Riemannium's profile - activity

HI, there. I tried to compute some examples with Sage manifolds and I got this:

sage: E2 = Manifold(2, 'E^2', latex_name=r'\mathbb{E}^2',start_index=1)

NotImplementedError Traceback (most recent call last) <ipython-input-37-4b1cf0743b4e> in <module>() ----> 1 E2 = Manifold(Integer(2), 'E^2', latex_name=r'\mathbb{E}^2',start_index=Integer(1))

/usr/lib/sagemath/src/sage/misc/lazy_import.pyx in sage.misc.lazy_import.LazyImport.__call__ (/usr/lib/sagemath//src/build/cythonized/sage/misc/lazy_import.c:3627)() 384 True 385 """ --> 386 return self._get_object()(args, *kwds) 387 388 def __repr__(self):

/usr/lib/sagemath/local/lib/python2.7/site-packages/sage/manifolds/manifold.py in Manifold(dim, name, latex_name, field, structure, start_index, **extra_kwds) 1653 else: 1654 raise NotImplementedError("manifolds of type {} are not ".format(structure) + -> 1655 "implemented") 1656 return TopologicalManifold(dim, name, field, structure, 1657 latex_name=latex_name, start_index=start_index,

NotImplementedError: manifolds of type smooth are not implemented

How could I fix it?

PS: My plan is to compute metric, connection, curvature, and riemann tensors. PS(II): Are differential forms implemented in Sage? Thanks!

I got this trying to compute the example christoffel symbols sage:

sage: var('r t theta phi')
(r, t, theta, phi)
sage: (r, t, theta, phi)
(r, t, theta, phi)
sage: sage: m = matrix(SR, [[(1-1/r),0,0,0],[0,-(1-1/r)^(-1),0,0],[0,0,-r^2,0],[0,0,0,-r^2*(sin(theta))^2]])
sage: sage: print m
[ -1/r + 1 0 0 0]
[ 0 1/(1/r - 1) 0 0]
[ 0 0 -r^2 0]
[ 0 0 0 -r^2*sin(theta)^2]
sage: [ -1/r + 1 0 0 0]

Moreover, I get...

sage: var('r t theta phi')
(r, t, theta, phi)
sage: m = matrix(SR, [[(1-1/r),0,0,0],[0,-(1-1/r)^(-1),0,0],[0,0,-r^2,0],[0,0,0,-r^2*(sin(theta))^2]])    
sage: def christoffel(i,j,k,vars,g):
....:        s = 0
....:        ginv = g^(-1)
....:        for l in range(g.nrows()):
....:               s = s + (1/2)*ginv[k,l]*(g[j,l].diff(vars[i])+g[i,l].diff(vars[j])-g[i,j].diff(vars[l]))
....:            return s
....:     
  File "<ipython-input-3-70e0eaa76f50>", line 6
    return s
            ^
IndentationError: unindent does not match any outer indentation level

What am I doing BAD?