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<head><title>firstOrderDeformation -- Makes a first order deformation.</title>
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<div><h1>firstOrderDeformation -- Makes a first order deformation.</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>firstOrderDeformation(mg,v)</tt><br/><tt>firstOrderDeformation(I,v)</tt></div>
</dd></dl>
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<li><div class="single">Inputs:<ul><li><span><tt>I</tt>, <span>an <a href="../../Macaulay2Doc/html/___Ideal.html">ideal</a></span>, monomial, reduced, in a <a href="../../Macaulay2Doc/html/___Polynomial__Ring.html" title="the class of all ordered monoid rings">PolynomialRing</a>, or</span></li>
<li><span><tt>I</tt>, <span>a <a href="../../Macaulay2Doc/html/___Monomial__Ideal.html">monomial ideal</a></span>, reduced</span></li>
<li><span><tt>mg</tt>, <span>a <a href="../../Macaulay2Doc/html/___Matrix.html">matrix</a></span>, row, with generators of a reduced monomial ideal.</span></li>
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<li><div class="single">Outputs:<ul><li><span><span>a <a href="___First__Order__Deformation.html">first order deformation</a></span></span></li>
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<div class="single"><h2>Description</h2>
<div><p>Generates a first order deformation <a href="../../Macaulay2Doc/html/_ideal.html" title="make an ideal">ideal</a> mg. If it is given an ideal I then <a href="../../Macaulay2Doc/html/_generators.html" title="provide matrix or list of generators">generators</a> of I are stored to have a reference for <a href="_parameters.html" title="Parameters of a deformation.">parameters</a>. You can also give non-minimal generators.</p>
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<table class="examples"><tr><td><pre>i1 : R=QQ[x_0..x_4];</pre>
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<tr><td><pre>i2 : addCokerGrading(R)
o2 = | -1 -1 -1 -1 |
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 1 0 |
| 0 0 0 1 |
5 4
o2 : Matrix ZZ <--- ZZ</pre>
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<tr><td><pre>i3 : I=ideal(x_0*x_1,x_1*x_2,x_2*x_3,x_3*x_4,x_4*x_0)
o3 = ideal (x x , x x , x x , x x , x x )
0 1 1 2 2 3 3 4 0 4
o3 : Ideal of R</pre>
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<tr><td><pre>i4 : mg=mingens I;
1 5
o4 : Matrix R <--- R</pre>
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<tr><td><pre>i5 : f=firstOrderDeformation(mg, vector {-1,1,0,0,0})
x
1
o5 = --
x
0
o5 : first order deformation space of dimension 1</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="___First__Order__Deformation.html" title="The class of all first order deformations of monomial ideals.">FirstOrderDeformation</a> -- The class of all first order deformations of monomial ideals.</span></li>
<li><span><a href="_dim_lp__First__Order__Deformation_rp.html" title="Compute the dimension of a deformation.">dim(FirstOrderDeformation)</a> -- Compute the dimension of a deformation.</span></li>
<li><span><a href="_add__Coker__Grading.html" title="Stores a cokernel grading in a polynomial ring.">addCokerGrading</a> -- Stores a cokernel grading in a polynomial ring.</span></li>
</ul>
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<div class="waystouse"><h2>Ways to use <tt>firstOrderDeformation</tt> :</h2>
<ul><li>firstOrderDeformation(Ideal,Vector)</li>
<li>firstOrderDeformation(Matrix,Vector)</li>
<li>firstOrderDeformation(MonomialIdeal,Vector)</li>
</ul>
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