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Diffstat (limited to 'data/points/generator/aurelien_alvarez_surfaces_in_R8.py')
| -rwxr-xr-x | data/points/generator/aurelien_alvarez_surfaces_in_R8.py | 90 |
1 files changed, 0 insertions, 90 deletions
diff --git a/data/points/generator/aurelien_alvarez_surfaces_in_R8.py b/data/points/generator/aurelien_alvarez_surfaces_in_R8.py deleted file mode 100755 index 57773c4c..00000000 --- a/data/points/generator/aurelien_alvarez_surfaces_in_R8.py +++ /dev/null @@ -1,90 +0,0 @@ -# This file is part of the Gudhi Library. The Gudhi library -# (Geometric Understanding in Higher Dimensions) is a generic C++ -# library for computational topology. -# -# Author(s): Aurélien Alvarez -# -# Copyright (C) 2016 Université d'Orléans (France) -# -# This program is free software: you can redistribute it and/or modify -# it under the terms of the GNU General Public License as published by -# the Free Software Foundation, either version 3 of the License, or -# (at your option) any later version. -# -# This program 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 General Public License for more details. -# -# You should have received a copy of the GNU General Public License -# along with this program. If not, see <http://www.gnu.org/licenses/>. - -import numpy as np -import random -from math import factorial - -I = complex(0,1) - -################################################# -################################################# - -#Surface réelle d'équation x.conj(y)^d + y.conj(z)^d + z.conj(x)^d = 0 dans P2(C) -#Équation affine (z=1) multipliée par sa conjuguée (d = 2) : x.conj(x)^2.y^4 + 2x^3.conj(x).y^2 + y + conj(x)^2 + x^5 = 0 -def equationAffineSurfaceReelle(x): - polynome = [0]*(degre**2+1) - for k in range(degre+1): - polynome[k*degre] = (-1)**degre*x*factorial(degre)/(factorial(k)*factorial(degre-k))*x**(k*degre)*np.conjugate(x)**(degre-k) - polynome[-2] += 1 - polynome[-1] += np.conjugate(x)**degre - return polynome - -################################################# -################################################# - -def calculRacines(equation,nombrePoints,module_x): - racines = [[1,0,0],[0,1,0],[0,0,1]] - for _ in range(nombrePoints): - x = module_x*(2*random.random()-1+I*(2*random.random()-1)) - fool = [[[x,y,1],[y,1,x],[1,x,y]] for y in np.roots(equation(x)) if abs(x*np.conjugate(y)**degre+y+np.conjugate(x)**degre) < 0.0001] - for bar in fool: - racines += bar - return racines - -################################################# -################################################# - -def plongementDansR8(pointDansCP2): - z0 = pointDansCP2[0] - z1 = pointDansCP2[1] - z2 = pointDansCP2[2] - a = z0*np.conjugate(z0) - b = z1*np.conjugate(z1) - c = z2*np.conjugate(z2) - normeCarree = a+b+c - a = a/normeCarree - b = b/normeCarree - u = z0*np.conjugate(z1)/normeCarree - v = z0*np.conjugate(z2)/normeCarree - w = z1*np.conjugate(z2)/normeCarree - return [a.real,b.real,u.real,u.imag,v.real,v.imag,w.real,w.imag] - -def plongementListeDansR8(listePointsDansCP2): - listePointsDansR8 = [] - for point in listePointsDansCP2: - listePointsDansR8 += [plongementDansR8(point)] - return listePointsDansR8 - -################################################# -################################################# - -degre = 3 -nombrePoints = 10**4 -module_x = 10 - -with open("surface.txt","w") as fichier: - bar = calculRacines(equationAffineSurfaceReelle,nombrePoints,module_x) - listePoints = plongementListeDansR8(bar) - fichier.write(str(len(bar)) + "\n") - for point in listePoints: - fichier.write(str(point[0]) + " " + str(point[1]) + " " + str(point[2]) + " " + str(point[3]) + " " + str(point[4]) + " " + str(point[5]) + " " + str(point[6]) + " " + str(point[7]) + "\n") - |