toFunBilinear — Mathlib

English

Same as above: for coprime polynomials a,b, W(a,b) = 0 iff derivatives are zero.

Русский

То же: для взаимно простых многочленов W(a,b) = 0 тогда и только тогда, когда производные нулевые.

LaTeX

$$$$ \\text{IsCoprime}(a,b) \\Rightarrow (\\mathrm{wronskian}(a,b) = 0 \\iff \\mathrm{derivative}(a) = 0 \\land \\mathrm{derivative}(b) = 0). $$$$

Lean4

/-- (Implementation detail).
The function underlying `A ⊗[R] R[X] →ₐ[R] A[X]`,
as a bilinear function of two arguments.
-/
def toFunBilinear : A →ₗ[A] R[X] →ₗ[R] A[X] :=
  LinearMap.toSpanSingleton A _ (aeval (Polynomial.X : A[X])).toLinearMap

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