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[GSoC] Functions: Fixes incorrect evaluation caused due to subfactorial in limit_seq expression #19515

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merged 4 commits into from Jun 9, 2020

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@sachin-4099 sachin-4099 commented Jun 8, 2020

Fixes: #9308

Brief description of what is fixed or changed

Incorrect limit_seq evaluation takes place because of subfactorial in limit_seq expression.

Ideally, we should have _eval_rewrite_as_factorial() and _eval_rewrite_as_gamma() functionalities for subfactorial.

This is implemented using the equation:

image

For further details: https://en.wikipedia.org/wiki/Derangement#Limit_of_ratio_of_derangement_to_permutation_as_n_approaches_%E2%88%9E

After this, we can simply rewrite the subfactorial term present in limit_seq expression to gamma, so that the evaluations take place correctly.

Other Comments

Regression Test has been added.

Release Notes

  • functions
    • Adds _eval_rewrite_as_factorial() and _eval_rewrite_as_gamma() functionalities for subfactorial

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sympy-bot commented Jun 8, 2020

Hi, I am the SymPy bot (v160). I'm here to help you write a release notes entry. Please read the guide on how to write release notes.

Your release notes are in good order.

Here is what the release notes will look like:

  • functions
    • Adds _eval_rewrite_as_factorial() and _eval_rewrite_as_gamma() functionalities for subfactorial (#19515 by @sachin-4099)

This will be added to https://github.com/sympy/sympy/wiki/Release-Notes-for-1.7.

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Fixes: #9308

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

**Incorrect limit_seq evaluation** takes place because of **subfactorial in limit_seq expression.**

Ideally, we should have `_eval_rewrite_as_factorial()` and `_eval_rewrite_as_gamma()`  functionalities for `subfactorial`.

This is implemented using the equation:

![image](https://user-images.githubusercontent.com/46645803/84059488-56a67100-a9d8-11ea-9705-fbea54aece7c.png)

For further details: https://en.wikipedia.org/wiki/Derangement#Limit_of_ratio_of_derangement_to_permutation_as_n_approaches_%E2%88%9E

After this, we can simply rewrite the `subfactorial` term present in `limit_seq expression` to `gamma`, so that the evaluations take place correctly.

#### Other Comments
Regression Test has been added.


#### Release Notes


<!-- BEGIN RELEASE NOTES -->
* functions
  * Adds `_eval_rewrite_as_factorial()` and `_eval_rewrite_as_gamma()`  functionalities for `subfactorial`
<!-- END RELEASE NOTES -->

Update

The release notes on the wiki have been updated.

@sachin-4099 sachin-4099 changed the title [GSoC] Functions: Fixes incorrect evaluation caused due to subfactorial in limit expression [GSoC] Functions: Fixes incorrect evaluation caused due to subfactorial in limit_seq expression Jun 8, 2020
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codecov bot commented Jun 8, 2020

Codecov Report

Merging #19515 into master will decrease coverage by 0.000%.
The diff coverage is 63.636%.

@@              Coverage Diff              @@
##            master    #19515       +/-   ##
=============================================
- Coverage   75.690%   75.689%   -0.001%     
=============================================
  Files          653       653               
  Lines       169873    169884       +11     
  Branches     40059     40059               
=============================================
+ Hits        128577    128584        +7     
- Misses       35686     35689        +3     
- Partials      5610      5611        +1     

@jksuom jksuom merged commit 2182b0c into sympy:master Jun 9, 2020
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limit(subfactorial(n)/factorial(n), n, oo) returns wrong result
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