics and Computer Science College of the Holy Cross
Email:
jlittle@holycross.edu
Journal:
Bull. Amer. Math. Soc.
57 (2020), 515-521
DOI:
https://doi.org/10.1090/bull/1690
Published electronically:
January 24, 2020
Review copyright:
© Copyright 2020
American Mathematical Society