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()`

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.

### 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
```

*clifford*version 1.0-8 Index]