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

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.

1 2 3 | ```
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.

1 2 3 4 5 6 7 8 9 10 | ```
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
``` |

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