Related papers: Numerical Schubert Calculus in Macaulay2
We describe an algorithm to compute a presentation of the pushforward module $f_*{\mathcal O}_{\mathcal{X}}$ for a finite map germ $f\colon \mathcal{X}\to ({\mathbb{C}}^{n+1},0)$, where $\mathcal{X}$ is Cohen-Macaulay of dimension $n$. The…
We introduce and study a new mathematical structure in the generalised (quantum) cohomology theory for Grassmannians. Namely, we relate the Schubert calculus to a quantum integrable system known in the physics literature as the asymmetric…
Many applications modeled by polynomial systems have positive dimensional solution components (e.g., the path synthesis problems for four-bar mechanisms) that are challenging to compute numerically by homotopy continuation methods. A…
We try to understand and justify Schubert Calculus the way Schubert did it.
A computing program in Matlab is given that computes amplitudes in scalar $\phi^3$ theory. The program is partitioned into several parts and a simple guide is given for its use.
A numerical program is presented which facilitates the computation of the full set of one-gluon loop diagrams (including ghost loop contributions), with M attached external gluon lines in all possible ways. The feasibility of such a task…
We present a Mathematica package for performing algebraic and numerical computations in cosmological models based on supersymmetric theories. The programs allow for (I) evaluation and study of the properties of a scalar potential in a large…
We establish a Schubert calculus for Bott-Samelson resolutions in the algebraic cobordism ring of a complete flag variety G/B.
This report is concerned with the efficiency of numerical methods for simulating quantum spin systems, with the aim to implement an improved method for simulation of a time-dependent Hamiltonian that displays chirped pulses at a high…
Numerical continuation methods track a solution path defined by a homotopy. The systems we consider are defined by polynomials in several variables with complex coefficients. For larger dimensions and degrees, the numerical conditioning…
Recently Gouveia, Thomas and the authors introduced the slack realization space, a new model for the realization space of a polytope. It represents each polytope by its slack matrix, the matrix obtained by evaluating each facet inequality…
The Clifford algebra of a n-dimensional Euclidean vector space provides a general language comprising vectors, complex numbers, quaternions, Grassman algebra, Pauli and Dirac matrices. In this work, we present an introduction to the main…
Mumford showed that Schottky subgroups of $PGL(2,K)$ give rise to certain curves, now called Mumford curves, over a non-Archimedean field K. Such curves are foundational to subjects dealing with non-Archimedean varieties, including…
This document is the manual for a free Mathematica package for computing with harmonic functions. This package allows the user to make calculations that would take a prohibitive amount of time if done without a computer. For example, the…
In the present paper by using Mathematica system a symbolic programming method for generation of the expressions of the expansion terms of atomic stationary perturbation theory (PT) is presented. For this purpose, the package named as…
Let V be a symplectic vector space and LG be the Lagrangian Grassmannian which parametrizes maximal isotropic subspaces in V. We give a presentation for the (small) quantum cohomology ring QH^*(LG) and show that its multiplicative structure…
We give a description of a new Macaulay2 package called SimplicialPosets. This package provides functions for working with simplicial posets and calculating their generalized Stanley-Reisner ideals. For practical purposes, we also introduce…
We describe the main functions of the Macaulay2 package Quasidegrees. The purpose of this package is to compute the quasidegree set of a finitely generated A-graded module presented as the cokernel of a monomial matrix. We provide examples…
We describe an algorithm for computing Macaulay dual spaces for multi-graded ideals. For homogeneous ideals, the natural grading is inherited by the Macaulay dual space which has been leveraged to develop algorithms to compute the Macaulay…
As a powerful tool in scientific computation, Mathematica offers us algebraic computation, but it does not provide functions to directly calculate commutators in quantum mechanics. Different from present software packets to deal with…