c_cpp/etc/calc/cscript/4dsphere.calc

   1 #!/usr/local/src/cmd/calc/calc -q -s -f
   2 /*
   3  * 4dsphere - determine if 6 points lie on the surface of a sphere in R^4
   4  *
   5  * usage:
   6  *      4dsphere x0 y0 z0 w0 x1 y1 z1 w1 ... x5 y5 z5 w5
   7  *
   8  *      x0 y0 z0 w0     point 0 in R^4
   9  *      x1 y1 z1 w1     point 1 in R^4
  10  *      ...             ...
  11  *      x5 y5 z5 w5     point 5 in R^4
  12  *
  13  * Copyright (C) 2001  Landon Curt Noll
  14  *
  15  * Calc is open software; you can redistribute it and/or modify it under
  16  * the terms of the version 2.1 of the GNU Lesser General Public License
  17  * as published by the Free Software Foundation.
  18  *
  19  * Calc is distributed in the hope that it will be useful, but WITHOUT
  20  * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
  21  * or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General
  22  * Public License for more details.
  23  *
  24  * A copy of version 2.1 of the GNU Lesser General Public License is
  25  * distributed with calc under the filename COPYING-LGPL.  You should have
  26  * received a copy with calc; if not, write to Free Software Foundation, Inc.
  27  * 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
  28  *
  29  * @(#) $Revision: 30.1 $
  30  * @(#) $Id: 4dsphere.calc,v 30.1 2007/03/16 11:12:11 chongo Exp $
  31  * @(#) $Source: /usr/local/src/bin/calc/cscript/RCS/4dsphere.calc,v $
  32  *
  33  * Under source code control:   2001/05/03 19:02:03
  34  * File existed as early as:    2001
  35  *
  36  * chongo <was here> /\oo/\     http://www.isthe.com/chongo/
  37  * Share and enjoy!  :-)        http://www.isthe.com/chongo/tech/comp/calc/
  38  */
  39
  40 /*
  41  * parse args
  42  */
  43 argc = argv();
  44 if (argc != 25) {
  45     fprintf(files(2), "usage: %s x0 y0 z0 w0 x1 y1 z1 w1 ... x5 y5 z5 w5\n",
  46         argv(0));
  47     exit;
  48 }
  49 x0 = eval(argv(1));
  50 y0 = eval(argv(2));
  51 z0 = eval(argv(3));
  52 w0 = eval(argv(4));
  53 x1 = eval(argv(5));
  54 y1 = eval(argv(6));
  55 z1 = eval(argv(7));
  56 w1 = eval(argv(8));
  57 x2 = eval(argv(9));
  58 y2 = eval(argv(10));
  59 z2 = eval(argv(11));
  60 w2 = eval(argv(12));
  61 x3 = eval(argv(13));
  62 y3 = eval(argv(14));
  63 z3 = eval(argv(15));
  64 w3 = eval(argv(16));
  65 x4 = eval(argv(17));
  66 y4 = eval(argv(18));
  67 z4 = eval(argv(19));
  68 w4 = eval(argv(20));
  69 x5 = eval(argv(21));
  70 y5 = eval(argv(22));
  71 z5 = eval(argv(23));
  72 w5 = eval(argv(24));
  73
  74 /*
  75  * verbose output setup
  76  */
  77 print "(":x0:",":y0:",":z0:",":w0:") ":;
  78 print "(":x1:",":y1:",":z1:",":w1:") ":;
  79 print "(":x2:",":y2:",":z2:",":w2:") ":;
  80 print "(":x3:",":y3:",":z3:",":w3:") ":;
  81 print "(":x4:",":y4:",":z4:",":w4:") ":;
  82 print "(":x5:",":y5:",":z5:",":w5:") ":;
  83
  84 /*
  85  *
  86  * Given the 5 points:
  87  *
  88  *      (x0,y1,z1,w1)
  89  *      (x1,y1,z1,w1)
  90  *      (x2,y2,z2,w2)
  91  *      (x3,y3,z3,w3)
  92  *      (x4,y4,z4,w4)
  93  *      (x5,y5,z5,w5)
  94  *
  95  * we can determine if they lie in the surface of 4D sphere in R^4 if the
  96  * following matrix is 0:
  97  *
  98  *      | x0^2+y0^2+z0^2+w0^2   x0      y0      z0      w0      1 |
  99  *      | x1^2+y1^2+z1^2+w1^2   x1      y1      z1      w1      1 |
 100  *      | x2^2+y2^2+z2^2+w2^2   x2      y2      z2      w2      1 |     = 0
 101  *      | x3^2+y3^2+z3^2+w3^2   x3      y3      z3      w3      1 |
 102  *      | x4^2+y4^2+z4^2+w4^2   x4      y4      z4      w4      1 |
 103  *      | x5^2+y5^2+z5^2+w5^2   x5      y5      z5      w5      1 |
 104  */
 105 if ((w0*(-x1*(-y2*(-z4*(z5^2+y5^2+x5^2+w5^2)
 106     -z3*(-z5^2+z4^2-y5^2+y4^2-x5^2+x4^2-w5^2+w4^2) +
 107     (z4^2+y4^2+x4^2+w4^2)*z5+ (z3^2+y3^2+x3^2+w3^2)*(z4-z5))
 108     +y3*((z4^2+y4^2+x4^2+w4^2)*z5-z4*(z5^2+y5^2+x5^2+w5^2))
 109     +z2*(-y4*(z5^2+y5^2+x5^2+w5^2)
 110     -y3*(-z5^2+z4^2-y5^2+y4^2-x5^2+x4^2-w5^2+w4^2)
 111     +y5*(z4^2+y4^2+x4^2+w4^2) + (y4-y5)*(z3^2+y3^2+x3^2+w3^2))
 112     -z3*(y5*(z4^2+y4^2+x4^2+w4^2) -y4*(z5^2+y5^2+x5^2+w5^2)) +
 113     (z2^2+y2^2+x2^2+w2^2)*(y4*z5+y3*(z4-z5) -y5*z4- (y4-y5)*z3) -
 114     (z3^2+y3^2+x3^2+w3^2)*(y4*z5-y5*z4)) +y1*(-x2*(-z4*(z5^2+y5^2+x5^2+w5^2)
 115     -z3*(-z5^2+z4^2-y5^2+y4^2-x5^2+x4^2-w5^2+w4^2) +
 116     (z4^2+y4^2+x4^2+w4^2)*z5+ (z3^2+y3^2+x3^2+w3^2)*(z4-z5))
 117     +x3*((z4^2+y4^2+x4^2+w4^2)*z5-z4*(z5^2+y5^2+x5^2+w5^2))
 118     +z2*(-x4*(z5^2+y5^2+x5^2+w5^2)
 119     -x3*(-z5^2+z4^2-y5^2+y4^2-x5^2+x4^2-w5^2+w4^2) +x5*(z4^2+y4^2+x4^2+w4^2)
 120     + (x4-x5)*(z3^2+y3^2+x3^2+w3^2)) -z3*(x5*(z4^2+y4^2+x4^2+w4^2)
 121     -x4*(z5^2+y5^2+x5^2+w5^2)) + (z2^2+y2^2+x2^2+w2^2)*(x4*z5+x3*(z4-z5)
 122     -x5*z4- (x4-x5)*z3) - (z3^2+y3^2+x3^2+w3^2)*(x4*z5-x5*z4))
 123     -x2*(-y3*((z4^2+y4^2+x4^2+w4^2)*z5-z4*(z5^2+y5^2+x5^2+w5^2))
 124     +z3*(y5*(z4^2+y4^2+x4^2+w4^2) -y4*(z5^2+y5^2+x5^2+w5^2))
 125     + (z3^2+y3^2+x3^2+w3^2)*(y4*z5-y5*z4))
 126     +y2*(-x3*((z4^2+y4^2+x4^2+w4^2)*z5-z4*(z5^2+y5^2+x5^2+w5^2))
 127     +z3*(x5*(z4^2+y4^2+x4^2+w4^2) -x4*(z5^2+y5^2+x5^2+w5^2)) +
 128     (z3^2+y3^2+x3^2+w3^2)*(x4*z5-x5*z4)) -z1*(-x2*(-y4*(z5^2+y5^2+x5^2+w5^2)
 129     -y3*(-z5^2+z4^2-y5^2+y4^2-x5^2+x4^2-w5^2+w4^2) +y5*(z4^2+y4^2+x4^2+w4^2)
 130     + (y4-y5)*(z3^2+y3^2+x3^2+w3^2)) +x3*(y5*(z4^2+y4^2+x4^2+w4^2)
 131     -y4*(z5^2+y5^2+x5^2+w5^2)) +y2*(-x4*(z5^2+y5^2+x5^2+w5^2)
 132     -x3*(-z5^2+z4^2-y5^2+y4^2-x5^2+x4^2-w5^2+w4^2)
 133     +x5*(z4^2+y4^2+x4^2+w4^2) + (x4-x5)*(z3^2+y3^2+x3^2+w3^2))
 134     -y3*(x5*(z4^2+y4^2+x4^2+w4^2) -x4*(z5^2+y5^2+x5^2+w5^2)) -
 135     (x4*y5-x5*y4)*(z3^2+y3^2+x3^2+w3^2) + (x4*y5+x3*(y4-y5) -x5*y4-
 136     (x4-x5)*y3)*(z2^2+y2^2+x2^2+w2^2)) -z2*(-x3*(y5*(z4^2+y4^2+x4^2+w4^2)
 137     -y4*(z5^2+y5^2+x5^2+w5^2)) +y3*(x5*(z4^2+y4^2+x4^2+w4^2)
 138     -x4*(z5^2+y5^2+x5^2+w5^2)) + (x4*y5-x5*y4)*(z3^2+y3^2+x3^2+w3^2))
 139     + (z1^2+y1^2+x1^2+w1^2)*(x2*(y4*z5+y3*(z4-z5) -y5*z4-
 140     (y4-y5)*z3) -x3*(y4*z5-y5*z4) -y2*(x4*z5+x3*(z4-z5) -x5*z4-
 141     (x4-x5)*z3) +y3*(x4*z5-x5*z4) - (x4*y5-x5*y4)*z3+
 142     (x4*y5+x3*(y4-y5) -x5*y4- (x4-x5)*y3)*z2) +
 143     (z2^2+y2^2+x2^2+w2^2)*(x3*(y4*z5-y5*z4) -y3*(x4*z5-x5*z4) +
 144     (x4*y5-x5*y4)*z3)) -x0*(-w1*(-y2*(-z4*(z5^2+y5^2+x5^2+w5^2)
 145     -z3*(-z5^2+z4^2-y5^2+y4^2-x5^2+x4^2-w5^2+w4^2) +
 146     (z4^2+y4^2+x4^2+w4^2)*z5+ (z3^2+y3^2+x3^2+w3^2)*(z4-z5))
 147     +y3*((z4^2+y4^2+x4^2+w4^2)*z5-z4*(z5^2+y5^2+x5^2+w5^2))
 148     +z2*(-y4*(z5^2+y5^2+x5^2+w5^2)
 149     -y3*(-z5^2+z4^2-y5^2+y4^2-x5^2+x4^2-w5^2+w4^2)
 150     +y5*(z4^2+y4^2+x4^2+w4^2) + (y4-y5)*(z3^2+y3^2+x3^2+w3^2))
 151     -z3*(y5*(z4^2+y4^2+x4^2+w4^2) -y4*(z5^2+y5^2+x5^2+w5^2)) +
 152     (z2^2+y2^2+x2^2+w2^2)*(y4*z5+y3*(z4-z5) -y5*z4- (y4-y5)*z3) -
 153     (z3^2+y3^2+x3^2+w3^2)*(y4*z5-y5*z4)) -y1*(w2*(-z4*(z5^2+y5^2+x5^2+w5^2)
 154     -z3*(-z5^2+z4^2-y5^2+y4^2-x5^2+x4^2-w5^2+w4^2) +
 155     (z4^2+y4^2+x4^2+w4^2)*z5+ (z3^2+y3^2+x3^2+w3^2)*(z4-z5))
 156     -w3*((z4^2+y4^2+x4^2+w4^2)*z5-z4*(z5^2+y5^2+x5^2+w5^2))
 157     -z2*(-w4*(z5^2+y5^2+x5^2+w5^2)
 158     -w3*(-z5^2+z4^2-y5^2+y4^2-x5^2+x4^2-w5^2+w4^2) +w5*(z4^2+y4^2+x4^2+w4^2)
 159     + (w4-w5)*(z3^2+y3^2+x3^2+w3^2)) +z3*(w5*(z4^2+y4^2+x4^2+w4^2)
 160     -w4*(z5^2+y5^2+x5^2+w5^2)) + (z2^2+y2^2+x2^2+w2^2)*(-w4*z5-w3*(z4-z5)
 161     +w5*z4+ (w4-w5)*z3) - (z3^2+y3^2+x3^2+w3^2)*(w5*z4-w4*z5))
 162     -w2*(-y3*((z4^2+y4^2+x4^2+w4^2)*z5-z4*(z5^2+y5^2+x5^2+w5^2))
 163     +z3*(y5*(z4^2+y4^2+x4^2+w4^2) -y4*(z5^2+y5^2+x5^2+w5^2))
 164     + (z3^2+y3^2+x3^2+w3^2)*(y4*z5-y5*z4))
 165     -y2*(w3*((z4^2+y4^2+x4^2+w4^2)*z5-z4*(z5^2+y5^2+x5^2+w5^2))
 166     -z3*(w5*(z4^2+y4^2+x4^2+w4^2) -w4*(z5^2+y5^2+x5^2+w5^2)) +
 167     (z3^2+y3^2+x3^2+w3^2)*(w5*z4-w4*z5)) +z1*(w2*(-y4*(z5^2+y5^2+x5^2+w5^2)
 168     -y3*(-z5^2+z4^2-y5^2+y4^2-x5^2+x4^2-w5^2+w4^2) +y5*(z4^2+y4^2+x4^2+w4^2)
 169     + (y4-y5)*(z3^2+y3^2+x3^2+w3^2)) -w3*(y5*(z4^2+y4^2+x4^2+w4^2)
 170     -y4*(z5^2+y5^2+x5^2+w5^2)) -y2*(-w4*(z5^2+y5^2+x5^2+w5^2)
 171     -w3*(-z5^2+z4^2-y5^2+y4^2-x5^2+x4^2-w5^2+w4^2)
 172     +w5*(z4^2+y4^2+x4^2+w4^2) + (w4-w5)*(z3^2+y3^2+x3^2+w3^2))
 173     +y3*(w5*(z4^2+y4^2+x4^2+w4^2) -w4*(z5^2+y5^2+x5^2+w5^2)) -
 174     (w5*y4-w4*y5)*(z3^2+y3^2+x3^2+w3^2) + (-w4*y5-w3*(y4-y5) +w5*y4+
 175     (w4-w5)*y3)*(z2^2+y2^2+x2^2+w2^2)) +z2*(w3*(y5*(z4^2+y4^2+x4^2+w4^2)
 176     -y4*(z5^2+y5^2+x5^2+w5^2)) -y3*(w5*(z4^2+y4^2+x4^2+w4^2)
 177     -w4*(z5^2+y5^2+x5^2+w5^2)) + (w5*y4-w4*y5)*(z3^2+y3^2+x3^2+w3^2))
 178     + (z1^2+y1^2+x1^2+w1^2)*(w2*(y4*z5+y3*(z4-z5) -y5*z4-
 179     (y4-y5)*z3) -w3*(y4*z5-y5*z4) +y2*(-w4*z5-w3*(z4-z5)
 180     +w5*z4+ (w4-w5)*z3) -y3*(w5*z4-w4*z5) + (w5*y4-w4*y5)*z3-
 181     (-w4*y5-w3*(y4-y5) +w5*y4+ (w4-w5)*y3)*z2) +
 182     (z2^2+y2^2+x2^2+w2^2)*(w3*(y4*z5-y5*z4) +y3*(w5*z4-w4*z5) -
 183     (w5*y4-w4*y5)*z3)) +y0*(-w1*(-x2*(-z4*(z5^2+y5^2+x5^2+w5^2)
 184     -z3*(-z5^2+z4^2-y5^2+y4^2-x5^2+x4^2-w5^2+w4^2) +
 185     (z4^2+y4^2+x4^2+w4^2)*z5+ (z3^2+y3^2+x3^2+w3^2)*(z4-z5))
 186     +x3*((z4^2+y4^2+x4^2+w4^2)*z5-z4*(z5^2+y5^2+x5^2+w5^2))
 187     +z2*(-x4*(z5^2+y5^2+x5^2+w5^2)
 188     -x3*(-z5^2+z4^2-y5^2+y4^2-x5^2+x4^2-w5^2+w4^2)
 189     +x5*(z4^2+y4^2+x4^2+w4^2) + (x4-x5)*(z3^2+y3^2+x3^2+w3^2))
 190     -z3*(x5*(z4^2+y4^2+x4^2+w4^2) -x4*(z5^2+y5^2+x5^2+w5^2)) +
 191     (z2^2+y2^2+x2^2+w2^2)*(x4*z5+x3*(z4-z5) -x5*z4- (x4-x5)*z3) -
 192     (z3^2+y3^2+x3^2+w3^2)*(x4*z5-x5*z4)) -x1*(w2*(-z4*(z5^2+y5^2+x5^2+w5^2)
 193     -z3*(-z5^2+z4^2-y5^2+y4^2-x5^2+x4^2-w5^2+w4^2) +
 194     (z4^2+y4^2+x4^2+w4^2)*z5+ (z3^2+y3^2+x3^2+w3^2)*(z4-z5))
 195     -w3*((z4^2+y4^2+x4^2+w4^2)*z5-z4*(z5^2+y5^2+x5^2+w5^2))
 196     -z2*(-w4*(z5^2+y5^2+x5^2+w5^2)
 197     -w3*(-z5^2+z4^2-y5^2+y4^2-x5^2+x4^2-w5^2+w4^2) +w5*(z4^2+y4^2+x4^2+w4^2)
 198     + (w4-w5)*(z3^2+y3^2+x3^2+w3^2)) +z3*(w5*(z4^2+y4^2+x4^2+w4^2)
 199     -w4*(z5^2+y5^2+x5^2+w5^2)) + (z2^2+y2^2+x2^2+w2^2)*(-w4*z5-w3*(z4-z5)
 200     +w5*z4+ (w4-w5)*z3) - (z3^2+y3^2+x3^2+w3^2)*(w5*z4-w4*z5))
 201     -w2*(-x3*((z4^2+y4^2+x4^2+w4^2)*z5-z4*(z5^2+y5^2+x5^2+w5^2))
 202     +z3*(x5*(z4^2+y4^2+x4^2+w4^2) -x4*(z5^2+y5^2+x5^2+w5^2))
 203     + (z3^2+y3^2+x3^2+w3^2)*(x4*z5-x5*z4))
 204     -x2*(w3*((z4^2+y4^2+x4^2+w4^2)*z5-z4*(z5^2+y5^2+x5^2+w5^2))
 205     -z3*(w5*(z4^2+y4^2+x4^2+w4^2) -w4*(z5^2+y5^2+x5^2+w5^2)) +
 206     (z3^2+y3^2+x3^2+w3^2)*(w5*z4-w4*z5)) +z1*(w2*(-x4*(z5^2+y5^2+x5^2+w5^2)
 207     -x3*(-z5^2+z4^2-y5^2+y4^2-x5^2+x4^2-w5^2+w4^2) +x5*(z4^2+y4^2+x4^2+w4^2)
 208     + (x4-x5)*(z3^2+y3^2+x3^2+w3^2)) -w3*(x5*(z4^2+y4^2+x4^2+w4^2)
 209     -x4*(z5^2+y5^2+x5^2+w5^2)) -x2*(-w4*(z5^2+y5^2+x5^2+w5^2)
 210     -w3*(-z5^2+z4^2-y5^2+y4^2-x5^2+x4^2-w5^2+w4^2)
 211     +w5*(z4^2+y4^2+x4^2+w4^2) + (w4-w5)*(z3^2+y3^2+x3^2+w3^2))
 212     +x3*(w5*(z4^2+y4^2+x4^2+w4^2) -w4*(z5^2+y5^2+x5^2+w5^2)) -
 213     (w5*x4-w4*x5)*(z3^2+y3^2+x3^2+w3^2) + (-w4*x5-w3*(x4-x5) +w5*x4+
 214     (w4-w5)*x3)*(z2^2+y2^2+x2^2+w2^2)) +z2*(w3*(x5*(z4^2+y4^2+x4^2+w4^2)
 215     -x4*(z5^2+y5^2+x5^2+w5^2)) -x3*(w5*(z4^2+y4^2+x4^2+w4^2)
 216     -w4*(z5^2+y5^2+x5^2+w5^2)) + (w5*x4-w4*x5)*(z3^2+y3^2+x3^2+w3^2)) +
 217     (z1^2+y1^2+x1^2+w1^2)*(w2*(x4*z5+x3*(z4-z5) -x5*z4- (x4-x5)*z3)
 218     -w3*(x4*z5-x5*z4) +x2*(-w4*z5-w3*(z4-z5) +w5*z4+ (w4-w5)*z3)
 219     -x3*(w5*z4-w4*z5) + (w5*x4-w4*x5)*z3- (-w4*x5-w3*(x4-x5) +w5*x4+
 220     (w4-w5)*x3)*z2) + (z2^2+y2^2+x2^2+w2^2)*(w3*(x4*z5-x5*z4)
 221     +x3*(w5*z4-w4*z5) - (w5*x4-w4*x5)*z3))
 222     -w1*(-x2*(-y3*((z4^2+y4^2+x4^2+w4^2)*z5-z4*(z5^2+y5^2+x5^2+w5^2))
 223     +z3*(y5*(z4^2+y4^2+x4^2+w4^2) -y4*(z5^2+y5^2+x5^2+w5^2))
 224     + (z3^2+y3^2+x3^2+w3^2)*(y4*z5-y5*z4))
 225     +y2*(-x3*((z4^2+y4^2+x4^2+w4^2)*z5-z4*(z5^2+y5^2+x5^2+w5^2))
 226     +z3*(x5*(z4^2+y4^2+x4^2+w4^2) -x4*(z5^2+y5^2+x5^2+w5^2)) +
 227     (z3^2+y3^2+x3^2+w3^2)*(x4*z5-x5*z4)) -z2*(-x3*(y5*(z4^2+y4^2+x4^2+w4^2)
 228     -y4*(z5^2+y5^2+x5^2+w5^2)) +y3*(x5*(z4^2+y4^2+x4^2+w4^2)
 229     -x4*(z5^2+y5^2+x5^2+w5^2)) + (x4*y5-x5*y4)*(z3^2+y3^2+x3^2+w3^2))
 230     + (z2^2+y2^2+x2^2+w2^2)*(x3*(y4*z5-y5*z4)
 231     -y3*(x4*z5-x5*z4) + (x4*y5-x5*y4)*z3))
 232     +x1*(-w2*(-y3*((z4^2+y4^2+x4^2+w4^2)*z5-z4*(z5^2+y5^2+x5^2+w5^2))
 233     +z3*(y5*(z4^2+y4^2+x4^2+w4^2) -y4*(z5^2+y5^2+x5^2+w5^2))
 234     + (z3^2+y3^2+x3^2+w3^2)*(y4*z5-y5*z4))
 235     -y2*(w3*((z4^2+y4^2+x4^2+w4^2)*z5-z4*(z5^2+y5^2+x5^2+w5^2))
 236     -z3*(w5*(z4^2+y4^2+x4^2+w4^2) -w4*(z5^2+y5^2+x5^2+w5^2)) +
 237     (z3^2+y3^2+x3^2+w3^2)*(w5*z4-w4*z5)) +z2*(w3*(y5*(z4^2+y4^2+x4^2+w4^2)
 238     -y4*(z5^2+y5^2+x5^2+w5^2)) -y3*(w5*(z4^2+y4^2+x4^2+w4^2)
 239     -w4*(z5^2+y5^2+x5^2+w5^2)) + (w5*y4-w4*y5)*(z3^2+y3^2+x3^2+w3^2))
 240     + (z2^2+y2^2+x2^2+w2^2)*(w3*(y4*z5-y5*z4)
 241     +y3*(w5*z4-w4*z5) - (w5*y4-w4*y5)*z3))
 242     -y1*(-w2*(-x3*((z4^2+y4^2+x4^2+w4^2)*z5-z4*(z5^2+y5^2+x5^2+w5^2))
 243     +z3*(x5*(z4^2+y4^2+x4^2+w4^2) -x4*(z5^2+y5^2+x5^2+w5^2))
 244     + (z3^2+y3^2+x3^2+w3^2)*(x4*z5-x5*z4))
 245     -x2*(w3*((z4^2+y4^2+x4^2+w4^2)*z5-z4*(z5^2+y5^2+x5^2+w5^2))
 246     -z3*(w5*(z4^2+y4^2+x4^2+w4^2) -w4*(z5^2+y5^2+x5^2+w5^2)) +
 247     (z3^2+y3^2+x3^2+w3^2)*(w5*z4-w4*z5)) +z2*(w3*(x5*(z4^2+y4^2+x4^2+w4^2)
 248     -x4*(z5^2+y5^2+x5^2+w5^2)) -x3*(w5*(z4^2+y4^2+x4^2+w4^2)
 249     -w4*(z5^2+y5^2+x5^2+w5^2)) + (w5*x4-w4*x5)*(z3^2+y3^2+x3^2+w3^2))
 250     + (z2^2+y2^2+x2^2+w2^2)*(w3*(x4*z5-x5*z4) +x3*(w5*z4-w4*z5)
 251     - (w5*x4-w4*x5)*z3)) -z0*(-w1*(-x2*(-y4*(z5^2+y5^2+x5^2+w5^2)
 252     -y3*(-z5^2+z4^2-y5^2+y4^2-x5^2+x4^2-w5^2+w4^2) +y5*(z4^2+y4^2+x4^2+w4^2)
 253     + (y4-y5)*(z3^2+y3^2+x3^2+w3^2)) +x3*(y5*(z4^2+y4^2+x4^2+w4^2)
 254     -y4*(z5^2+y5^2+x5^2+w5^2)) +y2*(-x4*(z5^2+y5^2+x5^2+w5^2)
 255     -x3*(-z5^2+z4^2-y5^2+y4^2-x5^2+x4^2-w5^2+w4^2)
 256     +x5*(z4^2+y4^2+x4^2+w4^2) + (x4-x5)*(z3^2+y3^2+x3^2+w3^2))
 257     -y3*(x5*(z4^2+y4^2+x4^2+w4^2) -x4*(z5^2+y5^2+x5^2+w5^2)) -
 258     (x4*y5-x5*y4)*(z3^2+y3^2+x3^2+w3^2) + (x4*y5+x3*(y4-y5) -x5*y4-
 259     (x4-x5)*y3)*(z2^2+y2^2+x2^2+w2^2)) -x1*(w2*(-y4*(z5^2+y5^2+x5^2+w5^2)
 260     -y3*(-z5^2+z4^2-y5^2+y4^2-x5^2+x4^2-w5^2+w4^2) +y5*(z4^2+y4^2+x4^2+w4^2)
 261     + (y4-y5)*(z3^2+y3^2+x3^2+w3^2)) -w3*(y5*(z4^2+y4^2+x4^2+w4^2)
 262     -y4*(z5^2+y5^2+x5^2+w5^2)) -y2*(-w4*(z5^2+y5^2+x5^2+w5^2)
 263     -w3*(-z5^2+z4^2-y5^2+y4^2-x5^2+x4^2-w5^2+w4^2)
 264     +w5*(z4^2+y4^2+x4^2+w4^2) + (w4-w5)*(z3^2+y3^2+x3^2+w3^2))
 265     +y3*(w5*(z4^2+y4^2+x4^2+w4^2) -w4*(z5^2+y5^2+x5^2+w5^2)) -
 266     (w5*y4-w4*y5)*(z3^2+y3^2+x3^2+w3^2) + (-w4*y5-w3*(y4-y5) +w5*y4+
 267     (w4-w5)*y3)*(z2^2+y2^2+x2^2+w2^2)) -w2*(-x3*(y5*(z4^2+y4^2+x4^2+w4^2)
 268     -y4*(z5^2+y5^2+x5^2+w5^2)) +y3*(x5*(z4^2+y4^2+x4^2+w4^2)
 269     -x4*(z5^2+y5^2+x5^2+w5^2)) + (x4*y5-x5*y4)*(z3^2+y3^2+x3^2+w3^2))
 270     -x2*(w3*(y5*(z4^2+y4^2+x4^2+w4^2) -y4*(z5^2+y5^2+x5^2+w5^2))
 271     -y3*(w5*(z4^2+y4^2+x4^2+w4^2) -w4*(z5^2+y5^2+x5^2+w5^2)) +
 272     (w5*y4-w4*y5)*(z3^2+y3^2+x3^2+w3^2)) +y1*(w2*(-x4*(z5^2+y5^2+x5^2+w5^2)
 273     -x3*(-z5^2+z4^2-y5^2+y4^2-x5^2+x4^2-w5^2+w4^2) +x5*(z4^2+y4^2+x4^2+w4^2)
 274     + (x4-x5)*(z3^2+y3^2+x3^2+w3^2)) -w3*(x5*(z4^2+y4^2+x4^2+w4^2)
 275     -x4*(z5^2+y5^2+x5^2+w5^2)) -x2*(-w4*(z5^2+y5^2+x5^2+w5^2)
 276     -w3*(-z5^2+z4^2-y5^2+y4^2-x5^2+x4^2-w5^2+w4^2) +w5*(z4^2+y4^2+x4^2+w4^2)
 277     + (w4-w5)*(z3^2+y3^2+x3^2+w3^2)) +x3*(w5*(z4^2+y4^2+x4^2+w4^2)
 278     -w4*(z5^2+y5^2+x5^2+w5^2)) - (w5*x4-w4*x5)*(z3^2+y3^2+x3^2+w3^2)
 279     + (-w4*x5-w3*(x4-x5) +w5*x4+ (w4-w5)*x3)*(z2^2+y2^2+x2^2+w2^2))
 280     +y2*(w3*(x5*(z4^2+y4^2+x4^2+w4^2) -x4*(z5^2+y5^2+x5^2+w5^2))
 281     -x3*(w5*(z4^2+y4^2+x4^2+w4^2) -w4*(z5^2+y5^2+x5^2+w5^2)) +
 282     (w5*x4-w4*x5)*(z3^2+y3^2+x3^2+w3^2)) + (w3*(x4*y5-x5*y4) +x3*(w5*y4-w4*y5)
 283     - (w5*x4-w4*x5)*y3)*(z2^2+y2^2+x2^2+w2^2) + (w2*(x4*y5+x3*(y4-y5)
 284     -x5*y4- (x4-x5)*y3) -w3*(x4*y5-x5*y4) +x2*(-w4*y5-w3*(y4-y5)
 285     +w5*y4+ (w4-w5)*y3) -x3*(w5*y4-w4*y5) + (w5*x4-w4*x5)*y3-
 286     (-w4*x5-w3*(x4-x5) +w5*x4+ (w4-w5)*x3)*y2)*(z1^2+y1^2+x1^2+w1^2))
 287     +z1*(-w2*(-x3*(y5*(z4^2+y4^2+x4^2+w4^2) -y4*(z5^2+y5^2+x5^2+w5^2))
 288     +y3*(x5*(z4^2+y4^2+x4^2+w4^2) -x4*(z5^2+y5^2+x5^2+w5^2)) +
 289     (x4*y5-x5*y4)*(z3^2+y3^2+x3^2+w3^2)) -x2*(w3*(y5*(z4^2+y4^2+x4^2+w4^2)
 290     -y4*(z5^2+y5^2+x5^2+w5^2)) -y3*(w5*(z4^2+y4^2+x4^2+w4^2)
 291     -w4*(z5^2+y5^2+x5^2+w5^2)) + (w5*y4-w4*y5)*(z3^2+y3^2+x3^2+w3^2))
 292     +y2*(w3*(x5*(z4^2+y4^2+x4^2+w4^2) -x4*(z5^2+y5^2+x5^2+w5^2))
 293     -x3*(w5*(z4^2+y4^2+x4^2+w4^2) -w4*(z5^2+y5^2+x5^2+w5^2)) +
 294     (w5*x4-w4*x5)*(z3^2+y3^2+x3^2+w3^2)) + (w3*(x4*y5-x5*y4)
 295     +x3*(w5*y4-w4*y5) - (w5*x4-w4*x5)*y3)*(z2^2+y2^2+x2^2+w2^2)) +
 296     (z0^2+y0^2+x0^2+w0^2)*(-w1*(x2*(y4*z5+y3*(z4-z5) -y5*z4- (y4-y5)*z3)
 297     -x3*(y4*z5-y5*z4) -y2*(x4*z5+x3*(z4-z5) -x5*z4- (x4-x5)*z3)
 298     +y3*(x4*z5-x5*z4) - (x4*y5-x5*y4)*z3+ (x4*y5+x3*(y4-y5) -x5*y4-
 299     (x4-x5)*y3)*z2) +x1*(w2*(y4*z5+y3*(z4-z5) -y5*z4- (y4-y5)*z3)
 300     -w3*(y4*z5-y5*z4) +y2*(-w4*z5-w3*(z4-z5) +w5*z4+ (w4-w5)*z3)
 301     -y3*(w5*z4-w4*z5) + (w5*y4-w4*y5)*z3- (-w4*y5-w3*(y4-y5) +w5*y4+
 302     (w4-w5)*y3)*z2) -w2*(x3*(y4*z5-y5*z4) -y3*(x4*z5-x5*z4) +
 303     (x4*y5-x5*y4)*z3) +x2*(w3*(y4*z5-y5*z4) +y3*(w5*z4-w4*z5) -
 304     (w5*y4-w4*y5)*z3) -y1*(w2*(x4*z5+x3*(z4-z5) -x5*z4- (x4-x5)*z3)
 305     -w3*(x4*z5-x5*z4) +x2*(-w4*z5-w3*(z4-z5) +w5*z4+ (w4-w5)*z3)
 306     -x3*(w5*z4-w4*z5) + (w5*x4-w4*x5)*z3- (-w4*x5-w3*(x4-x5) +w5*x4+
 307     (w4-w5)*x3)*z2) -y2*(w3*(x4*z5-x5*z4) +x3*(w5*z4-w4*z5) -
 308     (w5*x4-w4*x5)*z3) + (w3*(x4*y5-x5*y4) +x3*(w5*y4-w4*y5) -
 309     (w5*x4-w4*x5)*y3)*z2+ (w2*(x4*y5+x3*(y4-y5) -x5*y4- (x4-x5)*y3)
 310     -w3*(x4*y5-x5*y4) +x2*(-w4*y5-w3*(y4-y5) +w5*y4+ (w4-w5)*y3)
 311     -x3*(w5*y4-w4*y5) + (w5*x4-w4*x5)*y3- (-w4*x5-w3*(x4-x5) +w5*x4+
 312     (w4-w5)*x3)*y2)*z1) - (z1^2+y1^2+x1^2+w1^2)*(-w2*(x3*(y4*z5-y5*z4)
 313     -y3*(x4*z5-x5*z4) + (x4*y5-x5*y4)*z3) +x2*(w3*(y4*z5-y5*z4)
 314     +y3*(w5*z4-w4*z5) - (w5*y4-w4*y5)*z3) -y2*(w3*(x4*z5-x5*z4)
 315     +x3*(w5*z4-w4*z5) - (w5*x4-w4*x5)*z3) + (w3*(x4*y5-x5*y4)
 316     +x3*(w5*y4-w4*y5) - (w5*x4-w4*x5)*y3)*z2)) == 0) {
 317     print "are in the surface of a 4D sphere";
 318 } else {
 319     print "are NOT on a 4D sphere surface";
 320 }