mongePointWeightsWithCircumcenter

English

The weight function mongePointWeightsWithCircumcenter assigns to each vertex 1/(n+1) and to the circumcenter -2/(n+1).

Русский

Вектор весов mongePointWeightsWithCircumcenter задаёт каждому вершине значение 1/(n+1) и центр описания — -2/(n+1).

LaTeX

$$$$ \text{mongePointWeightsWithCircumcenter}(n)\bigl(pointIndex\_i\bigr) = \frac{1}{n+1}, \quad \text{mongePointWeightsWithCircumcenter}(n)\bigl(circumcenterIndex\bigr) = -\frac{2}{n+1}. $$$$

Lean4

/-- The weights for the Monge point of an (n+2)-simplex, in terms of
`pointsWithCircumcenter`. -/
def mongePointWeightsWithCircumcenter (n : ℕ) : PointsWithCircumcenterIndex (n + 2) → ℝ
  | pointIndex _ => ((n + 1 : ℕ) : ℝ)⁻¹
  | circumcenterIndex => -2 / ((n + 1 : ℕ) : ℝ)

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