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Prime fields are a very special case of finite fields, so unsurprisingly there are major implementation differences.

Those differences however should, as much as possible, be smoothed out in the user interface, and you are perfectly right in pointing out this inconsistency.

Fixing this is now tracked at

• Sage Trac ticket 31606: Make finite field element constructor accept lists for prime fields too

Similar tickets exist to make available methods more consistent for various implementation of finite fields:

• Sage Trac ticket 31294: Implement fetch_int method for non-givaro finite fields
• Sage Trac ticket 31605: Implement integer_representation method for non-givaro finite fields

Similarly there have been tickets to make some of the number field methods available for QQ too:

• Sage Trac ticket 23761: Add QQ to the category of number fields
• Sage Trac ticket 26239: QQ not isomorphic to itself