Add algorithm to compute real Gaunt coefficient

[AntiPhoton47]

I have coded a symbolic algorithm to compute the integral of three real spherical harmonics based on the outline presented in Homeier and Steinborn (1996). The appropriate import lines, references, and documentation have also been added throughout the entire file.

References to other Issues or PRs

I proposed these changes with the help of @smichr in pull request #24035, but I am new to GitHub and didnt merge the changes properly so I am opening a new pull request.

Brief description of what is fixed or changed

An algorithm to compute the real Gaunt coefficient has been added as a function titled real_gaunt, along with the appropriate import lines, references, and documentation scattered throughout the wigner.py file. A test function titled test_realgaunt was added to the testing file within the physics module as well. Lastly, the test functions for the clebsch-gordon function were all condensed down to one.

Other comments

The algorithm uses the already included Gaunt algorithm, but I can find another if this is problematic (due to copyright issues perhaps). Please also let me know if anyone finds any bugs or other conflicting lines.

EDIT: Very big thanks to Christopher Smith for suggesting a number of modifications that have made the program more concise and reduced the runtime significantly.

Release Notes

• physics.wigner
  • Added real_gaunt function to compute the integral of 3 real spherical harmonics.

[sympy-bot]

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Here is what the release notes will look like:

• physics.wigner
  • Added real_gaunt function to compute the integral of 3 real spherical harmonics. (#24070 by @AntiPhoton47)

This will be added to https://github.com/sympy/sympy/wiki/Release-Notes-for-1.12.

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<!-- Your title above should be a short description of what
was changed. Do not include the issue number in the title. -->

I have coded a symbolic algorithm to compute the integral of three real spherical harmonics based on the outline presented in Homeier and Steinborn (1996). The appropriate import lines, references, and documentation have also been added throughout the entire file.

#### References to other Issues or PRs
<!-- If this pull request fixes an issue, write "Fixes #NNNN" in that exact
format, e.g. "Fixes #1234" (see
https://tinyurl.com/auto-closing for more information). Also, please
write a comment on that issue linking back to this pull request once it is
open. -->

I proposed these changes with the help of @smichr in pull request #24035, but I am new to GitHub and didnt merge the changes properly so I am opening a new pull request.

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

An algorithm to compute the real Gaunt coefficient has been added as a function titled real_gaunt, along with the appropriate import lines, references, and documentation scattered throughout the wigner.py file. A test function titled test_realgaunt was added to the testing file within the physics module as well. Lastly, the test functions for the clebsch-gordon function were all condensed down to one.

#### Other comments

The algorithm uses the already included Gaunt algorithm, but I can find another if this is problematic (due to copyright issues perhaps). Please also let me know if anyone finds any bugs or other conflicting lines.

EDIT: Very big thanks to Christopher Smith for suggesting a number of modifications that have made the program more concise and reduced the runtime significantly.

#### Release Notes

<!-- Write the release notes for this release below between the BEGIN and END
statements. The basic format is a bulleted list with the name of the subpackage
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* solvers
  * Added a new solver for logarithmic equations.

* functions
  * Fixed a bug with log of integers.

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<!-- BEGIN RELEASE NOTES -->

* physics.wigner
  * Added `real_gaunt` function to compute the integral of 3 real spherical harmonics. 

<!-- END RELEASE NOTES -->

Update

The release notes on the wiki have been updated.

[smichr]

If, in this branch, you git reset head~8 and commit as "review edits" (and even squash that 4th commit into your 3rd commit) and then push here with git push -f AntiPhoton47 patch-1 that will clean up the several small additions that we have made.

[AntiPhoton47]

I'm still doing something wrong and i'm not sure what it is. I am in my local directory and I first entered git reset head~8, then I entered git commit -m "review edits", and finally I entered git push -f origin patch-1.

[AntiPhoton47]

The odd part is that my local clone is the version we had before I reset the head, but the version that was pushed to my remote repository is the original version I opened the pull request with.

[smichr]

Looks good to me. This will merge when tests pass.