The Bath algebraic number package
SYMSAC '86 Proceedings of the fifth ACM symposium on Symbolic and algebraic computation
ISSAC '89 Proceedings of the ACM-SIGSAM 1989 international symposium on Symbolic and algebraic computation
The computation of polynomial greatest common divisors over an algebraic number field
Journal of Symbolic Computation
Solving zero-dimensional algebraic systems
Journal of Symbolic Computation
A generalized Euclidean algorithm for computing triangular representations of algebraic varieties
Journal of Symbolic Computation
An FFT extension of the elliptic curve method of factorization
An FFT extension of the elliptic curve method of factorization
Efficient rational number reconstruction
Journal of Symbolic Computation
Computing GCDs of polynomials over algebraic number fields
Journal of Symbolic Computation
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Modern computer algebra
On Euclid's Algorithm and the Computation of Polynomial Greatest Common Divisors
Journal of the ACM (JACM)
On the design and implementation of Brown's algorithm over the integers and number fields
ISSAC '00 Proceedings of the 2000 international symposium on Symbolic and algebraic computation
AAECC-8 Proceedings of the 8th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Polynomial Gcd Computations over Towers of Algebraic Extensions
AAECC-11 Proceedings of the 11th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
In-place Arithmetic for Polinominals over Zn
DISCO '92 Proceedings of the International Symposium on Design and Implementation of Symbolic Computation Systems
Probabilistic algorithms for sparse polynomials
EUROSAM '79 Proceedings of the International Symposiumon on Symbolic and Algebraic Computation
A modular GCD algorithm over number fields presented with multiple extensions
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
Acceleration of Euclidean algorithm and extensions
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
Algebraic factoring and rational function integration
SYMSAC '76 Proceedings of the third ACM symposium on Symbolic and algebraic computation
A p-adic algorithm for univariate partial fractions
SYMSAC '81 Proceedings of the fourth ACM symposium on Symbolic and algebraic computation
P-adic reconstruction of rational numbers
ACM SIGSAM Bulletin
A sparse modular GCD algorithm for polynomials over algebraic function fields
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
| Hi-index | 0.00 |
Let L be an algebraic function field in k ≥ 0 parameters t;1;, ..., t;k;. Let f;1;, f;2; be non-zero polynomials in L[x]. We give two algorithms for computing their gcd. The first, a modular GCD algorithm, is an extension of the modular GCD algorithm of Brown for Z[x;1;,...,x;n;] and Encarnacion for Q(α)[x] to function fields. It is uses rational number and rational function reconstruction and trial division. The second, a fraction-free algorithm, is a modification of the Moreno Maza and Rioboo algorithm for computing gcds over triangular sets. The modification reduces coefficient growth in L to be linear. We show how to extend the modular GCD algorithm to work when the minimal polynomial for L is not irreducible. We give an empirical comparison of the two algorithms using implementations in Maple.