[sage-devel] Re: Conway's nimber field
The reference is Chapter 6 of ONAG (in particular Thm 49). The
terminology
of nimbers appears in Winning ways for your mathematical plays.
Michel
On Mar 20, 8:11 am, Michel [EMAIL PROTECTED] wrote:
Yes the basic reference is ONAG. I will put a more precise
reference in the source (but I need to go to the library
to fetch ONAG). Basically the two rules for multiplying
nimbers are
(1) The product of any number of distinct Fermat powers
is the ordinary product.
(2) If f is a Fermat power then f^2=3f/2 (where 3f/2 is
computed for the ordinary product).
Basically (1)(2) say that if f_n is the n't Fermat power then
f_n^2=f_n+f_{n-1}f_{n-2}...f_0
This realizes the nimber field as a tower of quadratic extensions.
To compute in the nimber field we write nimbers f^2 (f a Fermat
power) as l*f+r with l,rf and work recursively.
Michel
On 19 mrt, 21:29, David Joyner [EMAIL PROTECTED] wrote:
Are you using ONAG for the main reference? In any case, I would appreciate
a precise reference to a book or article on nimbers.
On 3/19/07, Michel [EMAIL PROTECTED] wrote:
Hi,
To acquant myself with sage's inner workings I have implemented
Conway's nimber field.
See
http://alpha.uhasselt.be/Research/Algebra/Members/nimbers/
Recall that the nimbers form a field whose underlying set is the
natural numbers. The addition is bitwise exclusive or but the
multiplication is complicated. GF(2^(2^n)) is isomorphic to the
nimbers that are less than 2^(2^n). Thus the full nimber field is
isomorphic to the union of GF(2^(2^n)) for all n.
Although my implenentation is still in pure python it seems to be not
much slower
than the standard finite fields GF(2^(2^n)) that one can create in
sage. However I didn't
do extensive testing. The basic arithmetic should be trivial to
rewrite in pyrex.
This is still a prototype. The most glaring ommission is that
coercions from and to
standard Galois fields are missing. Nevertheless if there are remarks/
comments I would
appreciate it very much.
Regards,
Michel
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[sage-devel] Re: polynomial quo_rem coercion
On Mar 22, 2007, at 1:42 PM, Joel B. Mohler wrote: This feels just a bit pedantic to me, but I think it might be a bug from some viewpoint. I'm looking at the polynomial function quo_rem and I see that it does it's own coercion manually. This feels a little wrong to me. I think it should go through the standard coercion routines. Here's a bug that results: sage: x=ZZ['x'].0 sage: y=QQ['x'].0 sage: (y+1).quo_rem(1/2*x) (2, 1) sage: (x+1).quo_rem(1/2*y) ... type 'exceptions.TypeError': no coercion of this rational to integer The bug is that I don't see why these two things are treated substantially differently. The reason I found this is because the simple TypeError exception did not provide the usual message about parents being mis-matched -- I think this is a bug in itself. Any comments? Exactly which quo_rem() method are you talking about? Which class? David --~--~-~--~~~---~--~~ 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: polynomial quo_rem coercion
On Thursday 22 March 2007 13:48, David Harvey wrote: This feels just a bit pedantic to me, but I think it might be a bug from some viewpoint. I'm looking at the polynomial function quo_rem and I see that it does it's own coercion manually. This feels a little wrong to me. I think it should go through the standard coercion routines. Here's a bug that results: sage: x=ZZ['x'].0 sage: y=QQ['x'].0 sage: (y+1).quo_rem(1/2*x) (2, 1) sage: (x+1).quo_rem(1/2*y) ... type 'exceptions.TypeError': no coercion of this rational to integer The bug is that I don't see why these two things are treated substantially differently. The reason I found this is because the simple TypeError exception did not provide the usual message about parents being mis-matched -- I think this is a bug in itself. Any comments? Exactly which quo_rem() method are you talking about? Which class? Hmm, yes, I was thinking of including that information -- I see I didn't. I think that any of them in polynomial_element_generic.py exhibit analogous behaviour. The one around line 897 is one specific instance. -- Joel --~--~-~--~~~---~--~~ 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: polynomial quo_rem coercion
Bug +1. Nick On Mar 22, 10:42 am, Joel B. Mohler [EMAIL PROTECTED] wrote: This feels just a bit pedantic to me, but I think it might be a bug from some viewpoint. I'm looking at the polynomial function quo_rem and I see that it does it's own coercion manually. This feels a little wrong to me. I think it should go through the standard coercion routines. Here's a bug that results: sage: x=ZZ['x'].0 sage: y=QQ['x'].0 sage: (y+1).quo_rem(1/2*x) (2, 1) sage: (x+1).quo_rem(1/2*y) ... type 'exceptions.TypeError': no coercion of this rational to integer The bug is that I don't see why these two things are treated substantially differently. The reason I found this is because the simple TypeError exception did not provide the usual message about parents being mis-matched -- I think this is a bug in itself. Any comments? -- Joel --~--~-~--~~~---~--~~ 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: polynomial quo_rem coercion
On Mar 22, 10:42 am, Joel B. Mohler [EMAIL PROTECTED] wrote: This feels just a bit pedantic to me, but I think it might be a bug from some viewpoint. I'm looking at the polynomial function quo_rem and I see that it does it's own coercion manually. This feels a little wrong to me. I think it should go through the standard coercion routines. Here's a bug that results: sage: x=ZZ['x'].0 sage: y=QQ['x'].0 sage: (y+1).quo_rem(1/2*x) (2, 1) sage: (x+1).quo_rem(1/2*y) ... type 'exceptions.TypeError': no coercion of this rational to integer The bug is that I don't see why these two things are treated substantially differently. The reason I found this is because the simple TypeError exception did not provide the usual message about parents being mis-matched -- I think this is a bug in itself. Any comments? quo_rem was written long before there was any standard coercion system. It makes sense to rewrite it now to use the canonical coercion model. Feel free to do so, or at least add something to trac. 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: Biopython package
Stupid of me not to try that - i.e. the 'http://'. Ah well. I have written to the biopython dev list to let them know of the SAGE- biopython connection. I tried to take a look at what was causing those installation hangups. It looks like its not the mxTextTools, but rather the components that immediately follow - namely the lack of Reportlab (optional, I've never used its functionality) and the compilation of part of Bio.PDB (basically a parser for molecular structure files). I cut out the relevant section and pasted it below. If I have time, I will try to figure out a workaround for this in the installation script. I am now spending a great deal of time working in the SAGE notebook environment, which should inspire me eventually to do more development work on SAGE. Here's the installation snippet of interest: *** Reportlab *** is either not installed or out of date. This package is optional, which means it is only used in a few specialized modules in Biopython. You probably don't need this if you are unsure. You can ignore this requirement, and install it later if you see ImportErrors. You can find Reportlab at http://www.reportlab.org/downloads.html. Do you want to continue this installation? (Y/n) *** Bio.KDTree *** NOT built by default The Bio.PDB.NeighborSearch module depends on the Bio.KDTree module, which in turn, depends on C++ code that does not compile cleanly on all platforms. Hence, Bio.KDTree is not built by default. Would you like to build Bio.KDTree ? (y/N) running build On Mar 20, 12:39 pm, William Stein [EMAIL PROTECTED] wrote: On Tuesday 20 March 2007 9:30 am, Hamptonio wrote: Just to clarify: the downloading problem isn't biopython-specific - I can't get anything fromwww.sagemath.orgthrough sage, only from a browser. For example, 'sage -optional' fails as well. Sorry, you have to do this (note the http://) -- I forgot to mention this before -- my mistake. export SAGE_SERVER=http://www.sagemath.org; sage -optional ... -MH On Mar 20, 10:31 am, Hamptonio [EMAIL PROTECTED] wrote: Woo-hoo! Thank you!!! I had the same error as before on my Mac Pro - the '... in open_local_file raise IOError(e.errno, e.strerror, e.filename) IOError: [Errno 2] No such file or directory: 'www.sagemath.org/ packages/optional/biopython-1.43.spkg' sage: Failed to download package biopython-1.43 fromwww.sagemath.org' error, so I manually downloaded the spkg fromwww.sagemath.org, and it installed fine apart from the weird need for 'enter' commands that you warned me about. I have tested a few of my more commonly used tasks and it seems to work. I can tell the biopython developers about this once the package download problems get a little sorted out. Thanks again, Marshall On Mar 20, 7:53 am, Hamptonio [EMAIL PROTECTED] wrote: Great! I am once again amazed by your speed. I set SAGE_SERVER as you said, but my attempt at installing fails to get the package. The output is appended below. I doing this on a PPC (G4) Apple powerbook, with sage 2.0 upgraded to 2.3. I had tried to read the documentation you suggested - I was only volunteering to try this because it seemed relatively simple! I've installed biopython 1.42 on linux, apple, and windows machines, but I haven't tried a normal install of 1.43 yet (its quite recent). I am not sure what mxTextTools is doing; in a python install I just do 'sudo python setup.py install' although I am not sure that the sudo is necessary. I'll also give this a try on the Mac Pro (Intel) in my office when I get in. Thanks, Marshall ~/sage-2.0:07:43:42:./sage -i biopython-1.43 Installing biopython-1.43 Calling sage-spkg on biopython-1.43 WARNING: Using SAGE_ROOT variable that was already set to '/Users/mh/ sage-2.0'. biopython-1.43 Machine: Darwin medmgmt-3.tajen.edu.tw 8.8.0 Darwin Kernel Version 8.8.0: Fri Sep 8 17:18:57 PDT 2006; root:xnu-792.12.6.obj~1/RELEASE_PPC Power Macintosh powerpc Deleting directories from past builds of previous/current versions of biopython-1.43 /Users/mh/sage-2.0/local/bin/sage-spkg: file /Users/mh/sage-2.0/ biopython-1.43 does not exist Attempting to download it.www.sagemath.org/packages/optional/biopython-1.43.spkg-- biopython-1.43.spkg [ Traceback (most recent call last): File /Users/mh/sage-2.0/local/bin/sage-download_package, line 53, in module if not download_file(optional/%s%F): File /Users/mh/sage-2.0/local/bin/sage-download_package, line 45, in download_file urllib.urlretrieve(url, file, reporthook) File /Users/mh/sage-2.0/local/lib/python2.5/urllib.py, line 89, in urlretrieve return _urlopener.retrieve(url, filename, reporthook, data) File /Users/mh/sage-2.0/local/lib/python2.5/urllib.py, line 222, in retrieve fp = self.open(url,
