formation of tensor products of chain complexes
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- Dominant language
- Macaulay2
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Description
`formation` works nicely for tensors of modules:
```m2
i16 : M = R^2;
i17 : formation(M ** M)
2 2
o17 = tensor (R , R )
o17 : Expression of class FunctionApplication
```
But for chain complexes only formation of direct sums works:
```m2
i1 : R = kk[x,y];
i2 : K = koszul vars R;
i3 : formation(K ++ K)
1 2 1 1 2 1
o3 = directSum (R <-- R <-- R , R <-- R <-- R )
0 1 2 0 1 2
o3 : Expression of class FunctionApplication
i4 : formation(K ** K) -- gives null
```
The new Complexes packages doesn't seem to support `formation` at all:
```
i10 : formation(K ** K)
stdio:10:1:(3): error: no method found for applying formation to:
1 4 6 4 1
argument : R <-- R <-- R <-- R <-- R (of class Complex)
0 1 2 3 4
```
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First steps
- Read the whole issue, then the project's contributing guide.
- Comment on the issue to say you are picking it up — it saves two people doing the same work.
- Fork the repository and make your change on a branch.
- Open a pull request that references the issue number.
Research direction
Start by reproducing the `formation(K ** K)` examples for chain complexes and compare them with `formation(K ++ K)` and module tensors. Read the `formation` handling in the Complexes package and determine how tensor products are represented. Done means formation supports the tensor-product complex without returning null or raising a missing-method error.
Written by the indexing model from the issue text.
Assessment
- Domain
- tooling
- Issue type
- Bug
- Difficulty
- 4/5
- Estimated time
- 3-5 days
- Activity status
- Stale
- Clarity
- Mostly clear
- Newbie friendliness
- 38/100