freegroup (version 1.1-8)

tietze: Tietze form for free group objects

Description

Translate an object of class free to and from Tietze form

Usage

# S3 method for free
tietze(x)
# S3 method for matrix
tietze(x)
vec_to_matrix(x)

Arguments

x

Object to be converted

Author

Robin K. S. Hankin

Details

The Tietze form for a word is a list of integers corresponding to the symbols of the word; typically \(a=1,b=2,c=3,d=4\), etc. Negative integers represent the inverses of the symbols. Thus c^4.d^-2.a.c becomes 3 3 3 3 -4 -4 1 3.

Function vec_to_matrix() is a low-level helper function that returns a two-row integer matrix. If given 0 or NULL, it returns a two-row, zero-column matrix.

Examples

(x <- rfree(10,3))
tietze(x)

vec_to_matrix(c(1,3,-1,-1,-1,2))

as.free(list(c(1,1,8),c(2,-4,-4)))

all(as.free(tietze(abc(1:30))) == abc(1:30))