# SumOfTwists -- the class of all sums of twists

## Description

This class is used internally as an abstract representation of a graded module as an infinite direct sum of twists of a coherent sheaf.
 i1 : R = QQ[x,y,z] o1 = R o1 : PolynomialRing i2 : X = Proj R o2 = X o2 : ProjectiveVariety i3 : OO_X(*) 1 o3 = OO (*) X o3 : SumOfTwists i4 : peek oo 1 o4 = SumOfTwists{OO , LowerBound{-infinity}} X i5 : OO_X(>=2) 1 o5 = OO (>=2) X o5 : SumOfTwists i6 : peek oo 1 o6 = SumOfTwists{OO , LowerBound{2}} X i7 : Ext^0(OO_X^1, OO_X^1) 1 o7 = QQ o7 : QQ-module, free i8 : Ext^0(OO_X^1, OO_X^1(*)) 1 o8 = R o8 : R-module, free

## Functions and methods returning an object of class SumOfTwists :

• "CoherentSheaf LowerBound" -- see LowerBound -- the class of lower bound objects
• "SheafOfRings LowerBound" -- see LowerBound -- the class of lower bound objects

## For the programmer

The object SumOfTwists is a type, with ancestor classes BasicList < Thing.