freegroup (version 1.2-1-1)

size: 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)

Value

These functions return an integer vector.

Arguments

a

Vector of free group objects

Author

Robin K. S. Hankin

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.

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)))