rank(DiagonalAction) -- of a diagonal action

Synopsis

• Function: rank

• Usage:

  rank D

• Inputs:
  • D, an instance of the type DiagonalAction
• Outputs:
  • an integer, the rank of the torus factor of a diagonal action

Description

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

See also

• DiagonalAction -- the class of all diagonal actions
• diagonalAction -- diagonal group action via weights