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<head><title>divideByVariable -- divide all columns by a (power of a) variable</title>
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<div><h1>divideByVariable -- divide all columns by a (power of a) variable</h1>
<div class="single"><h2>Description</h2>
<div><tt>divideByVariable(m,v)</tt> -- divide each column of the matrix 'm' by as high a power of the variable 'v' as possible.<br/><tt>divideByVariable(m,v,d)</tt> -- divide each column of the matrix 'm' by as high a power of the variable 'v' as possible, but divide by no more than v^d.<p/>
<table class="examples"><tr><td><pre>i1 : R = ZZ/101[a..d]
o1 = R
o1 : PolynomialRing</pre>
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<tr><td><pre>i2 : m = matrix{{a*b, a^2*c}, {a*b^2, a^4*d}}
o2 = | ab a2c |
| ab2 a4d |
2 2
o2 : Matrix R <--- R</pre>
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<tr><td><pre>i3 : divideByVariable(m,a)
o3 = (| b c |, 2)
| b2 a2d |
o3 : Sequence</pre>
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<tr><td><pre>i4 : divideByVariable(m,a,1)
o4 = (| b ac |, 1)
| b2 a3d |
o4 : Sequence</pre>
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We may eliminate this routine.</div>
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<div class="single"><h2>Caveat</h2>
<div>You can only divide by a variable, not a monomial, and you have little control on what power will be divided. This routine is mostly used by the saturation commands as a fast internal way of dividing.</div>
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<div class="waystouse"><h2>Ways to use <tt>divideByVariable</tt> :</h2>
<ul><li>divideByVariable(Matrix,RingElement)</li>
<li>divideByVariable(Matrix,RingElement,ZZ)</li>
</ul>
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