Macaulay2 / Macaulay2/M2

formation of tensor products of chain complexes

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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

  1. Read the whole issue, then the project's contributing guide.
  2. Comment on the issue to say you are picking it up — it saves two people doing the same work.
  3. Fork the repository and make your change on a branch.
  4. 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

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