Generalizations and Related Concepts
The resultant is sometimes defined for two homogeneous polynomials in two variables, in which case it vanishes when the polynomials have a common non-zero solution, or equivalently when they have a common zero on the projective line. More generally, the multivariate resultant or Macaulay's resultant of n homogeneous polynomials in n variables is a polynomial in their coefficients that vanishes when they have a common non-zero solution, or equivalently when the n hypersurfaces corresponding to them have a common zero in n–1 dimensional projective space. The multivariate resultant is, with Gröbner bases, one of the main tools of effective elimination theory (elimination theory on computers).
Read more about this topic: Resultant
Famous quotes containing the words related and/or concepts:
“Gambling is closely related to theft, and lewdness to murder.”
—Chinese proverb.
“Institutional psychiatry is a continuation of the Inquisition. All that has really changed is the vocabulary and the social style. The vocabulary conforms to the intellectual expectations of our age: it is a pseudo-medical jargon that parodies the concepts of science. The social style conforms to the political expectations of our age: it is a pseudo-liberal social movement that parodies the ideals of freedom and rationality.”
—Thomas Szasz (b. 1920)