isCoordinateZero -- checks if coordinate has absolute value less than a given tolerance

Synopsis

• Usage:

  isCoordinateZero(sol,k,tol)

• Inputs:
  • sol, a point, solution to a polynomial system
  • k, an integer, index of coordinate
  • tol, a real number, tolerance on the absolute value of the k-th coordinate
• Outputs:
  • a Boolean value, true if the k-th coordinate of solution has absolute value less than tol, false otherwise

Description

i1 : R = CC[x,y];

i2 : f = { x^3*y^5 + y^2 + x^2*y, x*y + x^2 - 1};

i3 : fSols = solveSystem(f, randomSeed=>3);

i4 : fSols/print
{-1, 0}
{1, 0}
{-1.59272, .964857}
{.742585+.425943*ii, .270685-1.00715*ii}
{-.764107, -.544612}
{1.33076-.335184*ii, -.62414+.513163*ii}
{-.894935-.624334*ii, .143333+1.14868*ii}
{1.33076+.335184*ii, -.62414-.513163*ii}
{-.894935+.624334*ii, .143333-1.14868*ii}
{.742585-.425943*ii, .270685+1.00715*ii}

o4 = {, , , , , , , , , }

o4 : List

i5 : isCoordinateZero(fSols_0,1,1.0e-10)

o5 = true

See also

• refineSolutions -- refines solutions of a system by increasing working precision
• zeroFilter -- returns solutions with k-th coordinate less than the given tolerance
• nonZeroFilter -- returns solutions with coordinate larger than given tolerance