7 citations · 12 across the 8 of their papers we have counts for
8 papers
On Two Signature Variants Of Buchberger's Algorithm Over Principal Ideal Domains
Maria Francis, Thibaut Verron
Signature-based algorithms have brought large improvements in the performances of Gröbner bases algorithms for polynomial systems over fields. Furthermore, they yield additional da…
Signature-based Möller's algorithm for strong Gröbner bases over PIDs
Maria Francis, Thibaut Verron
Signature-based algorithms are the latest and most efficient approach as of today to compute Gröbner bases for polynomial systems over fields. Recently, possible extensions of thes…
A Signature-based Algorithm for computing Computing Gröbner Bases over Principal Ideal Domains
Maria Francis, Thibaut Verron
Signature-based algorithms have become a standard approach for Gröbner basis computations for polynomial systems over fields, but how to extend these techniques to coefficients in…
On Gröbner Bases and Krull Dimension of Residue Class Rings of Polynomial Rings over Integral Domains
Maria Francis, Ambedkar Dukkipati
Given an ideal in , where is a Noetherian integral domain, we propose an approach to compute the Krull dimension of $A[x_1,\ldots,x_n]/\math…
On Ideal Lattices, Gröbner Bases and Generalized Hash Functions
Maria Francis, Ambedkar Dukkipati
In this paper, we draw connections between ideal lattices and multivariate polynomial rings over integers using Gröbner bases. Ideal lattices are ideals in the residue class ring,…
On Ideal Lattices and Gröbner Bases
Maria Francis, Ambedkar Dukkipati
In this paper, we draw a connection between ideal lattices and Gröbner bases in the multivariate polynomial rings over integers. We study extension of ideal lattices in $\mathbb{Z}…
Border Bases for Polynomial Rings over Noetherian Rings
Ambedkar Dukkipati, Nithish Pai, Maria Francis
The theory of border bases for zero-dimensional ideals has attracted several researchers in symbolic computation due to their numerical stability and mathematical elegance. As show…
Reduced Gröbner Bases and Macaulay-Buchberger Basis Theorem over Noetherian Rings
Maria Francis, Ambedkar Dukkipati
In this paper, we extend the characterization of , where to be a free -module to multivariate polynomial rings over any c…