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The following works for me:
sage: p = 2^31 - 1
sage: p.is_prime()
True
sage: k.<a> = GF( p^2 )
sage: R.<z> = PolynomialRing( k, sparse=True )
sage: R
Sparse Univariate Polynomial Ring in z over Finite Field in a of size 2147483647^2
sage: B1 = 858993459*a + 429496730
sage: B1^p
1288490188*a + 1717986918
sage: B1*z + (B1*z)^p
(1288490188*a + 1717986918)*z^2147483647 + (858993459*a + 429496730)*z
The only important place is the one with PolynomialRing( k, sparse=True ), so that a sparse polynomial of high power can be stored.
