Solved incorrect left limit result for atan at inf #25763

borgesaugusto · 2023-10-05T17:54:56Z

References to other Issues or PRs

Brief description of what is fixed or changed

As suggested by anutosh491 PoleError is raised in case the value is nan, which solves the bug. A test was added to check for this case.

Release Notes

functions
- Solved bug with atan when solving a left inf limit

sympy-bot · 2023-10-05T17:55:03Z

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functions
- Solved bug with atan when solving a left inf limit (#25763 by @borgesaugusto)

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#### References to other Issues or PRs
Fixes #25582 
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#### Brief description of what is fixed or changed
As suggested by [anutosh491](https://github.com/anutosh491) PoleError is raised in case the value is nan, which solves the bug. A test was added to check for this case.


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   * Solved bug with atan when solving a left inf limit 
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Update

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github-actions · 2023-10-05T19:12:41Z

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)

| Change   | Before [8059df73] <sympy-1.12^0>   | After [060f97a8]    |   Ratio | Benchmark (Parameter)                                                |
|----------|------------------------------------|---------------------|---------|----------------------------------------------------------------------|
| -        | 88.3±0.8ms                         | 58.5±0.2ms          |    0.66 | integrate.TimeIntegrationRisch02.time_doit(10)                       |
| +        | 21.9±0.1μs                         | 39.0±0.1μs          |    1.78 | integrate.TimeIntegrationRisch03.time_doit(1)                        |
| -        | 6.98±0.02ms                        | 3.84±0.02ms         |    0.55 | logic.LogicSuite.time_load_file                                      |
| -        | 2.12±0.01ms                        | 660±2μs             |    0.31 | polys.TimePREM_LinearDenseQuadraticGCD.time_op(3, 'sparse')          |
| -        | 10.4±0.06ms                        | 1.97±0.01ms         |    0.19 | polys.TimePREM_LinearDenseQuadraticGCD.time_op(5, 'sparse')          |
| -        | 367±0.9μs                          | 82.7±0.3μs          |    0.23 | polys.TimePREM_QuadraticNonMonicGCD.time_op(1, 'sparse')             |
| -        | 4.89±0.02ms                        | 364±0.7μs           |    0.07 | polys.TimePREM_QuadraticNonMonicGCD.time_op(3, 'sparse')             |
| -        | 10.6±0.06ms                        | 1.10±0ms            |    0.1  | polys.TimePREM_QuadraticNonMonicGCD.time_op(5, 'sparse')             |
| -        | 6.26±0.02ms                        | 3.99±0.01ms         |    0.64 | polys.TimeSUBRESULTANTS_LinearDenseQuadraticGCD.time_op(2, 'sparse') |
| -        | 27.2±0.1ms                         | 12.2±0.01ms         |    0.45 | polys.TimeSUBRESULTANTS_LinearDenseQuadraticGCD.time_op(3, 'sparse') |
| -        | 6.93±0.04ms                        | 1.18±0ms            |    0.17 | polys.TimeSUBRESULTANTS_QuadraticNonMonicGCD.time_op(1, 'sparse')    |
| -        | 16.4±0.05ms                        | 9.23±0.03ms         |    0.56 | polys.TimeSUBRESULTANTS_QuadraticNonMonicGCD.time_op(2, 'sparse')    |
| -        | 211±0.4ms                          | 71.4±0.1ms          |    0.34 | polys.TimeSUBRESULTANTS_QuadraticNonMonicGCD.time_op(3, 'sparse')    |
| -        | 6.39±0.01ms                        | 537±1μs             |    0.08 | polys.TimeSUBRESULTANTS_SparseGCDHighDegree.time_op(3, 'sparse')     |
| -        | 27.6±0.04ms                        | 863±3μs             |    0.03 | polys.TimeSUBRESULTANTS_SparseGCDHighDegree.time_op(5, 'sparse')     |
| -        | 612±3μs                            | 203±2μs             |    0.33 | polys.TimeSUBRESULTANTS_SparseNonMonicQuadratic.time_op(1, 'sparse') |
| -        | 6.49±0.01ms                        | 205±0.8μs           |    0.03 | polys.TimeSUBRESULTANTS_SparseNonMonicQuadratic.time_op(3, 'sparse') |
| -        | 17.0±0.04ms                        | 208±0.9μs           |    0.01 | polys.TimeSUBRESULTANTS_SparseNonMonicQuadratic.time_op(5, 'sparse') |
| -        | 162±0.7μs                          | 89.4±0.3μs          |    0.55 | solve.TimeMatrixOperations.time_rref(3, 0)                           |
| -        | 311±0.5μs                          | 109±0.8μs           |    0.35 | solve.TimeMatrixOperations.time_rref(4, 0)                           |
| -        | 32.0±0.2ms                         | 13.6±0.08ms         |    0.42 | solve.TimeSolveLinSys189x49.time_solve_lin_sys                       |

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

sympy/functions/elementary/trigonometric.py

anutosh491 · 2023-10-06T06:55:33Z

sympy/functions/elementary/tests/test_trigonometric.py

@@ -2160,3 +2160,7 @@ def test_as_real_imag():
 def test_issue_18746():
    e3 = cos(S.Pi*(x/4 + 1/4))
    assert e3.period() == 8
+
+
+def test_atan_inf_left():


I do believe that we would like to see some sort of PoleError here but I would like to test out more cases (think of cases that could go wrong) . the acot function is related to the atan function hence there is a possiblity of cases going wrong there too.

>>> atan(x).rewrite(acot) acot(1/x)

Also could you please change the name of the function (use test_issue_issue_number like other functions) and place it in sorted order

Also add the test here https://github.com/sympy/sympy/blob/master/sympy/series/tests/test_limits.py

anutosh491 · 2023-10-06T10:04:44Z

sympy/functions/elementary/trigonometric.py

@@ -2677,6 +2677,8 @@ def taylor_term(n, x, *previous_terms):
    def _eval_as_leading_term(self, x, logx=None, cdir=0):  # atan
        arg = self.args[0]
        x0 = arg.subs(x, 0).cancel()
+        if x0 is S.NaN:
+            raise PoleError()
        if x0.is_zero:


Also another thing being we would encounter this case in all inverse trigonometric functions (while calculating limits for asin(exp(x)), acsc(exp(x))). Just addressing an individual case might not help us overall, could you try tackling all cases that go wrong.

nan typically results when a substitution gives 0/0 (e.g. arg = sin(x)/x). It may be advisable to first try to compute x0 as a limit before raising PoleError.

e.g. limit(acos(sin(x)/x),x,oo) ? @borgesaugusto, what does that do in this PR?

With the "/ x" gives this result:
limit(acos(sin(x)),x,oo) -> I* log(I* AccumBounds(-1, 1) + AccumBounds(0, 1)) + pi/2

and

limit(acos(sin(x)/x),x,oo) gives:
"sympy.core.function.PoleError: Cannot expand sin(1/_w) around 0" in "sympy/functions/elementary/trigonometric.py" line 436" (The txt with the trace), ending with a NotImplementedError.

sympy_trace.txt

…for nan

borgesaugusto · 2023-10-06T12:12:35Z

I added the check to all the inverse trigonometric functions (except atan2) and moved the test to the suggested file (incorporating the asserts for the new functions and changing the name).
I don't see a more general way of doing it.

smichr · 2023-10-13T04:29:15Z

This seems like a positive step forward. Thanks, this is in.

borgesaugusto added 2 commits October 5, 2023 19:40

author: add Augusto Borges to .mailmap

238e868

trigonometric: Solves incorrect inf limit for atan

86fd144

borgesaugusto mentioned this pull request Oct 5, 2023

Incorrect limit for atan #25582

Closed

smichr reviewed Oct 5, 2023

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sympy/functions/elementary/trigonometric.py Show resolved Hide resolved

anutosh491 added the limits label Oct 6, 2023

anutosh491 reviewed Oct 6, 2023

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borgesaugusto added 2 commits October 6, 2023 13:17

Merge branch 'sympy:master' into iss_25582

d50f54c

Test moved to test_limits. All inverse trigonometric functions check …

c93f864

…for nan

smichr merged commit 458e3c4 into sympy:master Oct 13, 2023

borgesaugusto deleted the iss_25582 branch October 13, 2023 08:25

oscarbenjamin mentioned this pull request Oct 26, 2023

Limit at infinity of arctan(expression that goes to infinity) erroneously gives NaN or it doesn't compute. #25833

Closed

anutosh491 mentioned this pull request Oct 31, 2023

Issue with _eval_as_leading_term function for inverse trig/hyperbolic functions #25847

Closed

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borgesaugusto commented Oct 5, 2023

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