Implementation of elementary crystals

[bsalisbury1]

Implements the crystals T_lambda, R_lambda, C, and B_i for all types.

[tscrim]

Thanks for your work on this Ben.

[tscrim]

Hey Ben,

Could you reupload the version of the patch on the combinat queue? I had to make some minor tweaks due changes in #14402.

Thanks,
Travis

[bsalisbury1]

It's re-uploaded. Thanks, Travis and Anne, for reviewing and adjusting!

[tscrim]

Thanks Ben.

[aschilling]

Why does this patch import ../sage/combinat/crystals/kyoto_path_model into the documentation? That does not seem to exist.

So I set this back to needs work.

Best,

Anne

[aschilling]

In addition, I unfortunately get test failures:

sage -t elementary_crystals.py
**********************************************************************
File "elementary_crystals.py", line 335, in sage.combinat.crystals.elementary_crystals.TCrystal.Element._latex_
Failed example:
    latex(t)
Expected:
    {t_{\left(-1\right)e_{0} + \left(-3\right)e_{1} + \left(-3\right)e_{2} + \left(-3\right)e_{deltacheck}}}
Got:
    {t_{-e_{0} - 3e_{1} - 3e_{2} - 3e_{deltacheck}}}
**********************************************************************
File "elementary_crystals.py", line 563, in sage.combinat.crystals.elementary_crystals.RCrystal.Element._latex_
Failed example:
    latex(r)
Expected:
    {r_{e_{0} + \left(-1\right)e_{2}}}
Got:
    {r_{e_{0} - e_{2}}}
**********************************************************************

[bsalisbury1]

Thank you, Anne, for pointing this out, and thank you, Travis, for your help!

[tscrim]

Failing doctests were due to #13735. Idk how I mistakenly put the kyoto_path_model into the rst file... Thanks for catching this Anne.