Is there a way to put a subscript / latex with sklearn's set_output API ?

[VincentRouvreau]

The original discussion

Originally posted by @DavidLapous in #1202 (comment)

Otherwise I think we should do this, even though it's a bit ugly

Is there a way to put a subscript / latex with sklearn's set_output API ? Otherwise I think we should do this, even though it's a bit ugly

        return [f"H_{i}" for i in self.dim_list_]

Answer from @mglisse
https://stackoverflow.com/a/24392215/1918193 shows a way to turn 421 into ₄₂₁. This may be fine for printing, but if the user needs to recreate such a string to ask for "H₁₂", that's going to be way less convenient than "H12".
(since we technically compute cohomology, should it be "H^{i}"? )

_Answer from @DavidLapous
If the user wants to change the default option, that's his problem, non ? + a little bit of llm, and he'll find the solution soon enough. I think "H₁" looks better for the default option.

Answer from @mglisse
I think the question is what those names are used for. From your comments, they seem to be there for pretty printing. My comment is because I thought they were mostly used as indexes, so you would write result["H2"] to extract that part of the result (or result["H"+str(i)] if this is in a loop). In that case, using obscure unicode characters makes the user's life harder.
I don't have any experience with pandas, so let me ask @martinroyer what he thinks.

Answer from @martinroyer
@mglisse I think you are spot on, this allows to compute things like this:

where one potentially wants to access columns by key f"H{i}", and I'd say it is good as it is for now.

IRL

rips = RipsPersistence(homology_dimensions=[0, 2], n_jobs=-2)
diags_pandas = rips.set_output(transform="pandas").fit_transform(point_clouds)

print(diags_pandas.columns[0], diags_pandas.columns[1])
# "H0 H2"  or  "H₀ H₂"  or  "H_0 H_2"  or  "0 2"  -  What would be the best ?

# 1. "H0 H2" is the state of the art in GUDHI

# 2. "H₀ H₂" is nice but:
diags_pandas["H₀"]  # requires an extra method to transform H0 to H₀

# 3. "H_0 H_2" would be ok for LaTeX purpose but doesn't add that much

# 4. "0 2" TBC, but I think pandas allows integer as column name type
diags_pandas[0]  # would also be a nice way to play with data