# size

From freegroup v1.1-0
by Robin K S Hankin

##### Bignesses of a free object

Various metrics to say 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.

##### See Also

##### Examples

```
# NOT RUN {
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)))
# }
```

*Documentation reproduced from package freegroup, version 1.1-0, License: GPL-2*

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