term {clifford} | R Documentation |
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.
terms(x)
is.blade(x)
is.basisblade(x)
x |
Object of class |
Functions terms()
and coeffs()
are the
extraction methods. These are unordered vectors but the ordering is
consistent between them (an extended discussion of this phenomenon
is presented in the mvp
package).
Function term()
returns a clifford object that comprises
a single term with unit coefficient.
Function is.basisterm()
returns TRUE
if its
argument has only a single term, or is a nonzero scalar; the zero
clifford object is not considered to be a basis term.
Robin K. S. Hankin
C. Perwass. “Geometric algebra with applications in engineering”. Springer, 2009.
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