Computing kernel of a graded homomorpism in an algorithmic way

Question

For computing kernel of a module homomorphism we can use module-Grobner basis as described in notes talking about computing SyZyGies. But how can we compute kernel of a homomorphism between a graded rings? I was thinking that maybe I should consider the graded parts of the two rings as modules and then computing kernel of restriction of the graded homomorphism on them but then I have an infinite sequence of generators for these kernels, even if it be a right attempt then I should think about bringing out a finite generator for the main kernel. I somehow feel it's not a correct idea. Does anyone know how to compute these kernels? It is possible as for example Singular software compute defining ideal of Rees algebra which is kernel of a graded homomorphism, so there should be a computational method.