# Involutive Algorithms for Computing Groebner Bases

@inproceedings{PGerdt2005InvolutiveAF, title={Involutive Algorithms for Computing Groebner Bases}, author={Vladimir P.Gerdt}, year={2005} }

. In this paper we describe an efﬁcient involutive algorithm for construct- ing Gröbner bases of polynomial ideals. The algorithm is based on the concept of involutive monomial division which restricts the conventional division in a certain way. In the presented algorithm a reduced Gröbner basis is the internally ﬁxed subset of an involutive basis, and having computed the later, the former can be output without any extra computational costs. We also discuss some accounts of experimental…

## 31 Citations

### Computation of Pommaret Bases Using Syzygies

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An involutive variant of the signature based algorithm of Gao et al. to compute simultaneously a Grobner basis for a given ideal and for the syzygy module of the input basis to ensure the existence of a finite Pommaret basis is proposed.

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An algorithm for this transformation into an equivalent Gréobner basis form is presented and its implementation can be applied to automatic generation of difference schemes for linear partial differential equations and to reduction of Feynman integrals.

### Complementary decompositions of monomial ideals and involutive bases

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Complementary decompositions of monomial ideals—also known as Stanley decompositions—play an important role in many places in commutative algebra. In this article, we discuss and compare several…

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