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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function that rounds towards
-infinity.
Paul Zimmermann
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as a different method.
Paul Zimmermann
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- ---
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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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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sage
:
--
| Sage Version 3.4, Release Date: 2009-03-11 |
| Type notebook() for the GUI, and license() for information.|
--
sage: numerical_integral(sin(pi*exp(x/2)),0,2)[0]
-0.43734547482524966
Paul Zimmermann
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: *? enter
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 limit.
is known so far.
Paul Zimmermann
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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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rounding to nearest).
Paul Zimmermann
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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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):
return p
b1 = b1 + isqrt(b1)
Paul Zimmermann
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))
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 message
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 test suite as starting point.
Paul Zimmermann
with the (very naive) algorithm above.
Paul Zimmermann
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equivalent to integer linear programming (ILP),
see http://en.wikipedia.org/wiki/Integer_linear_programming#Integer_unknowns.
Paul Zimmermann
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that 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
to 'sage.interfaces.gp.GpElement'
with a smaller precision:
sage: a-a.parent()(c)
-1.0349334749767836598 E-13
sage: a-c
-1.0349334749767836598 E-13
sage: c
0.8414709848078965
sage: a.parent()(c)
0.841470984808
Paul Zimmermann
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To post
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
the sage build directory.
Regards,
Alfredo Portes
On Feb 2, 2008 8:19 AM, Paul Zimmermann [EMAIL
, which is usually at least
10 times slower than GF2X, up to degree 2^17 anyway. In that range
GF2X matches the speed of magma.)
for your information, on http://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
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.x,y = PolynomialRing(GF(2147483659))
sage: ideal([x^3-2*y^2,3*x+y^4]).groebner_basis()
...
type 'exceptions.TypeError': Singular error:
?
simplify,
and radical_simplify, but neither succeeds...
Paul Zimmermann
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(more probably 0 or 1).
Paul Zimmermann
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,
whereas previously it sometimes reported several (up to 5 or 6) ecm processes.
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
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 see a pointer
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?
Cheers,
Paul Zimmermann
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
Numpy /
In[3]:= Pi \\ N
Syntax::sntxf: Pi cannot be followed by \\ N.
In[4]:= f \\ g
Syntax::sntxf: f cannot be followed by \\ g.
please turn your '\' key by Pi/2:
In[2]:= f // g
Out[2]= g[f]
In[3]:= Pi // N
Out[3]= 3.14159
In[7]:= Pi + E // N + 5 // N
Out[7]= (5. + N)[5.85987]
Paul
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
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