diagInvariants -- ring of invariants of a diagonalizable group action

• Usage:

  diagInvariants(T,U,R)

• Inputs:
  • a matrix, whose rows are the values of the indeterminates under the torus action
  • a matrix, whose rows are the values of the indeterminates under action of the finite group
  • a ring, the basering
• Optional inputs:
  • allComputations (missing documentation) => ..., default value false,
  • grading (missing documentation) => ..., default value {},
• Outputs:
  • a monomial subalgebra, the ring of invariants

i1 : R=QQ[x,y,z,w];

i2 : T=matrix({{-1,-1,2,0},{1,1,-2,-1}});

              2       4
o2 : Matrix ZZ  <-- ZZ

i3 : U=matrix{{1,1,1,1,5},{1,0,2,0,7}}

o3 = | 1 1 1 1 5 |
     | 1 0 2 0 7 |

              2       5
o3 : Matrix ZZ  <-- ZZ

i4 : diagInvariants(T,U,R)

o4 = MonomialSubalgebra{cache => CacheTable{...1...}                                                                      }
                                        70 35     19 10   4 6 5   15 5 10   26 4 15   37 3 20   48 2 25   59   30   70 35
                        generators => {y  z  , x*y  z  , x y z , x  y z  , x  y z  , x  y z  , x  y z  , x  y*z  , x  z  }
                        ring => R

o4 : MonomialSubalgebra of R