#13180: Compare elements of finite fields somehow consistently
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Reporter: SimonKing | Owner: AlexGhitza
Type: defect | Status: new
Priority: major | Milestone: sage-5.2
Component: basic arithmetic | Keywords:
Work issues: | Report Upstream: N/A
Reviewers: | Authors:
Merged in: | Dependencies:
Stopgaps: |
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Finite fields are not ordered fields. But of course cmp can still be
applied to them. It would be nice to have a consistent way of comparison
of elements in different rings. In most cases, one gets the same answers:
{{{
sage: K = GF(2)
sage: K(0) < K(1)
True
sage: K = GF(4,'z')
sage: K(0) < K(1)
True
sage: K(0) < K('z')
True
sage: K = GF(3)
sage: K(0) < K(1)
True
sage: K(0) < K(-1)
True
sage: K = GF(9,'z')
sage: K(0) < K(1)
True
sage: K(0) < K(-1)
True
sage: K(0) < K('z')
True
sage: K = GF(3^100,'z')
sage: K(0) < K(1)
True
sage: K(0) < K(-1)
True
sage: K(0) < K('z')
True
}}}
But alas:
{{{
sage: K = GF(2^100,'z')
sage: K(0) < K(1)
False
sage: K(0) < K('z')
False
}}}
I suggest to make big finite fields of characteristic 2 behave like the
other fields.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13180>
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