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intersection of ring of valuations

NmzIntersectionValRings(M: MAT, M: Ring): LIST of RINGELEM

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 in 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.

/**/     use R::=QQ[x,y,z,w];
/**/     V := matrix([[0,1,2,3],[-1,1,2,1]]);
/**/     NmzIntersectionValRings(V,R);
[y, z, w, x*y, x^2*z, x*w, x*z]

See Also