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<head><title>homogenize -- homogenize with respect to a variable</title>
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<div><h1>homogenize -- homogenize with respect to a variable</h1>
<div class="single"><h2>Description</h2>
<div><tt>homogenize(m,v)</tt> -- homogenize the ring element, vector, matrix, or module <tt>m</tt> using the variable <tt>v</tt> in the ring of <tt>m</tt>.<br/><tt>homogenize(m,v,w)</tt> -- homogenize <tt>m</tt> using the variable <tt>v</tt>, so that the result is homogeneous with respect to the given list <tt>w</tt> of integers provided as weights for the variables.<p/>
<table class="examples"><tr><td><pre>i1 : R = ZZ/101[x,y,z,Degrees => {1,2,3}]
o1 = R
o1 : PolynomialRing</pre>
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<tr><td><pre>i2 : f = 1 + y + z^2
2
o2 = z + y + 1
o2 : R</pre>
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<tr><td><pre>i3 : homogenize(f,x)
6 4 2
o3 = x + x y + z
o3 : R</pre>
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<tr><td><pre>i4 : homogenize(f,x,{1,0,-1})
2 2
o4 = x z + y + 1
o4 : R</pre>
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The weights that may be used are limited (roughly) to the range -2^30 .. 2^30.<p/>
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<div class="single"><h2>Caveat</h2>
<div>If the homogenization overflows the monomial, this is not reported as an error.</div>
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<div class="waystouse"><h2>Ways to use <tt>homogenize</tt> :</h2>
<ul><li>homogenize(Ideal,RingElement)</li>
<li>homogenize(Matrix,RingElement)</li>
<li>homogenize(Matrix,RingElement,List)</li>
<li>homogenize(Module,RingElement)</li>
<li>homogenize(Module,RingElement,List)</li>
<li>homogenize(RingElement,RingElement)</li>
<li>homogenize(RingElement,RingElement,List)</li>
<li>homogenize(Vector,RingElement)</li>
<li>homogenize(Vector,RingElement,List)</li>
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