Dear GAP Forum and Bernhard,
Suppose we are given a finite dimensional quotient A = kQ/I of a path
algebra and two modules M and N over A, where we know that N is
a submodule of M. If M and N are given as two representations/
modules over A and you have not told QPA how N is a submodule of
M, then there is in general no way QPA can find the inclusion you are
thinking about. In general a module N can be a submodule of a given
module M in infinitely many ways. However, if you know by which
elements N is generated by inside M, say m_1, m_2,..., m_t, then the
command
gap> g := SubRepresentationInclusion(M, [m1,m2,...,mt]);
will produce an inclusion from a module N' isomorphic to N into M, but
where the images inside M are the same. Then to get an inclusion from
N you could find an isomorphism between N and N' by
gap> alpha := IsomorphismOfModules( N, N' );
and then find the composition alpha*g.
If you are just abstractly knowing that N is a submodule of M, then I
don't
know an algorithm to find an inclusion of N into M.
Best regards, Oeyvind Solberg.
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