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Normaliz :: intersectionValRings

intersectionValRings -- intersection of ring of valuations

Synopsis

Description

A discrete monomial valuation v on R=K[X1,...,Xn] is determined by the values v(Xj) of the indeterminates. This function computes the subalgebra S={f∈R: vi(f)≥0, i=1,...,r} that is the intersection of the valuation rings of the given valuations v1, ...,vr, 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=(vi(Xj)) whose rows correspond to the values of the indeterminates.

This method can be used with the options allComputations and grading.

i1 : R=QQ[x,y,z,w];
i2 : V0=matrix({{0,1,2,3},{-1,1,2,1}});

              2        4
o2 : Matrix ZZ  <--- ZZ
i3 : intersectionValRings(V0,R)

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

o3 : monomial subalgebra of R

See also

Ways to use intersectionValRings :