This is a type of hashtable storing the output of a pseudo-witness set computation using monodromy, with the following keys:
The following example demonstrates the output for the 3-uple embedding of P1 into P3, whose image is the twisted cubic:
i1 : R = CC[s,t]; |
i2 : W = numericalImageDegree(basis(3,R), ideal 0_R, Verbose => false); -- warning: experimental computation over inexact field begun -- results not reliable (one warning given per session) |
i3 : peek W o3 = PseudoWitnessSet{imageDegree => 3 } imageSlice => | (.025888+.714827i)y_1+(.461944+.775187i)y_2+(.074184+.808694i)y_3+(.127435+.254482i)y_4+1.84897+1.0891i | | (.89189+.231053i)y_1+(.909047+.314897i)y_2+(.362835+.706096i)y_3+(.741046+.108386i)y_4+2.04097-.925371i | isCompletePseudoWitnessSet => true sourceEquations => ideal 0 sourceSlice => 0 traceTest => 1.96932e-12 witnessPointPairs => {({.216572+.858035*ii, 1.25142+.497798*ii}, {-.468178-.510971*ii, -1.04763+.121949*ii, -.783536+1.40092*ii, 1.02945+2.21536*ii})} {({.892712+.673395*ii, .29398+.632944*ii}, {-.502996+1.3046*ii, -.660011+.57085*ii, -.531085+.120643*ii, -.327914-.0894633*ii}) } {({.023866-1.48479*ii, .280787+1.06704*ii}, {-.157831+3.27084*ii, -.543241-2.37168*ii, .864424+1.58777*ii, -.936945-.962513*ii})} 3 2 2 3 map => {s , s t, s*t , t } |
[1] J. D. Hauenstein and A. J. Sommese, Witness sets of projections. Appl. Math. Comput. 217(7) (2010), 3349-3354.
The object PseudoWitnessSet is a type, with ancestor classes HashTable < Thing.