🎮 pybertini.endgame¶

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Notes¶

Auto-generated docs¶

Endgame-specific things – endgames, configs¶

Endgames allow the computation of singular endpoints.

Flavors¶

There are two basic flavors of endgame implemented:

Power Series, commonly written PS or PSEG
Cauchy

Both estimate the cycle number and use it to compute a root at a time which is never tracked to. PSEG uses Hermite interpolation and extrapolation, and Cauchy uses loops around the target time coupled with the Cauchy integral formula. Both continue until two successive approximations of the root match to a given tolerance (pybertini.endgame.config.Endgame.final_tolerance).

The implementations of the endgames go with a particular tracker, hence there are six provided endgame types. Choose the one that goes with your selected tracker type. Adaptive Multiple Precision is a good choice.

Implementation reference¶

AMP Endgames¶

AMPCauchyEG
AMPPSEG

Fixed Double Precision Endgames¶

FixedDoublePSEG
FixedDoublePSEG

Fixed Multiple Precision Endgames¶

FixedMultiplePSEG
FixedMultiplePSEG

🎮 pybertini.endgame.config¶

Configs for endgames