valRing -- ring of valuations

A discrete monomial valuation v on R=K[X₁,...,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,...,n} for several such valuations v_i, i=1,...,r. The function needs the matrix V=(v_i(X_j)) 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

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.