I am having an issue with Physics[Vectors] in Maple 17, specifically an interference with PDEtools:-dchange. My apologies, this post is lengthy & a bit messy. I did upload a worksheet with the code; link at the end. The upload exhibits the UNWANTED behaviour in Maple 17.

Here are a few lines of code that exhibit the WANTED behaviour (change of variable and solving a de). it is run in Maple17 with Physics loaded but NOT Physics[Vectors]. The paste into Mapleprimes looks too messy to be useful so I am just showing the relevant lines; the file has everything:

-(diff(E1_(x, y, z, t), x, x))-(diff(E1_(x, y, z, t), y, y))-(diff(E1_(x, y, z, t), z, z)) = -mu*epsilon*(diff(E1_(x, y, z, t), t, t));

PDEtools:-dchange({x = r*cos(theta), z = r*sin(theta)}, -(diff(diff(E1_(x, y, z, t), x), x))-(diff(diff(E1_(x, y, z, t), y), y))-(diff(diff(E1_(x, y, z, t), z), z)) = -mu*epsilon*(diff(diff(E1_(x, y, z, t), t), t)), simplify);

subs(E1_(r, theta, y, t) = R(r)*exp(I*(-k*y+omega*t)), -((diff(diff(E1_(r, theta, y, t), y), y))*r^2+(diff(diff(E1_(r, theta, y, t), r), r))*r^2+(diff(E1_(r, theta, y, t), r))*r+diff(diff(E1_(r, theta, y, t), theta), theta))/r^2 = -mu*epsilon*(diff(diff(E1_(r, theta, y, t), t), t)));

dsolve((5));

So far this is all as expected.

Now I rerun this thing with Physics[Vectors] loaded rather than just Physics. Everything looks the same until I get to the line starting with subs(E1_ :

subs(E1_(r, theta, y, t) = R(r)*exp(I*(-k*y+omega*t)), -((diff(diff(E1_(r, theta, y, t), y), y))*r^2+(diff(diff(E1_(r, theta, y, t), r), r))*r^2+(diff(E1_(r, theta, y, t), r))*r+diff(diff(E1_(r, theta, y, t), theta), theta))/r^2 = -mu*epsilon*(diff(diff(E1_(r, theta, y, t), t), t)));

plus many more lines of expressions. I am not sure what is going wrong; but after the dchange the code behaves funky: I have had simplify producing similarly weird expressions etc.

Note that on Maple 15 this all works as expected and no issues show up for me. If the version of Physics I have on Maple 17.02 is bad; how do I change that? (I have not tried to update Physics separately, and it isn't obvious to me where to find it for Maple 17). It is sort-of an issue as I want to use this as a demo for students, who in fact will be running Maple 18... but I am stuck at 17 (and often using 15 at home) so I need this to work there (17), too.

TIA,

Mac Dude

dchangeTest.mw

Sometimes Maple can be endlessly frustrating!!

A recent question of mine on how to distribute integrals into a sum was answered:

http://www.mapleprimes.com/questions/201500-Integral-Of-A-Sum--Sum-Of-Integrals-In-Maple

Now I need the same thing, except (as part of a solution) Maple chose to use Intat rather than Int.

So I modify the rule I have to look like this:

ToSumInt:=Intat(A::algebraic*Sum(v::algebraic,r::{name,equation})*B::algebraic,u::{name,equation})=Sum(Intat(A*v*B,u),r);

.. and for the heck of it I cannot get Maple to accept this, no matter what type I make u to be. The error message always looks the same:

Error, invalid input: Intat expects its 2nd argument, dx_at_t, to be of type symbol = algebraic, but received u::{name, equation}

and you may replace the u::{name,equation} with any other u::type you care to think of.

Any help would be appreciated.

M.D.

Edit: Also, useInt will not replace the Intat (in the expression I want to apply the rule to) with Int.

I have an expression like this:

Since it is linear I want Maple to rewrite it into this:

(with the benefit that Maple then can solve it at least up to a point). i have tried to conceive a rule to do that but got stuck relatively quickly. Does anybody have a way to do this (in some genrality)?

Thanks,

Mac Dude.

Here is a problem I have with the Nabla operator:

I am working on a demonstration involving Maxwell's equations:

restart:with(Physics[Vectors]);
Setup(mathematicalnotation = true);
# Maxwell's eqn
M4 := `&x`(Nabla, B1_(x, y, z, t)) = mu*epsilon*(diff(E1_(x, y, z, t), t));

eval(subs(B1_(x,y,z,t)=Bxx(x,y,z,t)*_i+Bzz(x,y,z,t)*_k,M4)); # transverse magnetic field, no longitudinal (j) component

# Ok, this one is as expected.

eval(subs(B1_(x,y,z,t)=Bxx(x,y,z,t)*_i+Bzz(x,y,z,t)*_k,M4)) assuming real;

# Hmm... why is this zero?

eval assuming real seems to make them all zero. In this little example, Bxx and Bzz are just arbitrary functions and therefore the result cannot be zero in general. The bother here is that I later use a parametrization of the field (the Bxx and Bzz) which in fact does make curl(B) = 0. I wanted Maple to demonstrate that the parametrization does that, but it appears i can make the result zero for any B-field, which sort-of defeats the purpose. If I don't assume real, with the other parametrization Maple isn't getting anywhere...

So, how can I get correct results while declaring variables to be real when they are... ?

Thanks,

M.D.

Maxwell_test.mw

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