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<head><title>valRing -- ring of valuations</title>
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<div><h1>valRing -- ring of valuations</h1>
<div class="single"><h2>Synopsis</h2>
<ul><li><div class="list"><dl class="element"><dt class="heading">Usage: </dt><dd class="value"><div><tt>valRing(v,r)</tt></div>
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<li><div class="single">Inputs:<ul><li><span><span>a <a href="../../Macaulay2Doc/html/___Matrix.html">matrix</a></span>, values of the indeterminates</span></li>
<li><span><span>a <a href="../../Macaulay2Doc/html/___Ring.html">ring</a></span>, the basering</span></li>
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<li><div class="single">Outputs:<ul><li><span><span>an <a href="../../Macaulay2Doc/html/___Ideal.html">ideal</a></span>, the list of monomials generating the subalgebra of elements with valuation ≥0</span></li>
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<div class="single"><h2>Description</h2>
<div>A discrete monomial valuation v on R=K[X<sub>1</sub>,...,X<sub>n</sub>] is determined by the values v(X<sub>j</sub>) of the indeterminates. This function computes the subalgebra S={f∈R: v<sub>i</sub>(f)≥0, i=1,...,n} for several such valuations v<sub>i</sub>, i=1,...,r. The function needs the matrix V=(v<sub>i</sub>(X<sub>j</sub>)) as its input.<table class="examples"><tr><td><pre>i1 : R=QQ[x,y,z,w];</pre>
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<tr><td><pre>i2 : V0=matrix({{0,1,2,3},{-1,1,2,1}});
2 4
o2 : Matrix ZZ <--- ZZ</pre>
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<tr><td><pre>i3 : valRing(V0,R)
2
o3 = ideal (y, x*y, w, x*w, z, x*z, x z)
o3 : Ideal of R</pre>
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<div class="single"><h2>Caveat</h2>
<div>It is of course possible that S=K. At present, <tt>Normaliz</tt> cannot deal with the zero cone and will issue the (wrong) error message that the cone is not pointed.</div>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_val__Ring__Ideal.html" title="valuation ideal">valRingIdeal</a> -- valuation ideal</span></li>
<li><span><a href="_torus__Invariants.html" title="ring of invariants">torusInvariants</a> -- ring of invariants</span></li>
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<div class="waystouse"><h2>Ways to use <tt>valRing</tt> :</h2>
<ul><li>valRing(Matrix,Ring)</li>
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