Now MAGMA uses SS/FFT down to degree 16 at least, for 1000 bit.
But now they really screwed up their algorithm, because I can use MAGMA
to multiply 2400 degree polynomials considerably faster than they do it
themselves.
Anyhow, I found another trick for going to 2^(l+2) digit numbers for
the sam
Hmm, and David's script runs in 3.2s again. That throws a few theories
out the window.
So they didn't dump their algorithm because of round off errors, or
some bug.
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Hi,
I just installed the 64-bit MAGMA 2.13 binary on SAGE.
William
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Hi,
Since everybody is posting their patched version of Pyrex, I'll post
mine:
http://modular.math.washington.edu/tmp/pyrex-20061022.tar.bz2
Mine has full support for the new __index__ method.
It also supports correct cimports across directories (and sets
tp_name correctly in extension modul
I think I finally found the faster algorithm. It's just plain
Schoenhage-Strassen, but with a so called sqrt 2 trick.
Basically, if you want to do a multiplication for polynomials of degree
<= 2^l, you need to do a 2^l point FFT, which means you need to work in
a ring that has 2^l roots of unity.
On Oct 23, 2006, at 10:43 AM, Bill Hart wrote:
> At one stage MAGMA were boasting that their integer multiplication was
> a lot faster than GMP, but I suspect GMP has caught them up now, and I
> think it only made a difference to numbers of a million bits or more.
> MAGMA now seem to claim that
Bill Hart wrote:
> This page apparently answers the question definitively:
>
> http://magma.maths.usyd.edu.au/magma/Features/node93.html
And this paper tells me exactly what I want to know:
http://www.mathematik.hu-berlin.de/~gaggle/EVENTS/2006/BRENT60/presentations/Allan%20Steel%20-%20Reduce%2
On Oct 23, 2006, at 12:16 AM, William Stein wrote:
> Perhaps there is a fast way to tell whether a class is a Python class
> or a Pyrex
> class (say in the base class __add__ method), and always call
> _add_sibling_cdef
> if it's a Pyrex class and _add_sibling if it's a Python class. There
Hi,
See below. It looks like the MAGMA I installed on sage.math was the wrong
download,
i.e., 32-bit instead of 64-bit.
--- Forwarded message ---
From: "Allan Steel" <[EMAIL PROTECTED]>
To: "William Stein" <[EMAIL PROTECTED]>
Cc:
Subject: Re: algorithms
Date: Mon, 23 Oct 2006 08:14:31
This page apparently answers the question definitively:
http://magma.maths.usyd.edu.au/magma/Features/node93.html
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On Oct 23, 2006, at 12:16 AM, William Stein wrote:
> David H,
>
> Hi -- I'm concerned because I think the __add__, etc., architecture
> that you
> guys came up with (as of now) prevents implementation of any derived
> class's
> arithmetic in Python.
[...]
Wow, you're absolutely right, that r
William Stein wrote:
> I wonder why they switched from that faster algorithm to a slower one?
> Maybe it produced incorrect results (possibly due to rounding errors)?
I doubt they did. On their website there is no mention in their
changelogs of any change in the algorithm for multiplication of
On Monday 23 October 2006 10:37, William Stein wrote:
> Hi,
>
> Assuming I wake up in a few hours, I'm giving a talk to tons of algebraic
> geometers about SAGE at the IMA. You might find it interesting...
>
> http://modular.math.washington.edu/talks/2006-10-23-ima/ima.pdf
Quick correction:
Hi,
Assuming I wake up in a few hours, I'm giving a talk to tons of algebraic
geometers about SAGE at the IMA. You might find it interesting...
http://modular.math.washington.edu/talks/2006-10-23-ima/ima.pdf
See examples, notebooks, raw source here:
http://modular.math.washington.ed
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