TropicalGeometry: new positive tropicalizations

[YueRen]

This is the final pull request from the Leipzig workshop, adding the capability of computing positive tropicalizations for linear and binomial ideals (required for example for Telek-Rose).

It is a draft for now, as it is contingent on #4061 being merged. (I don't think it makes a lot of sense if tropical_variety returns a list of TropicalVariety while positive_tropical_variety returns a single TropicalVariety)

[codecov]

Codecov Report

Attention: Patch coverage is 84.21053% with 3 lines in your changes missing coverage. Please review.

Project coverage is 84.55%. Comparing base (3e86180) to head (a5778ed).

Files with missing lines	Patch %	Lines
src/TropicalGeometry/positive_variety.jl	84.21%	3 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #4447      +/-   ##
==========================================
- Coverage   84.55%   84.55%   -0.01%     
==========================================
  Files         672      673       +1     
  Lines       88880    88899      +19     
==========================================
+ Hits        75152    75167      +15     
- Misses      13728    13732       +4     

Files with missing lines	Coverage Δ
src/TropicalGeometry/positive_variety.jl	84.21% <84.21%> (ø)

... and 3 files with indirect coverage changes

[YueRen]

@MateTelek Would you be able to review this pull request for me?

[lgoettgens]

Suggested change

	Return the positive tropical variety of `I` as a `PolyhedralComplex` as per the definition in [SW05](@cite). Assumes that `I` is generated either by binomials or by linear polynomials and that `I` is defined either over
	Return the positive tropical variety of `I` as a `PolyhedralComplex` as per the definition in [SW05](@cite).
	Assumes that `I` is generated either by binomials or by linear polynomials and that `I` is defined either over

Break an overly long line. And good docstring style adds a paragraph break after the first sentence

[lgoettgens]

Have you checked by locally building the docs that this produces what you expect? From the first glance, I think that this may do weird linebreaks. Maybe one of the following is suitable for your case here?

Suggested change

	(a) the rational numbers and that `nu` encodes the trivial valuation,
	(b) the rational function field over the rational numbers and that `nu` encodes the t-adic valuation.
	1. the rational numbers and that `nu` encodes the trivial valuation,
	2. the rational function field over the rational numbers and that `nu` encodes the t-adic valuation.

Suggested change

	(a) the rational numbers and that `nu` encodes the trivial valuation,
	(b) the rational function field over the rational numbers and that `nu` encodes the t-adic valuation.
	- the rational numbers and that `nu` encodes the trivial valuation,
	- the rational function field over the rational numbers and that `nu` encodes the t-adic valuation.

[lgoettgens]

Suggested change

	if all(isequal(2),length.(gens(I)))
	if all(is_binomial, gens(I))

[lgoettgens]

Suggested change

	title = {The {{Tropical Totally Positive Grassmannian}}},
	title = {The Tropical Totally Positive Grassmannian},

our bibtex parser does not work well with braces inside of fields. It will keep the casing even without them (contrary to latex)

[lgoettgens]

It is a draft for now, as it is contingent on #4061 being merged. (I don't think it makes a lot of sense if tropical_variety returns a list of TropicalVariety while positive_tropical_variety returns a single TropicalVariety)

Is this comment obsolete or how did you proceed? I am asking since #4061 is not merged.