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GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it

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<Verb>CocycleCondition(R,n):: FreeRes, Int --> IntMat</Verb><P/>
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Inputs a free <M>\mathbb ZG</M>-resolution <M>R</M> of <M>\mathbb Z</M>
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and an integer
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<M>n \ge 1</M>.
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It returns an integer matrix <M>M</M> with the following property.
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Let <M>d</M> be the <M>\mathbb ZG</M>-rank of <M>R_n</M>.
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An integer vector <M>f=[f_1, ... , f_d]</M> then represents a
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<M>\mathbb ZG</M>-homomorphism <M>R_n \rightarrow
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\mathbb Z_q</M> which sends the
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<M>i</M>th generator of <M>R_n</M> to the integer <M>f_i</M> in the trivial
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<M>\mathbb ZG</M>-module <M>\mathbb Z_q=\mathbb Z/q{\mathbb Z}</M>
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(where possibly <M>q=0</M>). The homomorphism <M>f</M> is a cocycle if and
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only if <M>M^tf=0</M> mod <M>q</M>.
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