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<head><title>laurent -- Converts an exponent vector or a deformation into a Laurent monomial.</title>
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<div><h1>laurent -- Converts an exponent vector or a deformation into a Laurent monomial.</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>laurent(v,R)</tt><br/><tt>laurent(f)</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>v</tt>, <span>a <a href="../../Macaulay2Doc/html/___Vector.html">vector</a></span></span></li>
<li><span><tt>f</tt>, <span>a <a href="___First__Order__Deformation.html">first order deformation</a></span></span></li>
<li><span><tt>R</tt>, <span>a <a href="../../Macaulay2Doc/html/___Polynomial__Ring.html">polynomial ring</a></span></span></li>
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<li><div class="single">Outputs:<ul><li><span><span>a <a href="../../Macaulay2Doc/html/___Ring__Element.html">ring element</a></span></span></li>
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<div class="single"><h2>Description</h2>
<div><p>Converts the exponent vector v into a Laurent monomial in the variables of R. The result lies in <a href="../../Macaulay2Doc/html/_frac.html" title="construct a fraction field">frac</a> R. The number of variables of R has to match the length of v.</p>
<p>If given a <a href="___First__Order__Deformation.html" title="The class of all first order deformations of monomial ideals.">FirstOrderDeformation</a> it returns the corresponding laurent monomial.</p>
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<table class="examples"><tr><td><pre>i1 : R=QQ[x_0..x_4]
o1 = R
o1 : PolynomialRing</pre>
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<tr><td><pre>i2 : m=vector {1,-2,1,0,0}
o2 = | 1 |
| -2 |
| 1 |
| 0 |
| 0 |
5
o2 : ZZ</pre>
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<tr><td><pre>i3 : laurent(m,R)
x x
0 2
o3 = ----
2
x
1
o3 : frac(R)</pre>
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<table class="examples"><tr><td><pre>i4 : R=QQ[x_0..x_4]
o4 = R
o4 : PolynomialRing</pre>
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<tr><td><pre>i5 : addCokerGrading(R);
5 4
o5 : Matrix ZZ <--- ZZ</pre>
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<tr><td><pre>i6 : I=ideal(x_0*x_1,x_1*x_2,x_2*x_3,x_3*x_4,x_4*x_0)
o6 = ideal (x x , x x , x x , x x , x x )
0 1 1 2 2 3 3 4 0 4
o6 : Ideal of R</pre>
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<tr><td><pre>i7 : mg=mingens I;
1 5
o7 : Matrix R <--- R</pre>
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<tr><td><pre>i8 : f=firstOrderDeformation(mg, vector {-1,-1,0,2,0})
2
x
3
o8 = ----
x x
0 1
o8 : first order deformation space of dimension 1</pre>
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<tr><td><pre>i9 : laurent f
2
x
3
o9 = ----
x x
0 1
o9 : frac(R)</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_laurent.html" title="Converts an exponent vector or a deformation into a Laurent monomial.">laurent</a> -- Converts an exponent vector or a deformation into a Laurent monomial.</span></li>
</ul>
</div>
<div class="waystouse"><h2>Ways to use <tt>laurent</tt> :</h2>
<ul><li>laurent(FirstOrderDeformation)</li>
<li>laurent(Vector,PolynomialRing)</li>
</ul>
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