Absolute value of a free object

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

Author

Robin K. S. Hankin

Note

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

See also

subs

Examples

abs(abc(-5:5))
#>  [1] e.d.c.b.a d.c.b.a   c.b.a     b.a       a         0         a        
#>  [8] a.b       a.b.c     a.b.c.d   a.b.c.d.e

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

a
#>  [1] d^3.f^-2.b^2      d^-1.b.c          a^-1.c^-3.e^-3    e^-1.d^3.b^-3    
#>  [5] a^4.f.a           a^-2.g.d^-1       a^-2.g^3.a^-3.d^2 e^2.f^-1.c^-3    
#>  [9] b.g^3.d^2         a^8.f^-3         
abs(a)
#>  [1] d^3.f^2.b^2     d.b.c           a.c^3.e^3       e.d^3.b^3      
#>  [5] a^4.f.a         a^2.g.d         a^2.g^3.a^3.d^2 e^2.f.c^3      
#>  [9] b.g^3.d^2       a^8.f^3        

## following should all be TRUE:
all(size(abs(a+b))  <=  size(abs(a) + abs(b)))
#> [1] TRUE
all(total(abs(a+b)) <=  total(abs(a) + abs(b)))
#> [1] TRUE
all(number(abs(a+b)) <= number(abs(a) + abs(b)))
#> [1] TRUE

all(size(a+b)   <= size(abs(a) + abs(b)))
#> [1] TRUE
all(total(a+b)  <= total(abs(a) + abs(b)))
#> [1] TRUE
all(number(a+b) <= number(abs(a) + abs(b)))
#> [1] TRUE