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 computes the subalgebra S={f∈R: v
i(f)≥0, i=1,...,r} that is the intersection of the valuation rings of the given valuations v
1, ...,v
r, i.e. it consists of all elements of R that have a nonnegative value for all r valuations. It takes as input the matrix V=(v
i(X
j)) whose rows correspond to the values of the indeterminates.
This method can be used with the options
allComputations and
grading.
R=QQ[x,y,z,w]; |
V0=matrix({{0,1,2,3},{-1,1,2,1}}); |
intersectionValRings(V0,R) |