Journal of Symbolic Computation
Algorithmic algebra
Groebner basis under composition II
ISSAC '96 Proceedings of the 1996 international symposium on Symbolic and algebraic computation
On the stability of Groübner bases under specializations
Journal of Symbolic Computation
A criterion for detecting unnecessary reductions in the construction of Groebner bases
EUROSAM '79 Proceedings of the International Symposiumon on Symbolic and Algebraic Computation
On systems of algebraic equations with parametric exponents
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
Algorithms for the Functional Decomposition of Laurent Polynomials
Calculemus '09/MKM '09 Proceedings of the 16th Symposium, 8th International Conference. Held as Part of CICM '09 on Intelligent Computer Mathematics
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This paper presents a method for computing uniform Gröbner bases for certain ideals generated by polynomials with parametric exponents. The method proceeds by replacing monomials involving parametric exponents in the generators of an ideal with new variables, computing the reduced Gröbner basis for the resulting ideal with respect to a special monomial order, and then verifying whether the leading monomial ideal of the Gröbner basis satisfies some consistency conditions according to two criteria (of which one is derived from Buchberger graphs). When the consistency conditions are verified, a uniform Gröbner basis for the original ideal is obtained by substituting the new variables back to original monomials. The effectiveness and practical value of the method are demonstrated by its application to a family of ideals coming from the modeling of biological systems.