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Algebraic Programming and Differential Forms

Frank Zizza
Organization: Willamette University
Journal / Anthology

The Mathematica Journal
Year: 1992
Volume: 2
Issue: 1
Page range: 88-90

This article describes a general method for linear algebra and exterior algebra computations. The utilities MakeLinearObject, MakeLinearMap, and MakeMultilinearMap implement the properties of linearity, enabling the programmer to enter definitions of transformations of basis elements. Linear maps, derivations and bilinear operations can be handled with the same ease. The article concludes with an application to exterior algebras with differential forms.

Included is the package DifferentialForms.m, a package for symbolic computation with exterior differential forms in R^n. Functions implemented include ExteriorDerivative, Pair, Pullback, Push, Boundary, Integral, Chain, LieDerivative, Restrict, HomotopyOperater, and InvertMetric. Programming details of this package appeared in Volume II, Issue 1 of the Mathematica Journal in the article titled "Differential Forms and Algebraic Programming". Comments about the package are welcome at zizza@willamette.edu or Frank Zizza, Willamette University, D212, Salem Oregon 97301.

*Mathematics > Algebra > Linear Algebra

Pure Math, Pure Mathematics, Calculus, differential forms, tensors, Linear Algebra, the Mathematica Journal, TMJ, Vector Form, Alternating differential form, exterior derivative