#4218: Extensions of Finite Fields don't work well
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Reporter: justin | Owner: tbd
Type: defect | Status: new
Priority: major | Milestone:
Component: algebra | Keywords:
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The following sage snippets show (some of) the problems. First, we set
the stage:
{{{
sage: F1.<a> = GF(2^7)
sage: P1.<x>=PolynomialRing(F1)
sage: f=x^2+x+F1(1)
sage: F2=F1.extension(f,'u')
sage: F2
Univariate Quotient Polynomial Ring in u over Finite Field in a of size
2^7 with modulus u^2 + u + 1
sage: a in F2
True
}}}
First problem:
{{{
sage: for i in xrange(100):
....: r = F2.random_element()
....: if r != F2(0) and r != F2(1):
....: print "Yoicks! r=%s"%r
....:
sage:
}}}
No output means that 100 random elements of F2 are either
0 or 1, which seems somehow incorrect.
The next oddity is
{{{
sage: F1.order()
128
sage: F2.order()
---------------------------------------------------------------------------
NotImplementedError Traceback (most recent call
last)
/SandBox/Justin/sb/sage-3.1.1/<ipython console> in <module>()
/SandBox/Justin/sb/sage-3.1.1/ring.pyx in sage.rings.ring.Ring.order
(sage/rings/ring.c:4108)()
NotImplementedError:
}}}
Shouldn't .order() work for extensions as well as those directly defined?
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/4218>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
Reinventing the Wheel
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