Esempi in Python per Ricci, justicia

Esempio n. 1

from ET import *

B = Function('B')
A = Function('A')

t = Symbol('t')
r = Symbol('r')
theta = Symbol('theta')
phi = Symbol('phi')

g = Metric((-B(r), 0, 0, 0), (0, A(r), 0, 0), (0, 0, r**2, 0),
           (0, 0, 0, r**2 * sin(theta)**2))
x = (t, r, theta, phi)
C = Christoffel(g, x)
Rie = Riemann(C, x)
Ric = Ricci(Rie, x)
Rs = Rscalar(Ric)
G = ET(Ric, g, Rs)

print 'Initial metric:'
pprint(g.matrix())
#C.nonzero()
Ric.nonzero()
#Rie.nonzero()
#Rs.printing()
G.nonzero()

print 'Initial metric:'
pprint(gdd)
Gamma.nonzero()
Ric.nonzero()

Esempio n. 2

File: staticuniverse.py Progetto: gausstein/relativipy

t=Symbol('t')
r=Symbol('r')
theta=Symbol('theta')
phi=Symbol('phi')

A= Function('A')
K = Symbol('K')

#general, spherically symmetric metric
gdd=Matrix((
    (-1,0,0,0),
    (0, A(t)/(1 - K*r**2), 0, 0),
    (0, 0, A(t)*r**2, 0),
    (0, 0, 0, A(t)*r**2*sin(theta)**2)
    ))

g=Metric(gdd)
x=(t,r,theta,phi)
C=Christoffel(g,x)
Rie = Riemann(C,x)
Ric=Ricci( Rie,x)
Rs =Rscalar(Ric)


print 'Initial metric:'
pprint(gdd)
C.nonzero()
Ric.nonzero()
#Rie.nonzero()
#Rs.printing() 

Esempio n. 3

File: implementation.py Progetto: gausstein/relativipy

theta=Symbol('theta')
phi=Symbol('phi')

#general, spherically symmetric metric
gdd=Matrix((
    (-B(r),0,0,0),
    (0, A(r), 0, 0),
    (0, 0, r**2, 0),
    (0, 0, 0, r**2*sin(theta)**2)
    ))

g=Metric(gdd)
X=(t,r,theta,phi)
Gamma=Christoffel(g,X)
Rie = Riemann(Gamma,X)
Ric=Ricci(Rie,X)
Rs =Rscalar(Ric)

print 'Initial metric:'
pprint(gdd)

Gamma.nonzero()
Ric.nonzero()
#Rie.nonzero()
Rs.printing() 

print '-'*40
#Solving EFE for A and B
s = ( Ric.dd(1,1)/ A(r) ) + ( Ric.dd(0,0)/ B(r) )
pprint (s)
t = dsolve(s, A(r))

Esempio n. 4

File: implementation.py Progetto: gausstein/relativipy

r=Symbol('r')
theta=Symbol('theta')
phi=Symbol('phi')

#general, spherically symmetric metric
gdd=Matrix((
    (-B(r),0,0,0),
    (0, A(r), 0, 0),
    (0, 0, r**2, 0),
    (0, 0, 0, r**2*sin(theta)**2)
    ))

g=Metric(gdd)
X=(t,r,theta,phi)
Gamma=Christoffel(g,X)
Ric=Ricci(Riemann(Gamma,X),X)

def pprint_Gamma_udd(i,k,l):
    pprint(Eq(Symbol('Gamma^%i_%i%i' % (i,k,l)), Gamma.udd(i,k,l)))

def pprint_Ric_dd(i,j):
    pprint(Eq(Symbol('R_%i%i' % (i,j)), Ric.dd(i,j)))

print 'Initial metric:'
pprint(gdd)
print '-'*40
print 'Christoffel symbols:'
for i in [0,1,2,3]:
	for k in [0,1,2,3]:
		for l in [0,1,2,3]:
			if Gamma.udd(i,k,l) != 0 :

Esempio n. 5

File: sample-S2.py Progetto: eminamitani/differential-geometry

import Ricci
from sympy import *
from sympy.abc import phi, theta

coordinate = [theta, phi]
g = Matrix([[1, 0], [0, sin(theta) * sin(theta)]])

S2 = Ricci.Ricci(coordinate, g)
CF = S2.ChristoffelSymbol()
print(CF)

Esempio n. 6

from Christoffel import *
from Riemann import *
from Ricci import *
from Rscalar import *

t = Symbol('t')
r = Symbol('r')
theta = Symbol('theta')
phi = Symbol('phi')

A = Function('A')
K = Symbol('K')

#general, spherically symmetric metric
gdd = Matrix(((-1, 0, 0, 0), (0, A(t) / (1 - K * r**2), 0, 0),
              (0, 0, A(t) * r**2, 0), (0, 0, 0, A(t) * r**2 * sin(theta)**2)))

g = Metric(gdd)
x = (t, r, theta, phi)
C = Christoffel(g, x)
Rie = Riemann(C, x)
Ric = Ricci(Rie, x)
Rs = Rscalar(Ric)

print 'Initial metric:'
pprint(gdd)
C.nonzero()
Ric.nonzero()
#Rie.nonzero()
#Rs.printing()

Esempio n. 7

theta=Symbol('theta')
phi=Symbol('phi')

#general, spherically symmetric metric
gdd=Matrix((
    (-B(r),0,0,0),
    (0, A(r), 0, 0),
    (0, 0, r**2, 0),
    (0, 0, 0, r**2*sin(theta)**2)
    ))

g=Metric(gdd)
X=(t,r,theta,phi)
Gamma=Christoffel(g,X)
Rie = Riemann(Gamma,X)
Ric=Ricci(Rie,X)


print 'Initial metric:'
pprint(gdd)
print '-'*40
print 'Christoffel symbols:'
for i in [0,1,2,3]:
	for k in [0,1,2,3]:
		for l in [0,1,2,3]:
			if Gamma.udd(i,k,l) != 0 :
				Gamma.printing(i,k,l)
print'-'*40
print'Ricci tensor:'
for i in [0,1,2,3]:
   	for j in [0,1,2,3]: