print.RdPrint methods for free algebra objects. The indeterminates are represented using lowercase letters a-z (currently hard coded).
# S3 method for class 'freealg'
print(x,...)The print method does not change the internal representation of a
freealg object, which is a two-element list, the first of which
is a list of integer vectors representing words, and the second is a
numeric vector of coefficients.
The print method uses lowercase letters a-z to represent the indeterminates; this is currently hard coded:
> (x <- as.freealg("6abbbc + 7cax"))
free algebra element algebraically equal to
+ 6*abbbc + 7*cax
> unclass(x)
$indices
$indices[[1]]
[1] 1 2 2 2 3
$indices[[2]]
[1] 3 1 24
$coeffs
[1] 6 7
The print method has special dispensation for length-zero freealg objects but these are not handled entirely consistently.
The print method is sensitive to the value of
getOption("usecaret"), defaulting to “FALSE”. The default
is to use uppercase letters to represent multiplicative inverses. Thus,
the inverse of a appears as either “a^-1” if
usecaret is TRUE, and “A” if FALSE.
Carets become cumbersome for powers above the first. For example, the
default notation for \(aba^{-2}\) is abAA but becomes
aba^-1a^-1 if usecaret is TRUE.
The symbols for the indeterminates are currently hardcoded as
c(letters,LETTERS). The intent is to be able to signify 52
distinct indeterminates, a-z,A-Z. This works fine if option
usecaret is TRUE. But if option usecaret is
FALSE, this can be confusing: for example, indeterminate number 1
appears as a, and its inverse would appear as “A”.
But indeterminate number 27 also appears as “A”. They
look the same, but no warning is given: caveat emptor!
The method is also sensitive to getOption("mulsym"), defaulting
to NULL. This is the multiplication symbol used between the
coefficient and the indeterminate string. Sometimes an asterisk,
* or a space, might be useful. If mulsym takes its
default of NULL [or a length zero string], the print method
suppresses coefficients of \(\pm 1\).
Integers exceeding SHRT_MAX are reserved for infinitesimals,
which are printed as “da”; see the note at deriv.Rd
for details.
rfalg()
#> free algebra element algebraically equal to
#> + 13aaca + 3abbb + 5acc + 2baa + caaa + 4cb
x <- rfalg(inc=TRUE)
x # default
#> free algebra element algebraically equal to
#> + 3CC + 7BccB + AA + 5AbA + 4a + 2bba + 6bc
options("usecaret" = TRUE) # use caret
x
#> free algebra element algebraically equal to
#> + 3c^-1c^-1 + 7b^-1ccb^-1 + a^-1a^-1 + 5a^-1ba^-1 + 4a + 2bba + 6bc
options("usecaret" = FALSE) # back to the default
x
#> free algebra element algebraically equal to
#> + 3CC + 7BccB + AA + 5AbA + 4a + 2bba + 6bc
x <- freealg(list(5,1:4,3,8,7),c(1,1,1,3,22))
x
#> free algebra element algebraically equal to
#> + abcd + c + e + 22g + 3h
options(mulsym = "*")
x
#> free algebra element algebraically equal to
#> + 1*abcd + 1*c + 1*e + 22*g + 3*h
options(mulsym = NULL) # restore default