incorrect conversion of finite-field elements

[yyyyx4]

Example (Sage 10.8):

sage: GF(101^2)(GF(101^3).gen())
z2

The expected behaviour is failure (the generator of GF(101^2) does not lie in GF(101^3)).

[hemannt003]

Hi @yyyyx4 , I’d like to work on this.

It looks like the issue arises from allowing coercion between incompatible finite fields, where the extension degrees are not compatible (e.g., 2 does not divide 3).

I plan to:

• Add a validation step in the coercion/conversion logic to ensure that elements are only converted when there is a valid field embedding
• Raise an appropriate error when the source field is not a subfield of the target field

I’ll keep the fix minimal and aligned with existing coercion rules in Sage.

Please let me know if this approach sounds good!