numeric_to_clifford {clifford} R Documentation

## Coercion from numeric to Clifford form

### Description

Given a numeric value or vector, return a Clifford algebra element

### Usage

numeric_to_clifford(x)
as.1vector(x)
is.1vector(x)
scalar(x=1)
as.scalar(x=1)
is.scalar(C)
basis(n,x=1)
e(n,x=1)
pseudoscalar(n,x=1)
as.pseudoscalar(n,x=1)
is.pseudoscalar(C)


### Arguments

 x Numeric vector n Integer specifying dimensionality of underlying vector space C Object possibly of class Clifford

### Details

Function as.scalar() takes a length-one numeric vector and returns a Clifford scalar of that value (to extract the scalar component of a multivector, use const()).

Function is.scalar() is a synonym for is.real() which is documented at const.Rd.

Function as.1vector() takes a numeric vector and returns the linear sum of length-one blades with coefficients given by x; function is.1vector() returns TRUE if every term is of grade 1.

Function pseudoscalar(n) returns a pseudoscalar of dimensionality n and function is.pseudoscalar() checks for a Clifford object being a pseudoscalar.

Function numeric_to_vector() dispatches to either as.scalar() for length-one vectors or as.1vector() if the length is greater than one.

Function basis() returns a wedge product of basis vectors; function e() is a synonym. There is special dispensation for zero, so e(0) returns the Clifford scalar 1.

Function antivector() should arguably be described here but is actually documented at antivector.Rd.

### Author(s)

Robin K. S. Hankin

getcoeffs,antivector,const

### Examples


as.scalar(6)
as.1vector(1:8)

e(5:8)

Reduce(+,sapply(seq_len(7),function(n){e(seq_len(n))},simplify=FALSE))

pseudoscalar(6)

pseudoscalar(7,5) == 5*pseudoscalar(7)  # should be true



[Package clifford version 1.0-8 Index]