It worries me that the outputs live in different rings for different
classes, and the latter is not even a field :)

sage: x = ZZ['x'].0

sage: K.<a> = GF(11**11, name='a', modulus=x^11 - x + 1)
sage: type(K)
 <class 'sage.rings.finite_field.FiniteField_ext_pari'>
sage: K.modulus()
 x^11 - x + 1

sage: K.<a> = GF(5**5, name='a', modulus=x^5 - x + 1)
sage: type(K)
 <type 'sage.rings.finite_field_givaro.FiniteField_givaro'>
sage: K.modulus()
 a^5

Nick


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