32 citations
- University of BonnDE19 papers
- Centre National de la Recherche ScientifiqueFR4 papers
- Fraunhofer Institute for Intelligent Analysis and Information SystemsDE4 papers
- Université de MontpellierFR4 papers
- Fraunhofer Institute for Communication, Information Processing and ErgonomicsDE3 papers
- Université de LilleFR3 papers
- Coventry UniversityGB2 papers
- Joint Institute for Nuclear ResearchRU2 papers
- Laboratoire Paul PainlevéFR2 papers
- Slovak Academy of SciencesSK2 papers
- Alibaba Group (China)CN1 paper
- Artificial Intelligence Research InstituteES1 paper
5 papers · 1 filter
Tame Decompositions and Collisions
Konstantin Ziegler
A univariate polynomial f over a field is decomposable if f = g o h = g(h) for nonlinear polynomials g and h. It is intuitively clear that the decomposable polynomials form a small…
Normal form for Ritt's Second Theorem
Joachim von zur Gathen
Ritt's Second Theorem deals with composition collisions g o h = g* o h* of univariate polynomials over a field, where deg g = deg h*. Joseph Fels Ritt (1922) presented two types of…
Compositions and collisions at degree p^2
Raoul Blankertz, Joachim von zur Gathen, Konstantin Ziegler
A univariate polynomial f over a field is decomposable if f = g o h = g(h) for nonlinear polynomials g and h. In order to count the decomposables, one wants to know, under a suitab…
Counting reducible, powerful, and relatively irreducible multivariate polynomials over finite fields
Joachim von zur Gathen, Alfredo Viola, Konstantin Ziegler
We 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…
Counting decomposable univariate polynomials
Joachim von zur Gathen
A univariate polynomial f over a field is decomposable if it is the composition f = g(h) of two polynomials g and h whose degree is at least 2. We determine the dimension (over an…