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Coercion from numeric to Clifford form

numeric_to_clifford.Rd

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)

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 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

Robin K. S. Hankin

See also

getcoeffs,antivector,const,pseudoscalar

Examples


as.scalar(6)
#> Element of a Clifford algebra, equal to
#> scalar ( 6 )
as.1vector(1:8)
#> Element of a Clifford algebra, equal to
#> + 1e_1 + 2e_2 + 3e_3 + 4e_4 + 5e_5 + 6e_6 + 7e_7 + 8e_8

e(5:8)
#> Element of a Clifford algebra, equal to
#> + 1e_5678

Reduce(`+`,sapply(seq_len(7),function(n){e(seq_len(n))},simplify=FALSE))
#> Element of a Clifford algebra, equal to
#> + 1e_1 + 1e_12 + 1e_123 + 1e_1234 + 1e_12345 + 1e_123456 + 1e_1234567