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PHCpack :: isCoordinateZero

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

Synopsis

Description

A solution has a zero k-th coordinate when the abs function evaluates to a number less than the given tolerance.

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

Good values for the tolerance are relative to the accuracy and the condition number of the solution. To improve the accuracy of a solution, apply refineSolutions with a higher working precision.

See also

Ways to use isCoordinateZero :