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The Heaviside cover-up method, named after Oliver Heaviside, is a technique for quickly determining the coefficients when performing the partial-fraction expansion of a rational function in the case of linear factors. [1] [2] [3] [4]
The rational number / is unknown, and the goal of the problem is to recover it from the given information. In order for the problem to be solvable, it is necessary to assume that the modulus m {\displaystyle m} is sufficiently large relative to r {\displaystyle r} and s {\displaystyle s} .
In mathematics, the method of equating the coefficients is a way of solving a functional equation of two expressions such as polynomials for a number of unknown parameters. It relies on the fact that two expressions are identical precisely when corresponding coefficients are equal for each different type of term.
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).
Graphs of functions commonly used in the analysis of algorithms, showing the number of operations versus input size for each function. The following tables list the computational complexity of various algorithms for common mathematical operations.
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However, for rational coefficients, two aspects have to be taken care of: The output may involve huge integers which may make the computation and the use of the result problematic. To deduce the numeric values of the solutions from the output, one has to solve univariate polynomials with approximate coefficients, which is a highly unstable problem.
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