term {clifford}R Documentation

Deal with terms

Description

By basis vector, I mean one of the basis vectors of the underlying vector space R^n, that is, an element of the set \left\lbrace e_1,\ldots,e_n\right\rbrace. A term is a wedge product of basis vectors (or a geometric product of linearly independent basis vectors), something like e_{12} or e_{12569}. Sometimes I use the word “term” to mean a wedge product of basis vectors together with its associated coefficient: so 7e_{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 e_{12}=e_1\wedge e_2 and e_{12} + e_{13}=e_1\wedge(e_2+e_3) are blades, but e_{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

terms(x)
is.blade(x)
is.basisblade(x)

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


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


[Package clifford version 1.1-1 Index]