## A New Criterion for Normal Form Algorithms (1999)

Venue: | Proc. AAECC, volume 1719 of LNCS |

Citations: | 45 - 16 self |

### BibTeX

@INPROCEEDINGS{Mourrain99anew,

author = {B. Mourrain},

title = {A New Criterion for Normal Form Algorithms},

booktitle = {Proc. AAECC, volume 1719 of LNCS},

year = {1999},

pages = {430--443},

publisher = {Springer}

}

### Years of Citing Articles

### OpenURL

### Abstract

In this paper, we present a new approach for computing normal forms in the quotient algebra A of a polynomial ring R by an ideal I. It is based on a criterion, which gives a necessary and sufficient condition for a projection onto a set of polynomials, to be a normal form modulo the ideal I. This criterion does not require any monomial ordering and generalizes the Buchberger criterion of S-polynomials. It leads to a new algorithm for constructing the multiplicative structure of a zero-dimensional algebra. Described in terms of intrinsic operations on vector spaces in the ring of polynomials, this algorithm extends naturally to Laurent polynomials.