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 |
Details
Functions
terms()
andcoeffs()
are the extraction methods. These are unordered vectors but the ordering is consistent between them (an extended discussion of this phenomenon is presented in themvp
package).Function
term()
returns a clifford object that comprises a single term with unit coefficient.Function
is.basisterm()
returnsTRUE
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.
Author(s)
Robin K. S. Hankin
References
C. Perwass. “Geometric algebra with applications in engineering”. Springer, 2009.
See Also
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