I just tracked down a nasty bug completely messing up my math experiments 
to the following internal caching mechanism. In a clean Sage type:

sage: E = FiniteEnumeratedSet([ GF(97)(i) for i in [1,2,3,4,5,6]]); 
type(E[0])
<type 'sage.rings.finite_rings.integer_mod.IntegerMod_int'>

Restart Sage and type instead

sage: E = FiniteEnumeratedSet([1,2,3,4,5,6])
sage: type(E[0])
<type 'sage.rings.integer.Integer'>
sage: E = FiniteEnumeratedSet([ GF(97)(i) for i in [1,2,3,4,5,6]]); 
type(E[0])
<type 'sage.rings.integer.Integer'>

Many variations of this theme seem possible.

This was Sage 7.5.beta0.

Can someone knowledgeable help find the root cause and possible other 
places the bug could appear?

Best,
Johan

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