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Bertini input configuration -- a configuration option for a Bertini input file

Refer to Appendix E of SIAM Bertini book for full details and list of options.

MPType: Type of precision (0=double, 1=fixed higher, 2=adaptive).

PRECISION: Precision, in bits, when used MPType=1. Precision is capitalized here to not conflict with Precision.

ODEPredictor: Choice of predictor method (9 choices).

TrackTolBeforeEG: Before endgame zone, Newton error must be less than this for success.

TrackTolDuringEG: Same as previous, but during endgame.

FinalTol: Path is deemed successful if final two endpoint approximations agree to FinalTol.

MaxNorm: If SecurityLevel=0, path is truncated if two consecutive endpoint approximations exceed this value.

MinStepSizeBeforeEG: Path is truncated if stepsize drops below this level before endgame.

MinStepSizeDuringEG: Same as previous, but during endgame.

ImagThreshold: Endpoint deemed real if infinity norm is smaller than this.

CoeffBound: Useful only if MPType=2, bound on sum of coefficients of each polynomial.

DegreeBound: Useful only if MPType=2, bound on degree of each polynomial.

CondNumThreshold: Endpoint is deemed singular if multiple paths lead to it or condition number exceeds this.

RandomSeed: Useful to repeat runs with the same random numbers.

SingValZeroTol: Singular value is considered 0 if less than this value, when using fixed precision.

EndGameNum: Choice of endgame (1=power series, 2=Cauchy, 3=trackback Cauchy).

UseRegeneration: 1 to use regeneration for a zero-dimensional run.

SecurityLevel: 1 to avoid truncation of possibly-infinite paths.

ScreenOut: Level of output to the screen.

OutputLevel: Level of output to files.

StepsForIncrease: Number of consecutive Newton corrector successes before increase of stepsize.

MaxNewtonIts: Newton corrector step deemed failed if no convergence prior to this number of iterations.

MaxStepSize: Largest stepsize allowed.

MaxNumberSteps: Max number of steps for entire path. Path failure if number of steps exceeds this.

MaxCycleNum: Max cycle number considered during endgame.

RegenStartLevel: Level at which regeneration begins.

There are two recommended ways of using the optional arguments based on zero-dim solving and pos-dim solving.

(1) Specify individual parameters in a function call:

i1 : CC[x,y]; F = {x^2-1,y^2-1};
i3 : bertiniZeroDimSolve(F,BertiniInputConfiguration=>{RandomSeed=>0,TrackTolBeforeEG=>1e-6,FinalTol=>1e-100})

o3 = {{1, 1}, {1, -1}, {-1, 1}, {-1, -1}}

o3 : List

(2) Store your frequently used favorites in an OptionTable and pass it as the last argument in each function call:

i4 : opts = new OptionTable from {BertiniInputConfiguration=>{RandomSeed=>0,TrackTolBeforeEG=>1e-6,FinalTol=>1e-100}}

o4 = OptionTable{BertiniInputConfiguration => {RandomSeed => 0, TrackTolBeforeEG => .000001, FinalTol => 1e-100}}

o4 : OptionTable
i5 : G = {x^2+y^2-1};
i6 : bertiniPosDimSolve(G,opts)

o6 = a numerical variety with components in
     dim 1:  (dim=1,deg=2)

o6 : NumericalVariety