tietze: Tietze form for free group objects

In freegroup: The Free Group

Tietze form for free group objects

Description

Translate an object of class free to and from Tietze form

Usage

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

Arguments

x	Object to be converted

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.

Author(s)

Robin K. S. Hankin

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))

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