term: Deal with terms

Description Usage Arguments Details Author(s) References See Also Examples

Description

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By basis vector, I mean one of the basis vectors of the underlying vector space \mjeqnR^nR^n, that is, an element of the set \mjeqn\left\lbrace e_1,...,e_n\right\rbracee_1,...,e_n. A term is a wedge product of basis vectors (or a geometric product of linearly independent basis vectors), something like \mjeqne_12e_12 or \mjeqne_12569e_12569. Sometimes I use the word “term” to mean a wedge product of basis vectors together with its associated coefficient: so \mjeqn7e_127e_12 would be described as a term.

From Perwass: a blade is the outer product of a number of 1-vectors (or, equivalently, the wedge product of linearly independent 1-vectors). Thus \mjeqne_12=e_1\wedge e_2e_12=e_1 ^ e_2 and \mjeqne_12 + e_13=e_1\wedge(e_2+e_3)e_12+e_13=e1^(e2+e3) are blades, but \mjeqne_12 + e_34e_12+e_34 is not.

Function rblade(), documented at ‘rcliff.Rd’, returns a random blade.

Function is.blade() is not currently implemented: there is no easy way to detect whether a Clifford object is a product of 1-vectors.

Usage

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Arguments

x

Object of class clifford

Details

Author(s)

Robin K. S. Hankin

References

C. Perwass. “Geometric algebra with applications in engineering”. Springer, 2009.

See Also

clifford,rblade

Examples

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x <- rcliff()
terms(x)

is.basisblade(x)


a <- as.1vector(1:3)
b <- as.1vector(c(0,0,0,12,13))

a %^% b # a blade

clifford documentation built on Nov. 19, 2021, 1:06 a.m.