Basic principles of mechanical theorem proving in elementary geometrics
Journal of Automated Reasoning
A new method for solving algebraic systems of positive dimension
Discrete Applied Mathematics - Special volume on applied algebra, algebraic algorithms, and error-correcting codes
A generalized Euclidean algorithm for computing triangular representations of algebraic varieties
Journal of Symbolic Computation
Searching dependency between algebraic equations: an algorithm applied to automated reasoning
Artificial intelligence in mathematics
Decomposing polynomial systems into simple systems
Journal of Symbolic Computation
On the theories of triangular sets
Journal of Symbolic Computation - Special issue on polynomial elimination—algorithms and applications
Computing triangular systems and regular systems
Journal of Symbolic Computation
Computing the Radical of an Ideal in Positive Characteristic
Journal of Symbolic Computation
The calculation of radical ideals in positive characteristic
Journal of Symbolic Computation
Derivations and radicals of polynomial ideals over fields of arbitrary characteristic
Journal of Symbolic Computation - Computer algebra: Selected papers from ISSAC 2001
Properties of Gröbner bases under specializations
EUROCAL '87 Proceedings of the European Conference on Computer Algebra
An Algorithm for Transforming Regular Chain into Normal Chain
Computer Mathematics
Notes on triangular sets and triangulation-decomposition algorithms I: polynomial systems
SNSC'01 Proceedings of the 2nd international conference on Symbolic and numerical scientific computation
Decomposing polynomial sets into simple sets over finite fields: The zero-dimensional case
Computers & Mathematics with Applications
Characteristic set algorithms for equation solving in finite fields
Journal of Symbolic Computation
Algorithmic Thomas decomposition of algebraic and differential systems
Journal of Symbolic Computation
Hi-index | 5.23 |
This paper presents an algorithm for decomposing any positive-dimensional polynomial set into simple sets over an arbitrary finite field. The algorithm is based on some relationship established between simple sets and radical ideals, reducing the decomposition problem to the problem of computing the radicals of certain ideals. In addition to direct application of the algorithms of Matsumoto and Kemper, the algorithm of Fortuna and others is optimized and improved for the computation of radicals of special ideals. Preliminary experiments with an implementation of the algorithm in Maple and Singular are carried out to show the effectiveness and efficiency of the algorithm.