degree {weyl}

The degree of a weyl object

Description

The degree of a monomial weyl object \(x^a\partial^b\) is defined as \(a+b\). The degree of a general weyl object expressed as a linear combination of monomials is the maximum of the degrees of these monomials. Following Coutinho we have:

• \(\mathrm{deg}(d_1+d_2)\leq\max(\mathrm{deg}(d_1)+ \mathrm{deg}(d_2))\)

• \(\mathrm{deg}(d_1d_2) = \mathrm{deg}(d_1)+ \mathrm{deg}(d_2)\)

• \(\mathrm{deg}(d_1d_2-d_2d_1)\leq\mathrm{deg}(d_1)+ \mathrm{deg}(d_2)-2\)

Usage

deg(S)

Arguments

S

Object of class weyl

Value

Nonnegative integer (or \(-\infty\) for the zero Weyl object)

Note

The degree of the zero object is conventionally \(-\infty\).

Author(s)

Robin K. S. Hankin

Examples

(a <- rweyl())
deg(a)

d1 <- rweyl(n=2)
d2 <- rweyl(n=2)

deg(d1+d2) <= deg(d1) + deg(d2)
deg(d1*d2) == deg(d1) + deg(d2)
deg(d1*d2-d2*d1) <= deg(d1) + deg(d2) -2