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MonodromySolver :: sparseMonodromySolve

sparseMonodromySolve -- an "out of the box" polynomial system solver

Synopsis

Description

Blackbox monodromy solver for a square polynomial system without parameters. The example below finds all six intersection of a generic cubic F with its quadratic polar curve P.

i1 : setRandomSeed 2020;
i2 : R=CC[x,y,z];
i3 : F=random(3,R);
-- warning: experimental computation over inexact field begun
--          results not reliable (one warning given per session)
i4 : P=sum apply(gens R,g->diff(g,F)*random CC);
i5 : PS = polySystem {F,P,random(1,R)-1};
i6 : sols = sparseMonodromySolve PS;
i7 : for i from 0 to 5 list norm evaluate(PS, sols#i)

o7 = {1.57009e-16, 4.44089e-16, 7.1089e-16, 5.55112e-16, 1.07783e-15,
     ------------------------------------------------------------------------
     6.28037e-16}

o7 : List

For systems with dense support such as the above, the total number of paths tracked is generally not optimal, though timings may be comparable.

Ways to use sparseMonodromySolve :

For the programmer

The object sparseMonodromySolve is a method function with options.