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Ritt's Second Theorem deals with composition collisions g∘h=g⁎∘h⁎ of univariate polynomials over a field, where degg=degh⁎. Joseph Fels Ritt (1922) presented two types of such decompositions. His main result here is that these comprise all possibilities, up to some linear transformations. We present a normal form for Ritt's Second Theorem, which is unique in many cases, and clarify the relation between...
Earlier work has presented algorithms to factor and compute GCDs of symbolic Laurent polynomials, that is multivariate polynomials whose exponents are themselves integer-valued polynomials. This article extends the notion of univariate polynomial decomposition to symbolic polynomials and presents an algorithm to compute these decompositions. For example, the symbolic polynomial f(X) = 2Xn2+n - 4X...
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