rewrite constructbraidingtensor preprocessor

[Jutho]

This is an alternative to PR#94, that should also be correct if you have a tensor expression composed of a sum of different tensor network contractions. I've included the test cases from PR#94.

I think also _remove_braidingtensors will suffer from the same bugs as the old _construct_braidingtensors, so I probably will also rewrite this one before merging.

Also, it needs some more testing and it contains a branch that should not active and currently prints out a "huh". So I should not forget to remove this.

Maybe you can already test with your code and with MPSKit: @lkdvos and @Gertian .

[Jutho]

It is still easy to break @planar by doing things like adding /2 or other scalar expressions in tensor expressions, so I will need to debug/rewrite further.

[codecov]

Codecov Report

Attention: 57 lines in your changes are missing coverage. Please review.

Comparison is base (bb2b4cf) 80.57% compared to head (dc552e9) 81.43%.

Files	Patch %	Lines
src/planar/preprocessors.jl	77.36%	55 Missing ⚠️
src/planar/analyzers.jl	50.00%	2 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master      #95      +/-   ##
==========================================
+ Coverage   80.57%   81.43%   +0.85%     
==========================================
  Files          42       42              
  Lines        5453     5533      +80     
==========================================
+ Hits         4394     4506     +112     
+ Misses       1059     1027      -32     

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[Gertian]

@Jutho : Soon I'll have some fermionic PEPS that I want to contract and not optimize. This should be a great testcase :)

For now, both yours and Lukas fixes run but I don't know if the output is the correct one.

[Jutho]

When the test turn green, I think this is now ready. I have locally tested the current master of MPSKit with this on Julia 1.10, and all seems fine. Maybe there are additional tests from PEPSKit that @Gertian wants to try?

[Jutho]

Ok I will merge this. If there would still be issues with this in PEPSKit.jl @Gertian , let me know.

[Gertian]

@Jutho I'll see if my old code for contraction still works.

What is the current status for AD of planar fermionic diagrams ?

[lkdvos]

Somewhere near the top of my ever larger to-do list 😉 I'm a little hesitant to promise due dates, but maybe end of January-ish? Maybe @Jutho has more time?

[Gertian]

Great :)

I'm happy to hear it's still on your menu !

[Jutho]

Definitely still on the menu. I have a lot of grading to do the coming weeks, but if I need some distraction or procrastination, the AD rules for the planar operations might be a good candidate. However, you are also very welcome to give it a try yourself if you want :-).

[Gertian]

To be honest I have no idea where to get started with this.

[lkdvos]

https://github.com/Jutho/TensorKit.jl/tree/ld/planar-ad

This was a little more painful than I anticipated, but I think this could be a preliminary working version. Can you try it out? I wrote some small tests, but I can't say I am super confident about it.

[Gertian]

Thanks, I'll play around with it today.
I'll let you know what I found (or didn't find)