Description
Let T=(K
*)
r be the r-dimensional torus acting on the polynomial ring R=K[X
1,...,X
n] diagonally. Such an action can be described as follows: there are integers a
ij, i=1,...,r, j=1,...,n, such that (λ
1,...,λ
r)∈T acts by the substitution
X
j↦λ
1a1j*...*λ
rarjX
j, j=1,...,n.
The function takes the matrix (a
ij) as input and computes the ring of invariants R
T={f∈R: λf=f for all λ∈T}.
This method can be used with the options
allComputations and
grading.
i1 : R=QQ[x,y,z,w];
|
i2 : T=matrix({{-1,-1,2,0},{1,1,-2,-1}});
2 4
o2 : Matrix ZZ <--- ZZ
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i3 : torusInvariants(T,R)
2 2
o3 = QQ[y z, x*y*z, x z]
o3 : monomial subalgebra of R
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