GCD's and Factoring Multivariate Polynominals Using Gröbner Bases

@inproceedings{Gianni1985GCDsAF,
title={GCD's and Factoring Multivariate Polynominals Using Gr{\"o}bner Bases},
author={P. Gianni and Barry M. Trager},
booktitle={European Conference on Computer Algebra},
year={1985}
}

This paper shows how Grobner basis computations can be used to compute multivariate gcds, perform Hensel lifting, and reduce multivariate factorization to univariate. The essential idea is to produce an ideal containing the desired polynomial as an element of least degree. This polynomial must then appear in a total degree Grobner basis for the ideal. The construction is somewhat analogous to the recent lattice algorithms for polynomial factorization. A major difference is that we don't need to… CONTINUE READING