# numerical homotopy tracking options -- options for core functions of Numerical Algebraic Geometry

• [gamma]: (default gamma = 1). A parameter in the homotopy: H(t)=(1-t)^{tDegree} S + \gamma t^{tDegree} T.
• [tDegree]: (default tDegree = 1). A parameter in the homotopy: H(t)=(1-t)^{tDegree} S + \gamma t^{tDegree} T.
• [tStep]: (default tStep = .05). Initial step size.
• [tStepMin]: (default tStepMin = .000001). Minimal step size.
• [stepIncreaseFactor]: (default stepIncreaseFactor = 2). Determines how the step size is adjusted.
• [numberSuccessesBeforeIncrease]: (default numberSuccessesBeforeIncrease = 4). Determines how the step size is adjusted.
• [Predictor]: (default Predictor = RungeKutta4). A method to predict the next point on the homotopy path: choose between RungeKutta4, Tangent, Euler, Secant, Multistep, Certified. The option Certified provides certified tracking.
• [MultistepDegree]: (default MultistepDegree = 3). Degree of the Multistep predictor.
• [maxCorrSteps]: (default maxCorrSteps = 3). Max number of steps corrector takes before a failure is declared.
• [CorrectorTolerance]: (default CorrectorTolerance = .000001). Corrector succeeds if the relative error does not exceed this tolerance.
• [EndZoneFactor]: (default EndZoneFactor = .05). Determines the size of the "end zone", the interval at the end of the path where CorrectorTolerance is tighter.
• [InfinityThreshold]: (default InfinityThreshold = 1e9). Paths are truncated if the norm of the approximation exceeds the threshold.
• [Projectivize]: (default Projectivize = false). If true then the system is homogenized and the projective tracker is executed.
• [Normalize]: (default Normalize = false). Normalize the start and target systems w.r.t. the Bombieri-Weyl norm.
• [NoOutput]: (default NoOutput = false). If true, no output is produced (used by developers).
• [Iterations]: (default Iterations = 30). Number of refining iterations of Newton's method.
• [Bits]: (default Bits = infinity). Number of bits of precision.
• [ErrorTolerance]: (default ErrorTolerance = 1e-8). A bound on the desired estimated error.
• [ResidualTolerance]: (default ResidualTolerance = .0001). A bound on desired residual.
• [Precision]: (default Precision = 53). Precision of the floating-point numbers used in computation. If set to infinity(EXPERIMENTAL!) the precision in homotopy continuation adapts according to numerical conditioning. The default setting, DoublePrecision, forces fast arithmetic and linear algebra in standard precision. (Other settings invoke MPFR library.)