7.4.8 Barycenter of complex numbers
The barycenter,
or center of mass, of a set of points A1,
A2,…,An with masses
α1,α2,…,αn is
This formula makes sense even if the αj 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 arbitrary number of arguments:
each argument is a list lj=[Aj,αj] containing a point Aj (or the
affix of a point) and a weight αj 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,…,ln) returns the
barycenter of the points Aj weighted by the real coefficients
αj. If ∑αj=0, barycenter returns an
error.
Remark.
Note that the barycenter command returns a point, not an affix.
To output the point affix, you must input
affix(barycenter(l1,l2)) (see Section 26.12.1).
Example
| affix(barycenter([1+i,2],[1-i,1])) |
or:
| affix(barycenter([[1+i,2],[1-i,1]])) |