相关论文: Miura: Divisor Class Group Arithmetic

We introduce our package '+Ideals' for Magma, designed to perform the basic tasks related to ideals in number fields without pre-computing integral bases. It is based on Montes algorithm and a number of local techniques that we have…

In this paper we introduce a working generalization of the theory of Gr\"obner bases for algebras of partial difference polynomials with constant coefficients. One obtains symbolic (formal) computation for systems of linear or non-linear…

We compute divisors class groups of singular surfaces. Most notably we produce an exact sequence that relates the Cartier divisors and almost Cartier divisors of a surface to the those of its normalization. This generalizes Hartshorne's…

We introduce monomial divisibility diagrams (MDDs), a data structure for monomial ideals that supports insertion of new generators and fast membership tests. MDDs stem from a canonical tree representation by maximally sharing equal…

We present IntU package for Mathematica computer algebra system. The presented package performs a symbolic integration of polynomial functions over the unitary group with respect to unique normalized Haar measure. We describe a number of…

This is the second paper in a series of two in which a global algebraic number theory of the reals is formulated with the purpose of providing a unified setting for algebraic and transcendental number theory. In this paper, to any real…

The Amitsur subgroup of a variety with a group action measures the failure of the action to lift to the total spaces of its line bundles. We introduce the "numerical Amitsur group," which is an approximation of the ordinary Amitsur subgroup…

The Macaulay2 package CharacteristicClasses provides commands for the computation of the topological Euler characteristic, the degrees of the Chern classes and the degrees of the Segre classes of a closed subscheme of complex projective…

We show that if a divisor centered over a point on a smooth surface computes a minimal log discrepancy, then the divisor also computes a log canonical threshold. To prove the result, we study the asymptotic log canonical threshold of the…

Mixed Integer Programming (MIP) solvers rely on an array of sophisticated heuristics developed with decades of research to solve large-scale MIP instances encountered in practice. Machine learning offers to automatically construct better…

We form generating series of special divisors, valued in the Chow group and in the arithmetic Chow group, on the compactified integral model of a Shimura variety associated to a unitary group of signature (n-1,1), and prove their…

This article discusses a computational treatment of the localization A_L of an affine coordinate ring A at a prime ideal L and its associated graded ring Gr_a(A_L) with the means of standard basis techniques. Building on Mora's work, we…

We present a mixed-integer programming (MIP) model for scheduling quantum circuits to minimize execution time. Our approach maximizes parallelism by allowing non-overlapping gates (those acting on distinct qubits) to execute simultaneously.…

The recent emergence of novel computational devices, such as adiabatic quantum computers, CMOS annealers, and optical parametric oscillators, present new opportunities for hybrid-optimization algorithms that are hardware accelerated by…

We present a Mixed Integer Linear Program (MILP) approach in order to model the nonlinear problem of minimizing the tire noise. We first take more industrial constraints into account than in a former work of the authors. Then, we associate…

In this paper, we present an improved methodology to compute $\omega$-invariant of numerical semigroup. The approach is based on adapting a recent resolution method for optimizing a linear function over the set of efficient solutions of a…

Self-dual and complementary dual cyclic/abelian codes over finite fields form important classes of linear codes that have been extensively studied due to their rich algebraic structures and wide applications. In this paper, abelian codes…

Let $R$ be a commutative ring with nonzero identity and $I$ a proper ideal of $R$. The {\it ideal-based zero-divisor graph} of $R$ with respect to the ideal $I$, denoted by $\Gamma_I(R)$, is the graph on vertices $\{x \in R\setminus I \mid…

In previous work, the first author developed an algorithm for the computation of Hilbert modular forms. In this paper, we extend this to all totally real number fields of even degree and nontrivial class group. Using the algorithm over…

In this paper we present an algorithm to compute a Standard Basis for a fractional ideal $\mathcal{I}$ of the local ring $\mathcal{O}$ of an $n$-space algebroid curve with several branches. This allows us to determine the semimodule of…