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Bertini :: bertiniRefineSols

bertiniRefineSols -- sharpen solutions to a prescribed number of digits

Synopsis

Description

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)

Caveat

bertiniRefineSols will only refine non-singular solutions and does not currently work for homogeneous systems.

Ways to use bertiniRefineSols :