Author | Mignotte, Maurice. author |
---|---|
Title | Mathematics for Computer Algebra [electronic resource] / by Maurice Mignotte |
Imprint | New York, NY : Springer New York, 1992 |
Connect to | http://dx.doi.org/10.1007/978-1-4613-9171-5 |
Descript | XIV, 346 p. online resource |
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 dโAlembert -- 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. Berlekampโs method of factorization -- 5. The algorithm L3 -- 6. Factors of polynomials and lattices -- 7. The algorithm of factorization -- Index of Names