# size

0th

Percentile

##### 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.

abs

• size
• total
• number
• bigness
##### 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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