    |\^/|     Maple 14 (X86 64 LINUX)
._|\|   |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2010
 \  MAPLE  /  All rights reserved. Maple is a trademark of
 <____ ____>  Waterloo Maple Inc.
      |       Type ? for help.
#CheckSolutions.maple
#
#    File to check the reality of the numerically computed solutions
# to Dietmaier's Stewart platform.
> interface(quiet=true):
[alphaCertified, defaultSettings, loadOutput, printPoints,

    printPolynomialSystem, printSettings]


  alphaCertified v1.0.0 (October 27, 2010)
  Jonathan D. Hauenstein and Frank Sottile
         GMP v4.3.2 & MPFR v2.4.2


Analyzing 40 points using exact arithmetic.

Isolating 40 approximate solutions.

Classifying 40 distinct approximate solutions.

Rational certification results:

Number of points tested:           40
Certified approximate solutions:   40
Certified distinct solutions:      40
Certified real distinct solutions: 40

------------------------------------------------------------------------------------------------------------
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 solutions.
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.
------------------------------------------------------------------------------------------------------------
                                             -5                 -10
PointsData := Record(alpha = [0.5258978800 10  , 0.3649931080 10   ,

                   -11                 -11                 -11
    0.5421624043 10   , 0.4048685756 10   , 0.7065166602 10   ,

                   -12                 -9                 -11
    0.8367819211 10   , 0.1066599415 10  , 0.7443145312 10   ,

                   -9                 -12                 -6
    0.6397800316 10  , 0.5850923874 10   , 0.8609237651 10  ,

                   -11                 -9                 -11
    0.7885165295 10   , 0.6155035701 10  , 0.3742114769 10   ,

                   -10                 -12                 -9
    0.1246251725 10   , 0.5163602765 10   , 0.4326708875 10  ,

                   -10                 -9                 -5
    0.1912185102 10   , 0.2655578455 10  , 0.2757058278 10  ,

                   -11                 -11                 -5
    0.3022332451 10   , 0.1127451352 10   , 0.9027850057 10  ,

                   -9                 -12                 -9
    0.2964084769 10  , 0.5836676135 10   , 0.3285472762 10  ,

                   -10                 -7                 -9
    0.2139198819 10   , 0.6284863431 10  , 0.1980935565 10  ,

                   -11                 -9                 -7                 -9
    0.6268962432 10   , 0.1040308680 10  , 0.1248251817 10  , 0.1234516271 10  ,

                                     -9                 -11                 -10
    0.00001707147361, 0.1170847000 10  , 0.3999903873 10   , 0.3490402160 10   ,

                   -10                 -11                 -10
    0.1525087975 10   , 0.1945710874 10   , 0.1912787687 10   ], beta = [

                   -11                 -14                 -14
    0.3906470506 10   , 0.5291259560 10   , 0.2092047657 10   ,

                   -14                 -14                 -15
    0.1317577184 10   , 0.3799509939 10   , 0.8141931397 10   ,

                   -13                 -14                 -13
    0.1337242116 10   , 0.4436000915 10   , 0.4663122441 10   ,

                   -15                 -11                 -14
    0.8720975726 10   , 0.1418502537 10   , 0.2558459364 10   ,

                   -13                 -14                 -14
    0.2928066066 10   , 0.1065991858 10   , 0.6638453518 10   ,

                   -15                 -13                 -14
    0.8363541226 10   , 0.1948572228 10   , 0.3941329629 10   ,

                   -13                 -12                 -14
    0.1573121084 10   , 0.8576026169 10   , 0.2538194127 10   ,

                   -14                 -11                 -13
    0.1242453508 10   , 0.2323996011 10   , 0.2638830713 10   ,

                   -14                 -13                 -14
    0.1154841991 10   , 0.3990264937 10   , 0.4056411062 10   ,

                   -12                 -13                 -14
    0.5125580653 10   , 0.3078326850 10   , 0.4791878421 10   ,

                   -13                 -12                 -14
    0.1179320180 10   , 0.1026356888 10   , 0.8213910678 10   ,

                   -11                 -13                 -14
    0.7119205435 10   , 0.1242024646 10   , 0.1435820814 10   ,

                   -14                 -14                 -14
    0.7657488143 10   , 0.7353945789 10   , 0.1481187668 10   ,

                   -14                           7
    0.6022966054 10   ], gamma = [0.1346222579 10 , 6898.038242, 2591.539454,

    3072.826249, 1859.494175, 1027.743763, 7976.112945, 1677.895351,

    13719.99212, 670.9024377, 606924.3744, 3081.997474, 21020.82249,

    3510.453424, 1877.322364, 617.3943101, 22204.50858, 4851.624405,

                                7                                           7
    16880.95394, 0.3214843592 10 , 1190.741251, 907.4394691, 0.3884623732 10 ,

    11232.56886, 505.4090674, 8233.720852, 5273.624361, 122617.5893,

    6435.104723, 1308.247389, 8821.257347, 121619.6658, 15029.57994,

                   7
    0.2397946479 10 , 9426.922439, 2785.795995, 4558.155487, 2073.836303,

    1313.615361, 3175.823455], refinedPts = [[

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    isDistinctSoln = %1, isRealSoln = %1)

%1 := ["Yes", "Yes", "Yes", "Yes", "Yes", "Yes", "Yes", "Yes", "Yes", "Yes",

    "Yes", "Yes", "Yes", "Yes", "Yes", "Yes", "Yes", "Yes", "Yes", "Yes", "Yes",

    "Yes", "Yes", "Yes", "Yes", "Yes", "Yes", "Yes", "Yes", "Yes", "Yes", "Yes",

    "Yes", "Yes", "Yes", "Yes", "Yes", "Yes", "Yes", "Yes"]

