6.10.8  Barycenter of complex numbers: barycenter

The barycenter, or center of mass, of a set of points A₁, A₂,…,A_n with masses α₁,α₂,…,α_n is

This formula makes sense even if the α_j are not positive real numbers, and is still called the barycenter of the weighted points.

The barycenter command computes the barycenter of a set of weighted points.

• barycenter takes an unspecified number of arguments:
  each argument is a list l_j=[A_j,α_j] containing a point A_j (or the affix of a point) and a weight α_j for the point. The sum of the weights needs to be non-zero.
  These lists can also be given as two columns of a matrix.
• barycenter(l₁,l₂,…,l_n) returns the barycenter of the points A_j weighted by the real coefficients α_j. If ∑α_j = 0, barycenter returns an error.

Warning.
The barycenter command returns a point, not a complex number. To have a complex number in the output, the input must be affix(barycenter(l₁,l₂)) (see Section 13.13.1).

Example.
Input:

or:

Output: