generators(RingOfInvariants) -- the generators for a ring of invariants

Synopsis

• Function: generators

• Usage:

  generators S, gens S

• Inputs:
  • S, an instance of the type RingOfInvariants
• Optional inputs:
  • CoefficientRing => ..., default value null,
• Outputs:
  • a list, of algebra generators for the ring of invariants

Description

This method gets the algebra generators for a ring of invariants.

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 : S = R^T

o4 =             2
     QQ[x x x , x x x ]
         1 2 3   1 3 4

o4 : RingOfInvariants

i5 : gens S

               2
o5 = {x x x , x x x }
       1 2 3   1 3 4

o5 : List