#!/usr/bin/calc -q -s -f
/*
* 4dsphere - determine if 6 points lie on the surface of a sphere in R^4
*
* usage:
* 4dsphere x0 y0 z0 w0 x1 y1 z1 w1 ... x5 y5 z5 w5
*
* x0 y0 z0 w0 point 0 in R^4
* x1 y1 z1 w1 point 1 in R^4
* ... ...
* x5 y5 z5 w5 point 5 in R^4
*
* Copyright (C) 2001,2014 Landon Curt Noll
*
* Calc is open software; you can redistribute it and/or modify it under
* the terms of the version 2.1 of the GNU Lesser General Public License
* as published by the Free Software Foundation.
*
* Calc is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
* or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General
* Public License for more details.
*
* A copy of version 2.1 of the GNU Lesser General Public License is
* distributed with calc under the filename COPYING-LGPL. You should have
* received a copy with calc; if not, write to Free Software Foundation, Inc.
* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
*
* Under source code control: 2001/05/03 19:02:03
* File existed as early as: 2001
*
* chongo <was here> /\oo/\ http://www.isthe.com/chongo/
* Share and enjoy! :-) http://www.isthe.com/chongo/tech/comp/calc/
*/
/*
* parse args
*/
argc = argv();
if (argc != 25) {
fprintf(files(2), "usage: %s x0 y0 z0 w0 x1 y1 z1 w1 ... x5 y5 z5 w5\n",
argv(0));
exit;
}
x0 = eval(argv(1));
y0 = eval(argv(2));
z0 = eval(argv(3));
w0 = eval(argv(4));
x1 = eval(argv(5));
y1 = eval(argv(6));
z1 = eval(argv(7));
w1 = eval(argv(8));
x2 = eval(argv(9));
y2 = eval(argv(10));
z2 = eval(argv(11));
w2 = eval(argv(12));
x3 = eval(argv(13));
y3 = eval(argv(14));
z3 = eval(argv(15));
w3 = eval(argv(16));
x4 = eval(argv(17));
y4 = eval(argv(18));
z4 = eval(argv(19));
w4 = eval(argv(20));
x5 = eval(argv(21));
y5 = eval(argv(22));
z5 = eval(argv(23));
w5 = eval(argv(24));
/*
* verbose output setup
*/
print "(":x0:",":y0:",":z0:",":w0:") ":;
print "(":x1:",":y1:",":z1:",":w1:") ":;
print "(":x2:",":y2:",":z2:",":w2:") ":;
print "(":x3:",":y3:",":z3:",":w3:") ":;
print "(":x4:",":y4:",":z4:",":w4:") ":;
print "(":x5:",":y5:",":z5:",":w5:") ":;
/*
*
* Given the 5 points:
*
* (x0,y1,z1,w1)
* (x1,y1,z1,w1)
* (x2,y2,z2,w2)
* (x3,y3,z3,w3)
* (x4,y4,z4,w4)
* (x5,y5,z5,w5)
*
* we can determine if they lie in the surface of 4D sphere in R^4 if the
* following matrix is 0:
*
* | x0^2+y0^2+z0^2+w0^2 x0 y0 z0 w0 1 |
* | x1^2+y1^2+z1^2+w1^2 x1 y1 z1 w1 1 |
* | x2^2+y2^2+z2^2+w2^2 x2 y2 z2 w2 1 | = 0
* | x3^2+y3^2+z3^2+w3^2 x3 y3 z3 w3 1 |
* | x4^2+y4^2+z4^2+w4^2 x4 y4 z4 w4 1 |
* | x5^2+y5^2+z5^2+w5^2 x5 y5 z5 w5 1 |
*/
if ((w0*(-x1*(-y2*(-z4*(z5^2+y5^2+x5^2+w5^2)
-z3*(-z5^2+z4^2-y5^2+y4^2-x5^2+x4^2-w5^2+w4^2) +
(z4^2+y4^2+x4^2+w4^2)*z5+ (z3^2+y3^2+x3^2+w3^2)*(z4-z5))
+y3*((z4^2+y4^2+x4^2+w4^2)*z5-z4*(z5^2+y5^2+x5^2+w5^2))
+z2*(-y4*(z5^2+y5^2+x5^2+w5^2)
-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) + (y4-y5)*(z3^2+y3^2+x3^2+w3^2))
-z3*(y5*(z4^2+y4^2+x4^2+w4^2) -y4*(z5^2+y5^2+x5^2+w5^2)) +
(z2^2+y2^2+x2^2+w2^2)*(y4*z5+y3*(z4-z5) -y5*z4- (y4-y5)*z3) -
(z3^2+y3^2+x3^2+w3^2)*(y4*z5-y5*z4)) +y1*(-x2*(-z4*(z5^2+y5^2+x5^2+w5^2)
-z3*(-z5^2+z4^2-y5^2+y4^2-x5^2+x4^2-w5^2+w4^2) +
(z4^2+y4^2+x4^2+w4^2)*z5+ (z3^2+y3^2+x3^2+w3^2)*(z4-z5))
+x3*((z4^2+y4^2+x4^2+w4^2)*z5-z4*(z5^2+y5^2+x5^2+w5^2))
+z2*(-x4*(z5^2+y5^2+x5^2+w5^2)
-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)
+ (x4-x5)*(z3^2+y3^2+x3^2+w3^2)) -z3*(x5*(z4^2+y4^2+x4^2+w4^2)
-x4*(z5^2+y5^2+x5^2+w5^2)) + (z2^2+y2^2+x2^2+w2^2)*(x4*z5+x3*(z4-z5)
-x5*z4- (x4-x5)*z3) - (z3^2+y3^2+x3^2+w3^2)*(x4*z5-x5*z4))
-x2*(-y3*((z4^2+y4^2+x4^2+w4^2)*z5-z4*(z5^2+y5^2+x5^2+w5^2))
+z3*(y5*(z4^2+y4^2+x4^2+w4^2) -y4*(z5^2+y5^2+x5^2+w5^2))
+ (z3^2+y3^2+x3^2+w3^2)*(y4*z5-y5*z4))
+y2*(-x3*((z4^2+y4^2+x4^2+w4^2)*z5-z4*(z5^2+y5^2+x5^2+w5^2))
+z3*(x5*(z4^2+y4^2+x4^2+w4^2) -x4*(z5^2+y5^2+x5^2+w5^2)) +
(z3^2+y3^2+x3^2+w3^2)*(x4*z5-x5*z4)) -z1*(-x2*(-y4*(z5^2+y5^2+x5^2+w5^2)
-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)
+ (y4-y5)*(z3^2+y3^2+x3^2+w3^2)) +x3*(y5*(z4^2+y4^2+x4^2+w4^2)
-y4*(z5^2+y5^2+x5^2+w5^2)) +y2*(-x4*(z5^2+y5^2+x5^2+w5^2)
-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) + (x4-x5)*(z3^2+y3^2+x3^2+w3^2))
-y3*(x5*(z4^2+y4^2+x4^2+w4^2) -x4*(z5^2+y5^2+x5^2+w5^2)) -
(x4*y5-x5*y4)*(z3^2+y3^2+x3^2+w3^2) + (x4*y5+x3*(y4-y5) -x5*y4-
(x4-x5)*y3)*(z2^2+y2^2+x2^2+w2^2)) -z2*(-x3*(y5*(z4^2+y4^2+x4^2+w4^2)
-y4*(z5^2+y5^2+x5^2+w5^2)) +y3*(x5*(z4^2+y4^2+x4^2+w4^2)
-x4*(z5^2+y5^2+x5^2+w5^2)) + (x4*y5-x5*y4)*(z3^2+y3^2+x3^2+w3^2))
+ (z1^2+y1^2+x1^2+w1^2)*(x2*(y4*z5+y3*(z4-z5) -y5*z4-
(y4-y5)*z3) -x3*(y4*z5-y5*z4) -y2*(x4*z5+x3*(z4-z5) -x5*z4-
(x4-x5)*z3) +y3*(x4*z5-x5*z4) - (x4*y5-x5*y4)*z3+
(x4*y5+x3*(y4-y5) -x5*y4- (x4-x5)*y3)*z2) +
(z2^2+y2^2+x2^2+w2^2)*(x3*(y4*z5-y5*z4) -y3*(x4*z5-x5*z4) +
(x4*y5-x5*y4)*z3)) -x0*(-w1*(-y2*(-z4*(z5^2+y5^2+x5^2+w5^2)
-z3*(-z5^2+z4^2-y5^2+y4^2-x5^2+x4^2-w5^2+w4^2) +
(z4^2+y4^2+x4^2+w4^2)*z5+ (z3^2+y3^2+x3^2+w3^2)*(z4-z5))
+y3*((z4^2+y4^2+x4^2+w4^2)*z5-z4*(z5^2+y5^2+x5^2+w5^2))
+z2*(-y4*(z5^2+y5^2+x5^2+w5^2)
-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) + (y4-y5)*(z3^2+y3^2+x3^2+w3^2))
-z3*(y5*(z4^2+y4^2+x4^2+w4^2) -y4*(z5^2+y5^2+x5^2+w5^2)) +
(z2^2+y2^2+x2^2+w2^2)*(y4*z5+y3*(z4-z5) -y5*z4- (y4-y5)*z3) -
(z3^2+y3^2+x3^2+w3^2)*(y4*z5-y5*z4)) -y1*(w2*(-z4*(z5^2+y5^2+x5^2+w5^2)
-z3*(-z5^2+z4^2-y5^2+y4^2-x5^2+x4^2-w5^2+w4^2) +
(z4^2+y4^2+x4^2+w4^2)*z5+ (z3^2+y3^2+x3^2+w3^2)*(z4-z5))
-w3*((z4^2+y4^2+x4^2+w4^2)*z5-z4*(z5^2+y5^2+x5^2+w5^2))
-z2*(-w4*(z5^2+y5^2+x5^2+w5^2)
-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)
+ (w4-w5)*(z3^2+y3^2+x3^2+w3^2)) +z3*(w5*(z4^2+y4^2+x4^2+w4^2)
-w4*(z5^2+y5^2+x5^2+w5^2)) + (z2^2+y2^2+x2^2+w2^2)*(-w4*z5-w3*(z4-z5)
+w5*z4+ (w4-w5)*z3) - (z3^2+y3^2+x3^2+w3^2)*(w5*z4-w4*z5))
-w2*(-y3*((z4^2+y4^2+x4^2+w4^2)*z5-z4*(z5^2+y5^2+x5^2+w5^2))
+z3*(y5*(z4^2+y4^2+x4^2+w4^2) -y4*(z5^2+y5^2+x5^2+w5^2))
+ (z3^2+y3^2+x3^2+w3^2)*(y4*z5-y5*z4))
-y2*(w3*((z4^2+y4^2+x4^2+w4^2)*z5-z4*(z5^2+y5^2+x5^2+w5^2))
-z3*(w5*(z4^2+y4^2+x4^2+w4^2) -w4*(z5^2+y5^2+x5^2+w5^2)) +
(z3^2+y3^2+x3^2+w3^2)*(w5*z4-w4*z5)) +z1*(w2*(-y4*(z5^2+y5^2+x5^2+w5^2)
-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)
+ (y4-y5)*(z3^2+y3^2+x3^2+w3^2)) -w3*(y5*(z4^2+y4^2+x4^2+w4^2)
-y4*(z5^2+y5^2+x5^2+w5^2)) -y2*(-w4*(z5^2+y5^2+x5^2+w5^2)
-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) + (w4-w5)*(z3^2+y3^2+x3^2+w3^2))
+y3*(w5*(z4^2+y4^2+x4^2+w4^2) -w4*(z5^2+y5^2+x5^2+w5^2)) -
(w5*y4-w4*y5)*(z3^2+y3^2+x3^2+w3^2) + (-w4*y5-w3*(y4-y5) +w5*y4+
(w4-w5)*y3)*(z2^2+y2^2+x2^2+w2^2)) +z2*(w3*(y5*(z4^2+y4^2+x4^2+w4^2)
-y4*(z5^2+y5^2+x5^2+w5^2)) -y3*(w5*(z4^2+y4^2+x4^2+w4^2)
-w4*(z5^2+y5^2+x5^2+w5^2)) + (w5*y4-w4*y5)*(z3^2+y3^2+x3^2+w3^2))
+ (z1^2+y1^2+x1^2+w1^2)*(w2*(y4*z5+y3*(z4-z5) -y5*z4-
(y4-y5)*z3) -w3*(y4*z5-y5*z4) +y2*(-w4*z5-w3*(z4-z5)
+w5*z4+ (w4-w5)*z3) -y3*(w5*z4-w4*z5) + (w5*y4-w4*y5)*z3-
(-w4*y5-w3*(y4-y5) +w5*y4+ (w4-w5)*y3)*z2) +
(z2^2+y2^2+x2^2+w2^2)*(w3*(y4*z5-y5*z4) +y3*(w5*z4-w4*z5) -
(w5*y4-w4*y5)*z3)) +y0*(-w1*(-x2*(-z4*(z5^2+y5^2+x5^2+w5^2)
-z3*(-z5^2+z4^2-y5^2+y4^2-x5^2+x4^2-w5^2+w4^2) +
(z4^2+y4^2+x4^2+w4^2)*z5+ (z3^2+y3^2+x3^2+w3^2)*(z4-z5))
+x3*((z4^2+y4^2+x4^2+w4^2)*z5-z4*(z5^2+y5^2+x5^2+w5^2))
+z2*(-x4*(z5^2+y5^2+x5^2+w5^2)
-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) + (x4-x5)*(z3^2+y3^2+x3^2+w3^2))
-z3*(x5*(z4^2+y4^2+x4^2+w4^2) -x4*(z5^2+y5^2+x5^2+w5^2)) +
(z2^2+y2^2+x2^2+w2^2)*(x4*z5+x3*(z4-z5) -x5*z4- (x4-x5)*z3) -
(z3^2+y3^2+x3^2+w3^2)*(x4*z5-x5*z4)) -x1*(w2*(-z4*(z5^2+y5^2+x5^2+w5^2)
-z3*(-z5^2+z4^2-y5^2+y4^2-x5^2+x4^2-w5^2+w4^2) +
(z4^2+y4^2+x4^2+w4^2)*z5+ (z3^2+y3^2+x3^2+w3^2)*(z4-z5))
-w3*((z4^2+y4^2+x4^2+w4^2)*z5-z4*(z5^2+y5^2+x5^2+w5^2))
-z2*(-w4*(z5^2+y5^2+x5^2+w5^2)
-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)
+ (w4-w5)*(z3^2+y3^2+x3^2+w3^2)) +z3*(w5*(z4^2+y4^2+x4^2+w4^2)
-w4*(z5^2+y5^2+x5^2+w5^2)) + (z2^2+y2^2+x2^2+w2^2)*(-w4*z5-w3*(z4-z5)
+w5*z4+ (w4-w5)*z3) - (z3^2+y3^2+x3^2+w3^2)*(w5*z4-w4*z5))
-w2*(-x3*((z4^2+y4^2+x4^2+w4^2)*z5-z4*(z5^2+y5^2+x5^2+w5^2))
+z3*(x5*(z4^2+y4^2+x4^2+w4^2) -x4*(z5^2+y5^2+x5^2+w5^2))
+ (z3^2+y3^2+x3^2+w3^2)*(x4*z5-x5*z4))
-x2*(w3*((z4^2+y4^2+x4^2+w4^2)*z5-z4*(z5^2+y5^2+x5^2+w5^2))
-z3*(w5*(z4^2+y4^2+x4^2+w4^2) -w4*(z5^2+y5^2+x5^2+w5^2)) +
(z3^2+y3^2+x3^2+w3^2)*(w5*z4-w4*z5)) +z1*(w2*(-x4*(z5^2+y5^2+x5^2+w5^2)
-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)
+ (x4-x5)*(z3^2+y3^2+x3^2+w3^2)) -w3*(x5*(z4^2+y4^2+x4^2+w4^2)
-x4*(z5^2+y5^2+x5^2+w5^2)) -x2*(-w4*(z5^2+y5^2+x5^2+w5^2)
-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) + (w4-w5)*(z3^2+y3^2+x3^2+w3^2))
+x3*(w5*(z4^2+y4^2+x4^2+w4^2) -w4*(z5^2+y5^2+x5^2+w5^2)) -
(w5*x4-w4*x5)*(z3^2+y3^2+x3^2+w3^2) + (-w4*x5-w3*(x4-x5) +w5*x4+
(w4-w5)*x3)*(z2^2+y2^2+x2^2+w2^2)) +z2*(w3*(x5*(z4^2+y4^2+x4^2+w4^2)
-x4*(z5^2+y5^2+x5^2+w5^2)) -x3*(w5*(z4^2+y4^2+x4^2+w4^2)
-w4*(z5^2+y5^2+x5^2+w5^2)) + (w5*x4-w4*x5)*(z3^2+y3^2+x3^2+w3^2)) +
(z1^2+y1^2+x1^2+w1^2)*(w2*(x4*z5+x3*(z4-z5) -x5*z4- (x4-x5)*z3)
-w3*(x4*z5-x5*z4) +x2*(-w4*z5-w3*(z4-z5) +w5*z4+ (w4-w5)*z3)
-x3*(w5*z4-w4*z5) + (w5*x4-w4*x5)*z3- (-w4*x5-w3*(x4-x5) +w5*x4+
(w4-w5)*x3)*z2) + (z2^2+y2^2+x2^2+w2^2)*(w3*(x4*z5-x5*z4)
+x3*(w5*z4-w4*z5) - (w5*x4-w4*x5)*z3))
-w1*(-x2*(-y3*((z4^2+y4^2+x4^2+w4^2)*z5-z4*(z5^2+y5^2+x5^2+w5^2))
+z3*(y5*(z4^2+y4^2+x4^2+w4^2) -y4*(z5^2+y5^2+x5^2+w5^2))
+ (z3^2+y3^2+x3^2+w3^2)*(y4*z5-y5*z4))
+y2*(-x3*((z4^2+y4^2+x4^2+w4^2)*z5-z4*(z5^2+y5^2+x5^2+w5^2))
+z3*(x5*(z4^2+y4^2+x4^2+w4^2) -x4*(z5^2+y5^2+x5^2+w5^2)) +
(z3^2+y3^2+x3^2+w3^2)*(x4*z5-x5*z4)) -z2*(-x3*(y5*(z4^2+y4^2+x4^2+w4^2)
-y4*(z5^2+y5^2+x5^2+w5^2)) +y3*(x5*(z4^2+y4^2+x4^2+w4^2)
-x4*(z5^2+y5^2+x5^2+w5^2)) + (x4*y5-x5*y4)*(z3^2+y3^2+x3^2+w3^2))
+ (z2^2+y2^2+x2^2+w2^2)*(x3*(y4*z5-y5*z4)
-y3*(x4*z5-x5*z4) + (x4*y5-x5*y4)*z3))
+x1*(-w2*(-y3*((z4^2+y4^2+x4^2+w4^2)*z5-z4*(z5^2+y5^2+x5^2+w5^2))
+z3*(y5*(z4^2+y4^2+x4^2+w4^2) -y4*(z5^2+y5^2+x5^2+w5^2))
+ (z3^2+y3^2+x3^2+w3^2)*(y4*z5-y5*z4))
-y2*(w3*((z4^2+y4^2+x4^2+w4^2)*z5-z4*(z5^2+y5^2+x5^2+w5^2))
-z3*(w5*(z4^2+y4^2+x4^2+w4^2) -w4*(z5^2+y5^2+x5^2+w5^2)) +
(z3^2+y3^2+x3^2+w3^2)*(w5*z4-w4*z5)) +z2*(w3*(y5*(z4^2+y4^2+x4^2+w4^2)
-y4*(z5^2+y5^2+x5^2+w5^2)) -y3*(w5*(z4^2+y4^2+x4^2+w4^2)
-w4*(z5^2+y5^2+x5^2+w5^2)) + (w5*y4-w4*y5)*(z3^2+y3^2+x3^2+w3^2))
+ (z2^2+y2^2+x2^2+w2^2)*(w3*(y4*z5-y5*z4)
+y3*(w5*z4-w4*z5) - (w5*y4-w4*y5)*z3))
-y1*(-w2*(-x3*((z4^2+y4^2+x4^2+w4^2)*z5-z4*(z5^2+y5^2+x5^2+w5^2))
+z3*(x5*(z4^2+y4^2+x4^2+w4^2) -x4*(z5^2+y5^2+x5^2+w5^2))
+ (z3^2+y3^2+x3^2+w3^2)*(x4*z5-x5*z4))
-x2*(w3*((z4^2+y4^2+x4^2+w4^2)*z5-z4*(z5^2+y5^2+x5^2+w5^2))
-z3*(w5*(z4^2+y4^2+x4^2+w4^2) -w4*(z5^2+y5^2+x5^2+w5^2)) +
(z3^2+y3^2+x3^2+w3^2)*(w5*z4-w4*z5)) +z2*(w3*(x5*(z4^2+y4^2+x4^2+w4^2)
-x4*(z5^2+y5^2+x5^2+w5^2)) -x3*(w5*(z4^2+y4^2+x4^2+w4^2)
-w4*(z5^2+y5^2+x5^2+w5^2)) + (w5*x4-w4*x5)*(z3^2+y3^2+x3^2+w3^2))
+ (z2^2+y2^2+x2^2+w2^2)*(w3*(x4*z5-x5*z4) +x3*(w5*z4-w4*z5)
- (w5*x4-w4*x5)*z3)) -z0*(-w1*(-x2*(-y4*(z5^2+y5^2+x5^2+w5^2)
-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)
+ (y4-y5)*(z3^2+y3^2+x3^2+w3^2)) +x3*(y5*(z4^2+y4^2+x4^2+w4^2)
-y4*(z5^2+y5^2+x5^2+w5^2)) +y2*(-x4*(z5^2+y5^2+x5^2+w5^2)
-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) + (x4-x5)*(z3^2+y3^2+x3^2+w3^2))
-y3*(x5*(z4^2+y4^2+x4^2+w4^2) -x4*(z5^2+y5^2+x5^2+w5^2)) -
(x4*y5-x5*y4)*(z3^2+y3^2+x3^2+w3^2) + (x4*y5+x3*(y4-y5) -x5*y4-
(x4-x5)*y3)*(z2^2+y2^2+x2^2+w2^2)) -x1*(w2*(-y4*(z5^2+y5^2+x5^2+w5^2)
-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)
+ (y4-y5)*(z3^2+y3^2+x3^2+w3^2)) -w3*(y5*(z4^2+y4^2+x4^2+w4^2)
-y4*(z5^2+y5^2+x5^2+w5^2)) -y2*(-w4*(z5^2+y5^2+x5^2+w5^2)
-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) + (w4-w5)*(z3^2+y3^2+x3^2+w3^2))
+y3*(w5*(z4^2+y4^2+x4^2+w4^2) -w4*(z5^2+y5^2+x5^2+w5^2)) -
(w5*y4-w4*y5)*(z3^2+y3^2+x3^2+w3^2) + (-w4*y5-w3*(y4-y5) +w5*y4+
(w4-w5)*y3)*(z2^2+y2^2+x2^2+w2^2)) -w2*(-x3*(y5*(z4^2+y4^2+x4^2+w4^2)
-y4*(z5^2+y5^2+x5^2+w5^2)) +y3*(x5*(z4^2+y4^2+x4^2+w4^2)
-x4*(z5^2+y5^2+x5^2+w5^2)) + (x4*y5-x5*y4)*(z3^2+y3^2+x3^2+w3^2))
-x2*(w3*(y5*(z4^2+y4^2+x4^2+w4^2) -y4*(z5^2+y5^2+x5^2+w5^2))
-y3*(w5*(z4^2+y4^2+x4^2+w4^2) -w4*(z5^2+y5^2+x5^2+w5^2)) +
(w5*y4-w4*y5)*(z3^2+y3^2+x3^2+w3^2)) +y1*(w2*(-x4*(z5^2+y5^2+x5^2+w5^2)
-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)
+ (x4-x5)*(z3^2+y3^2+x3^2+w3^2)) -w3*(x5*(z4^2+y4^2+x4^2+w4^2)
-x4*(z5^2+y5^2+x5^2+w5^2)) -x2*(-w4*(z5^2+y5^2+x5^2+w5^2)
-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)
+ (w4-w5)*(z3^2+y3^2+x3^2+w3^2)) +x3*(w5*(z4^2+y4^2+x4^2+w4^2)
-w4*(z5^2+y5^2+x5^2+w5^2)) - (w5*x4-w4*x5)*(z3^2+y3^2+x3^2+w3^2)
+ (-w4*x5-w3*(x4-x5) +w5*x4+ (w4-w5)*x3)*(z2^2+y2^2+x2^2+w2^2))
+y2*(w3*(x5*(z4^2+y4^2+x4^2+w4^2) -x4*(z5^2+y5^2+x5^2+w5^2))
-x3*(w5*(z4^2+y4^2+x4^2+w4^2) -w4*(z5^2+y5^2+x5^2+w5^2)) +
(w5*x4-w4*x5)*(z3^2+y3^2+x3^2+w3^2)) + (w3*(x4*y5-x5*y4) +x3*(w5*y4-w4*y5)
- (w5*x4-w4*x5)*y3)*(z2^2+y2^2+x2^2+w2^2) + (w2*(x4*y5+x3*(y4-y5)
-x5*y4- (x4-x5)*y3) -w3*(x4*y5-x5*y4) +x2*(-w4*y5-w3*(y4-y5)
+w5*y4+ (w4-w5)*y3) -x3*(w5*y4-w4*y5) + (w5*x4-w4*x5)*y3-
(-w4*x5-w3*(x4-x5) +w5*x4+ (w4-w5)*x3)*y2)*(z1^2+y1^2+x1^2+w1^2))
+z1*(-w2*(-x3*(y5*(z4^2+y4^2+x4^2+w4^2) -y4*(z5^2+y5^2+x5^2+w5^2))
+y3*(x5*(z4^2+y4^2+x4^2+w4^2) -x4*(z5^2+y5^2+x5^2+w5^2)) +
(x4*y5-x5*y4)*(z3^2+y3^2+x3^2+w3^2)) -x2*(w3*(y5*(z4^2+y4^2+x4^2+w4^2)
-y4*(z5^2+y5^2+x5^2+w5^2)) -y3*(w5*(z4^2+y4^2+x4^2+w4^2)
-w4*(z5^2+y5^2+x5^2+w5^2)) + (w5*y4-w4*y5)*(z3^2+y3^2+x3^2+w3^2))
+y2*(w3*(x5*(z4^2+y4^2+x4^2+w4^2) -x4*(z5^2+y5^2+x5^2+w5^2))
-x3*(w5*(z4^2+y4^2+x4^2+w4^2) -w4*(z5^2+y5^2+x5^2+w5^2)) +
(w5*x4-w4*x5)*(z3^2+y3^2+x3^2+w3^2)) + (w3*(x4*y5-x5*y4)
+x3*(w5*y4-w4*y5) - (w5*x4-w4*x5)*y3)*(z2^2+y2^2+x2^2+w2^2)) +
(z0^2+y0^2+x0^2+w0^2)*(-w1*(x2*(y4*z5+y3*(z4-z5) -y5*z4- (y4-y5)*z3)
-x3*(y4*z5-y5*z4) -y2*(x4*z5+x3*(z4-z5) -x5*z4- (x4-x5)*z3)
+y3*(x4*z5-x5*z4) - (x4*y5-x5*y4)*z3+ (x4*y5+x3*(y4-y5) -x5*y4-
(x4-x5)*y3)*z2) +x1*(w2*(y4*z5+y3*(z4-z5) -y5*z4- (y4-y5)*z3)
-w3*(y4*z5-y5*z4) +y2*(-w4*z5-w3*(z4-z5) +w5*z4+ (w4-w5)*z3)
-y3*(w5*z4-w4*z5) + (w5*y4-w4*y5)*z3- (-w4*y5-w3*(y4-y5) +w5*y4+
(w4-w5)*y3)*z2) -w2*(x3*(y4*z5-y5*z4) -y3*(x4*z5-x5*z4) +
(x4*y5-x5*y4)*z3) +x2*(w3*(y4*z5-y5*z4) +y3*(w5*z4-w4*z5) -
(w5*y4-w4*y5)*z3) -y1*(w2*(x4*z5+x3*(z4-z5) -x5*z4- (x4-x5)*z3)
-w3*(x4*z5-x5*z4) +x2*(-w4*z5-w3*(z4-z5) +w5*z4+ (w4-w5)*z3)
-x3*(w5*z4-w4*z5) + (w5*x4-w4*x5)*z3- (-w4*x5-w3*(x4-x5) +w5*x4+
(w4-w5)*x3)*z2) -y2*(w3*(x4*z5-x5*z4) +x3*(w5*z4-w4*z5) -
(w5*x4-w4*x5)*z3) + (w3*(x4*y5-x5*y4) +x3*(w5*y4-w4*y5) -
(w5*x4-w4*x5)*y3)*z2+ (w2*(x4*y5+x3*(y4-y5) -x5*y4- (x4-x5)*y3)
-w3*(x4*y5-x5*y4) +x2*(-w4*y5-w3*(y4-y5) +w5*y4+ (w4-w5)*y3)
-x3*(w5*y4-w4*y5) + (w5*x4-w4*x5)*y3- (-w4*x5-w3*(x4-x5) +w5*x4+
(w4-w5)*x3)*y2)*z1) - (z1^2+y1^2+x1^2+w1^2)*(-w2*(x3*(y4*z5-y5*z4)
-y3*(x4*z5-x5*z4) + (x4*y5-x5*y4)*z3) +x2*(w3*(y4*z5-y5*z4)
+y3*(w5*z4-w4*z5) - (w5*y4-w4*y5)*z3) -y2*(w3*(x4*z5-x5*z4)
+x3*(w5*z4-w4*z5) - (w5*x4-w4*x5)*z3) + (w3*(x4*y5-x5*y4)
+x3*(w5*y4-w4*y5) - (w5*x4-w4*x5)*y3)*z2)) == 0) {
print "are in the surface of a 4D sphere";
} else {
print "are NOT on a 4D sphere surface";
}
Generated by dwww version 1.15 on Wed Jun 26 01:23:01 CEST 2024.