Remove redundant _parse_symbol methods

[fingolfin]

Also replace some uses of gens by symbols, and exploit that graded_polynomial_ring can take multiple symbol lists to simplify some of the code.

[thofma]

There is still a _parse_symbol method for this

[fingolfin]

Yes, though it is now only is used in a single file, Main.jl.

[codecov]

Codecov Report

Attention: Patch coverage is 97.29730% with 1 line in your changes missing coverage. Please review.

Project coverage is 84.42%. Comparing base (dac55d7) to head (1037bcb).
Report is 24 commits behind head on master.

Files with missing lines	Patch %	Lines
experimental/IntersectionTheory/src/blowup.jl	80.00%	1 Missing ⚠️

Additional details and impacted files

@@           Coverage Diff           @@
##           master    #4535   +/-   ##
=======================================
  Coverage   84.42%   84.42%           
=======================================
  Files         672      672           
  Lines       89164    89158    -6     
=======================================
- Hits        75273    75269    -4     
+ Misses      13891    13889    -2     

Files with missing lines	Coverage Δ
experimental/IntersectionTheory/src/Bott.jl	74.01% <100.00%> (ø)
experimental/IntersectionTheory/src/Main.jl	93.29% <100.00%> (+0.02%)	⬆️
experimental/IntersectionTheory/src/Misc.jl	96.87% <ø> (+10.76%)	⬆️
experimental/IntersectionTheory/src/blowup.jl	98.79% <80.00%> (-0.06%)	⬇️

... and 1 file with indirect coverage changes

[lgoettgens]

Suggested change

	R = graded_polynomial_ring(base, syms, vcat([1:r for r in ranks]...))[1]
	R = graded_polynomial_ring(base, syms, reduce(vcat, (1:r for r in ranks)))[1]

[fingolfin]

Fine by me, but the pattern occurs several times in this file, so perhaps they should be changed all at once.

[fingolfin]

Just to say:

julia> ranks = [3,1,5];

julia> @b vcat([1:r for r in $ranks]...)
92.871 ns (7 allocs: 336 bytes)

julia> @b reduce(vcat, (1:r for r in $ranks))
58.886 ns (7 allocs: 320 bytes)

julia> @b reduce(vcat, [1:r for r in $ranks])
48.961 ns (6 allocs: 320 bytes)

julia> @b reduce(vcat, 1:r for r in $ranks)
60.154 ns (7 allocs: 320 bytes)

So the version which does reduce over a vector is best here. None of these is great -- it could be done with a single allocation:

function parse_ranks(ranks)
  res = Vector{Int}(undef, sum(ranks))
  i = 1
  for r in ranks
    for j in 1:r
      res[i] = j
      i += 1
    end
  end
  return res
end

function parse_ranks2(ranks)
  res = sizehint!(Int[], sum(ranks))
  for r in ranks
    append!(res, 1:r)
  end
  return res
end

gives

julia> @b parse_ranks($ranks)
20.239 ns (2 allocs: 128 bytes)

julia> @b parse_ranks2($ranks)
36.541 ns (2 allocs: 128 bytes)

Of course none of this really matters, you just nerd-sniped me successfully ;-).

[lgoettgens]

The splatting version has the additional overhead of compiling a new method specialization every time you call it with a different number of arguments. This probably won't be caught by your chairmark

[fingolfin]

Sure, but I am not using the splatting version, I am using reduce with a Vector which was best in the micro benchmarks.

[fingolfin]

OK to merge this? Or any concerns?