dot-class | R Documentation |
The dot object is defined in the freealg package, and imported
here, so that idiom like .[x,y]
returns the commutator, that
is, x^-1 y^-1 xy
.
x |
Object of any class |
i,j |
elements to commute |
... |
Further arguments to |
Always returns an object of the same class as xy
.
Robin K. S. Hankin
.[as.free("x"), as.free("y")] .[abc(1:6),"z"] x <- rfree() y <- rfree() z <- rfree() .[x,y] == -x-y+x+y # should be TRUE abelianize(.[x,y]) ## Jacobi identity _not_ satisfied with this definition: is.id(.[x,.[y,z]] + .[y,.[z,x]] + .[z,.[x,y]]) ## But the Hall-Witt identity is: all(is.id(.[.[x,-y],z]^y + .[.[y,-z],x]^z + .[.[z,-x],y]^x))
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