77 citations · 186 across the 20 of their papers we have counts for
10 papers · 1 filter
Computing integral bases via localization and Hensel lifting
Janko Boehm, Wolfram Decker, Santiago Laplagne +1
We present a new algorithm for computing integral bases in algebraic function fields of one variable, or equivalently for constructing the normalization of a plane curve. Our basic…
Weak Lefschetz Property and Stellar Subdivisions of Gorenstein Complexes
Janko Boehm, Stavros Argyrios Papadakis
Assume sigma is a face of a Gorenstein* simplicial complex D. We investigate the question of whether the Weak Lefschetz Property of the Stanley-Reisner ring k[D] (over an infinite…
Bounds for the Betti numbers of successive stellar subdivisions of a simplex
Janko Boehm, Stavros Argyrios Papadakis
We give a bound for the Betti numbers of the Stanley-Reisner ring of a stellar subdivision of a Gorenstein* simplicial complex by applying unprojection theory. From this we derive…
The use of Bad Primes in Rational Reconstruction
Janko Boehm, Wolfram Decker, Claus Fieker +1
A standard method for finding a rational number from its values modulo a collection of primes is to determine its value modulo the product of the primes via Chinese remaindering, a…
Decomposition of Monomial Algebras: Applications and Algorithms
Janko Boehm, David Eisenbud, Max Joachim Nitsche
Considering finite extensions K[A] \subseteq K[B] of positive affine semigroup rings over a field K we have developed in [1] an algorithm to decompose K[B] as a direct sum of monom…
Decomposition of semigroup algebras
Janko Boehm, David Eisenbud, Max Joachim Nitsche
Let A \subseteq B be cancellative abelian semigroups, and let R be an integral domain. We show that the semigroup ring R[B] can be decomposed, as an R[A]-module, into a direct sum…
Parallel algorithms for normalization
Janko Boehm, Wolfram Decker, Santiago Laplagne +3
Given a reduced affine algebra A over a perfect field K, we present parallel algorithms to compute the normalization \bar{A} of A. Our starting point is the algorithm of Greuel, La…
Implementing the Kustin-Miller complex construction
Janko Boehm, Stavros Argyrios Papadakis
The Kustin-Miller complex construction, due to A. Kustin and M. Miller, can be applied to a pair of resolutions of Gorenstein rings with certain properties to obtain a new Gorenste…
On the structure of Stanley-Reisner rings associated to cyclic polytopes
Janko Boehm, Stavros Argyrios Papadakis
We study the structure of Stanley-Reisner rings associated to cyclic polytopes, using ideas from unprojection theory. Consider the boundary simplicial complex Delta(d,m) of the d-d…
Stellar subdivisions and Stanley-Reisner rings of Gorenstein complexes
Janko Boehm, Stavros Argyrios Papadakis
Unprojection theory aims to analyze and construct complicated commutative rings in terms of simpler ones. Our main result is that, on the algebraic level of Stanley-Reisner rings,…