as.1form: Coerce vectors to 1-forms

In wedge: The Exterior Calculus

Description

Given a vector, return the corresponding 1-form; the exterior derivative of a 0-form (that is, a scalar function)

Usage

as.1form(v)
grad(v)

Arguments

v	A vector with element i being df/dxi

Details

The exterior derivative of a k-form phi is a (k+1)-form d phi given by

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We can use the facts that

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and

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to calculate differentials of general k-forms. Specifically, if

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then

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The entry in square brackets is given by grad(). See the examples for appropriate R idiom.

Value

A one-form

Author(s)

Robin K. S. Hankin

See Also

kform

Examples

as.1form(1:9)  # note ordering of terms


as.1form(rnorm(20))

grad(c(4,7)) %^% grad(1:4)

wedge documentation built on Sept. 4, 2019, 9:02 a.m.