perfectly_odd's profile - activity

Is there a way to compute the "correct" distributional answer, -4*pi*dirac_delta(r), as the Laplacian of 1/r (in spheric

Reasons for asking: I'm doing calculations related to some problems in electromagnetism, and want to be able to compute fluxes, circulations, and similar integrals of vector fields over submanifolds of R^3. Ideally, I'd just define the surface or region of interest, then pass the (existing) field and domain to some built-in function to compute the relevant integral. Does such a thing exist at present?

Reasons for asking: My ultimate goal is to be able to integrate vector and form fields on surfaces defined by constraints in a 3D Euclidean space. A simple example would be the sphere (x^2 + y^2 + z^2 = R^2).

Thanks, @eric_g---looks like you got to all three of my submanifold-related questions. Apologies for being repetitious;

Again, thanks. I'll take a look at the ticket, but am not incredibly optimistic about my ability to implement this func

Reasons for asking: I'd like to integrate a differential form over, say, a finite cylinder, and then extract the boundary of the cylinder for further computations.

Thanks. I thought this might be the case, but wanted to make sure I wasn't missing something obvious.

Is there a way to define a submanifold of a Euclidean space by providing a list of implicit constraints, instead of by d

Is there a built-in way to integrate a vector or differential form field on an embedded submanifold of Euclidean space?

How can I define a submanifold-with-boundary of a Euclidean space in Sage? Reasons for asking: I'd like to integrate a d

Background: I'm using Sage to do some computations for a LaTeX document I'm preparing. My preferred approach is to include the script directly in the markup, using SageTeX to parse the code and print the results in TeX-readable form. The computations relevant to this question result in a longish list of numbers, most of which are of the form something*sqrt(pi). My intention is to include this list in a table, which I'm constructing using a little Python script I wrote. The script takes a lists of TeX-formatted strings and returns a string with the markup for a table with those strings as rows.

The problem: When I call the latex() function on the list elements to prepare them for serialization into the table, I get results like this: \frac{3}{7} \sqrt{7} \sqrt{\pi}. This is not at all how I would type this if I were "TeXifying" it myself---I'd much prefer \frac{3}{7} \sqrt{7 \pi}. Even \frac{3}{7} (7 \pi)^{1/2} would be preferable IMO.

Obviously, I could just generate a table and then copy-paste it into my document, tweaking where necessary. I could also try writing a little Python function to massage the output into the desired form. But it made me wonder if there is any way to control or customize the output of latex() beyond the basic delimiter-setting functions I found in the docs, and I think that'd be worthwhile to know in any event.

Specific question: Is there a way to "tell" Sage to avoid using \sqrt{} in its LaTeX output in favor of fractional exponents?

Thanks, Emmanuel---this is what I feared. I imagine writing a fully satisfactory solution to this problem that worked o

Thanks for the amazing response, @dsejas! I fully expected to have to write something like this myself if it came down

Is there a way to specify that `\sqrt{}`s should be avoided in favor of exponents when using the `latex()` function? Bac