Bug in canonical_height for dynamical systems?

[David Krumm]

The following few lines lead to a crash in Sage 10.0 with error message "TypeError: Not an element of the order." Is this an error on my part?

K.<a> = NumberField(3*x^2 + 1)
P.<z,w> = ProjectiveSpace(K, 1)
phi = DynamicalSystem_projective([a*(z^2 + w^2),z*w])
phi.canonical_height(P(a,1))

-- David

[Ben]

This looks like an error in .normalize_coordinates(). That function is
assuming that after you clear denominators, then the coefficients are in
the maximal order. This is clearly false. That function needs to be
fixed, please open an issue on github so we can track it and get it fixed.

As a workaround, you can scale phi so that all the coefficients are in
the maximal order (this does not change the canonical height calculation).

K.<a> = NumberField(3*x^2 + 1)
P.<z,w> = ProjectiveSpace(K, 1)
phi = DynamicalSystem_projective([a*(z^2 + w^2),z*w])

phi.scale_by(3)
phi.canonical_height(P(a,1))

Ben

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[Ben]

I've opened this issue is github:

https://github.com/sagemath/sage/issues/35797