Related papers: An algorithm for producing F-pure ideals

We present a randomized polynomial-time algorithm to generate a random integer according to the distribution of norms of ideals at most N in any given number field, along with the factorization of the integer. Using this algorithm, we can…

We determine, in a polynomial ring over a field, the arithmetical rank of certain ideals generated by a set of monomials and one binomial.

We present an algorithm for computing the integral closure of a reduced ring that is finitely generated over a finite field.

This paper presents algorithms for calculating the quadratic character and the norms of prime ideals in the ring of integers of any quadratic field. The norms of prime ideals are obtained by means of a sieve algorithm using the quadratic…

Let $K$ be the number field determined by a monic irreducible polynomial $f(x)$ with integer coefficients. In previous papers we parameterized the prime ideals of $K$ in terms of certain invariants attached to Newton polygons of higher…

In this note, we use estimates given in the recent preprint [Her11b]to deduce a formula for the F-pure threshold of a binomial hypersurface over a field of prime characteristic. These formulas are given in terms of the associated splitting…

We give an algorithm for computing the factor ring of a given ideal in a Dedekind domain with finite rank, which runs in deterministic and polynomial-time. We provide two applications of the algorithm: judging whether a given ideal is prime…

We present an algorithm to compute a primary decomposition of an ideal in a polynomial ring over the integers. For this purpose we use algorithms for primary decomposition in polynomial rings over the rationals resp. over finite fields, and…

We compute a number of invariants of singularities defined via the Frobenius morphism for seminormal affine toric varieties over fields of characteristic p > 0. Our main technical tool is a combinatorial description of the potential…

This paper presents some algorithmic techniques to compute explicitly the noetherian operators associated to a class of ideals and modules over a polynomial ring. The procedures we include in this work can be easily encoded in computer…

This paper presents a novel approach to constructing finite generating sets for infinitely generated ideals. By integrating algebraic and computational techniques, we provide a method to identify finite generators, demonstrated through…

We present an alternative method for computing primary decomposition of zero-dimensional ideals over finite fields. Based upon the further decomposition of the invariant subspace of the Frobenius map acting on the quotient algebra in the…

In this paper we develop a new technique to compute the Betti table of a monomial ideal. We present a prototype implementation of the resulting algorithm and we perform numerical experiments suggesting a very promising efficiency. On the…

In this paper, we introduce the notion of quasi-$F$-splitting for rings in mixed characteristic. By comparing quasi-$F$-splitting with perfectoid purity, we obtain a new inversion of adjunction-type result. Furthermore, we study the…

The $F$-pure threshold is a numerical invariant of prime characteristic singularities, that constitutes an analogue of the log canonical thresholds in characteristic zero. We compute the $F$-pure thresholds of determinantal ideals, i.e., of…

In this paper we give an algorithm to determine all finite matrix groups over a number field. Our algorithm is based on the representation theory of finite groups.

The aim of this paper is to show that there exists a deterministic algorithm that can be applied to compute the factors of a polynomial of degree 2, defined over a finite field, given certain conditions.

For a finite $\mathbb{Z}$-algebra $R$, i.e., for a $\mathbb{Z}$-algebra which is a finitely generated $\mathbb{Z}$-module, we assume that $R$ is explicitly given by a system of $\mathbb{Z}$-module generators $G$, its relation module ${\rm…

We describe an algorithm to count the number of distinct real zeros of a polynomial (square) system f. The algorithm performs O(n D kappa(f)) iterations where n is the number of polynomials (as well as the dimension of the ambient space), D…

We compute the $F$-pure threshold of some non-principal ideals which satisfy a geometric generic condition about their Newton polyhedron. We also contribute some evidence in favor of the conjectured equality between the $F$-pure threshold…