fix(integrals): handle degenerate case in Risch PRDE

[oscarbenjamin]

References to other Issues or PRs

Fixes #23948

Brief description of what is fixed or changed

Ensure that while the matrix is still empty it has the right number of columns.

Other comments

Release Notes

• integrals
  • A bug in the risch integration routine was fixed. Previously in certain conditions involving complicated integrands the routine would fail with AssertionError.

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• integrals
  • A bug in the risch integration routine was fixed. Previously in certain conditions involving complicated integrands the routine would fail with AssertionError. (#23959 by @oscarbenjamin)

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#### References to other Issues or PRs
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Fixes #23948

#### Brief description of what is fixed or changed

Ensure that while the matrix is still empty it has the right number of columns.

#### Other comments


#### Release Notes

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* integrals
   * A bug in the `risch` integration routine was fixed. Previously in certain conditions involving complicated integrands the routine would fail with `AssertionError`.
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Update

The release notes on the wiki have been updated.

[asmeurer]

Not really sure why I ever did it like this since it isn't this way in the book, but this line can just be used for both cases. I think I just didn't have a clear understanding of how empty matrices work, or possibly there was some bug with how they behaved back then, I don't know.

This is page 234 in Bronstein's book, ParamPolyRishDENoCancel1, for anyone checking. Really these docstrings ought to reference the exact pseudocode + page number in the book to make this easier.

[oscarbenjamin]

Maybe you did it like this because:

(Pdb) p Q[0].degree(DE.t)
-oo

[asmeurer]

Oh to be clear, the dc = -1 part is there because that's how it's written in the book (and the ambiguity of degree(0) is clearly the reason). I meant I don't know why I put the matrix definition inside of the if. In the book, it's separate.

[oscarbenjamin]

Okay, I see what you mean. I've moved the matrix definition out.

[asmeurer]

This line is also probably wrong

sympy/sympy/integrals/prde.py

Line 388 in 88664e6

M = Matrix()

[asmeurer]

Also I'm surprised that Matrix() with no arguments works (it creates a 0x0 matrix). I guess that's been around for some time, but IMO it's not great.

[oscarbenjamin]

This line is also probably wrong

Can you think of a test-case that would hit that line?

Also I'm surprised that Matrix() with no arguments works

Nothing like this surprises me any more.

[github-actions]

Benchmark results from GitHub Actions

Lower numbers are good, higher numbers are bad. A ratio less than 1
means a speed up and greater than 1 means a slowdown. Green lines
beginning with + are slowdowns (the PR is slower then master or
master is slower than the previous release). Red lines beginning
with - are speedups.

Significantly changed benchmark results (PR vs master)

Significantly changed benchmark results (master vs previous release)

       before           after         ratio
     [26f7bdbe]       [5eb59bda]
     <sympy-1.11^0>                 
-     1.35±0.05ms         833±30μs     0.62  solve.TimeSparseSystem.time_linear_eq_to_matrix(10)
-      3.90±0.2ms      1.49±0.09ms     0.38  solve.TimeSparseSystem.time_linear_eq_to_matrix(20)
-      7.38±0.2ms       2.21±0.2ms     0.30  solve.TimeSparseSystem.time_linear_eq_to_matrix(30)

Full benchmark results can be found as artifacts in GitHub Actions
(click on checks at the top of the PR).

[jksuom]

I think this is ready to be merged.