Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An Improvement over the GVW Algorithm for Inhomogeneous Polynomial
  Systems   The GVW algorithm is a signature-based algorithm for computing Gr\"obner
bases. If the input system is not homogeneous, some J-pairs with higher
signatures but lower degrees are rejected by GVW's Syzygy Criterion, instead,
GVW have to compute some J-pairs with lower signatures but higher degrees.
Consequently, degrees of polynomials appearing during the computations may
unnecessarily grow up higher and the computation become more expensive. In this
paper, a variant of the GVW algorithm, called M-GVW, is proposed and mutant
pairs are introduced to overcome inconveniences brought by inhomogeneous input
polynomials. Some techniques from linear algebra are used to improve the
efficiency. Both GVW and M-GVW have been implemented in C++ and tested by many
examples from boolean polynomial rings. The timings show M-GVW usually performs
much better than the original GVW algorithm when mutant pairs are found.
Besides, M-GVW is also compared with intrinsic Gr\"obner bases functions on
Maple, Singular and Magma. Due to the efficient routines from the M4RI library,
the experimental results show that M-GVW is very efficient.

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The categories of this paper are: adap-org
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The categories of this paper are: nlin
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The categories of this paper are: patt-sol
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The categories of this paper are: q-bio
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The categories of this paper are: q-alg
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The categories of this paper are: bayes-an
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The categories of this paper are: eess
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The categories of this paper are: acc-phys
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The categories of this paper are: ao-sci
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The categories of this paper are: atom-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: math-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: plasm-ph
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The categories of this paper are: physics