A discrete monomial valuation v on R=K[X
1,...,X
n] is determined by the values v(X
j) of the indeterminates. The function returns two ideals, both to be considered as lists of monomials. The first is the system of monomial generators of the subalgebra S={f∈R: v
i(f)≥0, i=1,...,n} for several such valuations v
i, i=1,...,r, the second the system of generators of the submodule M={f∈R: v
i(f)≥w
i, i=1,...,n} for integers w
1,...,w
r.
i1 : R=QQ[x,y,z,w];
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i2 : V=matrix({{0,1,2,3,4},{-1,1,2,1,3}});
2 5
o2 : Matrix ZZ <--- ZZ
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i3 : valRingIdeal(V,R)
2 2 2 2 2
o3 = {ideal (y, x*y, w, x*w, z, x*z, x z), ideal (z*w, x*z , z , y w, y z,
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2 4 4 2 3
x*y z, y , x*y , y*w , w )}
o3 : List
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