[sage-devel] Re: sage-2.5.alpha3
William Stein wrote: * w hart: quadratic sieve update (SAGE's qsieve command): It is MUCH faster, especially for large factorizations, on account of having implemented the large prime variant. it will factor an 81 digit number in 20 minutes. On the Athlon it is the fastest generally available implementation of the quadratic sieve in the world for certain sized factorizations, and only slightly behind at other sizes. Another example: n = next_prime(2^110)*next_prime(2^120) has these times on 32-bit 2Ghz linux: qsieve (107s), PARI (223s), Magma 2.13 (336s). Whoops, sorry, I've given you some wrong info William. That should have read well under 30 minutes. Also, unfortunately Jason P didn't take my Athlon improvements lying down. He's released a new version of msieve which again beats my sieve comprehensively on the Athlon. Work continues... At any rate, we are still miles ahead of LiDIA, MAGMA and Pari, etc. I also forgot to mention, the tuning parameters for the Athlon are currently commented out in QS.cpp. The tuning that is currently activated is for sage.math, i.e. 2.2GHz Opteron. Sorry about that. It appears I never got around to updating the makefile to take the architecture into account. Actually, if there is anyone who knows a lot about makefiles, I could really use a hand with this. C I know. makefile language I do not. Bill. --~--~-~--~~~---~--~~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://sage.scipy.org/sage/ and http://modular.math.washington.edu/sage/ -~--~~~~--~~--~--~---
[sage-devel] Re: sage-2.5.alpha3
To add to the success reports. Gentoo (Pentium 4): Builds fine and ... -- All tests passed! Total time for all tests: 1569.5 seconds -- Joel On Sun, May 06, 2007 at 09:24:19AM -0700, William Stein wrote: Hello, I've posted sage-2.5.alpha3 here: http://sage.math.washington.edu/home/was/sage2.5/ Feedback is welcome. This still won't build on OS X PowerPC or Cygwin, but should build on Linux and Intel OS X and pass make test there. Also, it should have most code that people have sent me for inclusion in SAGE. The official sage-2.5 is getting close, so any testing feedback is greatly appreciated. In particular, if people could try out some of the new features in sage-2.5, especially symbolic computation, this would be quite valuable. Here's a list of the main things that are new in sage-2.5.alpha3: 2.5: * new packages: - flintqs - ipython-0.8.0 (w stein) - maxima-5.12.0 (w stein) - python-2.5.1 (y qiang) -- important bug fixes - tachyon3d-0.98beta (w stein) * m abshoff: cputime bugfix for cygwin * m albrecht: major new singular library mode interface for SAGE which provides the world's fastest polynomial arithmetic to SAGE (not yet enabled by default!) * r bradshaw: tons of polynomial and power series optimizations; Coleman p-adic integration; Kedlaya for genus 1 * t clemens: source browser bugfix * p de napoli:fix some bugs in rationals and integers * d deshomme: (refereed by r bradshaw and w stein) very good support for Hida's quad-double field RQDF. * w hart: quadratic sieve update (SAGE's qsieve command): It is MUCH faster, especially for large factorizations, on account of having implemented the large prime variant. it will factor an 81 digit number in 20 minutes. On the Athlon it is the fastest generally available implementation of the quadratic sieve in the world for certain sized factorizations, and only slightly behind at other sizes. Another example: n = next_prime(2^110)*next_prime(2^120) has these times on 32-bit 2Ghz linux: qsieve (107s), PARI (223s), Magma 2.13 (336s). * d harvey: improvements, bug fixes. * d kohel:quaternion algebra improvements * k minola: tmp file clean bugfix; misc build fixes. * k minola, d joyner: updated the conway polynomial table * w stein and b moretti: major new symbolic calculus functionality * w stein:rewrite of SAGE/maxima interface. * c witty:(refereed by n alexandar) a new algebraic reals field (Qbar meet RR!). mpfr improvements --~--~-~--~~~---~--~~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://sage.scipy.org/sage/ and http://modular.math.washington.edu/sage/ -~--~~~~--~~--~--~---
[sage-devel] Re: sage-2.5.alpha3
For my OS X intel mac pro: All tests passed! Total time for all tests: 1516.7 seconds I also fired up the notebook and ran a few pieces of my own code, no problems. Marshall Hampton On May 6, 11:24 am, William Stein [EMAIL PROTECTED] wrote: Hello, I've posted sage-2.5.alpha3 here: http://sage.math.washington.edu/home/was/sage2.5/ Feedback is welcome. This still won't build on OS X PowerPC or Cygwin, but should build on Linux and Intel OS X and pass make test there. Also, it should have most code that people have sent me for inclusion in SAGE. The official sage-2.5 is getting close, so any testing feedback is greatly appreciated. In particular, if people could try out some of the new features in sage-2.5, especially symbolic computation, this would be quite valuable. Here's a list of the main things that are new in sage-2.5.alpha3: 2.5: * new packages: - flintqs - ipython-0.8.0 (w stein) - maxima-5.12.0 (w stein) - python-2.5.1 (y qiang) -- important bug fixes - tachyon3d-0.98beta (w stein) * m abshoff: cputime bugfix for cygwin * m albrecht: major new singular library mode interface for SAGE which provides the world's fastest polynomial arithmetic to SAGE (not yet enabled by default!) * r bradshaw: tons of polynomial and power series optimizations; Coleman p-adic integration; Kedlaya for genus 1 * t clemens: source browser bugfix * p de napoli:fix some bugs in rationals and integers * d deshomme: (refereed by r bradshaw and w stein) very good support for Hida's quad-double field RQDF. * w hart: quadratic sieve update (SAGE's qsieve command): It is MUCH faster, especially for large factorizations, on account of having implemented the large prime variant. it will factor an 81 digit number in 20 minutes. On the Athlon it is the fastest generally available implementation of the quadratic sieve in the world for certain sized factorizations, and only slightly behind at other sizes. Another example: n = next_prime(2^110)*next_prime(2^120) has these times on 32-bit 2Ghz linux: qsieve (107s), PARI (223s), Magma 2.13 (336s). * d harvey: improvements, bug fixes. * d kohel:quaternion algebra improvements * k minola: tmp file clean bugfix; misc build fixes. * k minola, d joyner: updated the conway polynomial table * w stein and b moretti: major new symbolic calculus functionality * w stein:rewrite of SAGE/maxima interface. * c witty:(refereed by n alexandar) a new algebraic reals field (Qbar meet RR!). mpfr improvements --~--~-~--~~~---~--~~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://sage.scipy.org/sage/ and http://modular.math.washington.edu/sage/ -~--~~~~--~~--~--~---
[sage-devel] Re: sage-2.5.alpha3
William, sage-2.5.alpha3 successfully passes all tests on my x86-Linux and x86_64-Linux machines. (I believe this is the first time that sage has passed ALL the tests for me. Yeah!) It fails the following two tests on my ia64-Linux machine: devel/sage-main/sage/plot/plot.py *** *** Error: TIMED OUT! *** *** devel/sage-main/sage/schemes/elliptic_curves/ell_generic.py First error message is: File ell_generic.py, line 220: sage: eqn = symbolic_expression(E); eqn Exception raised: Traceback (most recent call last): File /home/kate/sage/sage-2.5.alpha3-ia64-Linux/local/lib/ python2.5/docte st.py, line 1212, in __run compileflags, 1) in test.globs File doctest __main__.example_4[2], line 1, in module eqn = symbolic_expression(E); eqn###line 220: sage: eqn = symbolic_expression(E); eqn File sage_object.pyx, line 87, in sage_object.SageObject.__repr__ File /home/kate/sage/sage-2.5.alpha3-ia64-Linux/local/lib/ python2.5/site- packages/sage/calculus/equations.py, line 114, in _repr_ return %s%s%s %(paren(self._left), symbols[self._op], paren(self._righ t)) File /home/kate/sage/sage-2.5.alpha3-ia64-Linux/local/lib/ python2.5/site- packages/sage/calculus/equations.py, line 70, in paren return '(%s)'%repr(x) File sage_object.pyx, line 87, in sage_object.SageObject.__repr__ File /home/kate/sage/sage-2.5.alpha3-ia64-Linux/local/lib/ python2.5/site- packages/sage/calculus/calculus.py, line 2530, in _repr_ return self.simplify()._repr_(simplify=False) File /home/kate/sage/sage-2.5.alpha3-ia64-Linux/local/lib/ python2.5/site- packages/sage/calculus/calculus.py, line 1750, in simplify S = evaled_symbolic_expression_from_maxima_string(self._maxima_init_()) File /home/kate/sage/sage-2.5.alpha3-ia64-Linux/local/lib/ python2.5/site- packages/sage/calculus/calculus.py, line 4555, in evaled_symbolic_expression_fr om_maxima_string return symbolic_expression_from_maxima_string(maxima.eval(x)) File /home/kate/sage/sage-2.5.alpha3-ia64-Linux/local/lib/ python2.5/site- packages/sage/interfaces/expect.py, line 506, in eval return '\n'.join([self._eval_line(L) for L in code.split('\n') if L != ' ']) File /home/kate/sage/sage-2.5.alpha3-ia64-Linux/local/lib/ python2.5/site- packages/sage/interfaces/maxima.py, line 531, in _eval_line self._sendline(line) File /home/kate/sage/sage-2.5.alpha3-ia64-Linux/local/lib/ python2.5/site- packages/sage/interfaces/maxima.py, line 424, in _sendline self._sendstr(str) File /home/kate/sage/sage-2.5.alpha3-ia64-Linux/local/lib/ python2.5/site- packages/sage/interfaces/maxima.py, line 429, in _sendstr self._start() File /home/kate/sage/sage-2.5.alpha3-ia64-Linux/local/lib/ python2.5/site- packages/sage/interfaces/maxima.py, line 414, in _start Expect._start(self) File /home/kate/sage/sage-2.5.alpha3-ia64-Linux/local/lib/ python2.5/site- packages/sage/interfaces/expect.py, line 317, in _start raise RuntimeError, Unable to start %s%self.__name RuntimeError: Unable to start maxima When I run /home/kate/sage/sage-2.5.alpha3-ia64-Linux/local/bin/ maxima I get the maxima startup banner. Kate Minola University of Maryland, College Park --~--~-~--~~~---~--~~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://sage.scipy.org/sage/ and http://modular.math.washington.edu/sage/ -~--~~~~--~~--~--~---
[sage-devel] Re: sage-2.5.alpha3
William Stein wrote: Hello, I've posted sage-2.5.alpha3 here: http://sage.math.washington.edu/home/was/sage2.5/ Feedback is welcome. This still won't build on OS X PowerPC or Cygwin, but should build on Linux and Intel OS X and pass make test there. Also, it should have most code that people have sent me for inclusion in SAGE. The official sage-2.5 is getting close, so any testing feedback is greatly appreciated. real66m29.688s user53m59.447s sys 9m2.117s To install gap, gp, singular, etc., scripts in a standard bin directory, start sage and type something like sage: install_scripts('/usr/local/bin') at the SAGE command prompt. SAGE build/upgrade complete! [EMAIL PROTECTED] sage-2.5.alpha3]$ -- All tests passed! Total time for all tests: 1701.7 seconds This is on FC5: Linux paix.jaapspies.nl 2.6.20-1.2312.fc5smp #1 SMP Tue Apr 10 15:30:02 EDT 2007 i686 i686 i386 GNU/Linux Jaap --~--~-~--~~~---~--~~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://sage.scipy.org/sage/ and http://modular.math.washington.edu/sage/ -~--~~~~--~~--~--~---
[sage-devel] Re: sage-2.5.alpha3
On May 6, 9:39 pm, Jaap Spies [EMAIL PROTECTED] wrote: William Stein wrote: Hello, I've posted sage-2.5.alpha3 here: A couple issues from cygwin from alpha2. I am not sure that the two build patches I posted today are in alpha3, so I will postpone building alpha3 until tomorrow. - sympow doesn't work on cygwin - this is a known issue. - if $HOME is set to something unusual I get some errors like [10.0 s] sage -t devel/sage-main/sage/rings/ commutative_algebra_element.py[Errno 2] No such file or directory: '/ cygdrive/c/WinCoCoa4.5.2/emacs/.sage//temp/sprocket/1588/tmp_19' (my $HOME is set to /cygdrive/c/WinCoCoa4.5.2/emacs/) - might this be related to the file descriptor patch that went in earlier this week? Possibly this is totally unrelated to $HOME, but I have never seens this before. It looks like this is mainly an annoyance, so not high priority. - GAP doesn't start: ** File graph.py, line 2248: sage: S = SymmetricGroup(20) Exception raised: Traceback (most recent call last): File /sage-2.5.alpha2/local/lib/python2.5/doctest.py, line 1212, in __ru n compileflags, 1) in test.globs File doctest __main__.example_77[6], line 1, in module S = SymmetricGroup(Integer(20))###line 2248: sage: S = SymmetricGroup(20) File /sage-2.5.alpha2/local/lib/python2.5/site-packages/sage/ groups/perm_ gps/permgroup.py, line 1008, in __init__ PermutationGroup_generic.__init__(self, 'SymmetricGroup(%s)'%n, from_gro up = True) File /sage-2.5.alpha2/local/lib/python2.5/site-packages/sage/ groups/perm_ gps/permgroup.py, line 186, in __init__ self.gens() # so will check that group can be defined in GAP (e.g., no missing packages, etc.) File /sage-2.5.alpha2/local/lib/python2.5/site-packages/sage/ groups/perm_ gps/permgroup.py, line 456, in gens raise RuntimeError, (It might be necessary to install the database_gap optional SAGE package, if you haven't already.)\n%s%s RuntimeError: (It might be necessary to install the database_gap optional SA GE package, if you haven't already.) Failed to start GAP. Might be a local build issue - I will retry with alpha3. I had some odd issues with python, but because my build directory was nuked while playing atround with libsingular this will take a while. - _ns_image.dll issues: E:\cygwin\sage-2.5.alpha2\local\bin\python.exe: *** fatal error - unable to remap E:\cygwin\sage-2.5.alpha2\local\lib\python2.5\site- packages\matplotlib\_ns_ima ge.dll to same address as parent(0x1B0D) != 0x1B31 15 [main] python 1588 fork: child 1704 - died waiting for dll loading, errno 11 I have no idea where that one comes from. - some whitespace issues in calculus.py: sage -t devel/sage-main/sage/calculus/calculus.py ** File calculus.py, line 416: sage: f.display2d(onscreen=False) Expected: '\t\t\t\t\t 3\r\n\t\t\t\ty + x\r\n \t\t\t \r\n\t\t\t \t2\r\n\t\t\t\t 3 y + x + 1' Got: '\t\t\t\t\t 3\r\r\n\t\t\t\ty + x\r\r\n \t\t\t \r\r\n \t\t\t\t2\r\r\n\t\t\t\t 3 y + x + 1' ** 1 items had failures: 1 of 5 in __main__.example_8 ***Test Failed*** 1 failures. - problems in constants.py. I did patch ring_rqdf.pyx in order to make it compile on cygwin (it needed NAN and INFINTY), so this might be caused by me :(. Overall quad doubles seem not to work very well on cygwin (see the sympow issue). sage -t devel/sage-main/sage/functions/constants.py ** File constants.py, line 184: sage: RQDF(a) Exception raised: Traceback (most recent call last): File /sage-2.5.alpha2/local/lib/python2.5/doctest.py, line 1212, in __ru n compileflags, 1) in test.globs File doctest __main__.example_0[56], line 1, in module RQDF(a)###line 184: sage: RQDF(a) File real_rqdf.pyx, line 172, in real_rqdf.RealQuadDoubleField_class.__c all__ File /sage-2.5.alpha2/local/lib/python2.5/site-packages/sage/ calculus/cal culus.py, line 2446, in _real_rqdf_ return self.simplify()._real_rqdf_(field) File /sage-2.5.alpha2/local/lib/python2.5/site-packages/sage/ calculus/cal culus.py, line 2447, in _real_rqdf_ rops = [op._real_rqdf_(field) for op in self._operands] File /sage-2.5.alpha2/local/lib/python2.5/site-packages/sage/ calculus/cal culus.py, line 2447, in _real_rqdf_ rops = [op._real_rqdf_(field) for op in self._operands] File /sage-2.5.alpha2/local/lib/python2.5/site-packages/sage/ calculus/cal culus.py, line 2447, in _real_rqdf_ rops = [op._real_rqdf_(field) for op in self._operands] File /sage-2.5.alpha2/local/lib/python2.5/site-packages/sage/ calculus/cal culus.py, line
[sage-devel] Re: sage-2.5.alpha3
All tests pass on my machine, a Centrino running ubuntu feisty: didier On 5/6/07, William Stein [EMAIL PROTECTED] wrote: Hello, I've posted sage-2.5.alpha3 here: http://sage.math.washington.edu/home/was/sage2.5/ Feedback is welcome. This still won't build on OS X PowerPC or Cygwin, but should build on Linux and Intel OS X and pass make test there. Also, it should have most code that people have sent me for inclusion in SAGE. The official sage-2.5 is getting close, so any testing feedback is greatly appreciated. In particular, if people could try out some of the new features in sage-2.5, especially symbolic computation, this would be quite valuable. Here's a list of the main things that are new in sage-2.5.alpha3: 2.5: * new packages: - flintqs - ipython-0.8.0 (w stein) - maxima-5.12.0 (w stein) - python-2.5.1 (y qiang) -- important bug fixes - tachyon3d-0.98beta (w stein) * m abshoff: cputime bugfix for cygwin * m albrecht: major new singular library mode interface for SAGE which provides the world's fastest polynomial arithmetic to SAGE (not yet enabled by default!) * r bradshaw: tons of polynomial and power series optimizations; Coleman p-adic integration; Kedlaya for genus 1 * t clemens: source browser bugfix * p de napoli:fix some bugs in rationals and integers * d deshomme: (refereed by r bradshaw and w stein) very good support for Hida's quad-double field RQDF. * w hart: quadratic sieve update (SAGE's qsieve command): It is MUCH faster, especially for large factorizations, on account of having implemented the large prime variant. it will factor an 81 digit number in 20 minutes. On the Athlon it is the fastest generally available implementation of the quadratic sieve in the world for certain sized factorizations, and only slightly behind at other sizes. Another example: n = next_prime(2^110)*next_prime(2^120) has these times on 32-bit 2Ghz linux: qsieve (107s), PARI (223s), Magma 2.13 (336s). * d harvey: improvements, bug fixes. * d kohel:quaternion algebra improvements * k minola: tmp file clean bugfix; misc build fixes. * k minola, d joyner: updated the conway polynomial table * w stein and b moretti: major new symbolic calculus functionality * w stein:rewrite of SAGE/maxima interface. * c witty:(refereed by n alexandar) a new algebraic reals field (Qbar meet RR!). mpfr improvements --~--~-~--~~~---~--~~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://sage.scipy.org/sage/ and http://modular.math.washington.edu/sage/ -~--~~~~--~~--~--~---
[sage-devel] Re: sage-2.5.alpha3
On May 6, 9:24 am, William Stein [EMAIL PROTECTED] wrote: Hello, I've posted sage-2.5.alpha3 here: http://sage.math.washington.edu/home/was/sage2.5/ Feedback is welcome. On my machine running Debian testing, plotting-related tests fail with messages like: libpng error: Incompatible libpng version in application and library A mysterious error (perphaps a memory error?) occured, which may have crashed doctest. I think I understand why this is happening. Debian testing includes a new version of libpng (version 1.4, package names libpng14-1 and libpng14-dev). When matplotlib is compiled (in particular, the file _ns_image.cpp, which produces _ns_image.so), it uses a -I flag to include the png.h header file from SAGE's local version of libpng (version 1.2.16). However, when the resulting object file is linked, to actually produce _ns_image.so, it has no special -L flags, so it ends up linked against Debian's version 1.4 libpng. At runtime, libpng 1.4 notices that the application was compiled against the version 1.2.16 png.h header file; this is a fatal error, and exits SAGE. The fix is to change the matplotlib spkg-install, so that the _ns_image.so link command has the right -L flag to link against SAGE's libpng. (I don't know enough about the Python compile system to do this myself.) Carl Witty --~--~-~--~~~---~--~~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://sage.scipy.org/sage/ and http://modular.math.washington.edu/sage/ -~--~~~~--~~--~--~---
[sage-devel] Re: sage-2.5.alpha3
On 5/6/07, cwitty [EMAIL PROTECTED] wrote: I've posted sage-2.5.alpha3 here: http://sage.math.washington.edu/home/was/sage2.5/ Feedback is welcome. On my machine running Debian testing, plotting-related tests fail with messages like: libpng error: Incompatible libpng version in application and library A mysterious error (perphaps a memory error?) occured, which may have crashed doctest. I think I understand why this is happening. Debian testing includes a new version of libpng (version 1.4, package names libpng14-1 and libpng14-dev). When matplotlib is compiled (in particular, the file _ns_image.cpp, which produces _ns_image.so), it uses a -I flag to include the png.h header file from SAGE's local version of libpng (version 1.2.16). However, when the resulting object file is linked, to actually produce _ns_image.so, it has no special -L flags, so it ends up linked against Debian's version 1.4 libpng. At runtime, libpng 1.4 notices that the application was compiled against the version 1.2.16 png.h header file; this is a fatal error, and exits SAGE. The fix is to change the matplotlib spkg-install, so that the _ns_image.so link command has the right -L flag to link against SAGE's libpng. (I don't know enough about the Python compile system to do this myself.) Many thanks for tracking this down!! I greatly appreciate it. -- William --~--~-~--~~~---~--~~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://sage.scipy.org/sage/ and http://modular.math.washington.edu/sage/ -~--~~~~--~~--~--~---
[sage-devel] Re: sage-2.5.alpha3
On May 7, 7:45 am, William Stein [EMAIL PROTECTED] wrote: On 5/6/07, cwitty [EMAIL PROTECTED] wrote: I've posted sage-2.5.alpha3 here: http://sage.math.washington.edu/home/was/sage2.5/ Feedback is welcome. On my machine running Debian testing, plotting-related tests fail with messages like: libpng error: Incompatible libpng version in application and library A mysterious error (perphaps a memory error?) occured, which may have crashed doctest. I think I understand why this is happening. Debian testing includes a new version of libpng (version 1.4, package names libpng14-1 and libpng14-dev). When matplotlib is compiled (in particular, the file _ns_image.cpp, which produces _ns_image.so), it uses a -I flag to include the png.h header file from SAGE's local version of libpng (version 1.2.16). However, when the resulting object file is linked, to actually produce _ns_image.so, it has no special -L flags, so it ends up linked against Debian's version 1.4 libpng. At runtime, libpng 1.4 notices that the application was compiled against the version 1.2.16 png.h header file; this is a fatal error, and exits SAGE. The fix is to change the matplotlib spkg-install, so that the _ns_image.so link command has the right -L flag to link against SAGE's libpng. (I don't know enough about the Python compile system to do this myself.) Many thanks for tracking this down!! I greatly appreciate it. -- William This will probably solve this issue I reported above on cygwin, too: - _ns_image.dll issues: E:\cygwin\sage-2.5.alpha2\local\bin\python.exe: *** fatal error - unable to remap E:\cygwin\sage-2.5.alpha2\local\lib\python2.5\site- packages\matplotlib\_ns_image.dll to same address as parent(0x1B0D) != 0x1B31 15 [main] python 1588 fork: child 1704 - died waiting for dll loading, errno 11 Cheers, Michael --~--~-~--~~~---~--~~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://sage.scipy.org/sage/ and http://modular.math.washington.edu/sage/ -~--~~~~--~~--~--~---