free: Objects of class 'free'

In freegroup: The Free Group

Objects of class free

Description

Generate, and test for, objects of class free

Usage

free(x)
as.free(x)
is.free(x)
list_to_free(x)

Arguments

x	Function free() needs either a two-row matrix, or a list of two-row matrices; function as.free() attempts to coerce different types of argument before passing to free() (possibly via list_to_free())

Details

The basic structure of an element of the free group is a two-row matrix. The top row is the symbols (1=a, 2=b, 3=c, etc) and the bottom row is the corresponding power. Thus a^2ba^{-1}c^9 would be

> rbind(c(1,2,1,3),c(2,1,-1,9))
     [,1] [,2] [,3] [,4]
[1,]    1    2    1    3
[2,]    2    1   -1    9
>

Function free() needs either a two-row matrix or a list of two-row matrices. It is the only place in the package that sets the class of an object to free. Function as.free() is a bit more user-friendly and tries a bit harder to do the Right Thing.

The package uses setOldClass("free") for the dot methods.

Author(s)

Robin K. S. Hankin

See Also

char_to_free

Examples

free(rbind(1:5,5:1))

x <- rfree(10,3)
x
x+x
x-x
x[1:5]*(1:5)


as.free(c(4,3,2,2,2))
as.free("aaaabccccaaaaa")
as.free(c("a","A","abAAA"))

freegroup documentation built on April 3, 2025, 11:32 p.m.