24 citations · 68 across the 20 of their papers we have counts for
24 papers
Polynomial interpolation of partial functions in finite algebras with a Mal'cev term
Erhard Aichinger, Mario Kapl, Bernardo Rossi
We provide polynomial completeness results for finite algebras in congruence permutable varieties. In 2001, Idziak and Słomczy{ń}ska introduced the completeness concept of being \e…
Structured and Punctured Nullstellensätze
Erhard Aichinger, John R. Schmitt, Henry Zhan
A Nullstellensatz is a theorem providing information on polynomials that vanish on a certain set: David Hilbert's Nullstellensatz (1893) is a cornerstone of algebraic geometry, and…
On the complexity of solving equations over the symmetric group
Erhard Aichinger, Simon Grünbacher
The complexity of solving equations over finite groups has been an active area of research over the last two decades, starting with Goldmann and Russell, \emph{The complexity of so…
Strong Gröbner bases and linear algebra in multivariate polynomial rings over Euclidean domains
Erhard Aichinger
We provide a self-contained introduction to Gröbner bases of submodules of , where is a Euclidean domain, and explain how to use these bases to solve lin…
On when the union of two algebraic sets is algebraic
Erhard Aichinger, Mike Behrisch, Bernardo Rossi
In universal algebraic geometry, an algebra is called an equational domain if the union of two algebraic sets is algebraic. We characterize equational domains, with respect to poly…
Zero testing and equation solving for sparse polynomials on rectangular domains
Erhard Aichinger, Simon Grünbacher, Paul Hametner
We consider sparse polynomials in variables over a finite field, and ask whether they vanish on a set , where is a set of nonzero elements of the field. We see that if…