Boundary cases

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David Kohel

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Mar 4, 2013, 4:18:03 AM3/4/13
to sage-algebra, sage-...@gmail.com
In a ring of characteristic 0, it seems that 0^0 (= 1) is well-
defined.
In my view this is correct. It makes it much simpler to define the
matrix (e.g. FF a finite field):

G = matrix([ [ a^i for a in FF ] for i in range(k) ])

However, in finite fields or any of the the following rings, 0^0
gives an error:

FF.<w> = FiniteField(32)
FF = FiniteField(31)
PF.<x> = PolynomialRing(FF)

The correct behaviour can be faked in an isomorphic ring which
is a quotient of something in characteristic zero:

PZ.<x> = PolynomialRing(ZZ)
R = PZ.quotient_ring([x-1,31])

Here R(0)^0 (= 1) is fine. Is there any objection to reporting this
as a bug and fixing it?

--David
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