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

I have an equation with the following structure:

sin(a)-sin(b)=0;

Maple can solve this:

solve(%,[b]);

[[b=a]]

so it misses the 2nd solution (b=π-a). I can use the allsolutions qualifier:

solve(%,[b],allsolutions);

and now Maple returns an expression that, while correct, is really not conducive to further work without fairly massive substition work (_Z10 has to be 0 and the solutions wanted have _B10 0 and 1). In a classroom settng this is not helpful. Try as I might using the options to solve I have not found a way to make this into a list of the two solution I want without extensively mucking around with the expression. Is there any way to coerce solve to return something simpler?

I really want something like

[b=a,b=π-a]

TIA,

Mac Dude.

I need to get rid of the type "constant" for gamma. In Maple, gamma is defined as Euler's constant by default. While it is easy enough to unprotect(gamma) and then get rid of its value, Maple will refuse to solve an equation for gamma, as it remains of type constant even after deassigning it. So I need to regain gamma as a variable.

Some may feel this is an unwise thing to do. But it actually is not: I am writing a document involving physics, and gamma is the accepted symbol for the relativistic energy. I cannot avoid using that, lest mass confusion ensues (this involves students). I really don't want to write gammar instead. Euler's constant, otoh, does not figure at all in my document.

Note that I need a solution that works in Maple 15 and later as I am working in a heterogeneous environment as far as Maple versions are concerned.

Thanks in advance,

Mac Dude