solutionsWithMultiplicity -- replaces clusters of approximately equal points by single points with multiplicity

Synopsis

• Usage:

  M = solutionsWithMultiplicity S

• Inputs:
  • S, points
• Optional inputs:
  • Tolerance => ..., default value .000001, the tolerance of a numerical computation
• Outputs:
  • M, points with a multiplicity field

Description

Clusters the points and outputs a list with one point p per cluster with p.Multiplicity equal to the size of the cluster. If the multiplicity is not 1, then p.SolutionStatus is set to Singular; otherwise, it is inherited from one of the points in the cluster.

Whether two points are approximately equal is decided by the function areEqual that depends on Tolerance.

i1 : a = point {{0,1}}

o1 = a

o1 : Point

i2 : b = point {{0.000000001,1+0.00000000001*ii}}

o2 = b

o2 : Point

i3 : c = point {{0.001*ii,1}}

o3 = c

o3 : Point

i4 : M = solutionsWithMultiplicity {a,b,c}

o4 = {a, c}

o4 : List

i5 : peek M

o5 = {Point{Coordinates => {0, 1}}, Point{Coordinates => {.001*ii, 1}}}
            Multiplicity => 2             Multiplicity => 1

Caveat