this is now in trac: http://trac.sagemath.org/sage_trac/ticket/9913
Paul Zimmermann
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: continued_fraction(a, bits=150)
[2, 7314423575030504, 1, 83, 1, 2, 1, 108, 1, 20]
Paul Zimmermann
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Mezzarobba, Clément Pernet,
Nicolas M. Thiéry, Paul Zimmermann
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be better, and remainder could be provided
as a different method.
Paul Zimmermann
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on function for positive
quotient, but not for negative quotient, since the Python function seems to
round the quotient towards -infinity:
>>> (-6e-6) % 10e-6
4.0007e-06
>>> (6e-6) % (-10e-6)
-4.0007e-06
In C99 (and in MPFR) there is no mod/remainder function that
t/2 - ---
2 t
> convert(cos(log(t)),exp);
1/2 exp(ln(t) I) + 1/2 exp(-I ln(t))
Paul Zimmermann
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def HAVE___GMPN_ADD_NC did not work as expected,
or GMP-ECM was configured on a different system where __gmpn_add_nc
was available.
Paul Zimmermann
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and 'Full MatrixSpace of 2 by 2 dense
matrices over Symbolic Ring'
but v * m works:
sage: v * m
(a*d + e*c, b*d + e*d)
I find this rather counter-intuitive wrt mathematics. Is there any rationale?
Paul Zimmermann
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7;cos'. However with Sage 3.4
it works for me:
--
| Sage Version 3.4, Release Date: 2009-03-11 |
| Type notebook() for the GUI, and license() for information.|
--
sage: numerical_integral(s
Another quick option: is there a way to get a listing of all the
commands/functions/keywords used in SAGE (the top level not at the
source code level)?
try:
sage: *?
Hope this helps,
Paul Zimmermann
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William,
sorry to answer late:
> Paul -- does GMP-ECM have a by-design hard limit of 4095 digits? If
> so, then we have to give an error message from Sage immediately (raise
> a ValueError). If not, how do we get around the command line 4095
> digit limit?
no, GMP-ECM has no hard limi
> And here's a nicely formatted version of the release tour:
> http://mvngu.wordpress.com/2009/02/23/sage-33-released
this is very nice! I wonder how much time it took you to write this page.
Paul Zimmermann
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lution
is known so far.
Paul Zimmermann
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thank you Craig and William for your answers. Craig, I was using Sage 3.2,
(here on a different computer):
--
| Sage Version 3.2, Release Date: 2008-11-20 |
| Type notebook() for the GUI, and license() for
Hi,
on http://www.loria.fr/~zimmerma/exemple40.sage you can find a 500x360
integer matrix for which computing the Hermite Normal Form takes about
10 times longer in Sage than in Magma:
sage: C
500 x 360 dense matrix over Integer Ring
sage: time A=C.hermite_form()
CPU times: user 22.91 s,
ven perform an exact conversion (don't forget to divide
your reduced vectors by C at the end).
Damien Stehlé (in cc) might add more details.
Paul Zimmermann
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False), or plus 0.5005 ulp on the default printing if 3 digits
are left off (assuming rounding to nearest).
Paul Zimmermann
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sage-
has the advantage to guarantee correct
rounding (for the 150-bit binary result; if you are using the decimal
result above, you have to take into account the binary->decimal conversion
error, which is at most 1/2 ulp).
Paul Zimmermann
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To p
if is_pseudoprime(p):
return p
b1 = b1 + isqrt(b1)
Paul Zimmermann
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((-1,1))
sage: c=R((-1,1))
sage: w=R((-0.9,-0.6))
sage: x=R((-0.1,0.2))
sage: y=R((0.3,0.7))
sage: z=R((-0.2,0.1))
sage: f=(a*(w^2+x^2-y^2-z^2)+2*b*(x*y-w*z)+2*c*(x*z+w*y))/(w^2+x^2+y^2+z^2)
sage: f.lower()
-8.65853658536587
sage: f.upper()
21.6097560975610
Paul Zimmermann
--- Start of forwarded m
is the difficult one. As far as I know, he did implement his
algorithms in Axiom, including (partly) the algebraic case.
Implementing symbolic integration from scratch is a major task, that would
require years before reaching what Axiom can do. In any case, I suggest
reusing the Axiom
l of the
solution set with the (very naive) algorithm above.
Paul Zimmermann
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For more options, visi
equivalent to integer linear programming (ILP),
see http://en.wikipedia.org/wiki/Integer_linear_programming#Integer_unknowns.
Paul Zimmermann
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arise from the ongoing port as Sage-Combinat.
* on October 14, Robert Bradshaw will give a plenary demonstration of Sage.
If you have any questions, feel free to email me or any of the other organizers!
On behalf of the organizing committee,
Paul Zimmermann
PS: I take the opportunity to advertize
>
> Something very peculiar is happening. What? Why?
>
> Thank you,
>
> David Galant
my guess is that in a-c, c is converted to 'sage.interfaces.gp.GpElement'
with a smaller precision:
sage: a-a.parent()(c)
-1.0349334749767836598
2.10.2, which hopefully will fix that issue.
Paul
PS: you should be able to fix it by uncompressing libgcrypt-1.4.0.spkg in
spkg/standard, then add "CFLAGS="-O0 -g"; export CFLAGS" at the beginning
of file spkg-install, recompressing the archive, and doing again make in
t
/wwwmaths.anu.edu.au/~brent/gf2x.html you will
find an implementation up to 5 times faster than NTL's GF2X (for degree 2^20).
Paul Zimmermann
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Hi,
one of my colleagues discovered a limitation of SAGE: apparently one cannot
compute over multivariate ideals over GF(p) for p >= 2^31:
sage: R. = PolynomialRing(GF(2147483659))
sage: ideal([x^3-2*y^2,3*x+y^4]).groebner_basis()
...
: Singular error:
? `2147483659` greater than 21474
John,
> A variation of this, which would be useful in some elliptic curve
> calculations, would be a function
> RR(x).nearby_rational_whose_denominator_is_a_perfect_square().
>
> For either problem, is there a better solution than going through the
> continued fraction convergents until o
inconsistent or wrong results.
If one wants that (-1)^(1/3) simplifies to -1, the only clean solution I see
is to write a special function simplify_real to do that, but be prepared to
see inconsistent results.
Paul Zimmermann
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(2/(3*sqrt(3)) + 10/27)^(1/3) - 2/(9*(2/(3*sqrt(3)) + 10/27)^(1/3)) + 1/3
Quiz: how to simplify that expression to 1 within SAGE? I've tried simplify,
and radical_simplify, but neither succeeds...
Paul Zimmermann
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27; is much faster for large numbers.
Would it be possible to extend long by new methods like is_square, and get
rid of Integer?
I guess 'long' is based on GMP too, does it make sense to have two concurrent
interfaces to GMP integers?
Paul Zimmermann
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John,
> sage: [q for q in range(100) if q.is_square()]
>
> --rather, one has to do this
>
> sage: [q for q in range(100) if Integer(q).is_square()]
> [0, 1, 4, 9, 16, 25, 36, 49, 64, 81]
>
> or even this:
> sage: [Integer(q) for q in range(100) if Integer(q).is_square()]
> [0, 1, 4, 9,
point should give
you the number of corrections steps (more probably 0 or 1).
Paul Zimmermann
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> I have 2 documentation requests:
> [...]
I have a 3rd one: I am really missing a "SEE ALSO" field (or whatever you
want to call it) in the online documentation. It would be quite useful to
point users to related commands.
Paul
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Dear Andrzej,
> Im impressed again. Thank you so much
> I had only a rough idea and you are realy effective in SAGE (too).
> This time I have no additional concrete questions
> but I'm strongly interested in your general opinion
> concerning the comparison MAPLE-SAGE (any links?)
for flo
)
sage: I = singular.ideal([repr(eq1), repr(eq2), repr(eq3)])
sage: I2 = I.groebner()
sage: singular.reduce(repr(n12), I2)
0
In particular:
(1) is there a better way to normalize a rational expression that calling
factor? Apparently numerator alone does not do the job
. This is quite useful
for the user who is not aware of Gröbner bases (or the aware-user who prefers
a simple command). Does a similar command exist in SAGE?
Paul Zimmermann
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To u
es.
> Also, is there a way to rewrite one_curve using popen instead of pexpect?
I'm not sure it's worth the effort. It would be much better to write an
interface at the C level (see ticket #1550) if feasible.
Paul Zimmermann
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To
< in552.sage >& log &
where the file in552.sage, and the auxiliary files Primes.sage and
aliquot.sage can be downloaded from http://www.loria.fr/~zimmerma/tmp/xxx
(replace xxx by in552.sage, ...)
The problem will occur after a few minutes.
Any idea?
Paul Zimmermann
PS: I could not se
e.
> Turning that off will *probably* solve the problem.
by the way, I noticed while compiling sage-2.9 from source on my laptop
(Pentium M) that ATLAS ran MANY tuning tests, which did take VERY long.
Wouldn't it be possible to use some default machine parameters, like GMP does?
> > even better would be to adopt a computational model such that all
> > numerical computations can give only *one* correct result. Then you
> > could simply compare to the expected result with utilities like "diff".
>
> That would be nice but isn't realistic, since Sage includes systems like
>
.
even better would be to adopt a computational model such that all
numerical computations can give only *one* correct result. Then you
could simply compare to the expected result with utilities like "diff".
Paul Zimmermann
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> By the way, we'll definitely want to create an arbitrary precision find_root
> using MPFR etc. at some point -- that will be very exciting. (The above is
> just supposed to do some wimpy machine precision root finding.)
a possible starting point is http://komite.net/laurent/pro/these-20070228
> One interesting thing is that I made it so that
>
> f.find_root(a,b)
>
> works even if the sign of f(a) and f(b) are the same. In that case,
> it will find a min or max of f on the interval, and use that as a new
> endpoint as input to the root finding algorithm. The root finder
> itsel
// N
Out[3]= 3.14159
In[7]:= Pi + E // N + 5 // N
Out[7]= (5. + N)[5.85987]
Paul Zimmermann
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On http://sagemath.org/doc/html/ref/module-sage.calculus.calculus.html one
can read:
sage: var('x, u, v')
(x, u, v)
sage: f = expand((2*u*v^2-v^2-4*u^3)^2 * (-u)^3 * (x-sin(x))^3) # not
tested -- trac #946
This seems to work now:
sage: var('x, u, v')
sage: f = expand((2*u*v^2-v^2-4*u^3)^2
very useful (my machine has a load of 3-4). It would be
more useful to have to cpu time used by the spawned processes, or simply the
total cpu time used by SAGE and those processes.
Paul Zimmermann
def FindGroupOrder(p,s):
K = GF(p)
v = K(4*s)
u = K(s^2-5)
x = u^3
b = 4*x*v
a = (v-u
--
sage: x
x
sage: y
---
Traceback (most recent call last)
/users/spaces/zimmerma/Adm/Confs/07/SAGEdays6/ in ()
: name 'y' is not defined
>From a
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