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<head><title>valRingIdeal -- valuation ideal</title>
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<div><h1>valRingIdeal -- valuation ideal</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>valRingIdeal(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, the last column contains the lower bounds <tt>w_i</tt></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>a <a href="../../Macaulay2Doc/html/___List.html">list</a></span>, a list of two ideals</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. 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<sub>i</sub>(f)≥0, i=1,...,n} for several such valuations v<sub>i</sub>, i=1,...,r, the second the system of generators of the submodule M={f∈R: v<sub>i</sub>(f)≥w<sub>i</sub>, i=1,...,n} for integers w<sub>1</sub>,...,w<sub>r</sub>.<table class="examples"><tr><td><pre>i1 : R=QQ[x,y,z,w]; </pre>
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<tr><td><pre>i2 : V=matrix({{0,1,2,3,4},{-1,1,2,1,3}});
2 5
o2 : Matrix ZZ <--- ZZ</pre>
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<tr><td><pre>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,
------------------------------------------------------------------------
2 4 4 2 3
x*y z, y , x*y , y*w , w )}
o3 : List</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.html" title="ring of valuations">valRing</a> -- ring of valuations</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>valRingIdeal</tt> :</h2>
<ul><li>valRingIdeal(Matrix,Ring)</li>
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