Re: [sage-devel] Mac Launcher

2009-12-19 Thread Ivan Andrus
On Dec 18, 2009, at 7:38 AM, William Stein wrote:

> I wonder if somebody who understands the mac launcher for SAge could comment 
> on
> 
>   http://trac.sagemath.org/sage_trac/ticket/7700


Done.  I accepted the ticket and should get around to it after finals are done.

-Ivan

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[sage-devel] plot scale needs to be recomputed for different aspect_ratio

2009-12-19 Thread Henryk Trappmann
Hallo,

it seems currently (sage 4.2) that the plot scale is not recomputed
when changing the aspect_ratio, but simply graphically resized. This
leads to possibly overlapping numbers, and looks somehow squeezed.
Example:

p = plot(lambda x: 10*x, (0,1)); p.set_aspect_ratio(1); p

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[sage-devel] Re: plot scale needs to be recomputed for different aspect_ratio

2009-12-19 Thread Jason Grout
Henryk Trappmann wrote:
> Hallo,
> 
> it seems currently (sage 4.2) that the plot scale is not recomputed
> when changing the aspect_ratio, but simply graphically resized. This
> leads to possibly overlapping numbers, and looks somehow squeezed.
> Example:
> 
> p = plot(lambda x: 10*x, (0,1)); p.set_aspect_ratio(1); p
> 


I'm pretty sure the code for tick marks does not pay attention to the 
length of the axis in the picture, but only the length in data units. 
It would be an interesting problem to design a tick locator that cut out 
ticks based on the physical size in the picture of the axes.  This would 
be especially interesting since usually, you don't know how big (in the 
image) stuff is until you actually draw it, long after the ticks are all 
constructed and placed.

This should be forwarded to the matplotlib list and we should ask their 
opinion about it.

Thanks,

Jason

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[sage-devel] Re: plot scale needs to be recomputed for different aspect_ratio

2009-12-19 Thread Jason Grout
Jason Grout wrote:
> Henryk Trappmann wrote:
>> Hallo,
>>
>> it seems currently (sage 4.2) that the plot scale is not recomputed
>> when changing the aspect_ratio, but simply graphically resized. This
>> leads to possibly overlapping numbers, and looks somehow squeezed.
>> Example:
>>
>> p = plot(lambda x: 10*x, (0,1)); p.set_aspect_ratio(1); p
>>
> 
> 
> I'm pretty sure the code for tick marks does not pay attention to the 
> length of the axis in the picture, but only the length in data units. 
> It would be an interesting problem to design a tick locator that cut out 
> ticks based on the physical size in the picture of the axes.  This would 
> be especially interesting since usually, you don't know how big (in the 
> image) stuff is until you actually draw it, long after the ticks are all 
> constructed and placed.
> 
> This should be forwarded to the matplotlib list and we should ask their 
> opinion about it.


This example shows the problem in straight matplotlib code:

from matplotlib import pyplot as plt
import numpy
t = numpy.arange(0.0, 2.0, 0.01)
s = 10*t
plt.figure()
plt.plot(t,s)
plt.axes().set_aspect(1)
plt.savefig('test.png')

Thanks,

Jason

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Re: [sage-devel] input: and output: in docstrings

2009-12-19 Thread David Roe
> > I think that requiring them for every single function is excessive,
> > for example many functions don't take any parameters but self, or
> > don't return output.
>
> OK, good point.  How about requiring INPUT if there are any inputs
> beyond self, and requiring OUTPUT if there are any outputs?
>

This is what the patch at 7716 currently does (which I've updated to reflect
some comments; it still needs a reviewer).  Based on Robert's comments, I
would also suggest changing the coverage scripts to not require input or
output descriptions for functions that begin and end with underscores.  I'll
post a patch on 7716 to that effect shortly.


> > Also, what about arithmetic functions like
> > __neg__ and _mul_. (Specifically, I yesterday I was adding a bunch of
> > doctests to monsky-washnitzer, and the thought of adding (in my mind
> > superfluous) INPUT and OUTPUT blocks to these was not encouraging.
> > (I'm not just thinking about file size, developer time and vertical
> > screen real estate are valuable as well.)
>

Robert, are there any other kinds of functions that you can think of where
we don't need descriptions of the input/output?
David

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Re: [sage-devel] input: and output: in docstrings

2009-12-19 Thread David Roe
Currently we don't require documentation for __cinit__, __dealloc__ and
__new__.  Are there any other functions we want to add to that list?  I
could see an argument for _add_ and other arithmetic functions too.
David

On Sat, Dec 19, 2009 at 1:41 PM, David Roe  wrote:

>
> > I think that requiring them for every single function is excessive,
>> > for example many functions don't take any parameters but self, or
>> > don't return output.
>>
>> OK, good point.  How about requiring INPUT if there are any inputs
>> beyond self, and requiring OUTPUT if there are any outputs?
>>
>
> This is what the patch at 7716 currently does (which I've updated to
> reflect some comments; it still needs a reviewer).  Based on Robert's
> comments, I would also suggest changing the coverage scripts to not require
> input or output descriptions for functions that begin and end with
> underscores.  I'll post a patch on 7716 to that effect shortly.
>
>
>> > Also, what about arithmetic functions like
>> > __neg__ and _mul_. (Specifically, I yesterday I was adding a bunch of
>> > doctests to monsky-washnitzer, and the thought of adding (in my mind
>> > superfluous) INPUT and OUTPUT blocks to these was not encouraging.
>> > (I'm not just thinking about file size, developer time and vertical
>> > screen real estate are valuable as well.)
>>
>
> Robert, are there any other kinds of functions that you can think of where
> we don't need descriptions of the input/output?
> David
>
>

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Re: [sage-devel] input: and output: in docstrings

2009-12-19 Thread Robert Bradshaw
On Dec 19, 2009, at 10:59 AM, David Roe wrote:

> Currently we don't require documentation for __cinit__, __dealloc__  
> and __new__.  Are there any other functions we want to add to that  
> list?  I could see an argument for _add_ and other arithmetic  
> functions too.

A TESTS block is certainly a good thing to have for the arithmetic  
operators.

> David
>
> On Sat, Dec 19, 2009 at 1:41 PM, David Roe   
> wrote:
>
> > I think that requiring them for every single function is excessive,
> > for example many functions don't take any parameters but self, or
> > don't return output.
>
> OK, good point.  How about requiring INPUT if there are any inputs
> beyond self, and requiring OUTPUT if there are any outputs?
>
> This is what the patch at 7716 currently does (which I've updated to  
> reflect some comments; it still needs a reviewer).  Based on  
> Robert's comments, I would also suggest changing the coverage  
> scripts to not require input or output descriptions for functions  
> that begin and end with underscores.  I'll post a patch on 7716 to  
> that effect shortly.
>
> > Also, what about arithmetic functions like
> > __neg__ and _mul_. (Specifically, I yesterday I was adding a bunch  
> of
> > doctests to monsky-washnitzer, and the thought of adding (in my mind
> > superfluous) INPUT and OUTPUT blocks to these was not encouraging.
> > (I'm not just thinking about file size, developer time and vertical
> > screen real estate are valuable as well.)
>
> Robert, are there any other kinds of functions that you can think of  
> where we don't need descriptions of the input/output?

Not that I can think of at the moment.

- Robert


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[sage-devel] Re: input: and output: in docstrings

2009-12-19 Thread Simon King
Hi!

On 19 Dez., 21:23, Robert Bradshaw 
wrote:
> A TESTS block is certainly a good thing to have for the arithmetic  
> operators.

+1

For _add_ etc, the type of both in- and output is clear (IIRC,
coercion etc happens before). But it should certainly be tested.

2 cents
Simon

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[sage-devel] Scilab now GPL compatible?

2009-12-19 Thread Tim Lahey
It appears that Scilab 5 (http://www.scilab.org/) 
is now GPL v2 compatible according to their web site
and the FAQ for the license that they're using,

http://www.cecill.info/faq.en.html#compatible

Having an interface to Scilab would certainly be
nice. However, I don't think I'll have time to work
on it.

Cheers,

Tim.

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Re: [sage-devel] Scilab now GPL compatible?

2009-12-19 Thread William Stein
On Sat, Dec 19, 2009 at 12:44 PM, Tim Lahey  wrote:
> It appears that Scilab 5 (http://www.scilab.org/)
> is now GPL v2 compatible according to their web site
> and the FAQ for the license that they're using,
>
> http://www.cecill.info/faq.en.html#compatible

Excellent.  Is there _any_ valuable code/libraries/components/ideas in
Scilab that could be used in Sage?  (I hope yes!)  Or are they in
catchup mode with octave/gsl/numpy/scipy?   (I hope not.)  Is there
anything we can offer them...?

>
> Having an interface to Scilab would certainly be
> nice. However, I don't think I'll have time to work
> on it.

Ronan Paixao wrote a Sage/scilab interface over a year ago.

sage: print scilab('2+2')
4.


>
> Cheers,
>
> Tim.
>
> ---
> Tim Lahey
> PhD Candidate, Systems Design Engineering
> University of Waterloo
> http://www.linkedin.com/in/timlahey
>
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University of Washington
http://wstein.org

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Re: [sage-devel] Scilab now GPL compatible?

2009-12-19 Thread Tim Lahey

On 12-19-2009, at 3:50 PM, William Stein wrote:

> On Sat, Dec 19, 2009 at 12:44 PM, Tim Lahey  wrote:
>> It appears that Scilab 5 (http://www.scilab.org/)
>> is now GPL v2 compatible according to their web site
>> and the FAQ for the license that they're using,
>> 
>> http://www.cecill.info/faq.en.html#compatible
> 
> Excellent.  Is there _any_ valuable code/libraries/components/ideas in
> Scilab that could be used in Sage?  (I hope yes!)  Or are they in
> catchup mode with octave/gsl/numpy/scipy?   (I hope not.)  Is there
> anything we can offer them...?
> 

Scilab is under pretty active development. One of the really nice
things it has over most of the others is Scicos/Xcos which is a
Simulink-like environment.

Scilab also has a fair number of contributed toolboxes,

http://www.scilab.org/contrib/index_contrib.php?page=download

Note the various optimization libraries it interfaces with. 

It would be great if one could use Sage from Scilab and SciCos/Xcos.
One example is the Maxima-based mexfunctions generator,

http://www.scilab.org/contrib/index_contrib.php?page=displayContribution&fileID=1175

If one could have Sage as a symbolic toolbox and create symbolic
components for Scicos/Xcos, that would provide a lot of flexibility.
Especially since Scilab supports data collection.

>> 
>> Having an interface to Scilab would certainly be
>> nice. However, I don't think I'll have time to work
>> on it.
> 
> Ronan Paixao wrote a Sage/scilab interface over a year ago.
> 
> sage: print scilab('2+2')
>4.


Ooh. Nifty.

Thanks,

Tim.

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Re: [sage-devel] Scilab now GPL compatible?

2009-12-19 Thread Dr. David Kirkby
William Stein wrote:
> Excellent.  Is there _any_ valuable code/libraries/components/ideas in
> Scilab that could be used in Sage?  (I hope yes!)  Or are they in
> catchup mode with octave/gsl/numpy/scipy?   (I hope not.)  Is there
> anything we can offer them...?

Access to t2 for testing on Solaris. They might find that helpful.

Dave

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Re: [sage-devel] Re: input: and output: in docstrings

2009-12-19 Thread David Roe
Sounds good.  That's the current requirement.
David

On Sat, Dec 19, 2009 at 3:30 PM, Simon King  wrote:

> Hi!
>
> On 19 Dez., 21:23, Robert Bradshaw 
> wrote:
> > A TESTS block is certainly a good thing to have for the arithmetic
> > operators.
>
> +1
>
> For _add_ etc, the type of both in- and output is clear (IIRC,
> coercion etc happens before). But it should certainly be tested.
>
> 2 cents
> Simon
>
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[sage-devel] Something screwed up at http://www.sagemath.org/

2009-12-19 Thread Dr. David Kirkby
The site

http://www.sagemath.org/

is not displaying what is intended - it tells you nothing about Sage, except 
listing where to download it.

If one adds the /index.html on the end, so we get what I think is actually 
intended to be.

Has the server been reconfigured in some way? It looks like there is an issue

Dave

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Re: [sage-devel] Something screwed up at http://www.sagemath.org/

2009-12-19 Thread Alex Ghitza
On Sat, 19 Dec 2009 23:45:50 +, "Dr. David Kirkby" 
 wrote:
> The site
> 
> http://www.sagemath.org/
> 
> is not displaying what is intended - it tells you nothing about Sage, except 
> listing where to download it.
> 
> If one adds the /index.html on the end, so we get what I think is actually 
> intended to be.
> 

I am not seeing any problems.  http://www.sagemath.org/ and
http://www.sagemath.org/index.html look identical on my browser.


Best,
Alex

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Re: [sage-devel] Something screwed up at http://www.sagemath.org/

2009-12-19 Thread Dr. David Kirkby
Alex Ghitza wrote:
> On Sat, 19 Dec 2009 23:45:50 +, "Dr. David Kirkby" 
>  wrote:
>> The site
>>
>> http://www.sagemath.org/
>>
>> is not displaying what is intended - it tells you nothing about Sage, except 
>> listing where to download it.
>>
>> If one adds the /index.html on the end, so we get what I think is actually 
>> intended to be.
>>
> 
> I am not seeing any problems.  http://www.sagemath.org/ and
> http://www.sagemath.org/index.html look identical on my browser.
> 
> 
> Best,
> Alex
> 

Odd, they do not for me.

For http://www.sagemath.org/ I see:

-
  This is a mirror of Sage - Open Source Mathematics Software. Here, you can 
download Sage for your system and platform. Not sure what to download? Then 
follow the  download guide. For more information, visit the Sage website.
Sage Mirror Content

 * Download for Microsoft Windows — binary distribution for Windows
   o Live CD — Bootable Sage Live CD
 * Download for Linux — binary distribution for Linux
 * Download for Apple Mac OS X — binary distribution for Mac OS X
 * Download for Sun Solaris — binary distribution for Sun Solaris
 * Source Code — source code of Sage (older versions are here)

Additional Information

 * Metalinks for all Downloads — Metalinks provide fast, stable and 
resumeable downloads
 * Other Mirrors Worldwide — in case you need another mirror select one here

About
If you want to help Sage by creating a mirror, please contact the webmasters. 
If 
there are any problems with the mirror, please report it to the maintainer of 
the website or the sage-devel mailing list.
---

For http://www.sagemath.org/index.html I see:

Sage is a free open-source  mathematics software system licensed under the GPL. 
It combines the power of many existing open-source packages into a common 
Python-based interface.
Mission: Creating a viable free open source alternative to Magma, Maple, 
Mathematica and Matlab.


Donate · Acknowledgments · DevMap · Browse the Code · Questions?
4.2.1 Changelog · Spread the Word · Benchmarks · facebook fans

etc etc





i.e. I'm seeing very different things.

Could it be my IP address is seen to be in the UK, and so I'm being directed to 
a different mirror, outside the USA ??


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Re: [sage-devel] Something screwed up at http://www.sagemath.org/

2009-12-19 Thread Dr. David Kirkby
Dr. David Kirkby wrote:
> Alex Ghitza wrote:

>> I am not seeing any problems.  http://www.sagemath.org/ and
>> http://www.sagemath.org/index.html look identical on my browser.
>>
>>
>> Best,
>> Alex
>>
> 
> Odd, they do not for me.



> Could it be my IP address is seen to be in the UK, and so I'm being directed 
> to 
> a different mirror, outside the USA ??
> 
> 

Looking more closely, I see Alex is probably in Australia. Perhaps I'm seeing a 
different mirror. Perhaps something decides what mirror one sees, based on IP 
address.

Dave

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Re: [sage-devel] Something screwed up at http://www.sagemath.org/

2009-12-19 Thread Alex Ghitza
On Sun, 20 Dec 2009 00:04:19 +, "Dr. David Kirkby" 
 wrote:
> 
> Could it be my IP address is seen to be in the UK, and so I'm being directed 
> to 
> a different mirror, outside the USA ??
> 

Yes, that would be my guess now.  Harald would know exactly what's going
on, so hopefully he can enlighten us.


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Re: [sage-devel] Something screwed up at http://www.sagemath.org/

2009-12-19 Thread Tim Lahey

On 12-19-2009, at 7:08 PM, Dr. David Kirkby wrote:

> 
>> Could it be my IP address is seen to be in the UK, and so I'm being directed 
>> to 
>> a different mirror, outside the USA ??
>> 
>> 
> 
> Looking more closely, I see Alex is probably in Australia. Perhaps I'm seeing 
> a 
> different mirror. Perhaps something decides what mirror one sees, based on IP 
> address.
> 


Possibly. I'm in Canada and the home page is fine for me.

Cheers,

Tim.

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University of Waterloo
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[sage-devel] Re: Something screwed up at http://www.sagemath.org/

2009-12-19 Thread Simon King
Hi!

On 20 Dez., 01:08, "Dr. David Kirkby"  wrote:
> > Could it be my IP address is seen to be in the UK, and so I'm being 
> > directed to
> > a different mirror, outside the USA ??
>
> Looking more closely, I see Alex is probably in Australia. Perhaps I'm seeing 
> a
> different mirror. Perhaps something decides what mirror one sees, based on IP
> address.

I am in Ireland, so close enough to UK. But for me, the page looks
fine.

Cheers
Simon

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Re: [sage-devel] Something screwed up at http://www.sagemath.org/

2009-12-19 Thread Dr. David Kirkby
Tim Lahey wrote:
> On 12-19-2009, at 7:08 PM, Dr. David Kirkby wrote:
> 
>>> Could it be my IP address is seen to be in the UK, and so I'm being 
>>> directed to 
>>> a different mirror, outside the USA ??
>>>
>>>
>> Looking more closely, I see Alex is probably in Australia. Perhaps I'm 
>> seeing a 
>> different mirror. Perhaps something decides what mirror one sees, based on 
>> IP 
>> address.
>>
> 
> 
> Possibly. I'm in Canada and the home page is fine for me.
> 
> Cheers,
> 
> Tim.
> 
> ---
> Tim Lahey
> PhD Candidate, Systems Design Engineering
> University of Waterloo
> http://www.linkedin.com/in/timlahey
> 


It is not an IP address issue, but a browser issue. I just used 'wget'

bash-3.2$ wget  wget http://www.sagemath.org/

from home, and find the index.html it saves looks like I would expect, with the 
mission statement etc.

But I do not see that on my browser (Firefox 3.1b3 on OpenSolaris). This is 
from 
the same IP address.

When I go to my Vista laptop, so I see what is intended.

But I've looked at the Sage web sites loads of times with Firefox on my 
OpenSolaris box, and never had an issue.

Dave

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[sage-devel] Re: Something screwed up at http://www.sagemath.org/

2009-12-19 Thread Dr. David Kirkby
Dr. David Kirkby wrote:
> The site
> 
> http://www.sagemath.org/
> 
> is not displaying what is intended - it tells you nothing about Sage, 
> except listing where to download it.
> 
> If one adds the /index.html on the end, so we get what I think is 
> actually intended to be.
> 
> Has the server been reconfigured in some way? It looks like there is an 
> issue
> 
> Dave
> 


Here's a screen shot on my Sun Ultra 27 running Open Solaris 06/2009. This is 
an 
Intel Xeon box, not a SPARC.

http://sage.math.washington.edu/home/kirkby/sage-homepage.png

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[sage-devel] Re: Something screwed up at http://www.sagemath.org/

2009-12-19 Thread Dr. David Kirkby
Dr. David Kirkby wrote:
> Dr. David Kirkby wrote:
>> The site
>>
>> http://www.sagemath.org/
>>
>> is not displaying what is intended - it tells you nothing about Sage, 
>> except listing where to download it.
>>
>> If one adds the /index.html on the end, so we get what I think is 
>> actually intended to be.
>>
>> Has the server been reconfigured in some way? It looks like there is 
>> an issue
>>
>> Dave
>>
> 
> 
> Here's a screen shot on my Sun Ultra 27 running Open Solaris 06/2009. 
> This is an Intel Xeon box, not a SPARC.
> 
> http://sage.math.washington.edu/home/kirkby/sage-homepage.png
> 
> 

A couple of minutes after posting that link, so the site looks right again!

I've not been drinking, or smoking anything unusual, but this sure is very odd 
indeed.

Dave

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Re: [sage-devel] Re: Something screwed up at http://www.sagemath.org/

2009-12-19 Thread William Stein
On Sat, Dec 19, 2009 at 5:15 PM, Dr. David Kirkby
 wrote:
> Dr. David Kirkby wrote:
>> Dr. David Kirkby wrote:
>>> The site
>>>
>>> http://www.sagemath.org/
>>>
>>> is not displaying what is intended - it tells you nothing about Sage,
>>> except listing where to download it.
>>>
>>> If one adds the /index.html on the end, so we get what I think is
>>> actually intended to be.
>>>
>>> Has the server been reconfigured in some way? It looks like there is
>>> an issue
>>>
>>> Dave
>>>
>>
>>
>> Here's a screen shot on my Sun Ultra 27 running Open Solaris 06/2009.
>> This is an Intel Xeon box, not a SPARC.
>>
>> http://sage.math.washington.edu/home/kirkby/sage-homepage.png
>>
>>
>
> A couple of minutes after posting that link, so the site looks right again!
>
> I've not been drinking, or smoking anything unusual, but this sure is very odd
> indeed.

While sagemath.org was down for upgrades, I set it to redirect to that
mirror page.  I then changed it back, last night.  Your browser cache
was just confused.

William

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[sage-devel] Some thoughts and request for input on what kind of a plot object would be good for Jmol 3-D viewer in SAGE...

2009-12-19 Thread Jonathan
Dear SAGE community:
   The Jmol development team is starting to build a plot object into
Jmol that SAGE could just pass a group of surfaces/meshes to for
plotting.

  Initially we are talking about a 3-D plot object, which would take
care of scaling, axis ticks, axis labels and aspect ratios and allow
an interactive user interface to change these things inside the
notebook.

  However, I began wondering if we could make something more general
and if the SAGE community thinks it would be useful to them? How about
a generic plot object for any number of dimensions?  The basic idea is
that you could specify which triple of dimensions to use for the x,y,z
triplet and use a fourth dimension to specify a magnitude at a point
(plotable as a color intensity, scaled spheres or used to produce an
isosurface), a fourth and fifth dimension to specify a complex value
at a point (not sure how to plot that...scaled spheres of different
colors or a vector field only in one plane?), or a fourth, fifth and
sixth dimension to plot a vector field.  The key idea being that we
could choose the triple, qradruple, pentuple or hextuple to plot out
of any n-tuple.

Any thoughts on this more general idea?  Is anybody aware of
implementations of something like this that is open source? Or
something non-open source that we could look at for ideas about how
things should behave?  We would also welcome more input on the 3D
object properties.

Jonathan
a small part of the Jmol development team

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Re: [sage-devel] Some thoughts and request for input on what kind of a plot object would be good for Jmol 3-D viewer in SAGE...

2009-12-19 Thread Christopher Olah
On Sat, Dec 19, 2009 at 11:24 PM, Jonathan  wrote:
> Dear SAGE community:
>   The Jmol development team is starting to build a plot object into
> Jmol that SAGE could just pass a group of surfaces/meshes to for
> plotting.
>
>  Initially we are talking about a 3-D plot object, which would take
> care of scaling, axis ticks, axis labels and aspect ratios and allow
> an interactive user interface to change these things inside the
> notebook.
>
>  However, I began wondering if we could make something more general
> and if the SAGE community thinks it would be useful to them? How about
> a generic plot object for any number of dimensions?  The basic idea is
> that you could specify which triple of dimensions to use for the x,y,z
> triplet and use a fourth dimension to specify a magnitude at a point
> (plotable as a color intensity, scaled spheres or used to produce an
> isosurface), a fourth and fifth dimension to specify a complex value
> at a point (not sure how to plot that...scaled spheres of different
> colors or a vector field only in one plane?), or a fourth, fifth and
> sixth dimension to plot a vector field.  The key idea being that we
> could choose the triple, qradruple, pentuple or hextuple to plot out
> of any n-tuple.


It would be incredibly awesome if you could do this! Incredibly!

This topic was an obsession of mine about a year ago (I spent about a
month trying to think in four dimensions a year or so a go, after all
three is an arbitrary limit... and mostly failed). So, I have a few
suggestions:

First let's consider an R^a -> R^b function. We must be able to
present ℵ₁ unique b-tuples in a dimensions.

Increasing b is comparatively trivial (change intensity, colour,
shape, etc). The limiting agent is a.

We need to find more ways to present ℵ₁ values... There two options I
see are to use time (ie. the plot changes over time) and give user
controls to slide along dimensions. One could do this with @interact,
but it would be a lot better if it could be handled in jmol: it would
be smoother and hopefully one could change which dimensions were the
sliding ones and which ones were in 3-space with the click of a
button.



The other approach is to challenge that we are actually ℵ₁ values for
each axis. Sage already does this by not plotting each point
(impossible) and just meshing surfaces.

Consider x^2+y^2=9; it is a level set of an R^2->R function (and is in
fact a circle).  If we try to solve for x, we get:

x(y)=∓(9-y^2)^0.5

It's what I've labeled, in my abuse of an already obscure term, a
2-hyperfunction...

We can transform the function then into

x: s ⊂ R->{set}(R)
x(y)={ (9-y^2)^0.5, -(9-y^2)^0.5}
which obviously has the property |x(y)|=2. Thus, we could plot it with
the any approach we can use to plot an R->R^2. For example, we might
use a line and vary the r and b values. Theoretically, this approach
is feasible for any plot with a Hausdorff dimension of 1.

But I think this approach should be avoided. It would be harder to
implement and less intuitive for the end user.



Another thing that comes to mind is that if you move beyond three
dimensions, you will have to give up your triangle based meshes and
move to higher-dimensional equivalents. ...

>
> Any thoughts on this more general idea?  Is anybody aware of
> implementations of something like this that is open source? Or
> something non-open source that we could look at for ideas about how
> things should behave?  We would also welcome more input on the 3D
> object properties.
>
> Jonathan
> a small part of the Jmol development tea

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