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) ~/bertini 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) Temporary directory for input and output files:/var/folders/j_/gx42s4z576z_vj47_ym0j5xm0000gn/T/M2-74635-0/1 The version of Bertini you have installed on your computer was used for this run. Bertini is under ongoing development by D. Bates, J. Hauenstein, A. Sommese, and C. Wampler. 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+ 3.6293375664295463502309100705738928639868367720161625941979072156736995 19815048438950614193310022977e-316*ii o6 : CC (of precision 333) |
bertiniRefineSols will only refine non-singular solutions and does not currently work for homogeneous systems.