The constant term of a Clifford object

Get and set the constant term of a clifford object.

Usage

const(C,drop=TRUE)
is.real(C)
# S3 method for class '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

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.

Author

Robin K. S. Hankin

Examples


X <- clifford(list(1,1:2,1:3,3:5),6:9)
X
#> Element of a Clifford algebra, equal to
#> + 6e_1 + 7e_12 + 8e_123 + 9e_345
X <- X + 1e300
X
#> Element of a Clifford algebra, equal to
#> + 1e+300 + 6e_1 + 7e_12 + 8e_123 + 9e_345

const(X) # should be 1e300
#> [1] 1e+300

const(X) <- 0.6
const(X) # should be 0.6, no numerical error
#> [1] 0.6

# 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
#> Element of a Clifford algebra, equal to
#> + 6e_1 + 7e_12 + 8e_123 + 9e_345

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
#> Element of a Clifford algebra, equal to
#> + 0.6 + 6e_1 + 7e_12 + 8e_123 + 9e_345


x <- 2+rcliff(d=3,g=3)
jj <- x*cliffconj(x)
is.real(jj*rev(jj))   # should be TRUE
#> [1] TRUE