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<head><title>Example first order deformation -- Example accessing the data stored in a first order deformation.</title>
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<div><h1>Example first order deformation -- Example accessing the data stored in a first order deformation.</h1>
<div><p>Example for accessing the data stored in a first order deformation:</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,-1,0,2,0})
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 : f.gens
o6 = | x_3x_4 x_0x_4 x_2x_3 x_1x_2 x_0x_1 |
1 5
o6 : Matrix R <--- R</pre>
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<tr><td><pre>i7 : f.bigTorusDegree
o7 = | -1 |
| -1 |
| 0 |
| 2 |
| 0 |
5
o7 : ZZ</pre>
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<tr><td><pre>i8 : simplexRing f
o8 = R
o8 : PolynomialRing</pre>
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<tr><td><pre>i9 : target f
o9 = cokernel | x_3x_4 x_0x_4 x_2x_3 x_1x_2 x_0x_1 |
1
o9 : R-module, quotient of R</pre>
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<tr><td><pre>i10 : source f
o10 = image | x_3x_4 x_0x_4 x_2x_3 x_1x_2 x_0x_1 |
1
o10 : R-module, submodule of R</pre>
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<tr><td><pre>i11 : numerator f
o11 = | 0 |
| 0 |
| 0 |
| 2 |
| 0 |
5
o11 : ZZ</pre>
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<tr><td><pre>i12 : denominator f
o12 = | 1 |
| 1 |
| 0 |
| 0 |
| 0 |
5
o12 : ZZ</pre>
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<tr><td><pre>i13 : bigTorusDegree f
o13 = | -1 |
| -1 |
| 0 |
| 2 |
| 0 |
5
o13 : ZZ</pre>
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<tr><td><pre>i14 : numeratorMonomial f
2
o14 = x
3
o14 : R</pre>
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<tr><td><pre>i15 : degree f
o15 = 0
o15 : cokernel | -1 -1 -1 -1 |
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 1 0 |
| 0 0 0 1 |</pre>
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<tr><td><pre>i16 : grading f
o16 = | -1 -1 -1 -1 |
| 1 0 0 0 |
| 0 1 0 0 |
| 0 0 1 0 |
| 0 0 0 1 |
5 4
o16 : Matrix ZZ <--- ZZ</pre>
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<tr><td><pre>i17 : isHomogeneous f
o17 = true</pre>
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<tr><td><pre>i18 : relationsCoefficients f
o18 = 0
1
o18 : Matrix ZZ <--- 0</pre>
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<tr><td><pre>i19 : parameters f
o19 = | 0 |
| 0 |
| 0 |
| 0 |
| 1 |
5 1
o19 : Matrix ZZ <--- ZZ</pre>
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<tr><td><pre>i20 : dim f
o20 = 1</pre>
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<tr><td><pre>i21 : isNonzero f
o21 = true</pre>
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<tr><td><pre>i22 : isTrivial f
o22 = false</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_simplex__Ring.html" title="The underlying polynomial ring of a deformation or face or complex.">simplexRing</a> -- The underlying polynomial ring of a deformation or face or complex.</span></li>
<li><span><a href="_target_lp__First__Order__Deformation_rp.html" title="The target of a deformation.">target(FirstOrderDeformation)</a> -- The target of a deformation.</span></li>
<li><span><a href="_source_lp__First__Order__Deformation_rp.html" title="The source of a deformation.">source(FirstOrderDeformation)</a> -- The source of a deformation.</span></li>
<li><span><a href="_big__Torus__Degree.html" title="The big torus degree of a deformation.">bigTorusDegree</a> -- The big torus degree of a deformation.</span></li>
<li><span><a href="_numerator_lp__First__Order__Deformation_rp.html" title="The numerator of a deformation as a vector.">numerator(FirstOrderDeformation)</a> -- The numerator of a deformation as a vector.</span></li>
<li><span><a href="_denominator_lp__First__Order__Deformation_rp.html" title="The denominator of a deformation as a vector.">denominator(FirstOrderDeformation)</a> -- The denominator of a deformation as a vector.</span></li>
<li><span><a href="_numerator__Monomial.html" title="The numerator monomial of a deformation.">numeratorMonomial</a> -- The numerator monomial of a deformation.</span></li>
<li><span><a href="_denominator__Monomial.html" title="The denominator monomial of a deformation.">denominatorMonomial</a> -- The denominator monomial of a deformation.</span></li>
<li><span><a href="_degree_lp__First__Order__Deformation_rp.html" title="The small torus degree of a deformation.">degree(FirstOrderDeformation)</a> -- The small torus degree of a deformation.</span></li>
<li><span><a href="_grading_lp__First__Order__Deformation_rp.html" title="The small torus grading of a deformation.">grading(FirstOrderDeformation)</a> -- The small torus grading of a deformation.</span></li>
<li><span><a href="_is__Homogeneous_lp__First__Order__Deformation_rp.html" title="Check whether a deformation is homogeneous.">isHomogeneous(FirstOrderDeformation)</a> -- Check whether a deformation is homogeneous.</span></li>
<li><span><a href="_relations__Coefficients.html" title="Relations between the coefficients of a deformation.">relationsCoefficients</a> -- Relations between the coefficients of a deformation.</span></li>
<li><span><a href="_parameters.html" title="Parameters of a deformation.">parameters</a> -- Parameters of a deformation.</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="_is__Nonzero.html" title="Check whether a deformation is non-zero.">isNonzero</a> -- Check whether a deformation is non-zero.</span></li>
<li><span><a href="_is__Trivial.html" title="Check whether a deformation is trivial.">isTrivial</a> -- Check whether a deformation is trivial.</span></li>
<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>
<li><span><a href="_to__Hom.html" title="Convert a first order deformation into a homomorphism.">toHom</a> -- Convert a first order deformation into a homomorphism.</span></li>
<li><span><a href="_total__Space.html" title="Total space of a deformation.">totalSpace</a> -- Total space of a deformation.</span></li>
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