alpha {freegroup}

Alphabetical free group elements

Description

Produces simple vectors of free group elements based on the alphabet

Usage

alpha(v)
abc(v)

Arguments

v

Vector of integers

Details

Function alpha() takes an integer i and returns the letter i of the alphabet. Thus alpha(3) returns c. The function is vectorised: alpha(1:3) returns a b c.

Function abc() takes an integer i and returns letters 1 to i of the alphabet. Thus abc(4) returns a.b.c.d. The function is vectorised.

Remember that “letters of the alphabet” is just a phrase: above it refers to the default print method which can be changed, see the examples.

Author(s)

Robin K. S. Hankin

Examples

alpha(5)  # just the single letter 'e'
abc(5)    # product of a,b,c,d,e

alpha(1:26)  # the whole alphabet; c

all(alpha(1:26) == as.free(letters))  # should be TRUE

z <- alpha(26)  # variable 'z' is symbol 26, aka 'z'.
abc(1:10) ^ z

abc(-5:5)
alpha(-5:5)
sum(abc(-5:5))


## bear in mind that the symbols used are purely for the print method:
jj <- LETTERS[1:10]
options(freegroup_symbols = apply(expand.grid(jj,jj),1,paste,collapse=""))
alpha(c(66,67,68,69))   # sensible output
options(freegroup_symbols=NULL)   # restore to symbols to default letters
alpha(c(66,67,68,69))   # print method not very helpful now