Extract or Replace Parts of a clifford
Extract.RdExtract or replace subsets of cliffords.
Usage
# S3 method for class 'clifford'
C[index, ..., drop = FALSE]
# S3 method for class 'clifford'
C[index, ...] <- value
coeffs(x)
coeffs(x) <- value
list_modifier(B)
getcoeffs(C, B)
# S3 method for class 'clifford'
Im(z)
# S3 method for class 'clifford'
Re(z)Details
Extraction and replacement methods. The extraction method uses
getcoeffs() and the replacement method uses low-level helper
function c_overwrite().
In the extraction function a[index], if index is a list,
further arguments are ignored; if not, the dots are used. If
index is a list, its elements are interpreted as integer vectors
indicating which terms to be extracted (even if it is a disord
object). If index is a disord object, standard
consistency rules are applied. The extraction methods are designed so
that idiom such as a[coeffs(a)>3] works.
For replacement methods, the standard use-case is a[i] <- b in
which argument i is a list of integer vectors and b a
length-one numeric vector; (replacement vectors of length greater than
one are currently not implemented, whether or not they violate
disordR discipline). Otherwise, to manipulate parts of a
clifford object, use coeffs(a) <- value; disord
discipline is enforced. Idiom such as a[coeffs(a)<2] <- 0 is
implemented experimentally, as syntactic sugar for
coeffs(a)[coeffs(a)<2] <- 0. Replacement using a list-valued
index, as in A[i] <- value uses an ugly hack if value is
zero. Replacement methods are not yet finalised and not yet fully
integrated with the disordR package.
Idiom such as a[] <- b follows the spray package. If
b is a length-one scalar, then coeffs(a) <- b has the same
effect as a[] <- b.
Functions terms() [see term.Rd] and coeffs()
extract the terms and coefficients from a clifford object. These
functions return disord objects but the ordering is consistent
between them (an extended discussion of this phenomenon is presented
in the mvp package). Note that coeffs() returns
numeric(0) on the zero clifford object.
Function coeffs<-() (idiom coeffs(a) <- b) sets all
coefficients of a to b. This has the same effect as
a[] <- b.
Extracting or replacing a list with a repeated elements is usually a Bad
Idea (tm). However, if option warn_on_repeats is set to
FALSE, no warning will be given (and the coefficient will be the
sum of the coefficients of the term; see the examples).
Function getcoeffs() is a lower-level helper function that
lacks the succour offered by [.clifford(). It returns a named
numeric vector [not a disord object: the order of the elements
is determined by the order of argument B]. Compare standard
extraction, eg a[index], which returns a clifford object. The
names of the returned vector are determined by function
catterm().
Attempting to extract a coefficient of a term that includes a negative
index will throw an error. The coefficient of a term not present in
the Clifford object (including term with an index larger than
indicated by maxyterm()) will return zero.
The index for the constant is formally list(numeric(0)), but
this is a pain to type. Square bracket extraction and
getcoeffs() have special dispensation for zero entries, which
are translated by helper function list_modifier() to
numeric(0) and listified if necessary. The upshot is that
x[0] and getcoeffs(x,0) work as expected, returning the
constant.
Function Im() is a generic, which sets the real component of its
argument to zero (as per the onion package). Function
Re() is a convenience synonym for const().
Vignette getcoeffs gives a more extended discussion of function
getcoeffs().
Examples
A <- clifford(list(1,1:2,1:3),1:3)
B <- clifford(list(1:2,1:6),c(44,45))
A[1,c(1,3,4)]
#> Element of a Clifford algebra, equal to
#> + 1e_1
A[2:3, 4] <- 99
A[] <- B
X <- 5 + 6*e(1) -7*e(1:3) + 3*e(4:5)
X[0] # special dispensation for zero
#> Element of a Clifford algebra, equal to
#> scalar ( 5 )
X[0,drop=TRUE] # coerce to numeric
#> [1] 5
X[list(0,1:3)]
#> Element of a Clifford algebra, equal to
#> + 5 - 7e_123
getcoeffs(X,0)
#> e_0
#> 5
getcoeffs(X,list(1,0,1:3))
#> e_1 e_0 e_123
#> 6 5 -7
# clifford(list(1,1:2,1:2),1:3) # would give a warning
options("warn_on_repeats" = FALSE)
clifford(list(1,1:2,1:2),1:3) # works; 1e1 + 5e_12
#> Element of a Clifford algebra, equal to
#> + 1e_1 + 5e_12
options("warn_on_repeats" = TRUE) # return to default behaviour.