A New Scheme for Computing with Algebraically Closed Fields

Authors:
Allan Steel
Affiliations:
-
Venue:
ANTS-V Proceedings of the 5th International Symposium on Algorithmic Number Theory
Year:
2002

Citing 8
Cited 5

Solving zero-dimensional algebraic systems

Journal of Symbolic Computation
Efficient computation of zero-dimensional Gro¨bner bases by change of ordering

Journal of Symbolic Computation
The MAGMA algebra system I: the user language

Journal of Symbolic Computation - Special issue on computational algebra and number theory: proceedings of the first MAGMA conference
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms

The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
On the theories of triangular sets

Journal of Symbolic Computation - Special issue on polynomial elimination—algorithms and applications
About a New Method for Computing in Algebraic Number Fields

EUROCAL '85 Research Contributions from the European Conference on Computer Algebra-Volume 2
Algebraic factoring and rational function integration

SYMSAC '76 Proceedings of the third ACM symposium on Symbolic and algebraic computation
Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 3/e (Undergraduate Texts in Mathematics)

Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 3/e (Undergraduate Texts in Mathematics)

Equality in computer algebra and beyond

Journal of Symbolic Computation - Integrated reasoning and algebra systems
Lifting and recombination techniques for absolute factorization

Journal of Complexity
Computing with algebraically closed fields

Journal of Symbolic Computation
Dynamic Galois Theory

Journal of Symbolic Computation
A modular method for computing the splitting field of a polynomial

ANTS'06 Proceedings of the 7th international conference on Algorithmic Number Theory

Quantified Score

Hi-index	0.00

Visualization

Abstract

A new scheme is presented for computing with an algebraic closure of the rational field.It avoids factorization of polynomials over extension fields, but gives the illusion of a genuine field to the user.A technique of modular evaluation into a finite field ensures that a unique genuine field is simulated by the scheme and also provides fast optimizations for some critical operations.F ast modular matrix techniques are also used for several non-trivial operations.The scheme has been successfully implemented within the Magma Computer Algebra System.