change binomial registration

[isaacsas]

Closes #1028.

Uses @ChrisRackauckas's suggestion on how to handle this.

[codecov-commenter]

Codecov Report

Attention: 3 lines in your changes are missing coverage. Please review.

Comparison is base (dc7c7a9) 78.32% compared to head (bdf30c6) 78.04%.

Files	Patch %	Lines
src/extra_functions.jl	80.00%	3 Missing ⚠️

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Additional details and impacted files

@@            Coverage Diff             @@
##           master    #1029      +/-   ##
==========================================
- Coverage   78.32%   78.04%   -0.29%     
==========================================
  Files          28       28              
  Lines        3387     3398      +11     
==========================================
- Hits         2653     2652       -1     
- Misses        734      746      +12     

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[ChrisRackauckas]

  Candidates:
    binomial(n::Num, k::Real)
      @ Symbolics ~/work/Symbolics.jl/Symbolics.jl/src/wrapper-types.jl:142
    binomial(x::Number, k::Integer)
      @ Base intfuncs.jl:1145
  
  Possible fix, define
    binomial(::Num, ::Integer)

@shashi is there a reason why it's missing that dispatch?

[isaacsas]

This seems to fix the issue for me. The problem is several-fold. First, [Real,Integer] is never actually used by Symbolics in the macro (instead the types of the arguments are used if asserted, and if not Real is used). Even if it was used, however, it wouldn't help with the issue we have as we need a dispatch that allows the second input to be a BasicSymbolic{Real} (even though a user will pass an integer via the parameter map). This is what was previously defined via

@register_symbolic Base.binomial(n, k)::Int

Then there is the issue that we'd basically like to just say

@register_symbolic Base.binomial(n, k)::Int true
@register_symbolic Base.binomial(n, k::Int)::Int false

to get all the definitions, but this leads to overwriting of previous definitions involving Nums and such.

So the best solution I could come up with is to manually take the expressions from the second call to @register_symbolic and manually insert the non-redundant method definitions as I've now included.

[isaacsas]

It would be better if the macro could check what methods are already defined, and only output the new subset of method definitions from the set it generates.

[isaacsas]

Not sure why MTK tests are failing. binomial is not used anywhere in MTK from what I can see.