Bill Page _ again's profile - activity

This is nice. There is a lot of useful documentation: here but so far I could not easily find how compute the center of the algebra (elements that commute with all other elements) but perhaps this is defined in some other way?

I am looking for something similar to the Axiom/FriCAS domain AlgebraGivenByStructuralConstants which implements finite rank algebras over a commutative ring, given by the structural constants with respect to a fixed basis [a1,..,an] or equivalently in terms of generating equations of the form

a_i * a_j = gamma_ij1 * a_1 + ... + gamma_ijn * a_n

where gamma is a vector/list of length n of n by n matrices.

In particular I would like to be able to easily compute various properties of such algebras such as the conditions for idempotents etc. For example:

• http://axiom-wiki.newsynthesis.org/up...
• http://axiom-wiki.newsynthesis.org/Sa...

I had exactly the same problem on OpenSuse Leap 42.1. I downloaded the binary distribution sage-7.2-Fedora_23-x86_64.tar.bz2 from http://mirrors.mit.edu/sage/linux/64b... (since there is no OpenSuse binary). I extracted it and then ran 'make' (in spite of the fact that this was a binary distribution). Make ran for 20 minutes before giving this error. But the problem went away when I actually downloaded the source distribution instead from http://www.sagemath.org/download-sour.... Is 'make' supposed to work with the binary distribution?

http://en.wikipedia.org/wiki/Wirtinge...

I would agree that this is not implemented in Sage but I would disagree that it can be defined as a "simple combination of the usual derivatives". In particular it is necessary to consider the chain-rule. I have a prototype implementation in FriCAS (Axiom) that does this. In that context I am interested in collaboration and critical review.

http://axiom-wiki.newsynthesis.org/Sa...

From the point of view of complex analysis you might also want to look up references to polygenic functions, e.g. Kasner

http://www.ncbi.nlm.nih.gov/pmc/artic...

Thanks. This is cute, but as you say does not really answer the question. I am thinking of a way to make diff equivalent to your d operator, then dbar can be implemented simply by substituting a dummy variable for conjugate(x).

Or, can we differentiate holomorphic functions only?

Wirtinger defined two derivations in complex analysis for which we have: diff(x,conjugate(x)) = 0 and diff(conjugate(x),x) = 0.

http://en.wikipedia.org/wiki/Wirtinge...

Wirtinger calculus has important applications in optimization and has been extended to quaternion functions.

Is there any situation in which leaving diff(conjugate(x),x) unevaluated is an advantage?

Ok, yes with this option I do get a reasonable looking graph but I also get the message: verbose 0 (3998: plot.py, generate_plot_points) WARNING: When plotting, failed to evaluate function at 24999 points. verbose 0 (3998: plot.py, generate_plot_points) Last error message: ''

Thanks for the trac ticket.

Here is another one with a problem:

polar_plot(3*sqrt(cos(2*theta)),(theta, 0, 2*pi))

gives the follow graph:

> ![image description](http://)
> 
> Sorry, file uploading requires karma > 60

Arrrgh!

Well, ok try it yourslf. On my v.4.6.1 worksheet I see a plot with some weird discontinuity near the origin.

In Sage notebook v 4.6.1 I wrote:

var('theta')
polar_plot((1/sin(theta)),(theta, pi/12, pi/2))

I got

libpng error: Image width or height is zero in IHDR
Traceback (click to the left of this block for traceback)
...
RuntimeError: Error building image

What am I doing wrong?

In Sage notebook v 4.6.1 I wrote:

var('theta')
polar_plot((1/sin(theta)),(theta, pi/12, pi/2))

I got

libpng error: Image width or height is zero in IHDR
Traceback (click to the left of this block for traceback)
...
RuntimeError: Error building image

What am I doing wrong?