Gröbner basis

Known as: Multivariate division algorithm, Gröbner bases, Gröbner base 
In mathematics, and more specifically in computer algebra, computational algebraic geometry, and computational commutative algebra, a Gröbner basis… (More)
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2012
2012
We report on our experiences exploring state of the art Gröbner basis computation. We investigate signature based algorithms in… (More)
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Highly Cited
2009
Highly Cited
2009
This work presents a new framework for Gröbner basis computations with Boolean polynomials. Boolean polynomials can be modelled… (More)
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Highly Cited
2008
Highly Cited
2008
Schubert polynomials, which a priori represent cohomology classes of Schubert varieties in the flag manifold, also represent… (More)
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2007
2007
In this article, we discuss a Gröbner basis algorithm related to the stability of algebraic varieties in the sense of Geometric… (More)
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2006
2006
In the first sections we extend and generalize Gröbner basis theory to submodules of free right modules over monoid rings. Over… (More)
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Highly Cited
2004
Highly Cited
2004
This paper compares the XL algorithm with known Gröbner basis algorithms. We show that to solve a system of algebraic equations… (More)
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Highly Cited
2004
Highly Cited
2004
We extend the notion of regular sequence ([Mac16]) to overdetermined system of algebraic equations. We study generic properties… (More)
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Highly Cited
2002
Highly Cited
2002
This paper introduces a new efficient algorithm for computing Gröbner bases. We replace the Buchberger criteria by an optimal… (More)
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Highly Cited
1997
Highly Cited
1997
The objective of this note is the presentation of a procedure for converting a given Gröbner basis (Buchberger, 1965) of a… (More)
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Highly Cited
1992
Highly Cited
1992
Let K bean integral domain and let S be the polynomial ring K[Ui, ..,Ur ; X1, .-,X„ ] . For any finite F C S, we construct a… (More)
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