Basic principles of mechanical theorem proving in elementary geometrics
Journal of Automated Reasoning
Gröbner bases and primary decomposition of polynomial ideals
Journal of Symbolic Computation
Generalised characteristic polynomials
Journal of Symbolic Computation - Special issue on computational algebraic complexity
Irreducible decomposition of algebraic varieties via characteristic sets and Gro¨bner bases
Computer Aided Geometric Design
A new algorithm for the geometric decomposition of a variety
ISSAC '99 Proceedings of the 1999 international symposium on Symbolic and algebraic computation
A new approach to primary decomposition
Journal of Symbolic Computation - Special issue on computational algebra and number theory: proceedings of the second Magma conference
Decomposing Algebraic Varieties
ADG '98 Proceedings of the Second International Workshop on Automated Deduction in Geometry
Ritt-Wu's Decomposition Algorithm and Geometry Theorem Proving
Proceedings of the 10th International Conference on Automated Deduction
An algorithm for the computation of the radical of an ideal
Proceedings of the 2006 international symposium on Symbolic and algebraic computation
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In this paper, we introduce a modified Van der Waerden algorithm to decompose a variety into the union of irreducible varieties. We give an effective representation for irreducible varieties obtained by the algorithm, which allows us to obtain an irredundant decomposition easily. We show that in the zero dimensional case, the polynomial systems for the irreducible varieties obtained in the Van der Waerden algorithm generate prime ideals. As a consequence, we have an algorithm to decompose the radical ideal generated by a finite set of polynomials as the intersection of prime ideals and the degree of the polynomials in the computation is bounded by O(dn) where dis the degree of the input polynomials and nis the number of variables.