Convert character vectors to free objects
char_to_free.RdConvert character vectors to free objects
Details
Function char_to_matrix() gives very basic conversion between
character vectors and free objects. Current functionality is limited
to strings like “aaabaacd”, which would give
\(a^3ba^2cd\). It would be nice to take a string
like “a^3b^(-3)” but this is not yet implemented.
Function char_to_free() is a vectorized version that coerces
output to free.
Note
The function is not particularly robust; for example, passing anything other than letters a-z or A-Z will give possibly undesirable behaviour.
Upper-case letters A-Z are interpreted by char_to_matrix() as
the inverse of their corresponding lower-case equivalents. This
behaviour is inherited by char_to_free() and as.free(),
so that as.free("A") == inverse(as.free("a")).
Function char_to_free() is consistent with the default print
options (which are that the symbols are the lowercase letters a-z).
If you change the symbols' names, for example
options(freegroup_symbols=sample(letters)), then things can get
confusing. The print method does not change the internal
representation of a free object, which is a list of integer
matrices.
Examples
char_to_matrix("aaabcABC")
#> [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
#> jj 1 1 1 2 3 1 2 3
#> s 1 1 1 1 1 -1 -1 -1
rfree(10,3) + as.free('xxxxxxxxxxxx')
#> [1] c^2.b^3.a^2.x^12 b^-1.x^12 b^2.x^12 c^-3.x^12
#> [5] a^-3.x^12 b^3.c.a^-2.x^12 b^-2.x^12 c^3.a^2.c^2.x^12
#> [9] a^-3.c^-4.x^12 b^2.a^-3.b^-3.x^12
as.free(letters)*7
#> [1] a^7 b^7 c^7 d^7 e^7 f^7 g^7 h^7 i^7 j^7 k^7 l^7 m^7 n^7 o^7 p^7 q^7 r^7 s^7
#> [20] t^7 u^7 v^7 w^7 x^7 y^7 z^7
all(is.id(as.free(letters) + as.free(LETTERS)))
#> [1] TRUE
as.free('') # identity element
#> [1] 0