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I want to use Sage to give me the reduced incidence algebra of a poset P as a finite dimensional algebra generated by matrices, that I can use to input this algebra into GAP.

Question: How can I obtain a list of matrices that generate a finite dimensional algebra using Sage? A multiplication table would also be helpful and might be used to obtain the algebra in GAP.

Here how to use GAP to get an algebra:

A:=Algebra(GF(3),[[[1,0],[0,1]],[[0,1],[0,0]]]);

Here an example how to get the reduced incidence algebra using Sage:

n=5
P = posets.TamariLattice(n)

I = P.incidence_algebra(QQ)

T=I.reduced_subalgebra()
display(T.dimension())

I found the command "table()" (see http://sporadic.stanford.edu/reference/algebras/sage/algebras/finite_dimensional_algebras/finite_dimensional_algebra.html ) but it seems to not work to give me the matrices that generated the reduced incidence algebra here.

I want to use Sage to give me the reduced incidence algebra of a poset P as a finite dimensional algebra generated by matrices, that I can use to input this algebra into GAP.

Question: How can I obtain a list of matrices that generate a finite dimensional algebra using Sage? A multiplication table would also be helpful and might be used to obtain the algebra in GAP.

Here how to use GAP to get an algebra:algebra generated by matrices:

A:=Algebra(GF(3),[[[1,0],[0,1]],[[0,1],[0,0]]]);
A:=Algebra(Rationals,[[[1,0],[0,1]],[[0,1],[0,0]]]);

Here an example how to get the reduced incidence algebra using Sage:

n=5
P = posets.TamariLattice(n)

I = P.incidence_algebra(QQ)

T=I.reduced_subalgebra()
display(T.dimension())

I found the command "table()" (see http://sporadic.stanford.edu/reference/algebras/sage/algebras/finite_dimensional_algebras/finite_dimensional_algebra.html ) but it seems to not work to give me the matrices that generated the reduced incidence algebra here.