alphaCertified v1.0.0 (September 23, 2010) Jonathan D. Hauenstein and Frank Sottile GMP v4.3.2 & MPFR v2.4.2 Analyzing 8652 points using 256-bit floating point arithmetic. Isolating 8652 approximate solutions. Classifying 8652 distinct approximate solutions. Floating point (256 bits) certification results: Number of points tested: 8652 Certified approximate solutions: 8652 Certified distinct solutions: 8652 Certified real distinct solutions: 384 ------------------------------------------------------------------------------------------------------------ The following files have been created: approxSolns: A list of points that are certified approximate solutions. constantValues: A list of the values of alpha, beta, and gamma for the points. distinctSolns: A list of points that correspond to distinct solutuions. isApproxSoln: A list which describes if the ith point is an approximate solution. isDistinctSoln: A list which describes if the ith point is listed in 'distinctSolns'. isRealSoln: A list which describes if the ith point corresponds to a real solution. nonrealDistinctSolns: A list of points that correspond to distinct nonreal solutions. realDistinctSolns: A list of points that correspond to distinct real solutions. redundantSolns: A list of points that correspond to the same solution as one in 'distinctSolns'. refinedPoints: A list of points that are the best internally computed approximation of each solution. summary: A human-readable summary for each point - main output file. unknownPoints: A list of points that which cannot be certified as approximate solutions. ------------------------------------------------------------------------------------------------------------