Substitute and invert symbols

Substitute and invert specific symbols in a free object

Usage

subsu(X, from, to)
subs(X, ...)
flip(X, turn)

Arguments

X

Object of class free

from,to,turn

Objects coerced to class free specifying symbols to alter. These arguments are coerced to symbols using getlet(as.free())

...

Named arguments for substitution

Details

Function subsu(X,from,to) takes object X and transforms every symbol present in from into the symbol specified in to.

Function flip(X,turn) takes object X and replaces every symbol present in turn with its inverse.

Function discard(), documented at keep.Rd, effectively substitutes a symbol with the identity element (thereby discarding it).

Experimental function subs() is modelled on similar functionality in the freealg package and makes idiom such as subs(X,a='z') work as expected (viz, taking each instance of symbol a and replacing it with x).

Author

Robin K. S. Hankin

Note

Functions subs() and subsu() substitute for particular symbols, not free group elements. In particular, be careful with uppercase (inverse) symbols; because the power is discarded, substituting with x is the same as substituting for X. This behaviour might change in the future.

See also

abs,discard

Examples

subsu(abc(1:10),abc(5),'z')
#>  [1] z             z^2           z^3           z^4           z^5          
#>  [6] z^5.f         z^5.f.g       z^5.f.g.h     z^5.f.g.h.i   z^5.f.g.h.i.j
flip(abc(1:10),abc(5))
#>  [1] a^-1                               a^-1.b^-1                         
#>  [3] a^-1.b^-1.c^-1                     a^-1.b^-1.c^-1.d^-1               
#>  [5] a^-1.b^-1.c^-1.d^-1.e^-1           a^-1.b^-1.c^-1.d^-1.e^-1.f        
#>  [7] a^-1.b^-1.c^-1.d^-1.e^-1.f.g       a^-1.b^-1.c^-1.d^-1.e^-1.f.g.h    
#>  [9] a^-1.b^-1.c^-1.d^-1.e^-1.f.g.h.i   a^-1.b^-1.c^-1.d^-1.e^-1.f.g.h.i.j


o <- rfree(30,5,10)

# Following tests should all be TRUE:
size(flip(o,'a'))   == size(o)
#>  [1] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
#> [16] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
number(flip(o,'a')) == number(o)
#>  [1] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
#> [16] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
total(flip(o,'a'))  == total(o)
#>  [1] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
#> [16] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE

size(subsu(o,'a','b'))   <= size(o)
#>  [1] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
#> [16] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
number(subsu(o,'a','b')) <= number(o)
#>  [1] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
#> [16] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
total(subsu(o,'a','b'))  <= total(o)
#>  [1] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
#> [16] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE


frog <- rfree()
subs(frog,a='x')
#> [1] d^4.b^2           b^-4.d^2          d^-3              x^-2.d.x^2       
#> [5] d^2.x^3.c         d^-2.b^3.d^2.c^-3 x^-1.d^-1.x^4