Polynomial Decomposition and Its Applications
نویسندگان
چکیده
We present a simple algorithm for decomposing a polynomial H(x) into two constituent polynomials H(x) = f(g(x)), if such exist. Reversing a composition of two polynomials is shown to be reducible to a set of non-linear equations with a simple structure. While, in general, the solution of non-linear equations is quite complicated, we show that in this system the solution can be computed exactly using symbolic recurrence relations. We demonstrate the effectiveness of this result using some illustrative examples and also discuss interesting applications in geometric modeling: Reparameterization as an insecure watermarking tool and verifying the identity of a curve in two different representations.
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تاریخ انتشار 2003