#!/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.