feat(Mathematics): the Cauchy–Riemann criterion for Wirtinger derivatives

[pariandrea]

Adds the Cauchy–Riemann characterisation of holomorphy for the Wirtinger operators: a complex-valued
function on a complex normed space is ℂ-differentiable exactly when it is real-differentiable and
its anti-holomorphic Wirtinger derivatives vanish, in directional and in coordinate form.

The key step is that an ℝ-linear map commuting with multiplication by i is ℂ-linear.
Mathlib has this only for maps out of ℂ (ContinuousLinearMap.complexOfReal, used for its
one-variable differentiableAt_complex_iff_differentiableAt_real); ComplexLinear.lean gives the
arbitrary-domain form, which a many-variable Cauchy–Riemann argument needs.

The real-differentiability conjunct cannot be dropped: fderiv is 0 off the differentiability
locus, so the vanishing condition alone holds vacuously for a nowhere-differentiable function.

Added

Physlib/Mathematics/ForMathlib/ComplexLinear.lean (new)

• LinearMap.map_smul_of_commutesI: an ℝ-linear map pulls a complex scalar out of any direction
  along which it commutes with i.
• LinearMap.commutesI_of_basis: an ℝ-linear map commuting with i on a finite ℂ-basis commutes
  with it on every vector.
• ContinuousLinearMap.complexOfCommutesI: a continuous ℝ-linear map commuting with i in every
  direction, as a →L[ℂ] map.
• ContinuousLinearMap.complexOfCommutesI_apply (simp): complexOfCommutesI L h v = L v.

Physlib/Mathematics/Calculus/Wirtinger/Basic.lean

• clinear_of_dWirtingerAntiDir_eq_zero: converse of dWirtingerAntiDir_eq_zero_of_clinear.
• differentiableAt_complex_iff_dWirtingerAntiDir_eq_zero: Cauchy–Riemann, directional form.
• The section overview's paragraph on the real/complex derivative bridge now cites this criterion.

Physlib/Mathematics/Calculus/Wirtinger/Coordinate.lean

• differentiableAt_complex_iff_dWirtingerAntiCoord_eq_zero: Cauchy–Riemann in coordinates on
  ι → ℂ, the form ∂̄_Ī W = 0 takes in physics.

Removed: none. Wirtinger/Basic.lean drops its import of Mathlib.Analysis.Complex.Basic, now
implied by ComplexLinear.

Reviewer map

1. ComplexLinear.lean: the scalar law, the basis lemma, the bundled map.
2. Wirtinger/Basic.lean: the converse lemma, then the Cauchy–Riemann section.
3. Wirtinger/Coordinate.lean: the coordinate corollary.

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[nateabr]

claim

[github-actions]

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