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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 with its quadratic polar curve.

i1 : setRandomSeed 0;
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 : sparseMonodromySolve polySystem {F,P,random(1,R)-1}

o5 = {{.212986+.505809*ii, -.0640254-.418811*ii, .174869+.144954*ii},
     ------------------------------------------------------------------------
     {.040931+.735463*ii, -.751621+.636639*ii, -.809224+.075569*ii},
     ------------------------------------------------------------------------
     {.453473+.301343*ii, -1.01938-.509842*ii, -.592697-.68244*ii},
     ------------------------------------------------------------------------
     {-.147508-.127555*ii, -.071535-.796132*ii, .39264+.652917*ii},
     ------------------------------------------------------------------------
     {-1.08883+.94758*ii, -.222671+1.03031*ii, .185791+1.24332*ii},
     ------------------------------------------------------------------------
     {.449377+.392627*ii, .105165-.142662*ii, -.21861+.38705*ii}}

o5 : List

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

Ways to use sparseMonodromySolve :