Konstantin Ziegler
Composition collisions and projective polynomials.
Mon, 05/10/2010 - 15:01 — SomNambulAuthors: Joachim von zur Gathen, Konstantin Ziegler, Mark Giesbrecht
Subjects: Commutative Algebra
AbstractThe functional decomposition of polynomials has been a topic of great
interest and importance in pure and computer algebra and their applications.
The structure of compositions of (suitably normalized) polynomials f=g(h) over
finite fields is well understood in many cases, but quite poorly when the
degrees of both components are divisible by the characteristic p. This work
investigates the decomposition of polynomials whose degree is a power of p.Counting reducible, powerful, and relatively irreducible multivariate polynomials over finite fields.
Fri, 12/18/2009 - 16:01 — SomNambulAuthors: Joachim von zur Gathen, Alfredo Viola, Konstantin Ziegler
Subjects: Commutative Algebra
AbstractWe present counting methods for some special classes of multivariate
polynomials over a finite field, namely the reducible ones, the s-powerful ones
(divisible by the s-th power of a nonconstant polynomial), and the relatively
irreducible ones (irreducible but reducible over an extension field). One
approach employs generating functions, another one a combinatorial method. They
yield approximations with relative errors that essentially decrease
exponentially in the input size.
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