[sage-combinat-devel] WeylCharacterRing

2012-01-03 Thread Bruce
This seems to me to be either a bug or a deficiency:

sage: KZ = WeylCharacterRing('A1',base_ring=ZZ,style=coroots)
sage: KS =
WeylCharacterRing('A1',base_ring=SFASchur(ZZ),style=coroots)
sage: a = KZ([1])
sage: KS(a)

produces an error.

More generally I was hoping that given (commutative) rings R and S and
a ring homomorphism
phi : R -- S that the category framework would then provide the
homomorphism from
 WeylCharacterRing('A1',base_ring=R) to
WeylCharacterRing('A1',base_ring=S)
but in view of the above I have now lost confidence.

Is there a simple way to achieve this? Here R would probably be
symmetric functions and there are
several definitions of the same homomorphism, depending on the choice
of basis.

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Re: [sage-combinat-devel] Re: dot2tex, combinat

2012-01-03 Thread Nicolas M. Thiery
On Fri, Dec 30, 2011 at 11:25:28AM -0800, Travis Scrimshaw wrote:
 John,
I tried using it and I got the following error:
 
 Error: convert (from the ImageMagick suite) does not
 appear to be installed. Displaying PDFLaTeX output
 requires this program, so please install and try again.
 
 Go to http://www.imagemagick.org to download it.
 Latex error
 
This is likely because the pdf output from sage depends upon the
 tikz package. Additionally the tikzpicture environment requires the
 tikz package so I doubt the pdf would be compiled despite the above
 error.

I guess that this error is raised by sage.misc.latex._run_latex_.
This function requires ``convert`` to convert the produced pdf into a
png. Did you try installing imagemagick in the virtual machine? It
should be something like:

sudo apt-get install imagemagick

 The first issue should be easy enough to resolve and just make sure
 the base image for the Sage notebook download has the packages
 already installed.

Yes, the issue is more social than technical: it is about convincing
the virtual machine release manager that the extra kilobytes are worth
it. So this probably needs a discussion on sage-devel. The inclusion
(or not) of imagemagick is also to be discussed.

 For the second issue, do you know how the notebook communicates with
 the Sage in the VM and vice versa, or at least have some idea on
 where I could find the code? Also, could you tell me how Sage
 currently produces images/latex output to the notebook?

As you suspect, the Sage server is a typical web server, with AJAX and
the like for smooth interaction. But I am very unfamiliar with this
area, so please lookup the sources and/or ask on sage-devel.
For the notebook code, see SAGEROOT/devel/sagenb-main.

 I like your idea on sending the PDF directly the web browser, and I'm
 thinking we should have it as an option in the view() command since it
 is overkill in most cases and I don't know what kind of difficulties
 with pop-up blockers we might encounter. 

+1

 Also, to me this is somewhat of a hack solution unless we could
 somehow embed a pdf viewer in the notebook

I'd bet that some navigators allow for embedding a pdf viewer in the
middle of an html page; however I have no idea if this is
standardized. Anyway, for any complex picture, a separate window is as
good, if not better (I usually want to view the picture in
fullscreen).

 Anyways, I'll start a discussion on the sage-devel/trac and take a
 look at possibly cleaning up the patch.

Excellent. Thanks!

Happy new year,
Nicolas
--
Nicolas M. Thiéry Isil nthi...@users.sf.net
http://Nicolas.Thiery.name/

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Re: [sage-combinat-devel] WeylCharacterRing

2012-01-03 Thread Nicolas M. Thiery
On Tue, Jan 03, 2012 at 01:17:14AM -0800, Bruce wrote:
 This seems to me to be either a bug or a deficiency:
 
 sage: KZ = WeylCharacterRing('A1',base_ring=ZZ,style=coroots)
 sage: KS =
 WeylCharacterRing('A1',base_ring=SFASchur(ZZ),style=coroots)
 sage: a = KZ([1])
 sage: KS(a)
 
 produces an error.
 
 More generally I was hoping that given (commutative) rings R and S and
 a ring homomorphism
 phi : R -- S that the category framework would then provide the
 homomorphism from
  WeylCharacterRing('A1',base_ring=R) to
 WeylCharacterRing('A1',base_ring=S)
 but in view of the above I have now lost confidence.

This would be a natural feature, but it is indeed not yet implemented.
It should not be difficult, but requires a bit of thought to integrate
properly in the coercion framework. Please create a ticket! Maybe this
will trigger a volunteer :-)

 Is there a simple way to achieve this? Here R would probably be
 symmetric functions and there are several definitions of the same
 homomorphism, depending on the choice of basis.

You can construct the homomorphism by hand, and register it:

sage: KZ = WeylCharacterRing('A1',base_ring=ZZ,style=coroots)
sage: KS = WeylCharacterRing('A1',base_ring=SFASchur(ZZ),style=coroots)
sage: a = KZ([1])

sage: phi = KZ.module_morphism(KS.monomial)
sage: phi(a)
s[]*A1(1)
sage: phi.register_as_coercion()
sage: KS(a)
s[]*A1(1)

Note that the registering must be done early in the Sage session
(before any coercion lookup between KZ and KS.

Cheers,
Nicolas
--
Nicolas M. Thiéry Isil nthi...@users.sf.net
http://Nicolas.Thiery.name/

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