# bertiniRefineSols -- sharpen solutions to a prescribed number of digits

## Synopsis

• Usage:
S = bertiniRefineSols(d, F, l)
• Inputs:
• d, an integer, an integer specifying the number of digits of precision
• F, a list, a list of polynomials (system need not be square)
• l, a list, a list of points to be sharpened
• Optional inputs:
• BertiniInputConfiguration (missing documentation) => ..., default value {},
• IsProjective => ..., default value -1, optional argument to specify whether to use homogeneous coordinates
• Verbose => ..., default value false, Option to silence additional output
• Outputs:
• S, a list, a list of solutions of type Point

## 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) 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 = {[RF], [RF], [RF], [RF]} o4 : List i5 : coords = coordinates S_0 o5 = {-1.41421, -1.41421} o5 : List i6 : coords_0 o6 = -1.41421-1.11022e-16*ii o6 : CC (of precision 333)

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

## Ways to use bertiniRefineSols :

• "bertiniRefineSols(ZZ,List,List)"

## For the programmer

The object bertiniRefineSols is .