#15808: Remove genus2reduction
-------------------------------------+-------------------------------------
Reporter: jdemeyer | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.4
Component: packages: | Resolution:
standard | Merged in:
Keywords: | Reviewers:
Authors: Jeroen Demeyer | Work issues:
Report Upstream: N/A | Commit:
Branch: | 1068fef87401f820747d4f938a56d2429afbe4b0
public/ticket/15808 | Stopgaps:
Dependencies: #15767 |
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Comment (by jdemeyer):
Replying to [comment:13 pbruin]:
> Do you have a reference for the following manipulations?
They are based on looking at the PARI source code. But I must admit that I
don't understand everything 100% clearly.
The line
{{{
if minimal_equation.degree() == 5:
minimal_disc *= minimal_equation[5]**2
}}}
is based on
{{{
RgX_to_6(polr, &a0,&a1,&a2,&a3,&a4,&a5,&a6);
I.j10 = !signe(a0)? mulii(sqri(a1), ZX_disc(polr)): ZX_disc(polr);
}}}
The factor `2^(-12)` comes from
{{{
I.j10 = gmul2n(I.j10,-12);
}}}
and the multiplication by `2^(2*(d-1))` comes from
{{{
dd = polval(polr,gen_2) & (~1); /* = 2 floor(val/2) */
polr = gmul2n(polr, -dd);
}}}
which multiplies the whole polynomial by a power of 4.
Multiplying a polynomial of degree `d` by a constant `c` multiplies the
discriminant by `c^(d-1)`.
> Is the power of 2 in fact important?
I have no idea. I tried to reproduce as best as possible the output of the
old `genus2reduction` program. That is also the reason why I emulated the
`raw()` method and wrote to `divisors_to_string()` function: to check for
myself if the new output was the same as the old output. Modulo some small
details, this seems indeed to be the case.
--
Ticket URL: <http://trac.sagemath.org/ticket/15808#comment:14>
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