In theory there is no difference between theory and practice. In practice there is. Yogi Berra
A SINGULAR Introduction to Commutative Algebra offers a rigorous intro duction to …

Les bases de Gröbner constituent un outil important pour la résolution de systèmes
d'équations algébriques, et leur calcul est souvent la partie difficile de la résolution. Cette …

Let I be a homogeneous ideal of the polynomial ring K [x0,…, xn], where K is an arbitrary
field. Avoiding the construction of a minimal graded free resolution of I, we provide effective …

Regularity....................................................... 1 1.2 A Lemma from Homological Algebra and the
Equivalenceof the Definitions................................................ 3 1.3 Other Definitions and Further …

For Arithmetization-Oriented ciphers and hash functions Gr\" obner basis attacks are
generally considered as the most competitive attack vector. Unfortunately, the complexity of …

Let K be an infinite field and let m 1<⋯< mn be a generalized arithmetic sequence of positive
integers, ie, there exist h, d, m 1∈ Z+ such that mi= hm 1+(i− 1) d for all i∈{2,…, n}. We …

We consider several notions of genericity appearing in algebraic geometry and commutative
algebra. Special emphasis is put on various stability notions which are defined in a …

We improve certain degree bounds for Grobner bases of polynomial ideals in generic
position. We work exclusively in deterministically verifiable and achievable generic positions …

In this paper, we study generalized cryptographic semi-regular sequences, which are
expected to generic in the space of homogeneous polynomial sequences on which the …

Abstract Let R:= K [x 1,…, xn] be a polynomial ring over an infinite field K, and let I⊂ R be a
homogeneous ideal with respect to a weight vector ω=(ω 1,…, ω n)∈(Z+) n such that dim …