In Computer Algebra, Subresultant Theory provides a powerful method to construct algorithms solving problems for polynomials in one variable in an optimal way. So, using this method we can compute the greatest common divisor of two polynomials in one variable with integer coefficients avoiding the exponential growth of the coefficients that will appear if we use the Euclidean Algorithm.
In this note, generalizing a forgotten construction appearing in [Hab], we extend the Subresultant Theory to the multivariate case. In order to achieve this, first of all, we introduce the definition of subresultant sequence associated to two polynomials in one variable with coefficients in an integral domain and the properties of this sequence that we would like to extend to the multivariate case.
@article{urn:eudml:doc:39898,
title = {A subresultant theory of multivariate polynomials.},
journal = {Extracta Mathematicae},
volume = {5},
year = {1990},
pages = {150-152},
zbl = {0759.13011},
mrnumber = {MR1125689},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:39898}
}
González Vega, Laureano. A subresultant theory of multivariate polynomials.. Extracta Mathematicae, Tome 5 (1990) pp. 150-152. http://gdmltest.u-ga.fr/item/urn:eudml:doc:39898/