Re: [sage-support] Using PyWavelets in Sage
Hi,
On Fri, Sep 17, 2010 at 12:07 PM, j wade wrote:
> I would like to use PyWavelets (http://www.pybytes.com/pywavelets/) in
> Sage.
>
> I am running Sage 4.3.4 on Ubuntu 9.10.
>
> I have installed python-pywt using Synaptic File Manager, but I am not
> sure what to do beyond this. I have refreshed the libraries, and
> tried
>
> import scipy
> from scipy import pywt
>
> and
>
> import scipy
> import pywt
>
> but neither command recognizes pywt.
The above steps failed because by default Sage doesn't recognize
Python packages that you have installed system-wide. That is, the
package manager Synaptic installs packages system-wide, whereas the
packages (including Python ones) in Sage are installed specifically
under the SAGE_ROOT top-level directory. So when you issued
import pywt
from within a Sage session, Sage couldn't find pywt because PyWavelets
was not installed under a place where Sage would by default recognize.
> If someone out there is using pywavelets with Sage, I'd appreciate it
> if you could let me know how you were able to get it to work.
Here are the steps that should allow you to install and use PyWavelets
from within Sage.
(1) Download a source release of PyWavelets from
http://pypi.python.org/pypi/PyWavelets/. I downloaded
PyWavelets-0.2.0.tar.bz2 and uncompressed it.
(2) Get the absolute path to your local Sage installation. In my case, it's
/dev/shm/mvngu/sage-4.5.3
(3) Navigate to the top-level directory of the uncompressed PyWavelets
package and install it:
$ cd /path/to/PyWavelets-0.2.0/
$ /dev/shm/mvngu/sage-4.5.3/sage -python setup.py install
(4) Load Sage and start using PyWavelets:
$ /dev/shm/mvngu/sage-4.5.3/sage
--
| Sage Version 4.5.3, Release Date: 2010-09-04 |
| Type notebook() for the GUI, and license() for information.|
--
sage: import pywt
sage: pywt.families()
['haar', 'db', 'sym', 'coif', 'bior', 'rbio', 'dmey']
sage: w = pywt.Wavelet('db3')
sage: print w
Wavelet db3
Family name:Daubechies
Short name: db
Filters length: 6
Orthogonal: True
Biorthogonal: True
Symmetry: asymmetric
--
Regards
Minh Van Nguyen
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[sage-support] Using PyWavelets in Sage
I would like to use PyWavelets (http://www.pybytes.com/pywavelets/) in Sage. I am running Sage 4.3.4 on Ubuntu 9.10. I have installed python-pywt using Synaptic File Manager, but I am not sure what to do beyond this. I have refreshed the libraries, and tried import scipy from scipy import pywt and import scipy import pywt but neither command recognizes pywt. If someone out there is using pywavelets with Sage, I'd appreciate it if you could let me know how you were able to get it to work. -- 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 URL: http://www.sagemath.org
[sage-support] Re: bug in vector
On 9/16/10 9:01 PM, Jason Grout wrote: A patch will be up at #9928 in a few seconds fixing this. Patch is up; feel free to review it! Jason -- 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 URL: http://www.sagemath.org
[sage-support] Re: bug in vector
On 9/16/10 8:12 PM, VictorMiller wrote: Observe (using sage 4.5.2 on my mac): sage: import numpy sage: a = numpy.array([1,2,3]) sage: v = vector(a) Traceback (click to the left of this block for traceback) ... TypeError: unsupported operand type(s) for ** or pow(): 'NoneType' and 'int' The error message is particularly weird. The error comes because the order for testing input types is wrong (and so it tries to construct the vector space (None)^3 instead of ZZ^3). A patch will be up at #9928 in a few seconds fixing this. Jason -- 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 URL: http://www.sagemath.org
[sage-support] bug in vector
Observe (using sage 4.5.2 on my mac): sage: import numpy sage: a = numpy.array([1,2,3]) sage: v = vector(a) Traceback (click to the left of this block for traceback) ... TypeError: unsupported operand type(s) for ** or pow(): 'NoneType' and 'int' The error message is particularly weird. Victor -- 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 URL: http://www.sagemath.org
[sage-support] Re: inserting number into symbolic equation
> > Hi, I'm wondering if it is possible to insert a number into symbolic > > equation. For example: > > > sage: y = x^2 > > sage: diff(y) > >2*x > > > now is it possible to take the results of the derivative, define x as > > say 3, and get a numeric answer? Thanks > > Try this: > sage: g = diff(y) > sage: g > x |--> 2*x > sage: g(3) > 6 That usage is deprecated. "g" in this case would evaluate to the expression "2*x", not the function "x |--> 2*x". You can plug in a value for x using the "subs" method: sage: y = x^2 sage: diff(y) 2*x sage: diff(y).subs(x=3) 6 sage: diff(y).subs(x=pi) 2*pi Alternatively, if you define "y" as a function, "g" would be a function: sage: y(x) = x^2 sage: y x |--> x^2 sage: g = diff(y) sage: g x |--> 2*x sage: g(3) 6 sage: g(pi) 2*pi Hope this helps. -- Tianwei -- 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 URL: http://www.sagemath.org
[sage-support] Re: n() returns symbolic expression
> sage: a=(sqrt(4*(sqrt(3) - 5)*(sqrt(3) + 5) + 48) + 4*sqrt(3))/ > (sqrt(3) + 5) > sage: > a.imag().n() > 0.939469338708203*sin(0.500*pi) Here's a simpler example: sage: b = sqrt(-log(2)) sage: print b.imag().n() 0.832554611157698*sin(0.500*pi) -- Tianwei -- 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 URL: http://www.sagemath.org
Re: [sage-support] Re: installation problem
On Thu, 16 Sep 2010 at 07:43PM +0100, robin hankin wrote: > I did try to compile my own, but ran in to utter dependency hell. The Sage source should include very nearly everything it needs to build. There are very few dependencies. What kind of "dependency hell" did you run into? Dan -- --- Dan Drake - http://mathsci.kaist.ac.kr/~drake --- signature.asc Description: Digital signature
Re: [sage-support] integer factorization benchmarks
On 09/16/10 11:23 PM, Dr. David Kirkby wrote:
On 09/16/10 09:10 PM, Greg Marks wrote:
Out of curiosity...
At http://sagemath.org/tour-benchmarks.html the CPU time
given for factorization of the integer 2^512 - 1 with SAGE
version 4.1.1 is 92.29 sec. I just tried this with SAGE
version 4.5.2, running under 64-bit Linux on a laptop with
an Intel Core 2 Duo P8600 CPU @ 2.40 GHz and 2.9 GiB RAM,
and the same calculation required only 31.39 sec. CPU time.
(The same factorization, on the same computer, using Maple 14
required 185.43 sec., incidentally. I don't have a recent
version of Mathematica to compare.)
On Mathematica 7, Solaris x86 on a quad core 3.33 GHz Intel Xeon W3580.
I note Mathematica does not use many cores for this (I assume single
threaded). I would have thought this is the sort of thing that could
have been improved with a parallel algorithm, or perhaps for non-trivial
factorisations thats not so. But I would have thought it was.
In[3]:= Timing[ FactorInteger[2^512-1]]
Out[3]= {151.054, {{3, 1}, {5, 1}, {17, 1}, {257, 1}, {641, 1}, {65537, 1},
> {274177, 1}, {6700417, 1}, {67280421310721, 1}, {1238926361552897, 1},
> {59649589127497217, 1}, {5704689200685129054721, 1},
> {93461639715357977769163558199606896584051237541638188580280321, 1}}}
For context, on the Same machine,
sage: timeit('factor(2^512-1)')
5 loops, best of 3: 43.9 s per loop
However, this is a 32-bit build of Sage. Anything using large integers will be
significantly slower if using 32-bit words rather than 64-bit words, so I would
expect this to improve with a 64-bit build of Sage on OpenSolaris. But Sage
beats Mathematica by a factor of around 3.4, even though Sage is 32-bit and
Mathematica is 64-bit on this machine.
Dave
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Re: [sage-support] integer factorization benchmarks
On 09/16/10 09:10 PM, Greg Marks wrote:
Out of curiosity...
At http://sagemath.org/tour-benchmarks.html the CPU time
given for factorization of the integer 2^512 - 1 with SAGE
version 4.1.1 is 92.29 sec. I just tried this with SAGE
version 4.5.2, running under 64-bit Linux on a laptop with
an Intel Core 2 Duo P8600 CPU @ 2.40 GHz and 2.9 GiB RAM,
and the same calculation required only 31.39 sec. CPU time.
(The same factorization, on the same computer, using Maple 14
required 185.43 sec., incidentally. I don't have a recent
version of Mathematica to compare.)
On Mathematica 7, Solaris x86 on a quad core 3.33 GHz Intel Xeon W3580.
I note Mathematica does not use many cores for this (I assume single threaded).
I would have thought this is the sort of thing that could have been improved
with a parallel algorithm, or perhaps for non-trivial factorisations thats not
so. But I would have thought it was.
In[3]:= Timing[ FactorInteger[2^512-1]]
Out[3]= {151.054, {{3, 1}, {5, 1}, {17, 1}, {257, 1}, {641, 1}, {65537, 1},
> {274177, 1}, {6700417, 1}, {67280421310721, 1}, {1238926361552897, 1},
> {59649589127497217, 1}, {5704689200685129054721, 1},
> {93461639715357977769163558199606896584051237541638188580280321, 1}}}
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[sage-support] Re: integer factorization benchmarks
I just tried that on my laptop (2.4 GHz Intel Core 2 Duo, OS X 10.5) and it took 74 seconds for sage-3.2, 73 seconds for sage-4.6.alpha0. Since that difference is probably just noise, things haven't changed. -M. Hampton On Sep 16, 3:10 pm, Greg Marks wrote: > Out of curiosity... > > Athttp://sagemath.org/tour-benchmarks.htmlthe CPU time > given for factorization of the integer 2^512 - 1 with SAGE > version 4.1.1 is 92.29 sec. I just tried this with SAGE > version 4.5.2, running under 64-bit Linux on a laptop with > an Intel Core 2 Duo P8600 CPU @ 2.40 GHz and 2.9 GiB RAM, > and the same calculation required only 31.39 sec. CPU time. > (The same factorization, on the same computer, using Maple 14 > required 185.43 sec., incidentally. I don't have a recent > version of Mathematica to compare.) > > The documentation says SAGE calls PARI for this calculation. > Is the threefold improvement in speed due to any change in > the factorization algorithm between SAGE 4.1.1 and SAGE 4.5.2? > Or is it due to a difference in hardware, or something else? > > Best regards, > Greg Marks > > > | Greg Marks | > | Department of Mathematics and Computer Science | > | St. Louis University | > | St. Louis, MO 63103-2007 | > | U.S.A. | > | | > | Phone: (314)977-7206 | > | Fax: (314)977-1452 | > | Web:http://math.slu.edu/~marks | > -- 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 URL: http://www.sagemath.org
[sage-support] Re: integer factorization benchmarks
> The documentation says SAGE calls PARI for this calculation. > Is the threefold improvement in speed due to any change in > the factorization algorithm between SAGE 4.1.1 and SAGE 4.5.2? > Or is it due to a difference in hardware, or something else? And would it be even faster with the new PARI? Incidentally, many of these pages get out of date very quickly. For instance, the official doc also still implies we don't support OS X 64- bit - is this true? http://www.sagemath.com/doc/installation/source.html http://wiki.sagemath.org/SupportedPlatforms - kcrisman -- 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 URL: http://www.sagemath.org
[sage-support] integer factorization benchmarks
Out of curiosity... At http://sagemath.org/tour-benchmarks.html the CPU time given for factorization of the integer 2^512 - 1 with SAGE version 4.1.1 is 92.29 sec. I just tried this with SAGE version 4.5.2, running under 64-bit Linux on a laptop with an Intel Core 2 Duo P8600 CPU @ 2.40 GHz and 2.9 GiB RAM, and the same calculation required only 31.39 sec. CPU time. (The same factorization, on the same computer, using Maple 14 required 185.43 sec., incidentally. I don't have a recent version of Mathematica to compare.) The documentation says SAGE calls PARI for this calculation. Is the threefold improvement in speed due to any change in the factorization algorithm between SAGE 4.1.1 and SAGE 4.5.2? Or is it due to a difference in hardware, or something else? Best regards, Greg Marks | Greg Marks | | Department of Mathematics and Computer Science | | St. Louis University | | St. Louis, MO 63103-2007 | | U.S.A. | || | Phone: (314)977-7206 | | Fax: (314)977-1452 | | Web: http://math.slu.edu/~marks| -- 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 URL: http://www.sagemath.org
Re: [sage-support] Re: installation problem
On 09/16/10 07:43 PM, robin hankin wrote: Thanks for this Marshall. I did try to compile my own, but ran in to utter dependency hell. In the end I managed to get it to work by deleting some of the readline libraries, but I don't understand why that worked. Redline often causes problems on Sage. I know it has done on OpenSUSE Would you say that the google groups you point me towards is a more active forum than the sage-support mailing list? Thanks again Robin The mailing list is a Google group. Marshall just poined you to the same place. You can post via google groups or email. It's the same support forum. Dave -- 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 URL: http://www.sagemath.org
Re: [sage-support] Re: installation problem
Thanks for this Marshall.
I did try to compile my own, but ran in to utter dependency hell.
In the end I managed to get it to work by deleting some of the
readline libraries, but I don't understand why that worked.
Would you say that the google groups you point me towards
is a more active forum than the sage-support mailing list?
Thanks again
Robin
On Thu, Sep 16, 2010 at 7:17 PM, Marshall Hampton wrote:
> Your error message looks exactly like the one reported here a few
> months ago:
>
> http://groups.google.com/group/sage-support/browse_thread/thread/aba48495d9c09e03/f25d062b6764492f
>
> In that case it was somehow caused by an upgrade after installing the
> binary. One option would be to install a source version.
>
> -M. Hampton
>
> On Sep 16, 8:04 am, robin hankin wrote:
>> Hi. suse 11.3, trying to work with sage 4.5.3
>>
>> I get various problems when trying to execute sage
>> (transcript below).
>>
>> Any ideas?
>>
>> thanks
>>
>> rksh
>>
>> le112:~/Download/sage-4.5.3-linux-32bit-opensuse_11.1_i586-i686-Linux% ./sage
>> --
>> | Sage Version 4.5.3, Release Date: 2010-09-04 |
>> | Type notebook() for the GUI, and license() for information. |
>> --
>> sh: symbol lookup error: sh: undefined symbol: rl_filename_rewrite_hook
>> sh: symbol lookup error: sh: undefined symbol: rl_filename_rewrite_hook
>> sh: symbol lookup error: sh: undefined symbol: rl_filename_rewrite_hook
>> sh: symbol lookup error: sh: undefined symbol: rl_filename_rewrite_hook
>> sh: symbol lookup error: sh: undefined symbol: rl_filename_rewrite_hook
>> sh: symbol lookup error: sh: undefined symbol: rl_filename_rewrite_hook
>> sh: symbol lookup error: sh: undefined symbol: rl_filename_rewrite_hook
>> sh: symbol lookup error: sh: undefined symbol: rl_filename_rewrite_hook
>> sh: symbol lookup error: sh: undefined symbol: rl_filename_rewrite_hook
>> sh: symbol lookup error: sh: undefined symbol: rl_filename_rewrite_hook
>> sh: symbol lookup error: sh: undefined symbol: rl_filename_rewrite_hook
>> ERROR: An unexpected error occurred while tokenizing input
>> The following traceback may be corrupted or invalid
>> The error message is: ('EOF in multi-line statement', (69, 0))
>>
>> ERROR: An unexpected error occurred while tokenizing input
>> The following traceback may be corrupted or invalid
>> The error message is: ('EOF in multi-line statement', (47, 0))
>>
>> ---
>> RuntimeError Traceback (most recent call last)
>>
>> /home/rksh/Download/sage-4.5.3-linux-32bit-opensuse_11.1_i586-i686-Linux/local/lib/python2.6/site-packages/IPython/ipmaker.pyc
>> in force_import(modname)
>> 64 reload(sys.modules[modname])
>> 65 else:
>> ---> 66 __import__(modname)
>> 67
>> 68
>>
>> /home/rksh/Download/sage-4.5.3-linux-32bit-opensuse_11.1_i586-i686-Linux/local/bin/ipy_profile_sage.py
>> in ()
>> 5 preparser(True)
>> 6
>> > 7 import sage.all_cmdline
>> 8 sage.all_cmdline._init_cmdline(globals())
>> 9
>>
>> /home/rksh/Download/sage-4.5.3-linux-32bit-opensuse_11.1_i586-i686-Linux/local/lib/python2.6/site-packages/sage/all_cmdline.py
>> in ()
>> 12 try:
>> 13
>> ---> 14 from sage.all import *
>> 15 from sage.calculus.predefined import x
>> 16 preparser(on=True)
>>
>> /home/rksh/Download/sage-4.5.3-linux-32bit-opensuse_11.1_i586-i686-Linux/local/lib/python2.6/site-packages/sage/all.py
>> in ()
>> 62 get_sigs()
>> 63
>> ---> 64 from sage.misc.all import * # takes a while
>> 65
>> 66 from sage.misc.sh import sh
>>
>> /home/rksh/Download/sage-4.5.3-linux-32bit-opensuse_11.1_i586-i686-Linux/local/lib/python2.6/site-packages/sage/misc/all.py
>> in ()
>> 65 from sage_eval import sage_eval, sageobj
>> 66
>> ---> 67 from sage_input import sage_input
>> 68
>> 69 from cython import cython_lambda, cython_create_local_so
>>
>> /home/rksh/Download/sage-4.5.3-linux-32bit-opensuse_11.1_i586-i686-Linux/local/lib/python2.6/site-packages/sage/misc/sage_input.py
>> in ()
>> 161 """
>> 162
>> --> 163 from sage.misc.functional import parent
>> 164 import math
>> 165
>>
>> /home/rksh/Download/sage-4.5.3-linux-32bit-opensuse_11.1_i586-i686-Linux/local/lib/python2.6/site-packages/sage/misc/functional.py
>> in ()
>> 36
>> 37
>> ---> 38 from sage.rings.complex_double import CDF
>> 39 from sage.rings.real_double import RDF, RealDoubleElement
>> 40
>>
>> /home/rksh/Download/sage-4.5.3-linux-32bit-opensuse_11.1_i586-i686-Linux/local/bin/complex_double.pyx
>> in init sage.rings.complex_double
>> (sage/rings/complex_double.c:14319)()
>>
>> /home/rksh/Download/sage-4.5.3-linux-32bit-opensuse_11.1_i586-i686-Linux/local/l
[sage-support] Re: installation problem
Your error message looks exactly like the one reported here a few
months ago:
http://groups.google.com/group/sage-support/browse_thread/thread/aba48495d9c09e03/f25d062b6764492f
In that case it was somehow caused by an upgrade after installing the
binary. One option would be to install a source version.
-M. Hampton
On Sep 16, 8:04 am, robin hankin wrote:
> Hi. suse 11.3, trying to work with sage 4.5.3
>
> I get various problems when trying to execute sage
> (transcript below).
>
> Any ideas?
>
> thanks
>
> rksh
>
> le112:~/Download/sage-4.5.3-linux-32bit-opensuse_11.1_i586-i686-Linux% ./sage
> --
> | Sage Version 4.5.3, Release Date: 2010-09-04 |
> | Type notebook() for the GUI, and license() for information. |
> --
> sh: symbol lookup error: sh: undefined symbol: rl_filename_rewrite_hook
> sh: symbol lookup error: sh: undefined symbol: rl_filename_rewrite_hook
> sh: symbol lookup error: sh: undefined symbol: rl_filename_rewrite_hook
> sh: symbol lookup error: sh: undefined symbol: rl_filename_rewrite_hook
> sh: symbol lookup error: sh: undefined symbol: rl_filename_rewrite_hook
> sh: symbol lookup error: sh: undefined symbol: rl_filename_rewrite_hook
> sh: symbol lookup error: sh: undefined symbol: rl_filename_rewrite_hook
> sh: symbol lookup error: sh: undefined symbol: rl_filename_rewrite_hook
> sh: symbol lookup error: sh: undefined symbol: rl_filename_rewrite_hook
> sh: symbol lookup error: sh: undefined symbol: rl_filename_rewrite_hook
> sh: symbol lookup error: sh: undefined symbol: rl_filename_rewrite_hook
> ERROR: An unexpected error occurred while tokenizing input
> The following traceback may be corrupted or invalid
> The error message is: ('EOF in multi-line statement', (69, 0))
>
> ERROR: An unexpected error occurred while tokenizing input
> The following traceback may be corrupted or invalid
> The error message is: ('EOF in multi-line statement', (47, 0))
>
> ---
> RuntimeError Traceback (most recent call last)
>
> /home/rksh/Download/sage-4.5.3-linux-32bit-opensuse_11.1_i586-i686-Linux/local/lib/python2.6/site-packages/IPython/ipmaker.pyc
> in force_import(modname)
> 64 reload(sys.modules[modname])
> 65 else:
> ---> 66 __import__(modname)
> 67
> 68
>
> /home/rksh/Download/sage-4.5.3-linux-32bit-opensuse_11.1_i586-i686-Linux/local/bin/ipy_profile_sage.py
> in ()
> 5 preparser(True)
> 6
> > 7 import sage.all_cmdline
> 8 sage.all_cmdline._init_cmdline(globals())
> 9
>
> /home/rksh/Download/sage-4.5.3-linux-32bit-opensuse_11.1_i586-i686-Linux/local/lib/python2.6/site-packages/sage/all_cmdline.py
> in ()
> 12 try:
> 13
> ---> 14 from sage.all import *
> 15 from sage.calculus.predefined import x
> 16 preparser(on=True)
>
> /home/rksh/Download/sage-4.5.3-linux-32bit-opensuse_11.1_i586-i686-Linux/local/lib/python2.6/site-packages/sage/all.py
> in ()
> 62 get_sigs()
> 63
> ---> 64 from sage.misc.all import * # takes a while
> 65
> 66 from sage.misc.sh import sh
>
> /home/rksh/Download/sage-4.5.3-linux-32bit-opensuse_11.1_i586-i686-Linux/local/lib/python2.6/site-packages/sage/misc/all.py
> in ()
> 65 from sage_eval import sage_eval, sageobj
> 66
> ---> 67 from sage_input import sage_input
> 68
> 69 from cython import cython_lambda, cython_create_local_so
>
> /home/rksh/Download/sage-4.5.3-linux-32bit-opensuse_11.1_i586-i686-Linux/local/lib/python2.6/site-packages/sage/misc/sage_input.py
> in ()
> 161 """
> 162
> --> 163 from sage.misc.functional import parent
> 164 import math
> 165
>
> /home/rksh/Download/sage-4.5.3-linux-32bit-opensuse_11.1_i586-i686-Linux/local/lib/python2.6/site-packages/sage/misc/functional.py
> in ()
> 36
> 37
> ---> 38 from sage.rings.complex_double import CDF
> 39 from sage.rings.real_double import RDF, RealDoubleElement
> 40
>
> /home/rksh/Download/sage-4.5.3-linux-32bit-opensuse_11.1_i586-i686-Linux/local/bin/complex_double.pyx
> in init sage.rings.complex_double
> (sage/rings/complex_double.c:14319)()
>
> /home/rksh/Download/sage-4.5.3-linux-32bit-opensuse_11.1_i586-i686-Linux/local/lib/python2.6/site-packages/sage/rings/complex_field.pyc
> in ComplexField(prec, names)
> 84 if not C is None:
> 85 return C
> ---> 86 C = ComplexField_class(prec)
> 87 cache[prec] = weakref.ref(C)
> 88 return C
>
> /home/rksh/Download/sage-4.5.3-linux-32bit-opensuse_11.1_i586-i686-Linux/local/lib/python2.6/site-packages/sage/rings/complex_field.pyc
> in __init__(self, prec)
> 184 ParentWithGens.__init__(self, self._real_field(),
> ('I',), False, category = Fields())
[sage-support] Re: Simplifying symbolic expressions containing vectors and matrices
On 9/16/10 10:47 AM, miquel pericas wrote:
Hi,
I'm a collaborator of the author of the previous post. Let me try to
elaborate a little on what it is we want to do
Basically we are trying to simplify some complex symbolic expressions
we have generated which include matrices and vectors as variables.
Unfortunately these formulas are too long/complex to manipulate by
hand and we we are looking for some way to do this automatically.
Sage's manual explains how to simplify expressions with some
variables: The following example is extracted from the reference
manual
sage: var(’x, y, a, b, c’)
(x, y, a, b, c)
sage: f = x*(x-1)/(x^2 - 7) + y^2/(x^2-7) + 1/(x+1) + b/a + c/a; f
(x - 1)*x/(x^2 - 7) + y^2/(x^2 - 7) + b/a + c/a + 1/(x + 1)
sage: f.combine()
((x - 1)*x + y^2)/(x^2 - 7) + (b + c)/a + 1/(x + 1)
We want to do exactly the same, but in our case variables a,b,c, etc
would be vectors and matrices. Our question is: is it possible to use
sage to perform this kind of simplification with matrices and vectors?
Or, what is probably the same question, how can I generate variables
that are matrices and vectors?
It sounds like the thread I linked to in an earlier message on this
thread contains code that would do things like you are asking about.
http://groups.google.com/group/sage-devel/browse_thread/thread/cafb486c79a2eb3c/d0bb78d09a4fb52a
For example, here is an example from that thread:
sage: Alg = SymbolicMatrixAlgebra(QQ)
sage: A = Alg.matrix("A", 3, 2)
sage: B = Alg.matrix("B", 3, 2)
sage: C = Alg.matrix("C", 2, 2)
sage: D = Alg.matrix("D", 2, 3)
sage: x = D * (A+B) * C
sage: x
D B C + D A C
sage: x.transpose()
C^t B^t D^t + C^t A^t D^t
Of course, you can deal with a vector by declaring a 3 by 1 matrix, for
example:
sage: load('matrix.sage')
sage: Alg = SymbolicMatrixAlgebra(QQ)
sage: A = Alg.matrix("A",3,3)
sage: b = Alg.matrix("b",3,1)
sage: x = Alg.matrix("x",3,1) # a column vector
sage: A*x + A^2*x+A^3*x+A*b
A A A x + A A x + A b + A x
The code isn't complete, but it does do things like not assume matrices
commute, handle inverses and transposes, etc. I would love it if the
code was polished and included in Sage. I would probably make good use
of it too.
Thanks,
Jason
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[sage-support] Simplifying symbolic expressions containing vectors and matrices
Hi,
I'm a collaborator of the author of the previous post. Let me try to
elaborate a little on what it is we want to do
Basically we are trying to simplify some complex symbolic expressions
we have generated which include matrices and vectors as variables.
Unfortunately these formulas are too long/complex to manipulate by
hand and we we are looking for some way to do this automatically.
Sage's manual explains how to simplify expressions with some
variables: The following example is extracted from the reference
manual
sage: var(’x, y, a, b, c’)
(x, y, a, b, c)
sage: f = x*(x-1)/(x^2 - 7) + y^2/(x^2-7) + 1/(x+1) + b/a + c/a; f
(x - 1)*x/(x^2 - 7) + y^2/(x^2 - 7) + b/a + c/a + 1/(x + 1)
sage: f.combine()
((x - 1)*x + y^2)/(x^2 - 7) + (b + c)/a + 1/(x + 1)
We want to do exactly the same, but in our case variables a,b,c, etc
would be vectors and matrices. Our question is: is it possible to use
sage to perform this kind of simplification with matrices and vectors?
Or, what is probably the same question, how can I generate variables
that are matrices and vectors?
I tried the following, but it seems this is not really generating
matrices and vectors:
sage: A = matrix(RR, 1000, 1000, sparse=True).parent()
sage: A
Full MatrixSpace of 1000 by 1000 sparse matrices over Real Field with
53 bits of precision
sage: matr = var('matr', domain=A)
sage: V = vector(RR, 1000).parent()
sage: V
Vector space of dimension 1000 over Real Field with 53 bits of
precision
sage: vec = var('vec', domain=V)
I hope someone here will be able to shed some light on this or suggest
a different approach/tool for achieving the symbolic simplification we
are pursuing
Thank you very much in advance,
Miquel
On Sep 10, 2:44 pm, BSC-BCN wrote:
> Conjugate Gradient Algorithm
>
> 1.Compute r0:=b Ax0, p0:=r0
> 2.For j =0;1; ,until convergence Do:
> 3. aj :=(rj,rj)/(Apj,pj)
> 4.xj+1:= xj + ajpj
> 5.rj+1:=rj-ajApj
> 6.bj :=(rj+1,rj+1)/(rj,rj)
> 7.pj+1:=rj+1+bjpj
> 8.End Do
>
> Derivation for two steps in one go
>
> Compute r0:=bAx0, p0:=r0
> For j=0;2;,unitl convergence Do:
> aj := (rj,rj)/ (Apj,pj)
> xj+1:= xj + ajpj
> rj+1:=rj-ajApj
> bj :=(rj+1,rj+1)/(rj,rj)
> pj+1:=rj+1+bjpj
>
> aj+1 := (rj+1,rj+1)/ (APj+1,pj+1)
> xj+2:= xj+1 + aj+1pj+1
> rj+2:=rj+1-aj+1Apj+1
> bj+1 :=(rj+2,rj+2)/(rj+1,rj+1)
> pj+2:=rj+2+bj+1pj+1
>
> End Do
>
> All the equation must rely on the following initial variables:rj,pj,xj
> and on constant Matrix A
>
> Xj+2 have to be in function of rj,pj,xj and A it can't contain rj+1,pj
> +1,xj+1 and so on for rj+2, xj+2
>
> Some explanation:
>
> (rj,rj) is scalar-product of vectors rj,rj
> Apj is Matrix-vector multiplication where A is matrix and pj is a
> vector
> aj and bj are parametars
>
> I hope now is more clear what I want to do...As I said the expressions
> that I get are pretty big and I would like to use SAGE to try to
> simplify and make more compact. In case that I want to do 3 or more
> steps in one go the expressions would become even more bigger..
>
> Thanks
> Branimir
>
> On Sep 8, 3:23 pm, Jason Grout wrote:
>
> > On 9/8/10 7:45 AM, BSC-BCN wrote:
>
> > I hope you can understand
>
> > > me...
>
> > I don't think I really do, but this thread might contain some useful
> > things for you:
>
> >http://groups.google.com/group/sage-devel/browse_thread/thread/cafb48...
>
> > Thanks,
>
> > Jason
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[sage-support] installation problem
Hi. suse 11.3, trying to work with sage 4.5.3
I get various problems when trying to execute sage
(transcript below).
Any ideas?
thanks
rksh
le112:~/Download/sage-4.5.3-linux-32bit-opensuse_11.1_i586-i686-Linux% ./sage
--
| Sage Version 4.5.3, Release Date: 2010-09-04 |
| Type notebook() for the GUI, and license() for information.|
--
sh: symbol lookup error: sh: undefined symbol: rl_filename_rewrite_hook
sh: symbol lookup error: sh: undefined symbol: rl_filename_rewrite_hook
sh: symbol lookup error: sh: undefined symbol: rl_filename_rewrite_hook
sh: symbol lookup error: sh: undefined symbol: rl_filename_rewrite_hook
sh: symbol lookup error: sh: undefined symbol: rl_filename_rewrite_hook
sh: symbol lookup error: sh: undefined symbol: rl_filename_rewrite_hook
sh: symbol lookup error: sh: undefined symbol: rl_filename_rewrite_hook
sh: symbol lookup error: sh: undefined symbol: rl_filename_rewrite_hook
sh: symbol lookup error: sh: undefined symbol: rl_filename_rewrite_hook
sh: symbol lookup error: sh: undefined symbol: rl_filename_rewrite_hook
sh: symbol lookup error: sh: undefined symbol: rl_filename_rewrite_hook
ERROR: An unexpected error occurred while tokenizing input
The following traceback may be corrupted or invalid
The error message is: ('EOF in multi-line statement', (69, 0))
ERROR: An unexpected error occurred while tokenizing input
The following traceback may be corrupted or invalid
The error message is: ('EOF in multi-line statement', (47, 0))
---
RuntimeError Traceback (most recent call last)
/home/rksh/Download/sage-4.5.3-linux-32bit-opensuse_11.1_i586-i686-Linux/local/lib/python2.6/site-packages/IPython/ipmaker.pyc
in force_import(modname)
64 reload(sys.modules[modname])
65 else:
---> 66 __import__(modname)
67
68
/home/rksh/Download/sage-4.5.3-linux-32bit-opensuse_11.1_i586-i686-Linux/local/bin/ipy_profile_sage.py
in ()
5 preparser(True)
6
> 7 import sage.all_cmdline
8 sage.all_cmdline._init_cmdline(globals())
9
/home/rksh/Download/sage-4.5.3-linux-32bit-opensuse_11.1_i586-i686-Linux/local/lib/python2.6/site-packages/sage/all_cmdline.py
in ()
12 try:
13
---> 14 from sage.all import *
15 from sage.calculus.predefined import x
16 preparser(on=True)
/home/rksh/Download/sage-4.5.3-linux-32bit-opensuse_11.1_i586-i686-Linux/local/lib/python2.6/site-packages/sage/all.py
in ()
62 get_sigs()
63
---> 64 from sage.misc.all import * # takes a while
65
66 from sage.misc.sh import sh
/home/rksh/Download/sage-4.5.3-linux-32bit-opensuse_11.1_i586-i686-Linux/local/lib/python2.6/site-packages/sage/misc/all.py
in ()
65 from sage_eval import sage_eval, sageobj
66
---> 67 from sage_input import sage_input
68
69 from cython import cython_lambda, cython_create_local_so
/home/rksh/Download/sage-4.5.3-linux-32bit-opensuse_11.1_i586-i686-Linux/local/lib/python2.6/site-packages/sage/misc/sage_input.py
in ()
161 """
162
--> 163 from sage.misc.functional import parent
164 import math
165
/home/rksh/Download/sage-4.5.3-linux-32bit-opensuse_11.1_i586-i686-Linux/local/lib/python2.6/site-packages/sage/misc/functional.py
in ()
36
37
---> 38 from sage.rings.complex_double import CDF
39 from sage.rings.real_double import RDF, RealDoubleElement
40
/home/rksh/Download/sage-4.5.3-linux-32bit-opensuse_11.1_i586-i686-Linux/local/bin/complex_double.pyx
in init sage.rings.complex_double
(sage/rings/complex_double.c:14319)()
/home/rksh/Download/sage-4.5.3-linux-32bit-opensuse_11.1_i586-i686-Linux/local/lib/python2.6/site-packages/sage/rings/complex_field.pyc
in ComplexField(prec, names)
84 if not C is None:
85 return C
---> 86 C = ComplexField_class(prec)
87 cache[prec] = weakref.ref(C)
88 return C
/home/rksh/Download/sage-4.5.3-linux-32bit-opensuse_11.1_i586-i686-Linux/local/lib/python2.6/site-packages/sage/rings/complex_field.pyc
in __init__(self, prec)
184 ParentWithGens.__init__(self, self._real_field(),
('I',), False, category = Fields())
185 #self._populate_coercion_lists_()
--> 186
self._populate_coercion_lists_(coerce_list=[complex_number.RRtoCC(self._real_field(),
self)])
187
188 def __reduce__(self):
/home/rksh/Download/sage-4.5.3-linux-32bit-opensuse_11.1_i586-i686-Linux/local/lib/python2.6/site-packages/sage/rings/complex_number.so
in sage.rings.complex_number.RRtoCC.__init__
(sage/rings/complex_number.c:13971)()
/home/rksh/Download/sage-4.5.3-linux-32bit-opensuse_11.1_i586-i686-Linux/local/lib/python2.6/site-packages/sage/categories/map.so
in sage.categori
[sage-support] Re: Graphics3d Object face_list()
On 9/16/10 12:31 AM, TeamTeamUSA wrote: Answering my own question. The 3-tuples describe a triangle, the 4-tuples describe a quadrilateral - 2 triangles sharing 2 vertices. Can you please submit a patch clarifying the documentation? Thanks, Jason -- 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 URL: http://www.sagemath.org
