- Author:
- Maurice Mignotte
No abstract available.
Cited By
Magron V, Seidler H and de Wolff T Exact Optimization via Sums of Nonnegative Circuits and Arithmetic-geometric-mean-exponentials Proceedings of the 2019 on International Symposium on Symbolic and Algebraic Computation, (291-298)- Melczer S and Salvy B Symbolic-Numeric Tools for Analytic Combinatorics in Several Variables Proceedings of the ACM on International Symposium on Symbolic and Algebraic Computation, (333-340)
- Herman A and Tsigaridas E Bounds for the Condition Number of Polynomials Systems with Integer Coefficients Proceedings of the 17th International Workshop on Computer Algebra in Scientific Computing - Volume 9301, (210-219)
- Cheng J and Jin K (2015). A generic position based method for real root isolation of zero-dimensional polynomial systems, Journal of Symbolic Computation, 68:P1, (204-224), Online publication date: 1-May-2015.
- Pan V and Tsigaridas E Nearly optimal computations with structured matrices Proceedings of the 2014 Symposium on Symbolic-Numeric Computation, (21-30)
- Schirra S A Note on Sekigawa's Zero Separation Bound Proceedings of the 15th International Workshop on Computer Algebra in Scientific Computing - Volume 8136, (331-339)
- Pan V and Tsigaridas E On the boolean complexity of real root refinement Proceedings of the 38th International Symposium on Symbolic and Algebraic Computation, (299-306)
- Grimson R, Heintz J and Kuijpers B (2019). Evaluating geometric queries using few arithmetic operations, Applicable Algebra in Engineering, Communication and Computing, 23:3-4, (179-193), Online publication date: 1-Nov-2012.
- Strzeboński A and Tsigaridas E Univariate real root isolation in multiple extension fields Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation, (343-350)
- Strzebonski A and Tsigaridas E Univariate real root isolation in an extension field Proceedings of the 36th international symposium on Symbolic and algebraic computation, (321-328)
- Hansen K, Koucky M, Lauritzen N, Miltersen P and Tsigaridas E Exact algorithms for solving stochastic games Proceedings of the forty-third annual ACM symposium on Theory of computing, (205-214)
- Emiris I, Mourrain B and Tsigaridas E The DMM bound Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation, (243-250)
- Emiris I, Pan V and Tsigaridas E Algebraic and numerical algorithms Algorithms and theory of computation handbook, (17-17)
- Sasaki T and Terui A Computing clustered close-roots of univariate polynomials Proceedings of the 2009 conference on Symbolic numeric computation, (177-184)
- Hemmer M, Tsigaridas E, Zafeirakopoulos Z, Emiris I, Karavelas M and Mourrain B Experimental evaluation and cross-benchmarking of univariate real solvers Proceedings of the 2009 conference on Symbolic numeric computation, (45-54)
- Tsigaridas E and Emiris I (2008). On the complexity of real root isolation using continued fractions, Theoretical Computer Science, 392:1-3, (158-173), Online publication date: 20-Feb-2008.
- Poteaux A Computing monodromy groups defined by plane algebraic curves Proceedings of the 2007 international workshop on Symbolic-numeric computation, (36-45)
- Pérez-Díaz S, Sendra J and Sendra J (2006). Distance bounds of ε-points on hypersurfaces, Theoretical Computer Science, 359:1, (344-368), Online publication date: 14-Aug-2006.
- Eigenwillig A, Kettner L, Schömer E and Wolpert N (2006). Exact, efficient, and complete arrangement computation for cubic curves, Computational Geometry: Theory and Applications, 35:1-2, (36-73), Online publication date: 1-Aug-2006.
- Graillat S and Langlois P Pseudozero set of interval polynomials Proceedings of the 2006 ACM symposium on Applied computing, (1655-1659)
- Diaz---Toca G and Gonzalez---Vega L (2004). Various New Expressions for Subresultants and Their Applications, Applicable Algebra in Engineering, Communication and Computing, 15:3-4, (233-266), Online publication date: 1-Nov-2004.
- Sasaki T (2004). A theorem for separating close roots of a polynomial and its derivatives, ACM SIGSAM Bulletin, 38:3, (85-92), Online publication date: 1-Sep-2004.
- Grabmeier J, Kaltofen E and Weispfenning V Cited References Computer algebra handbook, (493-622)
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Index Terms
- Mathematics for computer algebra
Recommendations
Computer algebra
Encyclopedia of Computer ScienceComputer algebra is a branch of scientific computation. There are several characteristic features that distinguish computer algebra from numerical analysis, the other principal branch of scientific computation. (1) Computer algebra involves computation ...
Reviews
Attila Pethö
Computer algebra has become established as an important subject on the boundary between applied mathematics and computer science. Powerful symbolic computation programs such as Derive, MACSYMA, Maple, and Mathematica are widely used. Also, universities offer courses on computer algebra, but until now, no suitable textbooks for these courses have been available. Having published several scientific papers on computer algebra and taught the subject for many years, the author is well qualified to write this textbook. The original version, in French, appeared four years ago, and this English translation is welcome. The first chapter covers basic arithmetic. The next chapters treat number theory and the algebraic theory of polynomials. Subsequent chapters discuss the localization, distribution, and separation of roots of polynomials with real and complex coefficients, and factorization methods for polynomials over integers and over finite fields. The exposition is clear and readable. The author has found the right balance between theory and algorithms. Algorithms are presented both informally and formally. In addition, the book contains numerous exercises. I found the references deficient, however. Rather than list all references together at the end, the book cites publications in footnotes. Furthermore, the book omits references to closely related subjects such as the algebraic theory of polynomials in many variables and formal differentiation and integration. On the whole, however, the book is valuable for everyone who wishes to teach or learn about computer algebra.
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