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Case one has fractional expressions where factors in the denominator are unique. Case two has fractional expressions where some factors may repeat as powers of a binomial. In integral calculus we would want to write a fractional algebraic expression as the sum of its partial fractions in order to take the integral of each simple fraction ...
Linear fractional transformations leave cross ratio invariant, so any linear fractional transformation that leaves the unit disk or upper half-planes stable is an isometry of the hyperbolic plane metric space. Since Henri Poincaré explicated these models they have been named after him: the Poincaré disk model and the Poincaré half-plane model.
Using the preceding decomposition inductively one gets fractions of the form , with < = , where G is an irreducible polynomial. If k > 1 , one can decompose further, by using that an irreducible polynomial is a square-free polynomial , that is, 1 {\displaystyle 1} is a greatest common divisor of the polynomial and its derivative .
Any linear-fractional program can be transformed into a linear program, assuming that the feasible region is non-empty and bounded, using the Charnes-Cooper transformation. [1] The main idea is to introduce a new non-negative variable t {\displaystyle t} to the program which will be used to rescale the constants involved in the program ( α ...
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.
In mathematics, the method of clearing denominators, also called clearing fractions, is a technique for simplifying an equation equating two expressions that each are a sum of rational expressions – which includes simple fractions.
The Pentagon has failed its annual financial audit for the seventh year in a row. This means the Department of Defense (DOD) has failed every single audit it has been subjected to, but officials ...
In mathematical optimization, fractional programming is a generalization of linear-fractional programming. The objective function in a fractional program is a ratio of two functions that are in general nonlinear. The ratio to be optimized often describes some kind of efficiency of a system.
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