[with patch, with positive review] plotting Z_p as a fractal image

[robertwb]

See:

Albert A. Cuoco, Visualizing the p-adic Integers, The American Mathematical Monthly, Vol. 98, No. 4 (Apr., 1991), pp. 355-364

 http://www.jstor.org/stable/2323809?&Search=yes&term=numbers&term=p-adic&list=hide&searchUri=%2Faction%2FdoBasicSearch%3FQuery%3Dp-adic%2Bnumbers%26jc%3Dj100069&item=2&ttl=190&returnArticleService=showArticle

[malb]

cool, quick comment, there is a typo in the docstring: "algebraic an topological"

[robertwb]

Attached an updated patch with typo fixed.

[wdj]

This is a very neat feature, useful if you are teaching number theory or topology, say.

I didn't realize that the second patch was a replacement for the 1st patch, so I tried to apply them both and of course failed. The 1st patch works as claimed and passes sage -testall. (Actually, on my old machine,

The following tests failed:


        sage -t  devel/sage/sage/matrix/benchmark.py
        sage -t  devel/sage/sage/server/notebook/worksheet.py

but then they passes on retesting.)

My suggestion, and it really a very minor one, is that the "radius" where the points are plotted should be a parameter the user can reset. For example, if you graph a p=3 and a p=7 then they overlap maybe more that some would like. Not that I see this as important for teaching but might be a fun option for making cool pictures. Just an idea.

[wdj]

FYI, I added another example of the bottom of  http://wiki.sagemath.org/pics.

[robertwb]

Cool image at  http://wiki.sagemath.org/pics. :)

The "radius" can be changed with the pointsize parameter. Also, you could plot it with fewer points (as for p=3 or 7, the "points" you're seeing are probably a cluster of even smaller ones).

[wdj]

I am talking about a dufferent radius I think. To me

sage: P1 = Zp(3).plot(pointsize=1,rgbcolor=(0,1,0))
sage: P2 = Zp(7).plot(pointsize=2,rgbcolor=(1,0,0))

and

sage: P1 = Zp(3).plot(pointsize=1,rgbcolor=(0,1,0))
sage: P2 = Zp(7).plot(pointsize=3,rgbcolor=(1,0,0))

Look the same. I was wondering about a scaling parameter "distance", say, where

sage: P1 = Zp(3).plot(distance=1,rgbcolor=(0,1,0))

would plot the 3 triangles at (say) a circle of radius 1 from (0,0) as it does now, and

sage: P1 = Zp(3).plot(distance=2,rgbcolor=(0,1,0))

would plot the 3 triangles at (say) a circle of radius 2 from (0,0).

Is this possible without introducing a new parameter?

[craigcitro]

This looks good, barring the extra feature request wdj has. I'm going to give this positive review, and file another ticket with the extra feature request as an enhancement and assign it to robertwb.

I'm also adding a patch which adds an "r" to the docstring, in the hopes that this will cause less heartache with the reference manual.

Apply 3210-plot-Zp-typo-fix.patch followed by trac-3210-add-r.patch.

[craigcitro]

The new ticket is #3474.

[mabshoff]

Merged 3210-plot-Zp-typo-fix.patch and trac-3210-add-r.patch in Sage 3.0.4.alpha0