Counting reducible, powerful, and relatively irreducible multivariate polynomials over finite fields - Mathematics > Commutative AlgebraReport as inadecuate




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Abstract: We present counting methods for some special classes of multivariatepolynomials over a finite field, namely the reducible ones, the s-powerful onesdivisible by the s-th power of a nonconstant polynomial, and the relativelyirreducible ones irreducible but reducible over an extension field. Oneapproach employs generating functions, another one uses a combinatorial method.They yield exact formulas and approximations with relative errors thatessentially decrease exponentially in the input size.



Author: Joachim von zur Gathen, Alfredo Viola, Konstantin Ziegler

Source: https://arxiv.org/



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