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<head><title>fromDual -- ideal from inverse system</title>
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<div><h1>fromDual -- ideal from inverse system</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>fromDual g</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>g</tt>, <span>a <a href="___Matrix.html">matrix</a></span>, a one row matrix over a polynomial ring R, consisting of homogeneous polynomials</span></li>
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<li><div class="single">Outputs:<ul><li><span><span>a <a href="___Matrix.html">matrix</a></span>, a one row matrix f over R whose entries generate the homogeneous ideal { h in R | h . g = 0 }, where the action is by contraction (see <a href="_contract_lp__Matrix_cm__Matrix_rp.html" title="contract a matrix by a matrix">contract(Matrix,Matrix)</a>)</span></li>
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<div class="single"><h2>Description</h2>
<div>For other examples, and a more precise definition, see <a href="_inverse_spsystems.html" title="">inverse systems</a>.<table class="examples"><tr><td><pre>i1 : R = ZZ/32003[x_1..x_3];</pre>
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<tr><td><pre>i2 : g = random(R^1, R^{-4})
o2 = | -13746x_1^4+11433x_1^3x_2-14908x_1^2x_2^2+10772x_1x_2^3-7400x_2^4+
------------------------------------------------------------------------
5145x_1^3x_3+4181x_1^2x_2x_3-11130x_1x_2^2x_3+11719x_2^3x_3-4723x_1^2x_3
------------------------------------------------------------------------
^2-5777x_1x_2x_3^2+7518x_2^2x_3^2+12574x_1x_3^3-10597x_2x_3^3+13744x_3^4
------------------------------------------------------------------------
|
1 1
o2 : Matrix R <--- R</pre>
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<tr><td><pre>i3 : f = fromDual g
o3 = | x_2^2x_3+13223x_1x_3^2-10668x_2x_3^2-14800x_3^3
------------------------------------------------------------------------
x_1x_2x_3-11297x_1x_3^2+9797x_2x_3^2+12655x_3^3
------------------------------------------------------------------------
x_1^2x_3-6702x_1x_3^2+8756x_2x_3^2-15937x_3^3
------------------------------------------------------------------------
x_2^3-3378x_1x_3^2+4419x_2x_3^2-13724x_3^3
------------------------------------------------------------------------
x_1x_2^2-13565x_1x_3^2-1900x_2x_3^2-8306x_3^3
------------------------------------------------------------------------
x_1^2x_2+10557x_1x_3^2-4629x_2x_3^2+5093x_3^3
------------------------------------------------------------------------
x_1^3+9285x_1x_3^2+5412x_2x_3^2-13727x_3^3 |
1 7
o3 : Matrix R <--- R</pre>
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<tr><td><pre>i4 : res ideal f
1 7 7 1
o4 = R <-- R <-- R <-- R <-- 0
0 1 2 3 4
o4 : ChainComplex</pre>
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<tr><td><pre>i5 : betti oo
0 1 2 3
o5 = total: 1 7 7 1
0: 1 . . .
1: . . . .
2: . 7 7 .
3: . . . .
4: . . . 1
o5 : BettiTally</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_to__Dual.html" title="inverse system">toDual</a> -- inverse system</span></li>
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<div class="waystouse"><h2>Ways to use <tt>fromDual</tt> :</h2>
<ul><li><span><tt>fromDual(Matrix)</tt> (missing documentation<!-- tag: (fromDual,Matrix) -->)</span></li>
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