areEqual -- determine if solutions are equal

Synopsis

• Usage:

  b = areEqual(x,y)

• Inputs:
  • x, a solution or a list of solutions
  • y, a solution or a list of solutions
• Optional inputs:
  • Projective => ..., default value false, if true then solutions are considered as representatives of points in the projective space
  • Tolerance => ..., default value .000001, the tolerance of a numerical computation
• Outputs:
  • b, tells if x and y are approximately equal

Description

The inputs can be complex numbers, points, or lists of points (presented as points or lists of coordinates). The function returns false if the distance between x and y exceeds Tolerance and true, otherwise.

If Projective=>true then 1-\cos\alpha is compared with the Tolerance, where \alpha is the angle between x and y.

i1 : areEqual({{-1,1e-7},{1e-7*ii,-1}}, {{-1, 0}, {0, -1}})

o1 = true

i2 : areEqual({3*ii,2*ii,1+ii}, {-6,-4,-2+2*ii}, Projective=>true)  

o2 = false

For two points A and Bcalling A == Bis equivalent to areEqual(A,B), however, there is no way to specify the optional parameter.

i3 : A = point {{-1,1e-7}, {1e-7*ii,-1}}

o3 = A

o3 : Point

i4 : B = point {{-1,0}, {0, -1}}

o4 = B

o4 : Point

i5 : A == B

o5 = true

See also

• solveSystem -- solve a system of polynomial equations
• track -- track a linear segment homotopy given start and target system
• sortSolutions -- sort the list of solutions