Vol. 9, No. 1, 2019

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DiffAlg: a Differential algebra package

Manuel Dubinsky, César Massri, Ariel Molinuevo and Federico Quallbrunn

Vol. 9 (2019), 11–17
Abstract

In this article we present DiffAlg.m2, a differential algebra package for Macaulay2. It can perform the following operations: wedge products and exterior differentials of differential forms, contraction and Lie derivatives of differential forms with respect to a vector field and Lie brackets between vector fields.

Given a homogeneous differential operator of degree one D, the lack of an algebraic module structure attached to the kernel or image of D hinders the study of D. The main purpose of DiffAlg.m2 is to handle these spaces degree-wise.

Keywords
differential operators, exterior algebra, vector fields
Mathematical Subject Classification 2010
Primary: 14-04, 53-04
Supplementary material

Specialised routines for differential forms

Milestones
Received: 27 May 2015
Revised: 26 October 2018
Accepted: 19 November 2018
Published: 4 March 2019
Authors
Manuel Dubinsky
Departamento de Computación
Universidad de Avellaneda
Avellaneda
Argentina
César Massri
Departamento de Matemática
Universidad CAECE
Buenos Aires
Argentina
Ariel Molinuevo
Instituto de Matemática
Universidade Federal do Rio de Janeiro
Rio de Janeiro
Brazil
Federico Quallbrunn
Departamento de Matemática
Universidad de Buenos Aires
Pabellón I, Ciudad Universitaria
Buenos Aires
Argentina