## Maple 11 Physics Package: Indicial Notation Deriva...

I need to calculate derivative of a scalar function psi, which depends upon the scalar theta and tensor G[i] using the diff command and indicial notation capability of the recently included Physics package. My actual equation is longer, but here I am only including the terms needed to present my question. Please see below:

restart;

with(PDEtools):

> with(Physics):

Setup(dim=[3,+],spacetimeindices=lowercaselatin);

## Keep scaling and view when plot is within an array...

The code below is just to illustrate the issue. Is there any way to keep the chosen scaling and view when the plots are placed within an array? As the code below will show the scaling and view for a plot in an array has a mind of its own! I tried plotting a and b with both plots in them but with one in white - so it looked as if there was only one plot - but that did not work. restart; > with (plots): a:=plot(x^2/10,x=1..50,scaling=constrained,view=[0..120,0..800]): > b:=plot(-x^2+50*x,x=1..60,color=green,scaling=constrained,view=[0..120,0..800]): > display(a,b); > > g:=array(1..2):

## Efficient parametrization of unitary matrices...

Hello Maple community, although I'm using Maple (now version 11) for quite a while now, I still have problems in designing and writing efficient procedures. Within the context of quantum information theory, I want to write a procedure that parametrizes unitary matrices of arbitrary dimension NxN (in order to perform an optimization over this space). For the beginning, I just want to create random unitary matrices of a given dimension. For this, I implemented the formulas for the "Generalized Euler angle parametrization" (math-ph/0205016). This involves first the creation of N^2-1 matrices that serve as generators for SU(N) and, in a second step, several matrix exponentials and matrix products. These two steps I put in two procedures ("hermitian_basis" and "parametrize_unitary_Euler") (see the linked worksheet).

## There must be a more concise way to use fprintf...

I am writing a large number of variables to file to load into excel - it all works fine - with the code below. But there just has to be a neater way to do it. Can anyone help?
fd:=fopen(writefile,'WRITE','TEXT');
> for t from 1 to nops(files) by 1 do
> fprintf(fd
> ,"%a\t %a\t %a\t %a\t %a\t %a\t %a\t %a\t %a\t %a\t %a\t %a\t %a\t %a\t %a\t %a\t %a\t %a\t %a\t %a\t %a\t %a\t %a\t %a\t %a\t %a\t %a\t %a\t %a\t %a\t %a\t %a\t %a\t %a\t %a\t %a\t %a\t %a\t %a\t %a\t %a\t %a\t %a\t %a\t %a\t %a\t %a\t %a\t %a\t %a\t %a\t %a\t %a\t %a\t \n"

## 3D surface with curves...

I have succeeded in generating a nice plot of a surface in which I am interested, and have calculated geodesics on the surface. Is it possible to display one (or more) geodesic curves on a 3D plot of the surface? If so, would someone point me in the right direction to do so. I've looked at "multiple", but don't see how it's applicable to my problem. Don Ritchie

## animate a sphere

Maple
I am trying to animate a sphere/ so that it kinda looks like the globe rotating. This is what I have so far. Also if any body knows how to tilt a sphere so that it is on an angle. that would greatly help. with(plots):with(plottools): globe:=sphere([2.0, 1.5, 1.5], 1): display(globe,scaling=constrained,style=patch,axes=normal):

## puzzling substitution

by: Maple
Here's a substitution that briefly surprised me. It makes sense once you understand what is going on.
subs(true = false, proc() local i; for i to 3 do true; end do end proc);

proc()  end proc


## how to find why maple doesn't comlpete the command...

We have a maple 10 site license and I recently started to use maple for some challenging symbolic manipulation. Specifically I wanted to find the 3-dimensional eigenvectors A(u,w) and eigenvalues \lambda for a system of 8 partial differential equations. I was disappointed when maple completed most of the problem finding all 8 eigenvalues but only 6 of the 8 eigenvectors. In fact explicitly issuing Eigenvectors(A) command didn't seem to work as it ran for a long time with out returning so I ended up just issuing a series of LinearSolve(A-\lambda I|0) commands. This worked for the first 6 eigenvalues but for the last pair of eigenvalues maple just didn't do anything simply printing the command I issued. Maple didn't print any diagnostic information to let me know what went wrong. My question is when Maple doesn't evaluate a command how does one obtain information about what went wrong?

## Help!!! Rang Matrix...

Hello to evereybody!! I'm newbie with Maple and I've to do a program that calculates the rank of a Matrix, I can't use the comand rank or similar. I think it's something like: repeat If det(A) =/= 0 then rang := nº rows else reduce(a) until rows=1 or det(a) =/= 0 But i don't know how to codificate it in maple!! Help!!! Thanks for reading my problem... Sorry...If my english is bad i'm not from England or Usa

## Tupeplots/ Animation...

I was wondering if one could animate a tubeplot. if so i am trying to animate this tubeplot that i created so it can look like a tornado in action. tubeplot([20*t*cos(t+7),20*t*sin(t+7),20*t],t=0..20*Pi, radius=-100*exp(.00001*t), tubepoints=20, numpoints=100, color=grey); and if you can't does anybody know how I can animate a space curve similar to this to make it look like a tornado.

## Problem with singular()...

In this case there is a singularity at t=0, but the command singular() does not give it: singular(1/cos(1/t)); {t = 2/(Pi*(1+2*_Z1))} With the numeric range option it gives the correct answer: singular(1/cos(1/t), -1 .. 1); {t = 0}, {t = -2/(39*Pi)}, {t = -2/(37*Pi)}, {t = -2/(35*Pi)} etc. The command discont also gives the correct answer: discont(1/cos(1/t),t); {0, 2/(Pi*(1+2*_Z2))} I have maple 11.

## Elliptic Integrals...

I am trying to recreate a transcendental equation from a paper on buckling analysis. I have not been able to successfully manipulate equation (10) given on page 692 of the attached files into the final forms of equations (12) and (13), using the boundary conditions given in (11). Could someone take a look at my Maple worksheet and offer some suggestions that would yield an elliptic integral? Download 4865_Lo_p692.pdf
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