1 Introduction sparkling GeMSS spring up from the night sky a dazzling splendor to ever
beautify sequined glories that verily eye smack sparkling GeMSS spring up from night sky …

In 1965 Buchberger introduced an algorithmic approach to compute Gröbner bases. Later
on, he and many others presented various attempts to improve the computation by removing …

In this paper, based on the work pioneered by Aumasson and Meier, Dinur et al., and Guo et
al., we construct some new delicate structures from the roundreduced versions of …

The present paper extends a concept of the inverse of a matrix that its elements are fuzzy
numbers, which may be implemented to model imprecise and uncertain features of the …

Since Gentry discovered in 2009 the first fully homomorphic encryption scheme, the last few
years have witnessed dramatic progress on designing more efficient homomorphic …

Suppose $ k, p\!\in\!\mathbb {N} $ with $ p $ prime and $ f\!\in\!\mathbb {Z}[x] $ is a univariate
polynomial with degree $ d $ and all coefficients having absolute value less than $ p^ k …

We generalize signature Gröbner bases, previously studied in the free algebra over a field
or polynomial rings over a ring, to ideals in the mixed algebra R [x1,…, xk]⟨ y1,…, yn⟩ …

In this paper we present first steps in using signature-based Gröbner basis algorithms like
Faugère's F5 or GVW for computation over Euclidean rings. We present problems appearing …

Polynomial system solving arises in many application areas to model non-linear geometric
properties. In such settings, polynomial systems may come with degeneration which the end …

Signature-based algorithms have become a standard approach for computing Gröbner
bases in commutative polynomial rings. However, so far, it was not clear how to extend this …