相关论文: A package for computations with classical resultan…

In this paper we provide a description of the package \textit{PolyominoIdeals} for \textit{Macaulay2} that allows to deal with collections of cells, polyominoes and related binomial ideals.

Package-X, a Mathematica package for the analytic computation of one-loop integrals dimensionally regulated near 4 spacetime dimensions is described. Package-X computes arbitrarily high rank tensor integrals with up to three propagators,…

We consider an n-qubit quantum system with a Hamiltonian, defined by an expansion in the Pauli basis, and propose a new algorithm for classical computing the exponential of the Hamiltonian. The algorithm is based on the representation of…

We present Binomials, a package for the computer algebra system Macaulay2, which specializes well known algorithms to binomial ideals. These come up frequently in algebraic statistics and commutative algebra, and it is shown that…

This is an expository version of our paper [arXiv:1902.07384]. Our aim is to present recent Macaulay2 algorithms for computation of mixed multiplicities of ideals in a Noetherian ring which is either local or a standard graded algebra over…

A C# package is presented that allows a user for an input quantum circuit to generate a set of multivariate polynomials over the finite field Z_2 whose total number of solutions in Z_2 determines the output of the quantum computation…

Conical functions appear in a large number of applications in physics and engineering. In this paper we describe an extension of our module CONICAL for the computation of conical functions. Specifically, the module includes now a routine…

CylindricalAlgebraicDecomposition.m2 is the first implementation of Cylindrical Algebraic Decomposition (CAD) in Macaulay2. CAD decomposes space into 'cells' where input polynomials are sign-invariant. This package computes an Open CAD…

The R package lcmm provides a series of functions to estimate statistical models based on linear mixed model theory. It includes the estimation of mixed models and latent class mixed models for Gaussian longitudinal outcomes (hlme),…

New formulas are given for Chow forms, discriminants and resultants arising from (not necessarily normal) toric varieties of codimension 2. Exact descriptions are also given for the secondary polygon and for the Newton polygon of the…

The \texttt{StronglyStableIdeals} package for \textit{Macaulay2} provides a method to compute all saturated strongly stable ideals in a given polynomial ring with a fixed Hilbert polynomial. A description of the main method and auxiliary…

We describe a complete algorithm to compute millions of coefficients of classical modular forms in a few seconds. We also review operations on Euler products and illustrate our methods with a computation of triple product L-function of…

We demonstrate the feasibility of quantum computing for large-scale, realistic chemical systems through the development of a new interface using a quantum circuit simulator and CP2K, a highly efficient first-principles calculation software.…

This note describes a package for computing seminormalization of rings within Macaulay2.

Many applications in the sciences require numerically stable and computationally efficient evaluation of multivariate polynomials. Finding beneficial representations of polynomials, such as Horner factorisations, is therefore crucial.…

Multiple analogues of certain families of combinatorial numbers are recently constructed by the author in terms of well poised Macdonald functions, and some of their fundamental properties are developed. In this paper, we present…

We describe a recently revived version of the software package SubalgberaBases, which is distributed in the Macaulay2 computer algebra system. The package allows the user to compute and manipulate subagebra bases -- which are also known as…

We present here theoretical results coming from the implementation of the package called AMULT (automata with multiplicities in several noncommutative variables). We show that classical formulas are ``almost every time'' optimal,…

The software package developed in the MS thesis research implements functions for the intelligent guessing of polynomial sequence formulas based on user-defined expected sequence factors of the input coefficients. We present a specialized…

We present a new version of TaylUR, a Fortran 95 module to automatically compute the numerical values of a complex-valued function's derivatives with respect to several variables up to an arbitrary order in each variable, but excluding…