>From #17205:

sage: x, y = ZZ['x','y'].gens()
sage: GF(1091)['x','y'].random_element().degree(x) 
2
sage: GF(3037000453)['x','y'].random_element().degree(x) 
...
TypeError: x must be one of the generators of the parent.

I don't think the behavior should be different the polynomial rings over 
GF(1091) and GF(3037000453), but I don't know what the right behavior 
should be. Should x (which is one of the generators of ZZ[x,y]) be 
automatically coerced to an element of GF(p)[x,y] when we call 
elt.degree(x)?

-- 
John

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