Differences between revisions 3 and 4
 ⇤ ← Revision 3 as of 2007-09-30 16:50:35 → Size: 238 Editor: MikeHansen Comment: ← Revision 4 as of 2007-09-30 18:08:15 → ⇥ Size: 1034 Editor: SorooshYazdani Comment: My wishlist Deletions are marked like this. Additions are marked like this. Line 4: Line 4: 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.

# 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.

days5/proj/modules (last edited 2008-11-14 13:41:58 by anonymous)