Print clifford objects
print.RdPrint methods for Clifford algebra
Usage
# S3 method for class 'clifford'
print(x,...)
# S3 method for class 'clifford'
as.character(x,...)
catterm(a)Note
The print method does not change the internal representation of a
clifford object, which is a two-element list, the first of which
is a list of integer vectors representing terms, and the second is a
numeric vector of coefficients. The print method has special
dispensation for the zero clifford object.
The print method is sensitive to the value of options separate
and basissep. If option separate is FALSE (the
default), the method prints the basis blades in a compact form, as in
“e_134”. The indices of the basis vectors are separated
with the value of option basissep which is usually NULL;
but if \(n>9\), then setting option basissep to a comma
(“,”) might look good as it will print e_10,11,12
instead of e_101112:
options("basissep" = ",")If option separate is TRUE, the method prints the basis
vectors separately, as in e10 e11 e12:
options("separate" = TRUE)Function catterm() is a low-level helper function, used in the
print method, coercion to character, and also in function
getcoeffs() to set the names of its output. It takes an integer
vector like c(1,5,6) and returns a representation of the
corresponding basis blade, in this case “e_156”. Function
catterm() is where options basissep and separate
are processed. Special dispensation is needed for length-zero vectors,
for which the empty string is returned. This is needed to ensure that
the constant term (which has a basis blade of numeric(0)) is
treated appropriately. See also list_modifier() which deals with
this issue.
Experimental bespoke print method print_clifford_quaternion() and
print_clifford_pauli() is included. This are executed if option
clifford_print_special is quaternion; if NULL, then
print_clifford_default() is used. It is straightforward to add
further bespoke print methods if needed (modify
print.clifford()).
Examples
a <- rclifff(9)
a # default print method incomprehensible
#> Element of a Clifford algebra, equal to
#> + 6 - 8e_341215 + 2e_71315 + 6e_6791518 - 9e_258111213141720 +
#> 1e_25101214171820 - 2e_124510111920 - 6e_457811161920 - 3e_46891115161920 +
#> 7e_15610111415171920
options("separate" = TRUE)
a # marginally better
#> Element of a Clifford algebra, equal to
#> + 6 - 8e3 e4 e12 e15 + 2e7 e13 e15 + 6e6 e7 e9 e15 e18 - 9e2 e5 e8 e11 e12 e13
#> e14 e17 e20 + 1e2 e5 e10 e12 e14 e17 e18 e20 - 2e1 e2 e4 e5 e10 e11 e19 e20 -
#> 6e4 e5 e7 e8 e11 e16 e19 e20 - 3e4 e6 e8 e9 e11 e15 e16 e19 e20 + 7e1 e5 e6 e10
#> e11 e14 e15 e17 e19 e20
options("separate" = FALSE)
options(basissep=",")
a # clearer; YMMV
#> Element of a Clifford algebra, equal to
#> + 6 - 8e_3,4,12,15 + 2e_7,13,15 + 6e_6,7,9,15,18 - 9e_2,5,8,11,12,13,14,17,20 +
#> 1e_2,5,10,12,14,17,18,20 - 2e_1,2,4,5,10,11,19,20 - 6e_4,5,7,8,11,16,19,20 -
#> 3e_4,6,8,9,11,15,16,19,20 + 7e_1,5,6,10,11,14,15,17,19,20
options(basissep = NULL, maxdim=NULL) # restore default
options("maxdim" = 3)
signature(3)
a <- clifford(list(0,c(1,2),c(1,3),c(2,3)),6:9)
a
#> Element of a Clifford algebra, equal to
#> + 6 + 7e_12 + 8e_13 + 9e_23
options("clifford_print_special" = "quaternion")
a
#> A quaternion equal to:
#> +6 -7i -8j -9k
options("maxdim" = NULL)
options("clifford_print_special" = NULL)
signature(Inf)