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<head><title>totalSpace -- Total space of a deformation.</title>
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<div><h1>totalSpace -- Total space of a 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>totalSpace(f,R)</tt><br/><tt>totalSpace(L,R)</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>f</tt>, <span>a <a href="___First__Order__Deformation.html">first order deformation</a></span></span></li>
<li><span><tt>L</tt>, <span>a <a href="../../Macaulay2Doc/html/___List.html">list</a></span>, of <a href="___First__Order__Deformation.html" title="The class of all first order deformations of monomial ideals.">FirstOrderDeformation</a>s.</span></li>
<li><span><tt>T</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>an <a href="../../Macaulay2Doc/html/___Ideal.html">ideal</a></span></span></li>
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<div class="single"><h2>Description</h2>
<div><p>Compute the total space of a first order deformation f or a list of first order deformations. The polynomial ring T is used for the base. The number of variables of T should match <a href="_dim_lp__First__Order__Deformation_rp.html" title="Compute the dimension of a deformation.">dim(FirstOrderDeformation)</a> f (respectively the sum over the deformations in L).</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);
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,-1,0,2,0})
2
x
3
o5 = ----
x x
0 1
o5 : first order deformation space of dimension 1</pre>
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<tr><td><pre>i6 : S=QQ[t]
o6 = S
o6 : PolynomialRing</pre>
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<tr><td><pre>i7 : totalSpace(f,S)
2
o7 = ideal (x x , x x , x x , x x , t*x + x x )
3 4 0 4 2 3 1 2 3 0 1
o7 : Ideal of QQ[t, x , x , x , x , x ]
0 1 2 3 4</pre>
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<tr><td><pre>i8 : f1=firstOrderDeformation(mg, vector {0,-1,-1,0,2})
2
x
4
o8 = ----
x x
1 2
o8 : first order deformation space of dimension 1</pre>
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<tr><td><pre>i9 : S=QQ[t1,t2]
o9 = S
o9 : PolynomialRing</pre>
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<tr><td><pre>i10 : totalSpace({f,f1},S)
2 2
o10 = ideal (x x , x x , x x , t2*x + x x , t1*x + x x )
3 4 0 4 2 3 4 1 2 3 0 1
o10 : Ideal of QQ[t1, t2, x , x , x , x , x ]
0 1 2 3 4</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_first__Order__Deformation.html" title="Makes a first order deformation.">firstOrderDeformation</a> -- Makes a first order 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>
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<div class="waystouse"><h2>Ways to use <tt>totalSpace</tt> :</h2>
<ul><li>totalSpace(FirstOrderDeformation,PolynomialRing)</li>
<li>totalSpace(List,PolynomialRing)</li>
</ul>
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