Fix stale docstring examples; make power curvature follow the rational approximation - #3527

Description

Five docstrings shipped >>> examples that no longer ran. Fixing the last of them
surfaced a real behaviour bug in Power, which is also fixed here.

Docstring fixes

• cvxpy/utilities/einsum_utilities.py — the vendored NumPy helpers were renamed to
  drop their leading underscore, but the examples still called _find_contraction,
  _optimal_path, _greedy_path and _parse_einsum_input, so every one raised
  NameError. They were also nondeterministic by construction: set repr ordering and the
  generated einsum index symbols both vary between processes, and the # may vary marker
  is a NumPy refguide-check convention that plain doctest does not honour. They now
  assert sorted and structural output instead.
• cvxpy/constraints/constraint.py — Constraint.set_label had no
  import cvxpy as cp, so all four examples raised NameError. The variable is now named
  so its repr does not depend on the global variable counter.
• cvxpy/atoms/geo_mean.py — zero-weight terms are dropped from w, so the expected
  output no longer lists the 0.
• cvxpy/reductions/dgp2dcp/dgp2dcp.py — variables were defined as x1..x3 but used
  as x_1..x_3; cvxpy.reductions was referenced with only cp imported; and three
  calls had no expected output.

Behaviour fix in Power

The Power docstring states that domain, sign, monotonicity and curvature are determined
by the rational approximation p_used, not the input exponent. is_incr/is_decr
already did this, but is_atom_convex, is_atom_concave and sign_from_args still read
self.p.value. So two exponents that reduce to the same p_used were classified
differently:

                  before                after
power(x, 1)       AFFINE, UNKNOWN       AFFINE, UNKNOWN
power(x, 1.0001)  CONVEX, NONNEGATIVE   AFFINE, UNKNOWN
power(x, 1.001)   CONVEX, NONNEGATIVE   CONVEX, NONNEGATIVE

power(x, 1.0001) has p_used == 1 — mathematically identical to power(x, 1) after
approximation — yet was treated as convex with an implicit x >= 0. Those three methods
now consult p_used, following the pattern already established by is_incr/is_decr.
Parametrized exponents are unaffected: p_used is None keeps the previous fallback.

Note this is a semantic change to DCP curvature analysis and deserves a careful look,
even though the suite is green.

Issue link (if applicable): n/a

Type of change

• New feature (backwards compatible)
• New feature (breaking API changes)
• Bug fix
• Other (Documentation, CI, ...)

Contribution checklist

• Add our license to new files.
• Check that your code adheres to our coding style.
• Write unittests.
• Run the unittests and check that they're passing.
• Run the benchmarks to make sure your change doesn't introduce a regression.

Checklist notes, for transparency:

• Add our license to new files — no new files are added, so this does not apply.
• Write unittests — test_power_curvature_follows_rational_approximation in
  cvxpy/tests/test_atoms.py covers the curvature change. It was verified to fail against
  the previous behaviour (AssertionError: 'CONVEX' != 'AFFINE') and pass after. The
  docstring fixes are covered by the restored doctests themselves.
• Run the unittests — 2670 passed, 879 skipped, 0 failed locally. The 879 skips are
  solver-gated: only CLARABEL, SCS, SCIPY, HIGHS and OSQP were installed, so the
  commercial-solver paths through power were not exercised here and rely on CI.
• Run the benchmarks — not run. Left unchecked deliberately.

Also verified: pyright reports 0 errors, and all pre-commit hooks pass.

🤖 Generated with Claude Code