GR_stuff

christoffel.py

import sympy as sym 

x1, x2 = sym.symbols("x1 x2")
coord = [x1, x2]
g = sym.Matrix([[1,0],[0,x1**2]])
ginv = g.inv()

def christoffel(coord, g, ginv, index1, index2, index3):
	"""
	coord is the list of coordinates, eg coord = [r, theta, phi] 
	  where each coord entry is a SymPy symbol
	g is the metric matrix
	ginv is the inverse metric 
	index1 is the upper index. 
	index2 is the first lower index.
	index3 is the second lower index.
	"""
	chris = 0
	if g.shape[0] != g.shape[1]:
		print("You didn't define g correctly!")

	size = g.shape[0]

	for i in xrange(size):
		chris += 0.5*ginv[i,index1]*(sym.diff(g[i,index2],coord[index3])+sym.diff(g[i,index3],coord[index2])-sym.diff(g[index2,index3],coord[i]))

	return chris