size {freegroup}

Bignesses of a free object

Description

Various metrics to describe how “big” a free object is

Usage

size(a)
total(a)
number(a)
bigness(a)

Arguments

a

Vector of free group objects

Details

• The size of an object is the number of pure powers in it (this is the number of columns of the matrix representation of the word)

• The total of an object is the sum of the absolute values of its powers

• The number of an object is the number of distinct symbols in it

Thus size(a^2ba)=3, total(a^2ba)=4, and number(a^2ba)=2.

Function bigness() is a convenience wrapper that returns all three bigness measures.

Value

These functions return an integer vector.

Note

I would like to thank Murray Jorgensen for his insightful comments which inspired this functionality.

Author(s)

Robin K. S. Hankin

See Also

abs

Examples

(a <- rfree(20,6,4))
size(a)
total(a)
number(a)

a <- rfree(20,6,4)
b <- rfree(20,6,4)

## Following should all be TRUE
size(a+b)   <= size(a)  + size(b)
total(a+b)  <= total(a) + total(b)
number(a+b) <= number(a)+ number(b)

bigness(rfree(10,3,3))
bigness(allconj(rfree(1,6,1)))