Obtaining the evaluation map with QPA

Question

Given a finite dimensional quiver algebra $A$ and a module $M$ with $M^{*}=Hom_A(M,A)$.

Question: Is it possible to obtain the evaluation map $ev_M : M \rightarrow M^{**}$ in the GAP-package QPA for a given module $M$? Here $ev_M(m)=g(m)$ for $g \in M^{*}$.

This might allow one to obtain the $A$-module $Ext_A^1(Tr(M),A)$ (and thus $Ext_A^i(M,A)$ for all $i$ ) as an $A$-module as the kernel of $ev_M$.

Answer 1

With the latest addition to QPA, one can use the function FromIdentityToDoubleStarHomomorphism do the following:

gap> M;
<[ 0, 10, 7 ]>    
gap> f := FromIdentityToDoubleStarHomomorphism( M );
<<[ 0, 10, 7 ]> ---> <[ 3, 16, 13 ]>>
gap> Kernel( f );
<[ 0, 0, 0 ]>
gap> CoKernel( f );
<[ 3, 6, 6 ]>

which computes the natural homomorphism $M\to M^{**}$.