abs: Absolute value of a 'free' object

In freegroup: The Free Group

Absolute value of a free object

Description

Replaces every term's power with its absolute value

Usage

## S3 method for class 'free'
abs(x)

Arguments

x	Object of class free

Details

Replaces every term's power with its absolute value

Note

The function's name is motivated by the inequality in the examples section.

Author(s)

Robin K. S. Hankin

See Also

subs

Examples

abs(abc(-5:5))

a <- rfree(10,4,7)
b <- rfree(10,4,7)

a
abs(a)

## following should all be TRUE:
all(size(abs(a+b))  <=  size(abs(a) + abs(b)))
all(total(abs(a+b)) <=  total(abs(a) + abs(b)))
all(number(abs(a+b)) <= number(abs(a) + abs(b)))

all(size(a+b)   <= size(abs(a) + abs(b)))
all(total(a+b)  <= total(abs(a) + abs(b)))
all(number(a+b) <= number(abs(a) + abs(b)))

freegroup documentation built on June 25, 2024, 1:14 a.m.