refineSolutions -- refines solutions of a system by increasing working precision

Synopsis

Usage:

newSols = refineSolutions(f,sols,dp)
Inputs:
- f, a list, a system of polynomials
- sols, a list, solutions of the system f, each of type AbstractPoint (from a previous calculation)
- dp, an integer, the number of decimal places in working precision
Optional inputs:
- Verbose => ..., default value false, option to specify whether additional output is wanted
Outputs:
- newSols, a list, the solutions sols of f refined to increased precision of dp decimal places
Consequences:
- writes a system to a temporary file,
- invokes the command phc -v (with option 3),
- stores phc output in a temporary file,
- parses and prints the refined solutions.

The user can specify the number of decimal places desired to refine solutions.

Let us compute a square root with a working precision of 64 decimal places:

i1 : R = CC[x,y]; S = {x^2 - 1/3, x*y - 1}; ourRoots = solveSystem(S);

i4 : r0 = ourRoots#0#Coordinates#1

o4 = 1.73205080756888

o4 : CC (of precision 53)

i5 : newRoots = refineSolutions(S,ourRoots,64)

o5 = {{.57735, 1.73205}, {-.57735, -1.73205}}

o5 : List

i6 : newRoots#0 -- recall that solutions are of type Point

o6 = {.57735, 1.73205}

o6 : Point

i7 : r1 = newRoots#0#Coordinates#1

o7 = 1.73205080756887735414922460641658082304678611432812598193257967

o7 : CC (of precision 213)