Modern computer algebra

Summary

This highly successful textbook, widely regarded as the 'bible of computer algebra', gives a thorough introduction to the algorithmic basis of the mathematical engine in computer algebra systems.

Keywords

Algebra over a field, Computer science, Mathematics, Pure mathematics

References

XLIV. On the explicit values of Sturm's quotientsJ.J. Sylvester — 1853
Arithmetic specializations in polynomials.Vladimir G. Sprindžuk — 1983
Small Sample Algorithms for the Identification of PolynomialsJohn H. Rowland, John Cowles — 1986
Computational and Algorithmic Problems in Finite FieldsIgor E. Shparlinski — 1992
On the equivalence of polynomial GCD and squarefree factorization problemsDavid Y. Y. Yun — 1977
Residue arithmetic and its applications to computer technologyNicholas S. Szabó, Richard I. Tanaka — 1967
Schnelle Berechnung von KettenbruchentwicklungenA. Sch�nhage — 1971
Refined Analysis and Improvements on Some Factoring AlgorithmsC. P. Schnorr — 1981
Chebotarëv and his density theoremPeter Stevenhagen, H. W. Lenstra — 1996
THE SOLUTION OF THE PROBLEM OF INTEGRATION IN FINITE TERMSRobert H. Risch — 1970
A Hierarchy of Polynomial Time Lattice Basis Reduction AlgorithmsC. P. Schnorr — 1987
A method for obtaining digital signatures and public-key cryptosystemsRonald L. Rivest, Adi Shamir, Leonard M. Adleman — 1978
Factoring polynomials over finite fieldsLajos Rónyai — 1987
Further analysis of Coppersmith's block Wiedemann algorithm for the solution of sparse linear systems (extended abstract)Gilles Villard — 1997
XXIII. A method of determining by mere inspection the derivatives from two equations of any degreeJ.J. Sylvester — 1840
Effective polynomial computationRichard Zippel — 1993
Factorization of polynomials over finite fields.Richard G. Swan — 1962
Ring-Theoretic Properties of Certain Hecke AlgebrasRichard Taylor, Andrew Wiles — 1995
Complexity problems in computational theoryA. O. Slisenko — 1981
The JPEG still picture compression standardGregory K. Wallace — 1991

Cited by

Group-by Query Verification by Untrusted Clients on Outsourced Data StreamsSuman Nath, Ramarathnam Venkatesan — 2011
Algorithms for Solving Linear and Polynomial Systems of Equations over Finite Fields with Applications to CryptanalysisLawrence C. Washington, Gregory V. Bard — 2007
Quantum Fourier transforms for extracting hidden linear structures in finite fieldsJ. Niel de Beaudrap, Richard Cleve, John Watrous — 2000
Polynomial Systems Solving by Fast Linear AlgebraJean‐Charles Faugère, Pierrick Gaudry, Louise Huot — 2013
Computation Sequences for Series and PolynomialsYiming Zhang — 2013
Development of symbolic algorithms for certain algebraic processesAli Abd Rahman, Nor’aini Aris — 2007
Straight-line computation of the polynomial matrix inverseClaude-Pierre Jeannerod, Gilles Villard — 2006
Modular absolute decomposition of equidimensional polynomial idealsCristina Bertone — 2010
Book List for Algorithms and Data Structures Summer 2008Kurt Mehlhorn, Raimund Seidel — 2008
Improved Fast Gauss TransformChangjiang Yang, Ramani Duraiswami, Nail A. Gumerov — 2003
Certifying solutions to overdetermined and singular polynomial systems over QTulay Ayyildiz Akoglu, Jonathan D. Hauenstein, Ágnes Szántó — 2014
Time-space lower bounds for satisfiability and related problems on randomized machinesDieter van Melkebeek, Scott Diehl — 2008
On Lattice Methods in Integer OptimizationF.J. Von Heymann — 2013
Génération automatique de circuits pour le calcul de couplages cryptographiques en matérielNicolas Estibals — 2009
Irreducibility Certicates for Polynomials with Integer Coecien tsBart Kirkels — 2004
On the resultant of degree-deficient polynomialsA Lifshitz, Y. Bistritz — 2007
Lecture Notes on Computer AlgebraZiming Li — 2005
Algebraic Methods for Geometric ModelingJulien Wintz, MOURRAIN, Bernard — 2008
Application of Computer Algebra in List DecodingMuhammad F. I. Chowdhury — 2013
Hardware Acceleration Technologies in Computer Algebra: Challenges and ImpactSardar Anisul Haque — 2013

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