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I'm new to SageMath.

I was wondering how to form the conjugate of a complex scalar function on a Lorentzian manifold. This is useful for calculating Newman Penrose spin coefficients. According to the SageMath documentation, one can apply standard math functions (eg abs()) but as far as I can see there is no conjugate, real or imaginary part capability for scalar fields. For example trying conjugate(f) leads to:

"TypeError: cannot coerce arguments: no canonical coercion from Algebra of differentiable scalar fields on the 4-dimensional Lorentzian manifold M to Symbolic Ring".

On the other hand using SageManifolds to differentiate abs(f(t)) where f(t) is a scalar function leads to:

dabs(f) = 1/2(conjugate(d(f)/dt)f(t) + conjugate(f(t))*d(f)/dt)/abs(f(t)) dt

I'm not sure if this is a misunderstanding on my part or a missing feature.

I'm new to SageMath.

I was wondering how to form the conjugate of a complex scalar function function on a Lorentzian manifold. This is useful for calculating Newman Penrose Penrose spin coefficients. According to the SageMath documentation, one can can apply standard math functions (eg abs()) abs()) but as far as I can see there is is no conjugate, real or imaginary part capability for scalar fields. fields. For example trying conjugate(f) conjugate(f) leads to:

TypeError: cannot coerce arguments: no canonical canonical
coercion from Algebra of differentiable scalar fields on on
the 4-dimensional Lorentzian manifold M to Symbolic Ring".
Ring

dabs(f) = 1/2(conjugate(d(f)/dt)f(t) 1/2*(conjugate(d(f)/dt)*f(t) + conjugate(f(t))*d(f)/dt)/abs(f(t)) dt
dt