[Neclow]

Summary

Moves the notebooks into a docs/notebooks/ section and splits the single demo notebook by topic. Related to #170.

The "Notebooks" section of the docs now contains:

1. Getting started: sampling, Newick conversion, the matrix format, other tree formats (edges, ancestry, pairs), saving/loading files, and the built-in datasets
2. Tree operations: common ancestors and node depths, removing/adding leaves, rerooting, Queue Shuffle, Newick and taxon label utilities
3. Statistics: cophenetic distances, covariance/precision matrices, incidence matrices, balance indices, Robinson-Foulds distance
4. Optimisation: the former demo_opt.ipynb

A core concepts notebook (how the vector encodes a tree) is planned as a follow-up, between getting started and tree operations.

Notebook changes

• Content from demo.ipynb is kept, and the notebooks now also cover reroot, queue_shuffle, remove_branch_lengths, cov, precision, incidence, the balance indices (with a link to Khurana et al. 2024) and load_alignment
• Fixes: the get_pairs description (it returns pairs, not triplets), a cell that printed the wrong variable, list_models → list_methods, the "column-wise" argmax (it is row-wise), and the GradME score description
• The notebooks no longer os.chdir into py-phylo2vec or call the private _phylo2vec_core; the optimisation notebook downloads its data to a temporary directory instead of the package folder
• All notebooks were re-run, so every cell has up-to-date outputs. The optimisation notebook previously showed a FutureWarning and a local path in its output

Code fixes found while re-running the optimisation notebook

• HillClimbing used the deprecated reorder_v; it now calls queue_shuffle directly (results are identical, checked on 1,000 random trees)
• GradME.fit crashed at the end with recent jax (0.12), which requires a boolean where mask in jax.nn.softmax

Other changes

• .gitignore: the experimental notebooks/ rule is anchored to the root, as it also ignored docs/notebooks/
• CI: the notebook job executes getting started, tree operations and statistics. Optimisation is skipped, as it needs the [opt] extras, RAxML-NG and R
• README.md and installation.md point to the new optimisation page

The notebooks are moved unchanged in a separate commit, so that git records the renames. Merging with a merge commit rather than squashing keeps that history (git log --follow) for both notebooks.