The function RightModuleOverPathAlgebra(A, mats) assigns a zero-dimensional vector space to all isolated vertices, i.e. vertices that are not the source or target of any arrow. This causes bugs when some of QPA's methods are applied to quivers with isolated vertices: in some cases an incorrect result is returned, while in other cases an error occurs. This patch fixes most of these bugs (that I am aware of, at least) by using the function RightModuleOverPathAlgebra(A, dim_vector, gens) instead.
In addition to the methods I've updated, there are some methods using the function RightModuleOverPathAlgebra(A, mats) that I have not modified, namely the following:
1stSyzygy: This method does not seem to have any bugs, as the syzygy of a module is zero at all isolated vertices.
SubmoduleAsModule: This method seems to produce incorrect results in some cases, but I don't really understand what sort of results it's actually supposed to produce, nor do I fully understand the source code, so I have not attempted to modify it.
NaturalHomomorphismBySubAlgebraModule: I suspect that this method also produces incorrect results in some cases, but I haven't been able to find an example because I'm not sure what kind of input the method expects.
It might be relevant to update the last two of these methods at some point, but I've left them as they are for now.
The function
RightModuleOverPathAlgebra(A, mats)
assigns a zero-dimensional vector space to all isolated vertices, i.e. vertices that are not the source or target of any arrow. This causes bugs when some of QPA's methods are applied to quivers with isolated vertices: in some cases an incorrect result is returned, while in other cases an error occurs. This patch fixes most of these bugs (that I am aware of, at least) by using the functionRightModuleOverPathAlgebra(A, dim_vector, gens)
instead.In addition to the methods I've updated, there are some methods using the function
RightModuleOverPathAlgebra(A, mats)
that I have not modified, namely the following:1stSyzygy
: This method does not seem to have any bugs, as the syzygy of a module is zero at all isolated vertices.SubmoduleAsModule
: This method seems to produce incorrect results in some cases, but I don't really understand what sort of results it's actually supposed to produce, nor do I fully understand the source code, so I have not attempted to modify it.NaturalHomomorphismBySubAlgebraModule
: I suspect that this method also produces incorrect results in some cases, but I haven't been able to find an example because I'm not sure what kind of input the method expects.It might be relevant to update the last two of these methods at some point, but I've left them as they are for now.