Definition
For univariate monic polynomials P and Q over a field k, the resultant res(P,Q) is a polynomial function of their coefficients. It is defined as the product
of the differences of their root For non-monic polynomials with leading coefficients p and q, respectively, the above product is multiplied by pdegQqdegP.
Read more about this topic: Resultant
Famous quotes containing the word definition:
“The man who knows governments most completely is he who troubles himself least about a definition which shall give their essence. Enjoying an intimate acquaintance with all their particularities in turn, he would naturally regard an abstract conception in which these were unified as a thing more misleading than enlightening.”
—William James (18421910)
“Although there is no universal agreement as to a definition of life, its biological manifestations are generally considered to be organization, metabolism, growth, irritability, adaptation, and reproduction.”
—The Columbia Encyclopedia, Fifth Edition, the first sentence of the article on life (based on wording in the First Edition, 1935)
“One definition of man is an intelligence served by organs.”
—Ralph Waldo Emerson (18031882)