Covariant Derivative gives Error, why? (SAGE 7.5.1)
This simple code gives an Error:
f = function('f')
B=Manifold(2,'B',start_index=1)
polar.<R,Phi> = B.chart(R'R:(0,+oo) Phi:(0,2*pi):\Phi')
G = B.riemannian_metric('G')
G[1,1]=diff(f(R),R)
G[2,2]=f(R)^2
nabla=G.connection()
S=B.tensor_field(1,1)
S[1,1]=R^(0.5)
S[2,2]=R^3
S.display()
nabla(S)
Error: TypeError: unable to convert R to an integer
This Error doesn't occur either if I avoid the square root in S[1,1]=R^(0.5), for example by writing S[1,1]=R^(0.4) or if I avoid the dependence of the derivative of f in the first entry of the metric, for example by writing G[1,1]=f(R)^2.
This Error also doesn't occur in older Sage versions, for example Sage 7.1
Thanks a lot for help!