# size: Bignesses of a free object In RobinHankin/freegroup: The Free Group

## Description

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

## Usage

 ```1 2 3 4``` ```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

`abs`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17``` ```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))) ```