A discrete monomial valuation v on R=K[X
1,...,X
n] is determined by the values v(X
j) of the indeterminates. This function takes as input the matrix V=(v
i(X
j)), whose rows correspond to the values of the indeterminates for for r valuations v
1, ...,v
r, with an additional column holding lower bounds w
1,...,w
r ∈ℤ. It returns the subalgebra S={f∈R: v
i(f)≥0, i=1,...,n}, the intersection of the valuation rings of the r valuations, and a system of generators of the S-submodule M={f∈R: v
i(f)≥w
i, i=1,...,n} over R, which consists of the elements whose i-th valuation is greater or equal to the i-th bound w
i. If w
i>=0 for all i, then M is an ideal in S.
R=QQ[x,y,z,w]; |
V=matrix({{0,1,2,3,4},{-1,1,2,1,3}}); |
intersectionValRingIdeals(V,R) |