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Is there an easy way to define a purely symbolic riemannian metric on a manifold? Or do I need to initialize it like this g[0,0] = function('g00')(t,x,y,z) for example?

M = Manifold(4, 'M')
CM.<u,r,θ,φ> = M.chart(r'u r:(0,+oo) θ:(0,pi) φ:(0,2*pi)')
e = CM.coframe()
du = e[0]
dr = e[1]
dθ = e[2]
dφ = e[3]
V = function('V')
β = function('β')
γ = function('γ')
δ = function('δ')

(dθ * dφ + dφ * dθ).symmetries()
(dθ * dφ + dφ * dθ).symmetrize() == (dθ * dφ + dφ * dθ)

I want to define a (degenerate) metric:

 g = M.metric('g')
 g.set(dθ * dφ + dφ * dθ)

this fails because Sage does not believe the tensor field to be symmetric.

Thanks, this works of course. Just find it odd that g.set(...) does not explicitly check that the argument is symmetric.

Why does sage fail to detect the symmetry here? M = Manifold(4, 'M') CM.<u,r,θ,φ> = M.chart(r'u r:(0,+oo) θ:(0,pi)

oh, that is a pity. both in terms of writing it out and computationally. I will then use cadabra2 in the meantime for th

Keep metric purely symbolic Is there an easy way to define a purely symbolic riemannian metric on a manifold? Or do I ne

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