This method takes the list l of solutions of F and sharpens them to d digits using the sharpening module of Bertini.
i1 : R = CC[x,y]; |
i2 : F = {x^2-2,y^2-2}; |
i3 : sols = bertiniZeroDimSolve (F) o3 = {{1.41421, 1.41421}, {1.41421, -1.41421}, {-1.41421, 1.41421}, ------------------------------------------------------------------------ {-1.41421, -1.41421}} o3 : List |
i4 : S = bertiniRefineSols (100, F, sols) o4 = {{-1.41421, -1.41421}, {-1.41421, 1.41421}, {1.41421, -1.41421}, ------------------------------------------------------------------------ {1.41421, 1.41421}} o4 : List |
i5 : coords = coordinates S_0 o5 = {-1.41421, -1.41421} o5 : List |
i6 : coords_0 o6 = -1.414213562373095048801688724209698078569671875376948073176679737990732 478462107038850387534327641573+ 1.8146687832147731751154550352869464319934183860080812970989536078368497 59907524219475307096655011488e-316*ii o6 : CC (of precision 333) |
bertiniRefineSols will only refine non-singular solutions and does not currently work for homogeneous systems.