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Normaliz :: torusInvariants

torusInvariants -- ring of invariants of torus action

Synopsis

Description

Let T=(K*)r be the r-dimensional torus acting on the polynomial ring R=K[X1,...,Xn] diagonally. Such an action can be described as follows: there are integers aij, i=1,...,r, j=1,...,n, such that (λ1,...,λr)∈T acts by the substitution

Xj↦λ1a1j*...*λrarjXj, j=1,...,n.

The function takes the matrix (aij) as input and computes the ring of invariants RT={f∈R: λf=f for all λ∈T}.

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 : torusInvariants(T,R)

         2           2
o3 = QQ[x z, x*y*z, y z]

o3 : monomial subalgebra of R

See also

Ways to use torusInvariants :