dot: Class "dot"

In weyl: The Weyl Algebra

Class “dot”

Description

The dot object is defined so that idiom like .[x,y] returns the commutator, that is, xy-yx.

The dot object is generated by running script inst/dot.Rmd, which includes some further discussion and technical documentation, and creates file dot.rda which resides in the data/ directory.

The borcherds vignette discusses this in a more general context.

Usage

## S4 method for signature 'dot,missing,missing'
x[i, j, drop]
## S4 method for signature 'dot,ANY,missing'
x[i, j, drop]
## S4 method for signature 'dot,missing,ANY'
x[i, j, drop]
## S4 method for signature 'dot,matrix,matrix'
x[i, j, drop]
## S4 method for signature 'dot,ANY,ANY'
x[i, j, drop]
## S4 method for signature 'dot,function,function'
x[i, j, drop]

Arguments

x	An object of class dot (typically the pre-built object “.”)
i, j	Elements to commute
drop	Logical; passed to drop() in the default method

Value

Always returns an object of the same class as xy.

Author(s)

Robin K. S. Hankin

Examples

x <- rweyl(n=1,d=2)
y <- rweyl(n=1,d=2)
z <- rweyl(n=1,d=2)

.[x,.[y,z]] + .[y,.[z,x]] + .[z,.[x,y]]  # Jacobi identity

weyl documentation built on July 14, 2026, 1:07 a.m.