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valRing -- 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,...,n} for several such valuations vi, i=1,...,r. The function needs the matrix V=(vi(Xj)) as its input.
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 : valRing(V0,R)

                                     2
o3 = ideal (y, x*y, w, x*w, z, x*z, x z)

o3 : Ideal of R

Caveat

It is of course possible that S=K. At present, Normaliz cannot deal with the zero cone and will issue the (wrong) error message that the cone is not pointed.

See also

Ways to use valRing :