Macaulay2 / Macaulay2/M2

Issue with homology of matrices

Open
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Core
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Macaulay2
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Description

When computing the homology of matrices, Macaulay seems to have an issue with composing matrices over a polynomial ring.

```macaulay2
R = QQ[x]
M = matrix{{0,x},{0,0}}
homology(M,M)
```

returns

```
error: expected maps to be composable
```

Intended behavior would be to return QQ, since the kernel of M is R e1 and the image is xR e1.

On the other hand, it is able to return the homology of matrices whose composition is not zero, which isn't meaningful.
```macaulay2
R = QQ
M = matrix{{1,1},{0,0}}
homology(M,M)
```

returns
```
subquotient (| 1 |, | 1 1 |)
| -1 | | 0 0 |

2
ZZ-module, subquotient of ZZ
```

and it should probably just return an error.

Contributor guide

No contributing guide indexed for this repository

Research direction

Start at the homology(M,M) entry point and reproduce both matrix examples over QQ[x] and QQ. Trace how composability is checked and how nonzero compositions are handled; done means the first example returns the intended homology and the second reports an 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
35/100

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