<Chapter><Heading> Chain complexes</Heading> <Table Align="|l|" > <Row> <Item> <Index> ChevalleyEilenbergComplex</Index> <C> ChevalleyEilenbergComplex(X,n) </C> <P/> Inputs either a Lie algebra <M>X=A</M> (over the ring of integers <M>Z</M> or over a field <M>K</M>) or a homomorphism of Lie algebras <M>X=(f:A \longrightarrow B)</M>, together with a positive integer <M>n</M>. It returns either the first <M>n</M> terms of the Chevalley-Eilenberg chain complex <M>C(A)</M>, or the induced map of Chevalley-Eilenberg complexes <M>C(f):C(A) \longrightarrow C(B)</M>. <P/> (The homology of the Chevalley-Eilenberg complex <M>C(A)</M> is by definition the homology of the Lie algebra <M>A</M> with trivial coefficients in <M>Z</M> or <M>K</M>). <P/> This function was written by Pablo Fernandez Ascariz </Item> </Row> <Row> <Item> <Index> LeibnizComplex</Index> <C> LeibnizComplex(X,n) </C> <P/> Inputs either a Lie or Leibniz algebra <M>X=A</M> (over the ring of integers <M>Z</M> or over a field <M>K</M>) or a homomorphism of Lie or Leibniz algebras <M>X=(f:A \longrightarrow B)</M>, together with a positive integer <M>n</M>. It returns either the first <M>n</M> terms of the Leibniz chain complex <M>C(A)</M>, or the induced map of Leibniz complexes <M>C(f):C(A) \longrightarrow C(B)</M>. <P/> (The Leibniz complex <M>C(A)</M> was defined by J.-L.Loday. Its homology is by definition the Leibniz homology of the algebra <M>A</M>). <P/> This function was written by Pablo Fernandez Ascariz </Item> </Row> </Table> </Chapter>