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The runoff curve number (also called a curve number or simply CN) is an empirical parameter used in hydrology for predicting direct runoff or infiltration from rainfall excess. [1]
It follows that the roots of a polynomial with real coefficients are mirror-symmetric with respect to the real axis. This can be extended to algebraic conjugation: the roots of a polynomial with rational coefficients are conjugate (that is, invariant) under the action of the Galois group of the polynomial. However, this symmetry can rarely be ...
This is useful in solving such recurrences, since by using partial fraction decomposition we can write any proper rational function as a sum of factors of the form 1 / (ax + b) and expand these as geometric series, giving an explicit formula for the Taylor coefficients; this is the method of generating functions.
Rational function models can often be used to model complicated structure with a fairly low degree in both the numerator and denominator. This in turn means that fewer coefficients will be required compared to the polynomial model. Rational function models are moderately easy to handle computationally.
From coefficients in an algebraic extension to coefficients in the ground field (see below). From rational coefficients to integer coefficients (see below). From integer coefficients to coefficients in a prime field with p elements, for a well chosen p (see below).
In algebra, the partial fraction decomposition or partial fraction expansion of a rational fraction (that is, a fraction such that the numerator and the denominator are both polynomials) is an operation that consists of expressing the fraction as a sum of a polynomial (possibly zero) and one or several fractions with a simpler denominator.
The rational univariate representation or RUR is a representation of the solutions of a zero-dimensional polynomial system over the rational numbers which has been introduced by F. Rouillier. [10] A RUR of a zero-dimensional system consists in a linear combination x 0 of the variables, called separating variable, and a system of equations [11]
If a particular rational function occurs exactly once in the Padé table, it is called a normal approximant to f(z). If every entry in the complete Padé table is normal, the table itself is said to be normal. Normal Padé approximants can be characterized using determinants of the coefficients c n in the Taylor series expansion of f(z), as