FDerivPolarCoordRealSymm — Mathlib

English

The derivative of polarCoordReal.symm is given by the pair of derivatives: the first coordinate is the identity, the second component is the derivative of the polar coordinate on complex places composed with the second projection.

Русский

Производная полярной координаты симм равна паре производных: первая координата — тождество, вторая — производная полярной координаты на комплексных местах.

LaTeX

$$$FDerivPolarCoordRealSymm : realMixedSpace(K) \\to \\; realMixedSpace(K) \\\\; FDerivPolarCoordRealSymm = (fst) \\; \\times \\; (fderivPolarCoord\\_Symm \\circ snd)$$$

Lean4

/-- The derivative of `polarCoordReal.symm`, see `hasFDerivAt_polarCoordReal_symm`.
-/
def FDerivPolarCoordRealSymm : realMixedSpace K → realMixedSpace K →L[ℝ] realMixedSpace K := fun x ↦
  (fst ℝ _ _).prod <| (fderivPiPolarCoordSymm x.2).comp (snd ℝ _ _)

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