Hi Vincent,
On Mon, Jan 19, 2015 at 11:30 AM, Vincent Delecroix
<20100.delecr...@gmail.com> wrote:
> Hello Ondrej,
>
> For such questions of Sage usage, it is better to discuss on
> ask.sagemath.org or sage-support.
>
> You can also deal with all algebraic numbers at once with QQbar
>
> sage: sqrt3 = QQbar(sqrt(3))
> sage: sqrt5 = QQbar(sqrt(5))
>
> But then polynomials over QQbar are much slower.
Thanks, I'll ask there the next time. Since I started the thread here,
I'll keep it here so that everything is in one place.
So if you agree that I did things correctly, let's compare timings
(and lengths of expressions --- any idea how to get the number of
terms in a better way in Sage?):
sage: K.<sqrt3> = QuadraticField(3)
sage: L.<sqrt5> = K.extension(x^2-5)
sage: R.<a1,a2,a3,a4,a5> = L[]
sage: time f = (a1+a2+a3+sqrt5*a4+sqrt3*a5)^18
CPU times: user 2.43 s, sys: 3.94 ms, total: 2.44 s
Wall time: 2.44 s
sage: len(str(f).split("+"))
7315
Now compare this to CSymPy:
In [1]: from csympy import *
In [2]: var('a1 a2 a3 a4 a5 a6 a7')
Out[2]: (a1, a2, a3, a4, a5, a6, a7)
In [3]: %time f = ((a1+a2+a3+sqrt(5)*a4+sqrt(3)*a5)**18).expand()
CPU times: user 125 ms, sys: 7.73 ms, total: 133 ms
Wall time: 133 ms
In [4]: len(f.args)
Out[4]: 7315
You can also compare this to Sage symbolics (which should use the same
algorithm as CSymPy):
sage: var('a1 a2 a3 a4 a5 a6 a7')
(a1, a2, a3, a4, a5, a6, a7)
sage: %time f = ((a1+a2+a3+sqrt(5)*a4+sqrt(3)*a5)**18).expand()
CPU times: user 4.98 s, sys: 76.4 ms, total: 5.05 s
Wall time: 4.95 s
sage: len(f.operands())
7315
Which is also very slow.
I will try this in ginac directly, as that's what pynac is forked
from, maybe it's just the Python overhead. Also, I will carefully
check that we don't have a bug in csympy.
Ondrej
--
You received this message because you are subscribed to the Google Groups
"sage-devel" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to sage-devel+unsubscr...@googlegroups.com.
To post to this group, send email to sage-devel@googlegroups.com.
Visit this group at http://groups.google.com/group/sage-devel.
For more options, visit https://groups.google.com/d/optout.
