Mathematics for Computer Algebra

Mathematics for Computer Algebra by Maurice Mignotte.

This book corresponds to a mathematical course given in 1986/87 at the University Louis Pasteur, Strasbourg. This work is primarily intended for graduate students. The following are necessary prerequisites : a few standard definitions in set theory, the definition of rational integers, some elementa...

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Bibliographic Details
Main Author: Mignotte, Maurice (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: New York, NY : Springer New York : Imprint: Springer, 1992.
Edition:1st ed. 1992.
Series:Springer eBook Collection.
Subjects:
Algorithms.
Mathematical logic.
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
Table of Contents:
  • 1 Elementary Arithmetics
  • 1. Representation of an integer in basis B1
  • 2. Addition
  • 3. Subtraction
  • 4. Multiplication
  • 5. Euclidean division
  • 6. The cost of multiplication and division
  • 7. How to compute powers
  • 8. The g.c.d.
  • 9. The group G (n)
  • 10. The Chinese remainder theorem
  • 11. The prime numbers
  • 2 Number Theory, Complements
  • 1. Study of the group G(n)
  • 2. Tests of primality
  • 3. Factorization of rational integers
  • 3 Polynomials, Algebraic Study
  • 1. Definitions and elementary properties
  • 2. Euclidean division
  • 3. The Chinese remainder theorem
  • 4. Factorization
  • 5. Polynomial functions
  • 6. The resultant
  • 7. Companion matrix
  • 8. Linear recursive sequences
  • 4 Polynomials with complex coefficients
  • 1. The theorem of d’Alembert
  • 2. Estimates of the roots
  • 3. The measure of a polynomial
  • 4. Bounds for size of the factors of a polynomial
  • 5. The distribution of the roots of a polynomial
  • 6. Separation of the roots of a polynomial
  • 5 Polynomials with real coefficients
  • 1. Polynomials irreducible over ?
  • 2. The theorem of Rolle
  • 3. Estimates of real roots
  • 4. The number of zeros of a polynomial in a real interval
  • 5. Equations whose roots have a negative real part
  • 6/Polynomials over finite fields
  • 1. Finite fields
  • 2. Statistics on Hq[X]
  • 3. Factorization into a product of squarefree polynomials
  • 4. Factorization of the polynomials over a finite field
  • 5. Search for the roots of a polynomial in a finite field
  • 7 Polynomials with integer coefficients
  • 1. Principles of the algorithms of factorization
  • 2. The choice of the prime modulus
  • 3. Refining the factorization
  • 4. Berlekamp’s method of factorization
  • 5. The algorithm L3
  • 6. Factors of polynomials and lattices
  • 7. The algorithm of factorization
  • Index of Names.

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