<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>


