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RG_4x4_all.py
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RG_4x4_all.py
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#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Fri Nov 13 14:56:53 2020
@author: Thomas Stinglhamber (De La Physique)
"""
import sympy as sp
import numpy as np
from pprint import pprint
""" definition constantes """
t = sp.Symbol('t')
r = sp.Symbol('r')
o= sp.Symbol('o') # theta
p= sp.Symbol('p') # phi
G= sp.Symbol('G')
M= sp.Symbol('M')
u= sp.Symbol('u')
v= sp.Symbol('v')
K= sp.Symbol('K')
p_1 = sp.Symbol('p_1')
p_2 = sp.Symbol('p_2')
p_3 = sp.Symbol('p_3')
p_4 = sp.Symbol('p_4')
C = sp.Symbol('C')
""" Definition metrique """
g = [[(1-(2*G*M)/r) ,0,0,0],
[0,(1/(1-2*G*M/r)),0,0],
[0,0,r**2,0],
[0,0,0,r**2 * sp.sin(o)**2]]
""" variable de la métrique """
k=[t,r,o,p]
""" Chemin pour créer le fichier .txt avec le code LaTeX """
Path ="/Users/thomasstinglhamber/Desktop/RG_ALL/LaTeX_RG_4x4.txt"# changer pour mettre votre chemin
ToLaTeX = True # False pour pas générer le fichier.txt
#--------------------- Plus rien a modifier à partir d'ici -----------------------
f = open(Path, "w")
g2=sp.Matrix(([g[0][0],g[1][0],g[2][0],g[3][0]],
[g[0][1],g[1][1],g[2][1],g[3][1]],
[g[0][2],g[1][2],g[2][2],g[3][2]],
[g[3][0],g[3][1],g[3][2],g[3][3]]))
g_inv= g2.inv()
print("\u0332".join("Metrique : "))
pprint(g)
print()
def Christo4x4():
Christo = [[0,0,0,0],
[0,0,0,0],
[0,0,0,0],
[0,0,0,0],]
Christo_t = [[0,0,0,0],
[0,0,0,0],
[0,0,0,0],
[0,0,0,0],]
Christo_r = [[0,0,0,0],
[0,0,0,0],
[0,0,0,0],
[0,0,0,0],]
Christo_o = [[0,0,0,0],
[0,0,0,0],
[0,0,0,0],
[0,0,0,0],]
Christo_p = [[0,0,0,0],
[0,0,0,0],
[0,0,0,0],
[0,0,0,0],]
Christofell=[]
""" definition des symboles de Christofell """
print("\u0332".join("Symbole de Christofell: "))
for m in range(4):
for l in range(4):
for i in range(4):
for j in range(4):
Christo[i][j] = 1/2 * g_inv[l,m]*(sp.diff(g[l][i],k[j])+sp.diff(g[j][l],k[i])-sp.diff(g[i][j],k[l]))
if Christo[i][j] !=0:
print("C|",k[m],k[i],k[j],":",sp.simplify(Christo[i][j]) )
if m ==0:
Christo_t[i][j] =Christo[i][j]
if m ==1 :
Christo_r[i][j] =Christo[i][j]
if m ==2 :
Christo_o[i][j] =Christo[i][j]
if m ==3 :
Christo_p[i][j] =Christo[i][j]
Christofell =[Christo_t,Christo_r,Christo_o,Christo_p]
print()
for i in range(4):
print("Christofell selon",k[i],":")
pprint(Christofell[i])
print()
return Christofell
def Riemann(Christofell):
""" defintion de matrice utile apres pour indexation"""
Ri = [[0,0,0,0],
[0,0,0,0],
[0,0,0,0],
[0,0,0,0],]
Rl0=[[0,0,0,0],
[0,0,0,0],
[0,0,0,0],
[0,0,0,0],]
R_l0n0=[[0,0,0,0],
[0,0,0,0],
[0,0,0,0],
[0,0,0,0],]
R_l0n1=[[0,0,0,0],
[0,0,0,0],
[0,0,0,0],
[0,0,0,0],]
R_l0n2=[[0,0,0,0],
[0,0,0,0],
[0,0,0,0],
[0,0,0,0],]
R_l0n3=[[0,0,0,0],
[0,0,0,0],
[0,0,0,0],
[0,0,0,0],]
Rl1=[[0,0,0,0],
[0,0,0,0],
[0,0,0,0],
[0,0,0,0],]
R_l1n0=[[0,0,0,0],
[0,0,0,0],
[0,0,0,0],
[0,0,0,0],]
R_l1n1=[[0,0,0,0],
[0,0,0,0],
[0,0,0,0],
[0,0,0,0],]
R_l1n2=[[0,0,0,0],
[0,0,0,0],
[0,0,0,0],
[0,0,0,0],]
R_l1n3=[[0,0,0,0],
[0,0,0,0],
[0,0,0,0],
[0,0,0,0],]
R_l2n0=[[0,0,0,0],
[0,0,0,0],
[0,0,0,0],
[0,0,0,0],]
R_l2n1=[[0,0,0,0],
[0,0,0,0],
[0,0,0,0],
[0,0,0,0],]
R_l2n2=[[0,0,0,0],
[0,0,0,0],
[0,0,0,0],
[0,0,0,0],]
R_l2n3=[[0,0,0,0],
[0,0,0,0],
[0,0,0,0],
[0,0,0,0],]
Rl2=[[0,0,0,0],
[0,0,0,0],
[0,0,0,0],
[0,0,0,0],]
R_l3n0=[[0,0,0,0],
[0,0,0,0],
[0,0,0,0],
[0,0,0,0],]
R_l3n1=[[0,0,0,0],
[0,0,0,0],
[0,0,0,0],
[0,0,0,0],]
R_l3n2=[[0,0,0,0],
[0,0,0,0],
[0,0,0,0],
[0,0,0,0],]
R_l3n3=[[0,0,0,0],
[0,0,0,0],
[0,0,0,0],
[0,0,0,0],]
Rl3=[[0,0,0,0],
[0,0,0,0],
[0,0,0,0],
[0,0,0,0],]
R =[]
""" définition du tenseur de Riemann """
print("\u0332".join("Tenseur de Riemann :"))
for l in range(4):
for i in range(4):
for j in range(4):
for n in range(4):
for m in range(4):
Ri[j][n] = ((sp.diff(Christofell[l][i][j],k[n]))-(sp.diff(Christofell[l][i][n],k[j])) +((Christofell[m][i][j])*(Christofell[l][m][n]))-((Christofell[m][i][n])*(Christofell[l][m][j])))
if m==3:
if Ri[j][n] !=0:
print("R|",k[l],k[i],k[j],k[n],":",sp.simplify(Ri[j][n]))
if l==0:
if i ==0:
R_l0n0[j][n]= Ri[j][n]
if i ==1:
R_l0n1[j][n]= Ri[j][n]
if i ==2:
R_l0n2[j][n]= Ri[j][n]
if i ==2:
R_l0n3[j][n]= Ri[j][n]
if l==1:
if i ==0:
R_l1n0[j][n]= Ri[j][n]
if i ==1:
R_l1n1[j][n]= Ri[j][n]
if i ==1:
R_l1n2[j][n]= Ri[j][n]
if i ==2:
R_l1n3[j][n]= Ri[j][n]
if l==2:
if i ==0:
R_l2n0[j][n]= Ri[j][n]
if i ==1:
R_l2n1[j][n]= Ri[j][n]
if i ==1:
R_l2n2[j][n]= Ri[j][n]
if i ==2:
R_l2n3[j][n]= Ri[j][n]
if l==3:
if i ==0:
R_l3n0[j][n]= Ri[j][n]
if i ==1:
R_l3n1[j][n]= Ri[j][n]
if i ==1:
R_l3n2[j][n]= Ri[j][n]
if i ==2:
R_l3n3[j][n]= Ri[j][n]
Rl0 =[R_l0n0,R_l0n1,R_l0n2,R_l0n3]
Rl1 =[R_l1n0,R_l1n1,R_l1n2,R_l1n3]
Rl2 =[R_l2n0,R_l2n1,R_l2n2,R_l2n3]
Rl3 =[R_l3n0,R_l3n1,R_l3n2,R_l3n3]
R =[Rl0,Rl1,Rl2,Rl3]
print()
for i in range(4):
print("Riemann selon",k[i],":")
pprint(R[i])
print()
return R
def Ricci(R):
ricci1=[[0,0,0,0],
[0,0,0,0],
[0,0,0,0],
[0,0,0,0],]
ricci=[[0,0,0,0],
[0,0,0,0],
[0,0,0,0],
[0,0,0,0],]
""" Ricci """
print("\u0332".join("Tenseur de Ricci :"))
for l in range(4):
for i in range(4):
for j in range(4):
ricci1[i][j] = R[l][i][j][l]
if ricci1[i][j]!=0:
ricci[i][j]=ricci1[i][j]
print(ricci)
print()
return ricci
def Courbure_scalaire(ricci):
scalaire=[[0,0,0,0],
[0,0,0,0],
[0,0,0,0],
[0,0,0,0],]
""" courbure scalaire """
print("\u0332".join("Courbure scalaire :"))
for i in range(4):
for j in range(4):
scalaire[i][j]= g_inv[i,j]* ricci[i][j]
somme = scalaire[0][0]+scalaire[1][0]+scalaire[2][0]+scalaire[3][0]+scalaire[0][1]+scalaire[1][1]+scalaire[2][1]+scalaire[3][1]+scalaire[0][2]+scalaire[1][2]+scalaire[2][2]+scalaire[3][2]+scalaire[0][3]+scalaire[1][3]+scalaire[2][3]+scalaire[3][3]
print(somme)
return somme
"""--------------- Partie pour générer le code LaTeX ----------------- """
def PythonToLaTeX(Christofell,R,ricci,somme):
def pmatrix(a):
lines = str(a).replace('[', '').replace(']', '').replace(' - ','-').replace(' + ','+').splitlines()
rv = [r' $$\begin{pmatrix}']
rv += [' ' + ' ,& '.join(l.split()) + r'\\' for l in lines]
rv += [r'\end{pmatrix}$$']
return '\n'.join(rv)
def Tensor_matrix(a):
rv = [r'$$ \begin{pmatrix}']
for i in range(len(a)):
rv += [r' \begin{pmatrix}']
for j in range(len(a[i])):
lines = str(a[i][j]).replace('[', '').replace(']', '').replace(' - ','-').replace(' + ','+').splitlines()
rv += [' ' + ', & '.join(l.split()) + r'\\' for l in lines]
rv += [r'\end{pmatrix}\\']
rv += [r'\end{pmatrix}$$']
return '\n'.join(rv)
print('\setlength\parindent{0pt}',file=f)
print('\section{RG4x4}',file=f)
print('\subsection{Métrique}',file=f)
print(pmatrix(np.array(g)),'\n',file=f)
print('\subsection{Christofell}',file=f)
for m in range(4):
for i in range(4):
for j in range(4):
if Christofell[m][i][j] != 0:
print('$\Gamma^{',k[m],'}_{',k[i],k[j],'}',"=",Christofell[m][i][j],r'$\\', file=f)
else :pass
print('\n',file=f)
# =============================================================================
# for i in range(4):
# print('Symbole de Christofell selon $',k[i],'$ :\n',pmatrix(np.array(Christofell[i])) + '\n', file=f)
#
# =============================================================================
print('\subsection{Riemann}',file=f)
for l in range(4):
for i in range(4):
for j in range(4):
for n in range(4):
if R[l][i][j][n] !=0:
print('$R^{',k[l],'}_{',k[i],k[j],k[n],'}',"=",R[l][i][j][n],r'$\\', file=f)
print('\n',file=f)
# =============================================================================
# for i in range(4):
# print('Tenseur de Riemann selon $',k[i],'$ :\n',Tensor_matrix(np.array(R[i])) + '\n', file=f)
#
# =============================================================================
print('\subsection{Ricci}',file=f)
for l in range(4):
for i in range(4):
for j in range(4):
if R[l][i][j][l] !=0:
print('$R\mathrm{icci}_{',k[i],k[j],'}',"=",R[l][i][j][l],r'$\\', file=f)
print('\n',file=f)
# =============================================================================
# print('Tenseur de Ricci ','\n',pmatrix(np.array(ricci)) + '\n', file=f)
#
# =============================================================================
print('\paragraph{Courbure scalaire} ','\n','$$',somme , '$$',file=f)
f.close()
Christofell = Christo4x4()
R =Riemann(Christofell)
ricci =Ricci(R)
somme =Courbure_scalaire(ricci)
if ToLaTeX == True:
PythonToLaTeX(Christofell,R,ricci,somme)
f1 = open(Path, 'r')
input_data = f1.read()
f1.close()
theta_1 =' \sin(\\theta)'
theta_4 =' \cos(\\theta)'
theta_2 =' \\theta '
phi_2 =' \sin(\phi)'
phi_3 =' \cos(\phi)'
input_data = input_data.replace('o ', theta_2.replace('\t', '')).replace('p ' , ' \phi ').replace('**', '^').replace('cos(o)', theta_4.replace('\t', '')).replace('sin(o)', theta_1.replace('\t', '')).replace('sin(p)', phi_2).replace('cos(p)', phi_3).replace('*' , '').replace('1.00000000000000' , '1').replace('1.0/' , '1/').replace('1.0+' , '1+').replace('1.0-' , '1-').replace('1.0' , '')
f2 = open(Path, 'w')
f2.write(input_data)
f2.close()
print('\n','Fichier .txt généré')
else :pass