In mathematics, the formal derivative is an operation on elements of a polynomial ring or a ring of formal power series that mimics the form of the derivative from calculus. Though they appear similar, the algebraic advantage of a formal derivative is that it does not rely on the notion of a limit, which is in general impossible to define for a ring. Many of the properties of the derivative are true of the formal derivative, but some, especially those that make numerical statements, are not. The primary use of formal differentiation in algebra is to test for multiple roots of a polynomial.
Read more about Formal Derivative: Definition, Properties, Application To Finding Repeated Factors, Correspondence To Analytic Derivative
Famous quotes containing the words formal and/or derivative:
“It is in the nature of allegory, as opposed to symbolism, to beg the question of absolute reality. The allegorist avails himself of a formal correspondence between “ideas” and “things,” both of which he assumes as given; he need not inquire whether either sphere is “real” or whether, in the final analysis, reality consists in their interaction.”
—Charles, Jr. Feidelson, U.S. educator, critic. Symbolism and American Literature, ch. 1, University of Chicago Press (1953)
“When we say “science” we can either mean any manipulation of the inventive and organizing power of the human intellect: or we can mean such an extremely different thing as the religion of science the vulgarized derivative from this pure activity manipulated by a sort of priestcraft into a great religious and political weapon.”
—Wyndham Lewis (1882–1957)