clifford (version 1.1-2)

const: The constant term of a Clifford object

Description

Get and set the constant term of a clifford object.

Usage

const(C,drop=TRUE)
is.real(C)
# S3 method for clifford
const(x) <- value

Arguments

C, x

Clifford object

value

Replacement value

drop

Boolean, with default TRUE meaning to return the constant coerced to numeric, and FALSE meaning to return a (constant) Clifford object

Author

Robin K. S. Hankin

Details

Extractor method for specific terms. Function const() returns the constant element of a Clifford object. Note that const(C) returns the same as grade(C,0), but is faster. If C is a numeric vector, the first element is returned: any other elements are silently discarded, but this may change in future.

The R idiom in const<-() is slightly awkward:

> body(`const<-.clifford`)
{
  stopifnot(length(value) == 1)
  x <- x - const(x)
  return(x + value)
}

The reason that it is not simply return(x-const(x)+value) or return(x+value-const(x)) is to ensure numerical accuracy; see examples.

See Also

grade, clifford, getcoeffs, is.zero

Examples

X <- clifford(list(1,1:2,1:3,3:5), 6:9)
X
X <- X + 1e300
X

const(X) # should be 1e300

const(X) <- 0.6
const(X) # should be 0.6, no numerical error

# compare naive approach:

X <- clifford(list(1,1:2,1:3,3:5), 6:9) + 1e300
X + 0.6 - const(X)  # constant gets lost in the numerics

X <- clifford(list(1,1:2,1:3,3:5), 6:9) + 1e-300
X - const(X) + 0.6  # answer correct by virtue of left-associativity


x <- 2+rcliff(d=3, g=3)
jj <- x*cliffconj(x)
is.real(jj*rev(jj))   # should be TRUE