Tensor products, quotients, etc., of free modules

Comment from Mike: I'm highly interested in this functionality as I need it for a lot of things. It would be nice to be able to tensor over rings other than just the base ring.

Soroosh's Wish List: Here is a list of things that I think it would be nice to have in Sage. I think some of them are in already.

• kernel
• cokernel

• torsion: Given R-module M and an R-Ideal I, construct the submodule M[I]=\{m \in M | xm=0 \mbox{ for all } x \in I\}

• intersection: Given R-module M and two submodules N_1 and N_2, find the submodule N_1 \cap N_2

• sum: Given R-module M and two submodules N_1 and N_2, find the submodule N_1+N_2

• tensor product

• hom module: Given R-modules M_1 and M_2, construct the module Hom_R(M_1, M_2)

• Change of ring: Given R-modules M and an R-algebra A, construct the A-module M \otimes A.

• Annihilator
• Rank: Calculate the rank of an R-module M.
• direct sum
• treating ideals as an R-modules.