39 citations · 46 across the 8 of their papers we have counts for
9 papers · 1 filter
A C++ class for algebraic reliability computations
Anna Maria Bigatti, Patricia Pascual-Ortigosa, Eduardo Sáenz-de-Cabezón
We present the design and implementation of a \texttt{C++} class for reliability analysis of multi-state systems using an algebraic approach based on monomial ideals. The class is…
Saturations of Subalgebras, SAGBI Bases, and U-invariants
Anna Maria Bigatti, Lorenzo Robbiano
Given a polynomial ring over a field , an element , and a -subalgebra of , we deal with the problem of saturating with respect to , i.e. computing…
Ideals modulo a prime
John Abbott, Anna Maria Bigatti, Lorenzo Robbiano
The main focus of this paper is on the problem of relating an ideal in the polynomial ring to a corresponding ideal in $\mathbb F_p[x_1,\dots, x_n]…
Computing and Using Minimal Polynomials
John Abbott, Anna Maria Bigatti, Elisa Palezzato +1
Given a zero-dimensional ideal I in a polynomial ring, many computations start by finding univariate polynomials in I. Searching for a univariate polynomial in I is a particular ca…
Extremal behaviour in sectional matrices
Anna Maria Bigatti, Elisa Palezzato, Michele Torielli
In this paper we want to revive the object sectional matrix which encodes the Hilbert functions of successive hyperplane sections of a homogeneous ideal. We translate and/or reprov…
Groebner Bases for Everyone with CoCoA-5 and CoCoALib
John Abbott, Anna Maria Bigatti
We present a survey on the developments related to Groebner bases, and show explicit examples in CoCoA. The CoCoA project dates back to 1987: its aim was to create a "mathematician…