[sage-support] generating symmetric random matrices
I'd like to generate symmetric random matrices whose entries may be various distributions. Can I use random_matrix? In help (random_matrix), I haven't found any documentation on the *args and **kwds variables. --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Re: generating symmetric random matrices
On Tue, Jul 14, 2009 at 11:09 PM, pierre.du...@gmail.compierre.du...@gmail.com wrote: I'd like to generate symmetric random matrices whose entries may be various distributions. Can I use random_matrix? In help (random_matrix), I haven't found any documentation on the *args and **kwds variables. Unfortunately, I think you can't. You'll have to make a list v of the entries, then do A = matrix(n,v) Regarding random_matrix, if you do random_matrix(K,...) where K is a field, then each element of the matrix is computed by calling K.random_element, so you should see the docs on K.random_element. William -- William Stein Associate Professor of Mathematics University of Washington http://wstein.org --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Re: generating symmetric random matrices
You can also start with a random matrix A and then construct (A + A.transpose())/2, which would be symmetric. That might vary the distribution of the coefficients, though. Cheers Javier On Jul 15, 7:13 am, William Stein wst...@gmail.com wrote: On Tue, Jul 14, 2009 at 11:09 PM, pierre.du...@gmail.compierre.du...@gmail.com wrote: I'd like to generate symmetric random matrices whose entries may be various distributions. Can I use random_matrix? In help (random_matrix), I haven't found any documentation on the *args and **kwds variables. Unfortunately, I think you can't. You'll have to make a list v of the entries, then do A = matrix(n,v) Regarding random_matrix, if you do random_matrix(K,...) where K is a field, then each element of the matrix is computed by calling K.random_element, so you should see the docs on K.random_element. William -- William Stein Associate Professor of Mathematics University of Washingtonhttp://wstein.org --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Polynomial
Suppose f=2*x^2+3*x+1 is a polynomial in x. How efficiently we can calculate f^10 modulo 24? --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Re: Polynomial
Hi Santanu, On Wed, Jul 15, 2009 at 9:46 PM, Santanu Sarkarsarkar.santanu@gmail.com wrote: Suppose f=2*x^2+3*x+1 is a polynomial in x. How efficiently we can calculate f^10 modulo 24? For the ring of polynomials with coefficients over ZZ: -- | Sage Version 4.1, Release Date: 2009-07-09 | | Type notebook() for the GUI, and license() for information.| -- sage: K.x = ZZ[x] sage: f = 2*x^2 + 3*x + 1 sage: %timeit power_mod(f, 10, 24) 1 loops, best of 3: 93.7 µs per loop sage: %time power_mod(f, 10, 24) CPU times: user 0.00 s, sys: 0.00 s, total: 0.00 s Wall time: 0.00 s 16*x^20 + 8*x^18 + 12*x^12 + 12*x^11 + 21*x^10 + 6*x^9 + 21*x^8 + 18*x^6 + 12*x^5 + 6*x^4 + 12*x^3 + 17*x^2 + 6*x + 1 Here the coefficient ring is QQ: sage: K.x = QQ[x] sage: f = 2*x^2 + 3*x + 1 sage: %timeit power_mod(f, 10, 24) 1000 loops, best of 3: 374 µs per loop sage: %time power_mod(f, 10, 24) CPU times: user 0.00 s, sys: 0.00 s, total: 0.00 s Wall time: 0.00 s 0 So it looks to be pretty fast :-) -- Regards Minh Van Nguyen --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Re: Polynomial
On Wednesday 15 July 2009, Santanu Sarkar wrote: Suppose f=2*x^2+3*x+1 is a polynomial in x. How efficiently we can calculate f^10 modulo 24? sage: P.x = PolynomialRing(Zmod(24)) sage: f = 2*x^2+3*x+1 sage: type(f) type 'sage.rings.polynomial.polynomial_zmod_flint.Polynomial_zmod_flint' sage: %timeit f**10 10 loops, best of 3: 19 µs per loop Cheers, Martin -- name: Martin Albrecht _pgp: http://pgp.mit.edu:11371/pks/lookup?op=getsearch=0x8EF0DC99 _otr: 47F43D1A 5D68C36F 468BAEBA 640E8856 D7951CCF _www: http://www.informatik.uni-bremen.de/~malb _jab: martinralbre...@jabber.ccc.de --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Re: Polynomial
On Jul 15, 1:46 pm, Santanu Sarkar sarkar.santanu@gmail.com wrote: Suppose f=2*x^2+3*x+1 is a polynomial in x. How efficiently we can calculate f^10 modulo 24? quite fast i think: sage: R.x = PolynomialRing(Integers(24), x) sage: R Univariate Polynomial Ring in x over Ring of integers modulo 24 sage: f = 2*x^2+3*x+1 sage: type(f) type 'sage.rings.polynomial.polynomial_zmod_flint.Polynomial_zmod_flint' sage: f^10 16*x^20 + 8*x^18 + 12*x^12 + 12*x^11 + 21*x^10 + 6*x^9 + 21*x^8 + 18*x^6 + 12*x^5 + 6*x^4 + 12*x^3 + 17*x^2 + 6*x + 1 sage: %timeit f**10 1 loops, best of 3: 52.1 µs per loop sage: %timeit f**100 1 loops, best of 3: 91.6 µs per loop sage: %timeit f**1000 1000 loops, best of 3: 591 µs per loop h --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Re: Polynomial
For the ring of polynomials with coefficients over ZZ: -- | Sage Version 4.1, Release Date: 2009-07-09 | | Type notebook() for the GUI, and license() for information.| -- sage: K.x = ZZ[x] sage: f = 2*x^2 + 3*x + 1 sage: %timeit power_mod(f, 10, 24) 1 loops, best of 3: 93.7 µs per loop This is about 5x slower than the native way using FLINT's zmod_poly on my machine: sage: K.x = ZZ[x] sage: f = 2*x^2 + 3*x + 1 sage: %timeit power_mod(f, 10, 24) 1 loops, best of 3: 104 µs per loop sage: P.x = PolynomialRing(Zmod(24)) sage: f = 2*x^2 + 3*x + 1 sage: %timeit f**10 10 loops, best of 3: 19.3 µs per loop Cheers, Martin -- name: Martin Albrecht _pgp: http://pgp.mit.edu:11371/pks/lookup?op=getsearch=0x8EF0DC99 _otr: 47F43D1A 5D68C36F 468BAEBA 640E8856 D7951CCF _www: http://www.informatik.uni-bremen.de/~malb _jab: martinralbre...@jabber.ccc.de --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] query
I want to test the limits order of nilpotency class of certain infinite groups. How should I go about it? Please help. Thanking you in advance. Arun India -- Arun Muktibodh --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Re: Newb basic algebra question
sage: foo = (x-1)^2/(x+2)^2 + 2*(x-1)/(x+2) sage: bar = foo*(x+2) sage: bar (x + 2)*((x - 1)^2/(x + 2)^2 + 2*(x - 1)/(x + 2)) How come (x+2) isn't canceling in each of the parts? Probably because x might be -2. Also, you have to explicitly simplify to do any non-trivial transformations (because it may be expensive to do so). sage: bar.simplify_full() 3*(x^2 - 1)/(x + 2) Ah, this is great; thank you! After perusing the documentation, it seems that simplify_full applies simplify_trig, simplify_rational, and simplify_radical. And simplify_rational is exactly what takes care of this. -Doug --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] More python questions than sage questions
Two more basic questions I'm hoping you can help with:
1. My workstyle so far is to edit my .sage file in emacs and then load
it into sage on the command line. Sometimes I want my program to stop
in the middle so I can more closely examine/verify what it's doing.
I've been inserting a line that just says stop to do this and it
causes sage/Python to stop with an error message and a short stack
trace. This works, but it's kind of messy. raise Exception
('spam','eggs') does pretty much the same thing. Is there a way to
tell sage/Python to stop running without raising an error?
2. Is there a way to reset sage/Python from the command-line as if I
was restarting? I can't even find a command that will clear all my
global variables, although that might be enough.
Any help will be much appreciated!
Thanks, Doug
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[sage-support] Problem building Sage 4.1 from source on Fedora 11
Hi all, I have a problem while trying to compile Sage version 4.1 from source on Fedora 11. The kernel build is 2.6.29.5-191.fc11.x86_64, running on an AMD Phenom 9650 Quad-Core with 3 GB RAM. The building process aborts after an hour or so, and gives the error message posted below. If you need a bigger part of the install.log or anything please ask. Thanks! - - - creating build/temp.linux-x86_64-2.6/sage/ext gcc -fno-strict-aliasing -DNDEBUG -g -fwrapv -O3 -Wall -Wstrict- prototypes -fPIC -I/home/esteban/Downloads/Internet/sage-4.1/local// include -I/home/esteban/Downloads/Internet/sage-4.1/local//include/ csage -I/home/esteban/Downloads/Internet/sage-4.1/devel//sage/sage/ext -I/home/esteban/Downloads/Internet/sage-4.1/local/include/python2.6 -c sage/ext/fast_callable.c -o build/temp.linux-x86_64-2.6/sage/ext/ fast_callable.o -w error: could not create 'build/temp.linux-x86_64-2.6': File exists cc1plus: warning: command line option -Wstrict-prototypes is valid for Ada/C/ObjC but not for C++ cc1plus: warning: command line option -Wstrict-prototypes is valid for Ada/C/ObjC but not for C++ sage: There was an error installing modified sage library code. ERROR installing SAGE real6m14.724s user10m14.630s sys 0m51.278s sage: An error occurred while installing sage-4.1 Please email sage-devel http://groups.google.com/group/sage-devel explaining the problem and send the relevant part of of /home/esteban/Downloads/Internet/sage-4.1/install.log. Describe your computer, operating system, etc. If you want to try to fix the problem, yourself *don't* just cd to /home/esteban/Downloads/Internet/sage-4.1/spkg/build/sage-4.1 and type 'make'. Instead type /home/esteban/Downloads/Internet/sage-4.1/sage -sh in order to set all environment variables correctly, then cd to /home/esteban/Downloads/Internet/sage-4.1/spkg/build/sage-4.1 (When you are done debugging, you can type exit to leave the subshell.) make[1]: *** [installed/sage-4.1] Error 1 make[1]: Leaving directory `/media/Esteban/Downloads/Internet/sage-4.1/ spkg' real119m46.505s user78m27.545s sys 17m48.474s Error building Sage. --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Re: More python questions than sage questions
Doug wrote:
Two more basic questions I'm hoping you can help with:
1. My workstyle so far is to edit my .sage file in emacs and then load
it into sage on the command line. Sometimes I want my program to stop
in the middle so I can more closely examine/verify what it's doing.
I've been inserting a line that just says stop to do this and it
causes sage/Python to stop with an error message and a short stack
trace. This works, but it's kind of messy. raise Exception
('spam','eggs') does pretty much the same thing. Is there a way to
tell sage/Python to stop running without raising an error?
One thing you can do is use pdb, the python debugger (example from
http://www.electricmonk.nl/log/2008/06/25/breakpoint-induced-python-debugging-with-ipython/).
from IPython.Debugger import Tracer; debug_here = Tracer()
def ham():
x = 5
debug_here()
raise NotImplementedError('Use the source, luke!')
ham()
will put you into the python debugging loop, where you can examine
variables, step through the code, etc. Just put these two lines
somewhere in your code where you want it to stop. See also
http://www.nabble.com/debugging-in-ipython-td20047930.html for another
way to set a breakpoint.
Another way to enter this is to just turn pdb on in Sage (actually ipython):
sage: %pdb on
Now any errors will drop you into the debugger.
And thirdly, you can just wait until an error shows up and type
sage: %debug
to examine the variable values, etc. when that error was thrown.
Fourthly, you can use pdb to run the function directly:
import pdb
pdb.run('Networks.FindPathLengthsFromNode(g, 0)')
2. Is there a way to reset sage/Python from the command-line as if I
was restarting? I can't even find a command that will clear all my
global variables, although that might be enough.
Check out the (oddly enough named :) reset function:
sage: reset?
from the reset docs:
sage: x = 5
sage: reset()
sage: x
x
Thanks,
Jason
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[sage-support] Re: query
I don't think this is implemented yet in Sage. On Wed, Jul 15, 2009 at 8:55 AM, arun Muktibodhamukti2...@gmail.com wrote: I want to test the limits order of nilpotency class of certain infinite groups. How should I go about it? Please help. Thanking you in advance. Arun India -- Arun Muktibodh --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Re: More python questions than sage questions
This is all awesome info; I've got some reading to do! and I can't
believe I didn't try reset!
Thanks! Doug
On Jul 15, 11:30 am, Jason Grout jason-s...@creativetrax.com wrote:
Doug wrote:
Two more basic questions I'm hoping you can help with:
1. My workstyle so far is to edit my .sage file in emacs and then load
it into sage on the command line. Sometimes I want my program to stop
in the middle so I can more closely examine/verify what it's doing.
I've been inserting a line that just says stop to do this and it
causes sage/Python to stop with an error message and a short stack
trace. This works, but it's kind of messy. raise Exception
('spam','eggs') does pretty much the same thing. Is there a way to
tell sage/Python to stop running without raising an error?
One thing you can do is use pdb, the python debugger (example
fromhttp://www.electricmonk.nl/log/2008/06/25/breakpoint-induced-python-d...).
from IPython.Debugger import Tracer; debug_here = Tracer()
def ham():
x = 5
debug_here()
raise NotImplementedError('Use the source, luke!')
ham()
will put you into the python debugging loop, where you can examine
variables, step through the code, etc. Just put these two lines
somewhere in your code where you want it to stop. See
alsohttp://www.nabble.com/debugging-in-ipython-td20047930.htmlfor another
way to set a breakpoint.
Another way to enter this is to just turn pdb on in Sage (actually ipython):
sage: %pdb on
Now any errors will drop you into the debugger.
And thirdly, you can just wait until an error shows up and type
sage: %debug
to examine the variable values, etc. when that error was thrown.
Fourthly, you can use pdb to run the function directly:
import pdb
pdb.run('Networks.FindPathLengthsFromNode(g, 0)')
2. Is there a way to reset sage/Python from the command-line as if I
was restarting? I can't even find a command that will clear all my
global variables, although that might be enough.
Check out the (oddly enough named :) reset function:
sage: reset?
from the reset docs:
sage: x = 5
sage: reset()
sage: x
x
Thanks,
Jason
--~--~-~--~~~---~--~~
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To unsubscribe from this group, send email to
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URLs: http://www.sagemath.org
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[sage-support] Re: More python questions than sage questions
On Wed, Jul 15, 2009 at 9:06 AM, Dougmcke...@gmail.com wrote:
This is all awesome info; I've got some reading to do! and I can't
believe I didn't try reset!
Also, try typing
sage: trace?
William
Thanks! Doug
On Jul 15, 11:30 am, Jason Grout jason-s...@creativetrax.com wrote:
Doug wrote:
Two more basic questions I'm hoping you can help with:
1. My workstyle so far is to edit my .sage file in emacs and then load
it into sage on the command line. Sometimes I want my program to stop
in the middle so I can more closely examine/verify what it's doing.
I've been inserting a line that just says stop to do this and it
causes sage/Python to stop with an error message and a short stack
trace. This works, but it's kind of messy. raise Exception
('spam','eggs') does pretty much the same thing. Is there a way to
tell sage/Python to stop running without raising an error?
One thing you can do is use pdb, the python debugger (example
fromhttp://www.electricmonk.nl/log/2008/06/25/breakpoint-induced-python-d...).
from IPython.Debugger import Tracer; debug_here = Tracer()
def ham():
x = 5
debug_here()
raise NotImplementedError('Use the source, luke!')
ham()
will put you into the python debugging loop, where you can examine
variables, step through the code, etc. Just put these two lines
somewhere in your code where you want it to stop. See
alsohttp://www.nabble.com/debugging-in-ipython-td20047930.htmlfor another
way to set a breakpoint.
Another way to enter this is to just turn pdb on in Sage (actually ipython):
sage: %pdb on
Now any errors will drop you into the debugger.
And thirdly, you can just wait until an error shows up and type
sage: %debug
to examine the variable values, etc. when that error was thrown.
Fourthly, you can use pdb to run the function directly:
import pdb
pdb.run('Networks.FindPathLengthsFromNode(g, 0)')
2. Is there a way to reset sage/Python from the command-line as if I
was restarting? I can't even find a command that will clear all my
global variables, although that might be enough.
Check out the (oddly enough named :) reset function:
sage: reset?
from the reset docs:
sage: x = 5
sage: reset()
sage: x
x
Thanks,
Jason
--
William Stein
Associate Professor of Mathematics
University of Washington
http://wstein.org
--~--~-~--~~~---~--~~
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URLs: http://www.sagemath.org
-~--~~~~--~~--~--~---
[sage-support] Re: Polynomial
On Wed, Jul 15, 2009 at 5:03 AM, Martin Albrechtm...@informatik.uni-bremen.de wrote: For the ring of polynomials with coefficients over ZZ: -- | Sage Version 4.1, Release Date: 2009-07-09 | | Type notebook() for the GUI, and license() for information. | -- sage: K.x = ZZ[x] sage: f = 2*x^2 + 3*x + 1 sage: %timeit power_mod(f, 10, 24) 1 loops, best of 3: 93.7 µs per loop This is about 5x slower than the native way using FLINT's zmod_poly on my machine: sage: K.x = ZZ[x] sage: f = 2*x^2 + 3*x + 1 sage: %timeit power_mod(f, 10, 24) 1 loops, best of 3: 104 µs per loop sage: P.x = PolynomialRing(Zmod(24)) sage: f = 2*x^2 + 3*x + 1 sage: %timeit f**10 10 loops, best of 3: 19.3 µs per loop Cheers, Martin That's not surprising given what power_mod does. Do power_mod?? to see. It's generic code that does the arithmetic in the parent ring, then calls mod after each multiply. so in the above first example, zmod_poly is never used. So this sounds to me like a good opportunity to improve power_mod in some cases! -- William --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Cython Modules
I want to include some of my cython code as a sage module. I followed the directions for adding the .pyx file to the sage library at http://www.sagemath.org/doc/developer/coding_in_other.html. However, when I run sage -b I get this: -- sage: Building and installing modified Sage library files. Installing c_lib scons: `install' is up to date. Updating Cython code Building modified file sage/my_stuff/interpolators.pyx. python `which cython` --embed-positions --incref-local-binop -I/home/ evlutte/opt/sage-3.2.3/devel/sage-main -o sage/my_stuff/ interpolators.c sage/my_stuff/interpolators.pyx sage/my_stuff/interpolators.pyx -- /home/evlutte/opt/sage-3.2.3/ local//lib/python/site-packages//sage/my_stuff/interpolators.pyx Time to execute 1 commands: 1.00808811188 seconds Finished compiling Cython code (time = 1.51264286041 seconds) running install running build running build_py package init file 'sage/my_stuff/__init__.py' not found (or not a regular file) package init file 'sage/my_stuff/__init__.py' not found (or not a regular file) running build_ext building 'sage.my_stuff.interpolators' extension gcc -fno-strict-aliasing -DNDEBUG -g -fwrapv -O3 -Wall -Wstrict- prototypes -fPIC -I/home/evlutte/opt/sage-3.2.3/local//include -I/home/ evlutte/opt/sage-3.2.3/local//include/csage -I/home/evlutte/opt/ sage-3.2.3/devel//sage/sage/ext -I/home/evlutte/opt/sage-3.2.3/local/ include/python2.6 -c sage/my_stuff/interpolators.c -o build/temp.linux- i686-2.6/sage/my_stuff/interpolators.o -w sage/my_stuff/interpolators.c:139:31: error: numpy/arrayobject.h: No such file or directory sage/my_stuff/inte ... and lots more error stuff Below are the contents of interpolators.pyx Can anyone tell me what I'm doing wrong? include ../ext/interrupt.pxi include '../ext/cdefs.pxi' include '../ext/stdsage.pxi' import numpy as np cimport numpy as np from math import pi cdef double TWOPI = 2*pi class PSpline(): def __init__(self,pts,shift = (0,0), int reverse = 0): self.pts = pts self.shift = shift self.reverse = reverse cdef int N = len(pts) self.N = N def value(self,float t0): if self.reverse == 1: t0 = TWOPI-t0 while t0 = TWOPI: t0 -= TWOPI t1 = (t0 * self.N/(TWOPI)) pt1 = self.pts[int(t1)] pt2 = self.pts[(int(t1) + 1)%self.N] return np.complex(self.shift[0] + pt1[0] + (pt2[0] - pt1[0])* (t1-int(t1)),self.shift[1] + pt1[1] + (pt2[1] - pt1[1])*(t1-int(t1))) def derivative(self,float t): if self.reverse == 1: t0 = TWOPI-t0 while t0 = TWOPI: t0 -= TWOPI t1 = (t0 * self.N/(TWOPI)) pt1 = self.pts[int(t1)] pt2 = self.pts[(int(t1) + 1)%self.N] return np.complex((pt2[0] - pt1[0])*self.N/(TWOPI),(pt2[1] - pt1[1])*self.N/(TWOPI)) class CCSpline(): def __init__(self,cps): cdef int N,i,k,B B = len(cps) N = len(cps[0]) self.avec = np.zeros([B,N],dtype = np.complex128) self.bvec = np.zeros([B,N],dtype = np.complex128) self.cvec = np.zeros([B,N],dtype = np.complex128) self.dvec = np.zeros([B,N],dtype = np.complex128) for k in range(B): pts = cps[k] yvec = np.zeros(N,dtype = np.complex128) for i in xrange(N): yvec[i] = 3*(pts[(i-1)%N]-2*pts[i]+pts[(i+1)%N]) bmat = np.zeros([N,N],dtype = np.complex128) for i in xrange(N): bmat[i,i] = 4 bmat[(i-1)%N,i] = 1 bmat[(i+1)%N,i] = 1 bvec = (np.linalg.solve(bmat,yvec)) cvec = np.zeros(N,dtype = np.complex128) for i in range(N): cvec[i] = pts[(i+1)%N] - pts[i] - 1./3.*bvec[(i+1)%N] - 2./3. * bvec[i] dvec = pts avec = range(N) for i in range(N): avec[i] = 1./3.*(bvec[(i+1)%N] - bvec[i]) self.avec[k] = avec self.bvec[k] = bvec self.cvec[k] = cvec self.dvec[k] = dvec self.N = N def value(self,t0,k=0): cdef float t = (t0/TWOPI*self.N)%self.N cdef int j = int(t) return self.avec[k,j]*(t-j)**3+self.bvec[k,j]*(t-j) **2+self.cvec[k,j]*(t-j)+self.dvec[k,j] def derivative(self,t0,k=0): cdef float t = (t0/TWOPI*self.N)%self.N cdef int j = int(t) return 3*self.avec[k,j]*(t-j)**2+2*self.bvec[k,j]*(t-j) +self.cvec[k,j] --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Re: Polynomial
That's not surprising given what power_mod does. Do power_mod?? to see. It's generic code that does the arithmetic in the parent ring, then calls mod after each multiply. so in the above first example, zmod_poly is never used. This reminds me: Why do we have power_mod() when pow() does the same thing when given three arguments? Maybe this was discussed before and I just can't recall it. Martin -- name: Martin Albrecht _pgp: http://pgp.mit.edu:11371/pks/lookup?op=getsearch=0x8EF0DC99 _otr: 47F43D1A 5D68C36F 468BAEBA 640E8856 D7951CCF _www: http://www.informatik.uni-bremen.de/~malb _jab: martinralbre...@jabber.ccc.de --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Re: Polynomial
On Wed, Jul 15, 2009 at 11:23 AM, Martin
Albrechtm...@informatik.uni-bremen.de wrote:
That's not surprising given what power_mod does. Do power_mod?? to
see. It's generic code that does the arithmetic in the parent ring,
then calls mod after each multiply. so in the above first example,
zmod_poly is never used.
This reminds me: Why do we have power_mod() when pow() does the same thing
when given three arguments? Maybe this was discussed before and I just can't
recall it.
Hmm. Pow's third argument is often ignored:
sage: K.x = ZZ[x]
sage: f = 2*x^2 + 3*x + 1
sage: timeit('power_mod(f,10,24)')
625 loops, best of 3: 162 µs per loop
sage: timeit('pow(f,10,24)')
625 loops, best of 3: 11.9 µs per loop
That seems fast, but :
sage: pow(f,10,24)
1024*x^20 + 15360*x^19 + 108800*x^18 + 483840*x^17 + 1514880*x^16 +
3549312*x^15 + 6456480*x^14 + 9336960*x^13 + 10901460*x^12 +
10377180*x^11 + 8097453*x^10 + 5188590*x^9 + 2725365*x^8 + 1167120*x^7
+ 403530*x^6 + 110916*x^5 + 23670*x^4 + 3780*x^3 + 425*x^2 + 30*x + 1
sage: power_mod(f,10,24)
16*x^20 + 8*x^18 + 12*x^12 + 12*x^11 + 21*x^10 + 6*x^9 + 21*x^8 +
18*x^6 + 12*x^5 + 6*x^4 + 12*x^3 + 17*x^2 + 6*x + 1
So, ouch.
sage: P.x = PolynomialRing(Zmod(24))
sage: f = 2*x^2 + 3*x + 1
sage: timeit('f^10')
625 loops, best of 3: 27.6 µs per loop
-- William
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[sage-support] Re: Polynomial
On Wed, 15 Jul 2009 11:29:37 -0700
William Stein wst...@gmail.com wrote:
On Wed, Jul 15, 2009 at 11:23 AM, Martin
Albrechtm...@informatik.uni-bremen.de wrote:
That's not surprising given what power_mod does. Do power_mod?? to
see. It's generic code that does the arithmetic in the parent
ring, then calls mod after each multiply. so in the above first
example, zmod_poly is never used.
This reminds me: Why do we have power_mod() when pow() does the
same thing when given three arguments? Maybe this was discussed
before and I just can't recall it.
See #5082, and a duplicate #5652.
Cheers,
Burcin
Hmm. Pow's third argument is often ignored:
sage: K.x = ZZ[x]
sage: f = 2*x^2 + 3*x + 1
sage: timeit('power_mod(f,10,24)')
625 loops, best of 3: 162 µs per loop
sage: timeit('pow(f,10,24)')
625 loops, best of 3: 11.9 µs per loop
That seems fast, but :
sage: pow(f,10,24)
1024*x^20 + 15360*x^19 + 108800*x^18 + 483840*x^17 + 1514880*x^16 +
3549312*x^15 + 6456480*x^14 + 9336960*x^13 + 10901460*x^12 +
10377180*x^11 + 8097453*x^10 + 5188590*x^9 + 2725365*x^8 + 1167120*x^7
+ 403530*x^6 + 110916*x^5 + 23670*x^4 + 3780*x^3 + 425*x^2 + 30*x + 1
sage: power_mod(f,10,24)
16*x^20 + 8*x^18 + 12*x^12 + 12*x^11 + 21*x^10 + 6*x^9 + 21*x^8 +
18*x^6 + 12*x^5 + 6*x^4 + 12*x^3 + 17*x^2 + 6*x + 1
So, ouch.
sage: P.x = PolynomialRing(Zmod(24))
sage: f = 2*x^2 + 3*x + 1
sage: timeit('f^10')
625 loops, best of 3: 27.6 µs per loop
-- William
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[sage-support] Re: How can calculate the time of execution of a command in sage
Thanks, I'll try it.
Cheers Gustavo
On Jul 14, 10:42 pm, Simon King simon.k...@uni-jena.de wrote:
Hi Gustavo!
On 15 Jul., 03:17, Gustavo Rama gdr...@gmail.com wrote:
But how con you get the time of execution in a variable?
Using cputime or walltime: No problem, since they return a number.
Using timeit:
Remember that you could obtain a timing doing
sage: timeit('f=factorial(400).factor()')
625 loops, best of 3: 955 µs per loop
In order to assign the result of the timing to a variable, do
sage: T = timeit.eval('f=factorial(400).factor()')
Then, the necessary information is contained in the attribute 'stats'
of T:
sage: T.stats
(625, 3, 3, 953.62396240234375, '\xc2\xb5s')
So, the first entry gives the number of loops, the second the number
of runs, the third I don't understand, the fourth gives the
computation time, with units given by the last entry. Anyway:
sage: print %d loops, best of %d: %.*g %s per loop % T.stats
625 loops, best of 3: 954 µs per loop
Note that this only gives the walltime. Note also that it is not so
nice to compare different timings: It might be that one timing
measures the time in microseconds and the other in milliseconds - IMHO
this is an oddity.
Cheers,
Simon
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[sage-support] sort a list
How does one sort a list in Sage? I have tried L1=[56,2,4,10] Sort_ = L1.sort() and nothing is produced. I need it to calculate Quartiles. Is there a Quatile function in any of the modules? Thanks --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Re: sort a list
Hi Mikie, On Thu, Jul 16, 2009 at 5:14 AM, Mikiethephantom6...@hotmail.com wrote: How does one sort a list in Sage? I have tried L1=[56,2,4,10] Sort_ = L1.sort() and nothing is produced. Try this: -- | Sage Version 4.1, Release Date: 2009-07-09 | | Type notebook() for the GUI, and license() for information.| -- sage: L = [56, 2, 4, 10] sage: L [56, 2, 4, 10] sage: L.sort() sage: L [2, 4, 10, 56] That sort() function is built into Python. -- Regards Minh Van Nguyen --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Re: sort a list
On Jul 15, 2009, at 12:14 , Mikie wrote: How does one sort a list in Sage? I have tried L1=[56,2,4,10] Sort_ = L1.sort() and nothing is produced. As the saying goes, RTFM :-} sage: L1=[56,2,4,10] sage: L1.sort? Type: builtin_function_or_method Base Class: type 'builtin_function_or_method' String Form:built-in method sort of list object at 0x8a586c0 Namespace: Interactive Docstring: L.sort(cmp=None, key=None, reverse=False) -- stable sort *IN PLACE*; cmp(x, y) - -1, 0, 1 Class Docstring: attribute '__doc__' of 'builtin_function_or_method' objects sage: L1 [2, 4, 10, 56] HTH Justin -- Justin C. Walker, Curmudgeon at Large Institute for the Absorption of Federal Funds --- If it weren't for carbon-14, I wouldn't date at all. --- --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Re: sort a list
This is not about RTFM, because L1.sort() doesn't produce any result. It just modifies the original list in place. I think that Mikie wants to assign the sorted list to another list. In that case what you need is the sorted command: sage: L1 = [56,2,4,10] sage: sort_L1 = sorted(L1) sage: sort_L1 [2,4,10,56] On Wed, Jul 15, 2009 at 2:19 PM, Justin C. Walker jus...@mac.com wrote: On Jul 15, 2009, at 12:14 , Mikie wrote: How does one sort a list in Sage? I have tried L1=[56,2,4,10] Sort_ = L1.sort() and nothing is produced. As the saying goes, RTFM :-} sage: L1=[56,2,4,10] sage: L1.sort? Type: builtin_function_or_method Base Class: type 'builtin_function_or_method' String Form:built-in method sort of list object at 0x8a586c0 Namespace: Interactive Docstring: L.sort(cmp=None, key=None, reverse=False) -- stable sort *IN PLACE*; cmp(x, y) - -1, 0, 1 Class Docstring: attribute '__doc__' of 'builtin_function_or_method' objects sage: L1 [2, 4, 10, 56] HTH Justin -- Justin C. Walker, Curmudgeon at Large Institute for the Absorption of Federal Funds --- If it weren't for carbon-14, I wouldn't date at all. --- --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Re: Sage Unum
I was able to find a solution to my problem. If anyone else wants to do the same thing, I added the following function to unum/__init_.py. def round(self, sig_fig): ''' returns a string representation of the number w/ units showing only the set number of significant digits ''' return '%s %s' % (round(self.asNumber(),sig_fig), self.strUnit ()) This just gives you a method to print the number of desired digits. On Jul 14, 12:08 pm, dw dwe...@structuralcomponents.net wrote: I've been evaluating Sage for engineering applications. The one missing part, which after reading this forum I've realized is currently being worked on, is unit support. The best solution I've been able to use so far is Unum. It works well in my application, but in the notebook I'd like to be able to limit the number of digits shown. I'd previously been using print '%.3f to set the display, but it doesn't work with Unum numbers. I'm sure this would be better asked in an Unum forum, but I haven't found one and it seems a few people here have used the package. Also, on a more general note. Can you set the significant digits displayed throughout a notebook somehow? Thanks. --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Re: sort a list
Carlos, just what I needed. I have looked in scipy, but no Quartiles. On Jul 15, 1:26 pm, Carlos Córdoba ccordob...@gmail.com wrote: This is not about RTFM, because L1.sort() doesn't produce any result. It just modifies the original list in place. I think that Mikie wants to assign the sorted list to another list. In that case what you need is the sorted command: sage: L1 = [56,2,4,10] sage: sort_L1 = sorted(L1) sage: sort_L1 [2,4,10,56] On Wed, Jul 15, 2009 at 2:19 PM, Justin C. Walker jus...@mac.com wrote: On Jul 15, 2009, at 12:14 , Mikie wrote: How does one sort a list in Sage? I have tried L1=[56,2,4,10] Sort_ = L1.sort() and nothing is produced. As the saying goes, RTFM :-} sage: L1=[56,2,4,10] sage: L1.sort? Type: builtin_function_or_method Base Class: type 'builtin_function_or_method' String Form: built-in method sort of list object at 0x8a586c0 Namespace: Interactive Docstring: L.sort(cmp=None, key=None, reverse=False) -- stable sort *IN PLACE*; cmp(x, y) - -1, 0, 1 Class Docstring: attribute '__doc__' of 'builtin_function_or_method' objects sage: L1 [2, 4, 10, 56] HTH Justin -- Justin C. Walker, Curmudgeon at Large Institute for the Absorption of Federal Funds --- If it weren't for carbon-14, I wouldn't date at all. Hide quoted text - - Show quoted text - --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Re: sort a list
Hi! On 15 Jul., 21:26, Carlos Córdoba ccordob...@gmail.com wrote: This is not about RTFM, because L1.sort() doesn't produce any result. It just modifies the original list in place. ... and this is precisely what the manual tells you. However, you are right: I think that Mikie wants to assign the sorted list to another list. In that case what you need is the sorted command: The sorted command is probably the answer to Mikie's question. Cheers, Simon --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Re: How can calculate the time of execution of a command in sage
The third entry gives the precicion.
On Jul 15, 4:12 pm, Gustavo Rama gdr...@gmail.com wrote:
Thanks, I'll try it.
Cheers Gustavo
On Jul 14, 10:42 pm, Simon King simon.k...@uni-jena.de wrote:
Hi Gustavo!
On 15 Jul., 03:17, Gustavo Rama gdr...@gmail.com wrote:
But how con you get the time of execution in a variable?
Using cputime or walltime: No problem, since they return a number.
Using timeit:
Remember that you could obtain a timing doing
sage: timeit('f=factorial(400).factor()')
625 loops, best of 3: 955 µs per loop
In order to assign the result of the timing to a variable, do
sage: T = timeit.eval('f=factorial(400).factor()')
Then, the necessary information is contained in the attribute 'stats'
of T:
sage: T.stats
(625, 3, 3, 953.62396240234375, '\xc2\xb5s')
So, the first entry gives the number of loops, the second the number
of runs, the third I don't understand, the fourth gives the
computation time, with units given by the last entry. Anyway:
sage: print %d loops, best of %d: %.*g %s per loop % T.stats
625 loops, best of 3: 954 µs per loop
Note that this only gives the walltime. Note also that it is not so
nice to compare different timings: It might be that one timing
measures the time in microseconds and the other in milliseconds - IMHO
this is an oddity.
Cheers,
Simon
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[sage-support] Re: Sage Unum
thank you very much for sharing this! maurizio On 15 Lug, 21:47, dw dwe...@structuralcomponents.net wrote: I was able to find a solution to my problem. If anyone else wants to do the same thing, I added the following function to unum/__init_.py. def round(self, sig_fig): ''' returns a string representation of the number w/ units showing only the set number of significant digits ''' return '%s %s' % (round(self.asNumber(),sig_fig), self.strUnit ()) This just gives you a method to print the number of desired digits. On Jul 14, 12:08 pm, dw dwe...@structuralcomponents.net wrote: I've been evaluating Sage for engineering applications. The one missing part, which after reading this forum I've realized is currently being worked on, is unit support. The best solution I've been able to use so far is Unum. It works well in my application, but in the notebook I'd like to be able to limit the number of digits shown. I'd previously been using print '%.3f to set the display, but it doesn't work with Unum numbers. I'm sure this would be better asked in an Unum forum, but I haven't found one and it seems a few people here have used the package. Also, on a more general note. Can you set the significant digits displayed throughout a notebook somehow? Thanks. --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Re: import module for all notebooks
Correction to my last post. I thought that was working, but it seems the module was still imported from a previous import call. I've added the line to the all.py file, do I need to re-build sage in any way for this to take effect? I've tried restarting the server with no luck. On Jul 9, 2:08 pm, dw dwe...@structuralcomponents.net wrote: That's exactly what I needed. Thank you. The second solution you posted was right on. --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] numerical eigenforms
What is going on here? Does this only work for even weights? rje sage: n=numerical_eigenforms(15,3);n.ap(2) [] --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Re: import module for all notebooks
I did try your first suggestion again, and that worked. Since I'm running one instance of notebook under a single user, this works great. Thanks again. On Jul 15, 4:25 pm, dw dwe...@structuralcomponents.net wrote: Correction to my last post. I thought that was working, but it seems the module was still imported from a previous import call. I've added the line to the all.py file, do I need to re-build sage in any way for this to take effect? I've tried restarting the server with no luck. On Jul 9, 2:08 pm, dw dwe...@structuralcomponents.net wrote: That's exactly what I needed. Thank you. The second solution you posted was right on. --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Re: query
Thank you so much On 7/15/09, David Joyner wdjoy...@gmail.com wrote: I don't think this is implemented yet in Sage. On Wed, Jul 15, 2009 at 8:55 AM, arun Muktibodhamukti2...@gmail.com wrote: I want to test the limits order of nilpotency class of certain infinite groups. How should I go about it? Please help. Thanking you in advance. Arun India -- Arun Muktibodh -- Arun Muktibodh --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Save our Souls
Hi, I’m away for three weeks and I want to let my PC doing some calculations during 20 days. Now, I’m running the risk that after a few days the computer stops et cetera, so that the results are lost. What are save ways to store results? I expect that the total output is a few Mb. What I would like to avoid is a slow process (subroutine) that does the trick. Any ideas? Thanks in advance! Rolandb --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Problem with larger sws files
Hi, Already in March I reported this problem. http://groups.google.com/group/sage-support/browse_thread/thread/1dbc0160a9d70c5/ae5e660def75547?q=#0ae5e660def75547 Uploading a small file is going well, but a file larger then 3Mb takes ages where after the connection is aborted. Using Sage 4.1, VMware (Windows). Your help is much appreciated! Rolandb --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
[sage-support] Re: Save our Souls
Rolandb ha scritto: Hi, I’m away for three weeks and I want to let my PC doing some calculations during 20 days. Now, I’m running the risk that after a few days the computer stops et cetera, so that the results are lost. Among others precautions, you should to write your IP somewhere, so that you can solve problem by ssh. Laurent --~--~-~--~~~---~--~~ To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support-unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URLs: http://www.sagemath.org -~--~~~~--~~--~--~---
