areEqual -- determine if solutions are equal

Synopsis

• Usage:

  b = areEqual(x,y)

• Inputs:

  • x, a solution or list of solutions
  • y, a solution or list of solutions
• Optional inputs:

  • Projective => default value false, if true, then solutions are considered as representatives of points in the projective space
  • Tolerance => ..., -- specifies the tolerance of a numerical computation
• Outputs:

  • b, a Boolean value, a Boolean value: whether x and y are approximately equal

Description

i1 : R = CC[x,y];

i2 : s = solveSystem {x^2+y^2-1, x*y}

o2 = {{-1, 1.04882e-15+7.59064e-16*ii}, {1, -1.04882e-15-7.59064e-16*ii},
     ------------------------------------------------------------------------
     {-6.15976e-16+1.67394e-16*ii, 1}, {6.15976e-16-1.67394e-16*ii, -1}}

o2 : List

i3 : areEqual(sortSolutions s / coordinates, {{-1, 0}, {0, -1}, {0, 1}, {1, 0}})

o3 = true