On Dec 5, 2007 8:01 PM, William Stein <[EMAIL PROTECTED]> wrote:
> On Dec 5, 2007 4:17 PM, Robert Miller <[EMAIL PROTECTED]> wrote:
> >
> > Does anyone have any thoughts on the following? Luke Wolcott showed me
> > this example- the traceback looks suspect, but I don't know about the
> > internals here. Is this just something that is too big?
> >
> > {{{id=14|
> > P = QQ[2^(1/2), 2^(1/3), 2^(1/5)]
> > }}}
> >
> > {{{id=11|
> > P.gens()
> > ///
> > (sqrt2, a, b)
> > }}}
> >
> > {{{id=10|
> > aaa,bbb,ccc = P.gens()
> > }}}
> >
> > {{{id=17|
> > print aaa.absolute_minpoly();
> > print bbb.absolute_minpoly();
> > print ccc.absolute_minpoly();
> > ///
> > x^2 - 2
> > x^3 - 2
> > x^5 - 2
> > }}}
> >
> > {{{id=19|
> > P.order(aaa)
>
> I'm really glad Michael and you reported this.
>
> In the situation above, aaa satisfies only a quadratic polynomial so
> there is no possible way it will generate an order in a degree 8 field,
> since the index [O_K : ZZ[aaa]] is clearly infinite. Sage should
> quickly detect this and give an error message, but doesn't for some
> reason. By the way, the following code is equivalent to the code
> above but much simpler:
>
> sage: P.<a,b,c> = QQ[2^(1/2), 2^(1/3), 2^(1/5)]
> sage: P.order([1,a])
> *should* go boom very quickly.
>
> This is now trac #1407:
>
> http://trac.sagemath.org/sage_trac/ticket/1407
I've posted a patch there that fixes the "constructing an order in
a relative extension" problem:
http://trac.sagemath.org/sage_trac/ticket/1407
>
> Also, I noticed that you guys found a lib-singular bug in reduction of
> multivariate
> polynomials modulo p yesterday. This was easy to replicate:
>
> sage: R.<x,y> = QQ[]
> sage: S.<xx,yy> = GF(5)[]
> sage: S(5*x*y + x + 17*y)
> 0*xx*yy + xx + 2*yy
>
> I've filed a trac ticket about this:
> http://trac.sagemath.org/sage_trac/ticket/1406
>
>
>
> -- William
>
--
William Stein
Associate Professor of Mathematics
University of Washington
http://wstein.org
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