Differences between revisions 2 and 4 (spanning 2 versions)

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∈M|xm=0 for all x∈I}
intersection: Given R-module M and two submodules N1 and N2, find the submodule N1⋂N2
sum: Given R-module M and two submodules N1 and N2, find the submodule N1+N2
tensor product
hom module: Given R-modules M1 and M2, construct the module HomR(M1,M2)
Change of ring: Given R-modules M and an R-algebra A, construct the A-module M⊗A.
Annihilator
Rank: Calculate the rank of an R-module M.
direct sum
treating ideals as an R-modules.

-  ⇤ ← Revision 2 as of 2007-09-30 12:43:13 → 
  Size: 56
  Editor: was
  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.
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+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  $M [I] = {m \in M | x m = 0 for all x \in I}$ 
 * 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  $H o m_{R} (M_{1}, M_{2})$ 
 * 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.

Diff for "days5/proj/modules"

Tensor products, quotients, etc., of free modules