- Usage:
`intersectionValRings(v,r)`

- Outputs:
- an object of class MonomialSubalgebra, the subalgebra consisting of the elements with valuation ≥0 for all given valuations

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∈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.

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 |

- intersectionValRingIdeals -- intersection of valuation ideals

- intersectionValRings(Matrix,Ring)