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Comment:

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My wishlist

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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 Rmodule M and an RIdeal I, construct the submodule $M[I]=\{m \in M  xm=0 \mbox{ for all } x \in I\}$ * intersection: Given Rmodule M and two submodules $N_1$ and $N_2$, find the submodule $N_1 \cap N_2$ * sum: Given Rmodule M and two submodules $N_1$ and $N_2$, find the submodule $N_1+N_2$ * tensor product * hom module: Given Rmodules $M_1$ and $M_2$, construct the module $Hom_R(M_1, M_2)$ * Change of ring: Given Rmodules M and an Ralgebra A, construct the Amodule $M \otimes A$. * Annihilator * Rank: Calculate the rank of an Rmodule M. * direct sum * treating ideals as an Rmodules. 
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 Rmodule M and an RIdeal I, construct the submodule M[I]=\{m \in M  xm=0 \mbox{ for all } x \in I\}
intersection: Given Rmodule M and two submodules N_1 and N_2, find the submodule N_1 \cap N_2
sum: Given Rmodule M and two submodules N_1 and N_2, find the submodule N_1+N_2
 tensor product
hom module: Given Rmodules M_1 and M_2, construct the module Hom_R(M_1, M_2)
Change of ring: Given Rmodules M and an Ralgebra A, construct the Amodule M \otimes A.
 Annihilator
 Rank: Calculate the rank of an Rmodule M.
 direct sum
 treating ideals as an Rmodules.