rank(DiagonalAction) -- of a diagonal action

Synopsis

• Function: rank
• Usage:
rank D
• Inputs:
• Outputs:
• an integer, the rank of the torus factor of a diagonal action

Description

This function is provided by the package InvariantRing.

Use this function to recover the rank of the torus factor of a diagonal action.

The following example defines an action of a two-dimensional torus on a polynomial ring in four variables.

 i1 : R = QQ[x_1..x_4] o1 = R o1 : PolynomialRing i2 : W = matrix{{0,1,-1,1},{1,0,-1,-1}} o2 = | 0 1 -1 1 | | 1 0 -1 -1 | 2 4 o2 : Matrix ZZ <--- ZZ i3 : T = diagonalAction(W, R) * 2 o3 = R <- (QQ ) via | 0 1 -1 1 | | 1 0 -1 -1 | o3 : DiagonalAction i4 : rank T o4 = 2