Write free objects backwards

Write free objects in reverse order

Usage

backwards(x)

Arguments

x

Object of class free

Author

Robin K. S. Hankin

Note

For each element of a free object, function backwards() writes the symbols in reverse order. It is distinct from rev(), see examples.

Function backwards is an involution: it is its own inverse.

Examples

abc(1:5)
#> [1] a         a.b       a.b.c     a.b.c.d   a.b.c.d.e
backwards(abc(1:5))
#> [1] a         b.a       c.b.a     d.c.b.a   e.d.c.b.a
rev(abc(1:5))
#> [1] a.b.c.d.e a.b.c.d   a.b.c     a.b       a        

x <- rfree(10,5)
backwards(backwards(x)) == x  # involution
#>  [1] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
all(abelianize(x) == abelianize(backwards(x))) # should be TRUE
#> [1] TRUE