Macaulay2 / Macaulay2/M2

Feature request: singularLocus efficiency

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Macaulay2
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Description

The method `singularLocus` in M2 is not very efficient. I recently looked at the file [`bir.m2`](http://goo.gl/eT4rCR) written by Giovanni Staglianò for his [article](http://dx.doi.org/10.1016/j.jsc.2015.11.004), where one gets the option to use `Singular` to carry out this computation. For example, here is a test case.
```macaulay2
R = ZZ/11[x_0..x_3];
I = ideal apply(10, i->random_3 R);
elapsedTime isSmooth(I, Use=>Singular); -- 0.0754029 seconds elapsed
elapsedTime isSmooth(I, Use=>M2); -- 3.26353 seconds elapsed
```
Is it possible to make this an official feature, which will make `singularLocus` much more usable?
**Update**: The above example is a bit degenerate. Here is a better one.
```macaulay2
I = Grassmannian(1,4,CoefficientRing=>ZZ/101);
R = ring I;
J = I + ideal(random_1 R, random_2 R);
elapsedTime isSmooth(J, Use=>Singular); -- 2.72101 seconds elapsed
elapsedTime isSmooth(J, Use=>M2); -- 18.1278 seconds elapsed
```

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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 with M2's singularLocus implementation and the referenced bir.m2 implementation, then trace how isSmooth handles Use=>M2 and Use=>Singular. Done means Singular-backed computation is available as an official option for singularLocus and the two supplied examples produce the expected behavior and timing comparison.

Written by the indexing model from the issue text.

Assessment

Domain
tooling
Issue type
Feature
Difficulty
4/5
Estimated time
3-5 days
Activity status
Stale
Clarity
Mostly clear
Newbie friendliness
35/100

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