In Physics[Vectors] the operation ChangeBasis exists to change between different coordinate systems (Carthesian, cylindrical and spherical). The cylindrical system uses the third coordinate (_k) as its axis.

As it happens, in my work the axis of the cylindrial system should be the 2nd one (_j). I do not want to reformulate everything as this would become non-standard and confusing. I am wondering whether it is conceivable to "retrofit" the Physics package to allow for that. At issue are not so much the formulae; I can do the transformation "by hand", but that is a bit clumsy and I am looking for a way to have this integrated better in the Physics package so that all other operations (e.g. Nabla) do the expected.

I have looked for and not found something like an "addBasis" command. Am I missing something obvious here? I should add that some of my work happens on Maple 15 (Mac OS X PPC so no upgrade possible); if something like this was added recently I may have missed it, although I do have access to Maple 17 as well so I could use that version for this particular problem. Is the source of Physics actually open?

TIA,

Mac Dude

I am trying to get a Fourier transform of a Gaussian:

so I say

and get

The Fouriertransform of a Gaussian is well known and the result I expect is something like

exp(1/2*sigma^2*omega^2)

ignoring normalizations & other factors. I know that I can add functions to inttrans, but I kind-of expected inttrans[fourier] to know how to transform a Gaussian, it is a commonly used transformation. Even if I set phi0 to 0 it does not produce anything useful.

???

Mac Dude

I have the following d.e.:

I need to change the s variable into a different one, where the new variable is defined by

(the old s shows up in the limit of the integral)

I tried dchange, but it chokes on this as I don't have an explicit representation of s in terms of Theta.

(I know the overall solution as other people smarter than me have solved this a long time ago, but I 'd like to have the derivation to understand it).

Mac Dude

This is one of these silly ones that crop up every-so-often (and yes, beta, gamma are just the relativistic v/c and energy):

gamma=1/sqrt(1-beta^2);
solve(%,beta);

comes up with ±I*sqrt(-gamma^2+1)/gamma.

While this is not wrong it is nothing I want to throw at any student trying hard enough as it is to keep his/her head above water. What I want is beta=sqrt(1-1/gamma^2) and I am having a devil of a time getting Maple to do this. even doing it "by hand" the I comes in the moment I take the sqrt. "assuming" does not help (and when I try ...assuming beta::positive, gamma > 1 I get an error claiming these to be inconsistent).

What gives?

Mac Dude

In physics as in math, we often use delta to indicate a (small but finite) variation in a parameter (e.g. delta x). Sometimes Delta (capital delta) is used for a larger variation, and there are even constructs like delta Delta x (a small variation of a larger variation in x). (Don't laugh or frown, this is being done & makes sense in certain situations.)

How do I write this best in Maple, esp. when I use 2-d math and am working on a (live-) script that may be handed out to others incl. students,? I.e. the appearance matters. Just writing delta x is interpreted (in 2-d input) as delta*x which is not what is meant (and leads to funny effects after the first simplify). If I write deltax (one word) then delta does not typeset in its proper greek form, which becomes an issue if you have many of these. I can write delta(x) and that often works (as long as you don't try to differentiate by x), but the typeset equation does not look right either (delta is not a function of x).

Is there a god way of doing this, or am I hitting a wall here?

TIA,

Mac Dude