Macaulay2 / Macaulay2/M2

LinearTruncations

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package issue
Dominant language
Macaulay2
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Merged PRs (30d)
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Description

The function `isLinearComplex` in the package `LinearTruncations` isn't quite correct:

Here is the code I see:
```m2
isLinearComplex ChainComplex := F -> (
if F == 0 then return true;
t := degreeLength ring F;
range := toList(min F..max F-1);
if #(unique degrees F_(range_0)) != 1 then return false;
dF := apply(range, i -> (degrees(F_i))/sum);
mindF := dF_(min F)_0;
all(range, i -> max(dF_i) === mindF+i-range_0)
)
```

Problems:
- dF starts at 0, not at min F.
- range doesn't include the last module `F_(max F)` in the list, so if the degrees there are not making it a linear complex, it will not be detected.
- t is set, but doesn't appear to be being used.

An example:

```m2
needsPackage "LinearTruncations"
R = QQ[a..d]
M = matrix{{a,b,c},{b,c,d}}
C = res(coker M, LengthLimit => 2)
betti C
assert not isLinearComplex C -- fails. If there were a trailing zero, it would have worked...!
```
I noticed these while seeing about migrating this to the new Complexes package (which is delicate, as TateOnProducts is the hardest package to migrate!).

If you want, I can fix this, so it will work with the new Complexes package as well.

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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 in the LinearTruncations package at the isLinearComplex function and reproduce the reported example with QQ[a..d], M, and res. Check the degree range and dF calculations against the stated endpoint cases, then rerun assert not isLinearComplex C; done means the example is detected as non-linear without relying on a trailing zero.

Written by the indexing model from the issue text.

Assessment

Domain
tooling
Issue type
Bug
Difficulty
2/5
Estimated time
1-3 hours
Activity status
Active
Clarity
Mostly clear
Newbie friendliness
72/100

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