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<head><title>SumOfTwists -- the class of all sums of twists</title>
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<div><h1>SumOfTwists -- the class of all sums of twists</h1>
<div class="single"><h2>Description</h2>
<div>This class is used internally as an abstract representation of a graded module as an infinite direct sum of twists of a coherent sheaf.<table class="examples"><tr><td><pre>i1 : R = QQ[x,y,z]
o1 = R
o1 : PolynomialRing</pre>
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<tr><td><pre>i2 : X = Proj R
o2 = X
o2 : ProjectiveVariety</pre>
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<tr><td><pre>i3 : OO_X(*)
1
o3 = OO (*)
X
o3 : SumOfTwists</pre>
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<tr><td><pre>i4 : peek oo
1
o4 = SumOfTwists{OO , LowerBound{-infinity}}
X</pre>
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<tr><td><pre>i5 : OO_X(>=2)
1
o5 = OO (>=2)
X
o5 : SumOfTwists</pre>
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<tr><td><pre>i6 : peek oo
1
o6 = SumOfTwists{OO , LowerBound{2}}
X</pre>
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<tr><td><pre>i7 : Ext^0(OO_X^1, OO_X^1)
1
o7 = QQ
o7 : QQ-module, free</pre>
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<tr><td><pre>i8 : Ext^0(OO_X^1, OO_X^1(*))
1
o8 = R
o8 : R-module, free</pre>
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<div class="waystouse"><h2>Functions and methods returning an object of class SumOfTwists :</h2>
<ul><li><span>CoherentSheaf LowerBound, see <span><a href="___Lower__Bound.html" title="the class of lower bound objects">LowerBound</a> -- the class of lower bound objects</span></span></li>
<li><span>SheafOfRings LowerBound, see <span><a href="___Lower__Bound.html" title="the class of lower bound objects">LowerBound</a> -- the class of lower bound objects</span></span></li>
</ul>
<h2>Methods that use an object of class SumOfTwists :</h2>
<ul><li><span><a href="___Ext^__Z__Z_lp__Coherent__Sheaf_cm__Sum__Of__Twists_rp.html" title="global Ext">Ext^ZZ(CoherentSheaf,SumOfTwists)</a> -- global Ext</span></li>
<li><span>Ext^ZZ(SheafOfRings,SumOfTwists), see <span><a href="___Ext^__Z__Z_lp__Coherent__Sheaf_cm__Sum__Of__Twists_rp.html" title="global Ext">Ext^ZZ(CoherentSheaf,SumOfTwists)</a> -- global Ext</span></span></li>
<li><span><a href="___H__H^__Z__Z_sp__Sum__Of__Twists.html" title="coherent sheaf cohomology module">HH^ZZ SumOfTwists</a> -- coherent sheaf cohomology module</span></li>
</ul>
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<div class="waystouse"><h2>For the programmer</h2>
<p>The object <a href="___Sum__Of__Twists.html" title="the class of all sums of twists">SumOfTwists</a> is <span>a <a href="___Type.html">type</a></span>, with ancestor classes <a href="___Basic__List.html" title="the class of all basic lists">BasicList</a> < <a href="___Thing.html" title="the class of all things">Thing</a>.</p>
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