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2017-05-10 15:41:48 +0200 commented answer How can I specify a (possibly non-associative) algebra over a finite (small) set of generators by means of structure constants?

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?

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2017-05-09 21:09:47 +0200 asked a question How can I specify a (possibly non-associative) algebra over a finite (small) set of generators by means of structure constants?

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:

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2016-07-26 04:17:14 +0200 answered a question Problem in installing SAGE

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?

2015-03-25 03:31:09 +0200 answered a question Complex analysis. Compute bar derivative

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...

2014-09-03 15:29:10 +0200 commented answer Why is diff(conjugate(x),x) unevaluated?

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).

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2014-09-03 03:25:09 +0200 asked a question Why is diff(conjugate(x),x) unevaluated?

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?

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2011-11-07 07:37:49 +0200 commented answer polar_plot((1/sin(theta)),(theta, pi/12, pi/2))

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: ''

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2011-11-04 11:08:55 +0200 answered a question polar_plot((1/sin(theta)),(theta, pi/12, pi/2))

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.

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2011-11-01 20:57:13 +0200 asked a question polar_plot((1/sin(theta)),(theta, pi/12, pi/2))

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?

2011-11-01 20:56:02 +0200 asked a question polar_plot((1/sin(theta)),(theta, pi/12, pi/2))

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?