After having Maple for a week I'm happy with it but still have to learn a lot about the kinds of problems it can solve.  Here is a problem I solved many years ago whose solution I have misplaced.  I'm wondering if Maple could help me recover my solution.

Write an expression for ab (a and b real) using only the unit (1) and the operations of adding, subtracting, and taking the reciprocal.

I'm also curious whether this is a well-known problem.  As I recall, I didn't find any references to it when I worked on it before.

Special Relativity has been around for ~100 years, General Relativity for ~90 years.  I'm hoping that with the assistance of Maple and Mapleprimes I may be able to do some tensor calculus to better understand Einstein.  Perhaps the twin paradox is within my reach.  Perhaps even the orbit of Mercury.

In the following worksheet, evalf[4997](... does what I expected and evalf[4998](... does not.

View 4937_Page147.mw on MapleNet or Download 4937_Page147.mw
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See (3) and (10) in the worksheet.

Something I've been wondering about...

i am solving a heat equations with maple but i didn't work out. if you guys can get it out plz give me code. thanx a million

diff(u1(x,t),t)=diff(diff(u1(x,t),x),x))-a*(u1(x,t)-u2(x,t))+b*(u3(x,t)-u1(x,t))
diff(u2(x,t),t)=diff(diff(u2(x,t),x),x))-c*(u2(x,t)-u3(x,t))+a*(u1(x,t)-u2(x,t))
diff(u3(x,t),t)=diff(diff(u3(x,t),x),x))-b*(u3(x,t)-u1(x,t))+c*(u2(x,t)-u3(x,t))

i need the expression of the u1(x,t)，u2(x,t)，u3(x,t) and the a,b,c are constants.

Looking forward to hearing from you!!!

I've just reformatted my computer and NEED to reinstall Maple 11 ASAP,
assignments are due soon.
I am having trouble installing it

1st time Installing)

   Everything was alrite until my cd-drive went haywire and the installiation frooze
   i then ended the task (task manager), maple as far as i know created the folder 
  program files, a few files there but NO WORKING PROGRAM is there leading to my second attempt to reinstall

2nd time installing)

"Maple 11 already installed"
  confused i decided to explore maple 11 folder, attempt an uninstall

Hello,

Another interesting undocumented package in the Maple 11.02 Library.

My oldest son, Stuart, recently completed a Science Fair project on sudoku puzzles. While I am fairly good at solving sudoku puzzles, the mathematics is something that is completely outside my area of expertise. After seeing the paper by Hurzberg and Murty in the Notices of the AMS (June/July 2007) and additional papers by Felgenhauer and Jarvis (http://www.afjarvis.staff.shef.ac.uk/maths/felgenhauer_jarvis_spec1.pdf)  and Russell and Jarvis (http://www.afjarvis.staff.shef.ac.uk/maths/russell_jarvis_spec2.pdf) and Jarvis' sudoku webpage (http://www.afjarvis.staff.shef.ac.uk/sudoku/), I felt that I had a reasonable understanding of some of the basic ideas involved in counting unique sudoku puzzles. While I had nothing to add to the mathematical ideas, I did see the potential to create a tool to visualize these ideas. The result is the worksheet I just uploaded to MaplePrimes:

View 178_Sudoku3-20-03-08.mw on MapleNet or Download 178_Sudoku3-20-03-08.mw
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I just received and installed Maple 11.  (Maplesoft wouldn't sell me the student version, but I learned they have an unadvertised Home User version which is reasonable.  You have to call on the phone to order it.)  So far it's working well, but I can't figure out how to get an exact (symbolic) solution to a quartic with integer coefficients.

Of all the ways to decompose a numerical (floating point) matrix, my favorite is the singular value decomposition (SVD).  There are a lot of applications of the SVD (see my dissertation for one related to polynomial algebra) but my favorite ones are probably two applications related to image processing.

The first one I want to talk about comes from the cover of James Demmel's book "Applied Numerical Linear Algebra": image compression.  This example gives a really cool intuitive understanding of the Rank of Matrix and is also nice excuse to play with Maple's ImageTools package.

So, the first thing you need a test image. I used the classic image compression benchmark of a Mandrill.

Read this in with:

mandrill:=ImageTools:-Read("4.2.03.tiff");

The result is a 512x512x3 array.  In order to do something with this, we need to make it into a matrix so, call

manmat:=convert(ArrayTools:-Reshape(mandrill, 512*3, 512), Matrix);

Now we can compute a singular value decomposition of the image:

(U, S, V) := LinearAlgebra:-SingularValues(manmat, output = ['U', 'S', 'Vt']);

Now we can zero-out small singular values and multiply things back together to create low-rank approximations of the matrix that are also compressed versions of the image.
Rank 32 will give us 1/8 of the data (64 dimension 512 vectors: 32 rows of U, 32 columns of V, and the 32 corresponding singular values) but still a pretty good image:

rank32approx:=MatrixMatrixMultiply(`.`(U, DiagonalMatrix(S[1..32], 3*512, 512)), V, outputoptions = [order = C_order]);

This reshape it back to an image and display:

Preview((Reshape(rank32approx, 512, 512, 3)));

Taking things down to rank 8, is leaving only 1/32 of the data, but it is amazing how what is left resembles the original image:

rank8approx:=MatrixMatrixMultiply(`.`(U, DiagonalMatrix(S[1..8], 3*512, 512)), V, outputoptions = [order = C_order]);
Preview((Reshape(rank8approx, 512, 512, 3)));

To look at more images in order of descending rank, take a look at my worksheet:
Download 5480_SVD-face-colour-improved.mw
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Next time: eigenfaces

A colleague showed this to me earlier this afternoon. I can explain, and accept, most of Maple's responses. I do have one case where I believe Maple could do better.

This arose during the creation of some Maple materials to support the derivation of the Integral Test for series convergence. Consider:

restart;
I1 := Int( 1/x^p, x=1..infinity );
                                /infinity      
                               |          1    
                               |          -- dx
                               |           p   
                              /1          x    

The time for Easter eggs will soon be here.

And using LibraryTools to browse and poke about in Maple's .mla files can show a few undocumented items.

Here's one below, that's an interesting part of a package.

I would like Maple to assist me with the following definite double integral:

int(int(x/(x^2+y^2+z^2)^(3/2), y = -b .. b), z = c .. a+c)

so far, I have failed.  Can anybody help?

Here is my worksheet:

View 4937_Page92.mw on MapleNet or Download 4937_Page92.mw
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I'm asking Maple for simple things only, yet still (5 years later) I get nothing.

I'm creating 3 contour plots for potential functions in 3 bordering regions of 3-space,

because a continuous potential function isn't possible to define. 

After an entire worksheet worth of variable definitions and series expansions, i say simply:

CPA:=contourplot3d(VI(a,b,c,d,e)......)

CPB:=contourplot3d(VII(a,b,c,d,e)......)

CPC:=contourplot3d(VIII(a,b,c,d,e).......)