series - Fixes series expansion around float failing with NotImplementedError

[praneethratna]

References to other Issues or PRs

Brief description of what is fixed or changed

Fixes #23432 and now series(1/sqrt(1-x**2), x, 0.5) returns

0.769800358919501 + 1.539600717839*(x - 0.5)**2 + 2.39493444997178*(x - 0.5)**3 + 4.33369090947275*(x - 0.5)**4 + 7.75502583800386*(x - 0.5)**5 + 0.769800358919501*x + O((x - 1/2)**6, (x, 1/2))

instead of NotImplementedError.

Other comments

Release Notes

• series
  • fixes bug in series and now series expansion with float does not give NotImplementedError.

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• series
  • fixes bug in series and now series expansion with float does not give NotImplementedError. (#23456 by @praneethratna)

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#### Brief description of what is fixed or changed
Fixes #23432 and now `series(1/sqrt(1-x**2), x, 0.5)` returns 
```
0.769800358919501 + 1.539600717839*(x - 0.5)**2 + 2.39493444997178*(x - 0.5)**3 + 4.33369090947275*(x - 0.5)**4 + 7.75502583800386*(x - 0.5)**5 + 0.769800358919501*x + O((x - 1/2)**6, (x, 1/2))
```
instead of `NotImplementedError`.

#### Other comments


#### Release Notes

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  * Added a new solver for logarithmic equations.

* functions
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<!-- BEGIN RELEASE NOTES -->
* series
  * fixes bug in `series` and now series expansion with float does not give `NotImplementedError`.
<!-- END RELEASE NOTES -->

Update

The release notes on the wiki have been updated.

[praneethratna]

CC @jksuom

[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
     [77f1d79c]       [ed4e06ef]
     <sympy-1.10.1^0>                 
+       114±0.8ms          202±3ms     1.77  sum.TimeSum.time_doit

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

[praneethratna]

When I'm trying to add a test case, with the following change - Even though the answer is correct, I'm getting an AssertionError. @jksuom could you help me out here?

diff --git a/sympy/series/tests/test_series.py b/sympy/series/tests/test_series.py
index 34b598a415..f526b3bf0d 100644
--- a/sympy/series/tests/test_series.py
+++ b/sympy/series/tests/test_series.py
@@ -362,3 +362,11 @@ def test_issue_21245():
 def test_issue_21938():
     expr = sin(1/x + exp(-x)) - sin(1/x)
     assert expr.series(x, oo) == (1/(24*x**4) - 1/(2*x**2) + 1 + O(x**(-6), (x, oo)))*exp(-x)
+
+
+def test_issue_23432():
+    expr = 1/sqrt(1 - x**2)
+    assert expr.series(x, 0.5) == \
+        0.769800358919501 + 1.539600717839*(x - 0.5)**2 +\
+        2.39493444997178*(x - 0.5)**3 + 4.33369090947275*(x - 0.5)**4 +\
+        7.75502583800386*(x - 0.5)**5 + 0.769800358919501*x + O((x - 1/2)**6, (x, 1/2))

[jksuom]

sympy/sympy/core/power.py

Lines 1735 to 1739 in a189657

	if not d.is_positive:
	g = g.simplify()
	_, d = g.leadterm(x)
	if not d.is_positive:
	raise NotImplementedError()

Two changes: First, two lines between lines 1736 and 1737:

              if g.is_zero:
                  return f**e

Second, 4 lines in place of 1739:

                  g = ((b - f)/f).expand()
                  _, d = g.leadterm(x)
                  if not d.is_positive:
                      raise NotImplementedError()

[jksuom]

Even though the answer is correct, I'm getting an AssertionError.

Comparisons of expressions containing Floats are notoriously hard to implement. It seems that when a Float is printed, it is truncated, and when the printed expression is input and sympified, it will again be slightly modified so it will often not be exactly the same as the original Float. Comparison of printed strings is sometimes used as a work-around, but that should probably be avoided.

It is possible to use almosteq but that would make the test fairly complicated as all the Floats should be compared pairwise. In this case, I think that it would suffice to devise a test that would show that no error will be raised; for example, that expr.series(x, 0.5) is an Add.

[praneethratna]

@jksuom I have added the test case - assert expr.series(x, 0.5) != NotImplementedError , but I'm not sure whether it is the right way or not.

[jksuom]

The purpose of the tests is to give an indication of possible regressions when new code is added. assert expr.series(x, 0.5) != NotImplementedError would allow almost any changes to the series expansion; for example, it would pass even if an error of a different type were raised.
I think that a test of the following type would suffice in most cases:

res = expr.series(x, 0.5)
assert res.is_Add and len(res.args) == 7

[jksuom]

Can you squash the commits? A single commit with a message would suffice.

[jksuom]

Thanks, this is ready to go.