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potentialLowerBound -- the potential which is equal to the minimal number of new points guaranteed to be discovered

Description

This is an option for the Potential option for monodromySolve when we use selectBestEdgeAndDirection option to select edge and direction. This option observes discovered and undiscovered points first, and then follows the homotopy which has the minimal number of new points guaranteed to be found.

i1 : R = CC[a,b,c,d][x,y];
 
i2 : polys = polySystem {a*x+b*y^2,c*x*y+d};
 
i3 : (V, npaths) = monodromySolve(polys,SelectEdgeAndDirection=>selectBestEdgeAndDirection, Potential=>potentialLowerBound)

o3 = (HomotopyNode{...7...}, 3)

o3 : Sequence
 
i4 : G = V.Graph;
 
i5 : apply(toList G.Edges,e->e.Potential12)--potentials for all edges of a given direction

o5 = {0, 0, 0, 0}

o5 : List

See also

For the programmer

The object potentialLowerBound is a function closure.