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I started to notice strange things happening to Maple help pages lately when I google something. I think someone is changing them from inside Maplesoft? Now they look hard to read since I see text below another text and also can't copy it to retype it in my notebook since the syntax is not even valid. Here is a screen shot

http://www.maplesoft.com/support/help/maple/view.aspx?path=FileTools%2fText%2fOpen

 

I thought at first my browser was playing games on me. But I tried it with firefox and Chrome and after refreshing, and the pages still look mangled like the above.

Since I find it hard to believe someone at Maplesoft will make help pages like the above on purpose, where text falls below the line and it not even possible to interpret it when one wants to copy it, since the syntax is not even valid Maple syntax, I would have to imagine there is a bug somewhere inthe help pages generation.  But if so, someone must have seen it before me. I can't be the only person in the world who is googling Maple help.

This is why I am asking.

Is everyone seeing the same thing I am seeing? I am on windows 7, using Latest browsers.

Hello,

I want to simplify a fraction by cancelind the powers of ten. When the factors in front of the powers are short, it works fine with 'simplify', but with such long decimal numbers, Maple does not want to cancel down. How can I force it?

Example:

 

 

Regards, Yader

I do not understand why I am getting permission denied trying to create a file.

restart;
fd := FileTools[Text][Open]("C:\\foo.txt", create=true,overwrite=true);

     Error, (in FileTools:-Text:-Open) permission denied

I am running the above on my PC, from Maple, using the same user which is me. I can ofcourse create a file on my C drive outside of Maple. So I do not understand why it says permission denied. Also tried "C:/foo.txt". Also tried

         fd := FileTools[Text][Open]("C:\\foo.txt", create,overwrite);

Any idea what can be the problem? and how to determine why it is giving this error? I am on windows 7, using Maple 2015.

http://www.maplesoft.com/support/help/maple/view.aspx?path=FileTools%2fText%2fOpen

http://www.maplesoft.com/support/help/maple/view.aspx?path=IO_errors

"permission denied" - An attempt was made to read from a file on which the user does not have
read permissions, or write to a file on which the user does not have write permissions."

Well, I do have write permission to make a file on my C drive !

I tried using fopen, and got same error

restart;
  try     
     fd := fopen("C:\\foo.txt",APPEND,TEXT);
  catch:
     print(`Unable to open file, error is`);
     print(StringTools:-FormatMessage(lastexception[2]));
  end try:

                 Unable to open file, error is
                      "permission denied"

So I have no idea why I keep getting permission denied.

 

diff(y(x), x, x)+2*(diff(y(x), x))/x+af(x)*g(y(x))=0

restart

"n:=5:  y[0]:=0:  f(x):=1:  g(y):=e^(-y): L:=x^(-2)(ⅆ)/(ⅆ x) (x^(2)(ⅆ)/(ⅆ x) ):  L^(-1)(y):=(∫)[0]^(x)x^(-2)(∫)[0]^(x)x^(2)dxdx:  "

"for m from 1 to n do:  `&varkappa;`[m]:={[[0,m<=1],[1,m>1]]:   R[m]:=simplifyL^(-1)((d^(2)y[m-1])/(dx^(2))+(2)/(x)(&DifferentialD;y[m-1])/(&DifferentialD; x)+f(x)g(y) );  y[m]:=simplify(y[m-1]*`&varkappa;`[m]-R[m]):  od;"

``

plz help me, I m trying to solve homotopy analysis method for lane emden, what additional steps I have to taken in above programming?

Download LE_EQ.mw

Hi,

  Excuse me, I have the following code

  

###########################

with(combinat);
with(LinearAlgebra);
f:=([1,2,3]);
permute(f);

n:=3;
g:=array(1..n);

for i from 1 to n do
  g[i]:=i;
end do;

permute(g);

###########################

 The output ends up with

 

Error, (in combinat:-permute) 1st argument must be a list, set or a non-negative integer

 

 It seems that maple will not generate permutation of g... How to generate the permutation of array g? i.e. by assigning all variables automatically.

 

Thank you very much!

 

Hi, 

     I was just curious about the difference between defining tensors as arrays/matricies/TensorArrays vs defining them as algebraic symbols. I found that defining them as an expression lead to the wrong answer, and I was forced to define a tensor (LKh) as an array. I've attached a worksheet demonstrating my problem.

I apologize for the amount of tensors needed to find this problem, but it is the only one I have reproduced the issue. I basically define the metric
Metric = g_
auxillary tensor = h
Killing vector = K
LieDerivative of h, wrt K = LKh (not a tensor array)
LieDerivative of h, wrt K = LKh2 (tensor array)
Then I compare two expressions, rho1 and rho2 computed from LKh and LKh2 and they disagree. 


MapleQuestion.mw

Thanks!

I ran into a problem mentioned here before: With lots of code in one execution group, the standard GUI editor becomes very slow at least in older versions of Maple (I have reason to believe that this is mostly fixed in Maple 17 and, presumably, newer). With one of my packages this has become enough of a problem to force me to deal with it (and Modules and Packages have to be all in one execution group). I have some machines that cannot go beyond Maple 15 so I keep my stuff compatible with it (so far not a big sacrifice).

The fix is rather easy: In the GUI, export the code as "Maple Input" which creates a file with extension .mpl. Then, in the GUI have a small file that uses "read" to read-in and execute the code (of the module). In my case, I have the necessary LibTools statement to save as a .mla right after the package code ends so, bingo, I have just updated the package. I edit the .mpl file in Emacs.

So I installed Joe Riel's Emacs mode maplev-mode.el. This works rather well. However, it took not long for it to show its age: it does not recognize the multi-line comments (*...*). This is kind-of bad as this forces me to not use quotes in the comments since they mess-up the keyword highlighting esp. when using single quotes as in "I'll" and so on. Likewise, maplev-indent-buffer messes up the whole buffer as it interprets the multiline comments as code.

So my question is: is someone still working on this and using it?? I guess I can work around some of these things, but it would be nice if this worked.

Incidentally, my version of maplev-mode.el seems to be dated June 2005.

I know Joe is here on occasion, maybe he can chime in. It is not absolutely fatal; I could forgo using maplev, but if I am forced to go this route of readin in the package; using maplev-mode at least gives me something in return. Unfortunately my elisp skills are not quite up to fixing this myself; at least not in a reasonable time.

If it is relevant: I use Emacs 22.1 on Mac OS X. Yes, I could upgrade to at least Emace 23.4, if that were the issue.

Thanks in advance,

Mac Dude

I have the following paper:

http://projecteuclid.org/download/pdf_1/euclid.dmj/1077490637

 

Now I wanted to check Fritz John's claim in the proof of Theorem 1.1, he says that equation (7) can be easily verified for case i=1,k=2.

 

Now at first I tried to calculate by hand, but it's just a lengthy calculation, so now I turned to maple to check its validity, I get that this claim is false, am I wrong in my code? if yes, then how to change it?

 

P.S

I changed between xi and x and eta and y.

In the following is the code:

 

v := (((x_1-y_1)/(x_3-y_3))^2+((x_2-y_2)/(x_3-y_3))^2+1)^(1/2)*u((-x_1*y_3+x_3*y_1+x_2-y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2-x_1+y_1)/(x_3-y_3), (-x_1*y_3+x_3*y_1-x_2+y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2+x_1-y_1)/(x_3-y_3)); 1; diff(diff(v/((x_1-y_1)^2+(x_2-y_2)^2+(x_3-y_3)^2), x_1), y_2); 1; diff(diff(v/((x_1-y_1)^2+(x_2-y_2)^2+(x_3-y_3)^2), x_2), y_1); 1; evalb(diff(diff(v/((x_1-y_1)^2+(x_2-y_2)^2+(x_3-y_3)^2), x_1), y_2) = diff(diff(v/((x_1-y_1)^2+(x_2-y_2)^2+(x_3-y_3)^2), x_2), y_1))

((x_1-y_1)^2/(x_3-y_3)^2+(x_2-y_2)^2/(x_3-y_3)^2+1)^(1/2)*u((-x_1*y_3+x_3*y_1+x_2-y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2-x_1+y_1)/(x_3-y_3), (-x_1*y_3+x_3*y_1-x_2+y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2+x_1-y_1)/(x_3-y_3))

 

u((-x_1*y_3+x_3*y_1+x_2-y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2-x_1+y_1)/(x_3-y_3), (-x_1*y_3+x_3*y_1-x_2+y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2+x_1-y_1)/(x_3-y_3))*(x_1-y_1)*(x_2-y_2)/(((x_1-y_1)^2/(x_3-y_3)^2+(x_2-y_2)^2/(x_3-y_3)^2+1)^(3/2)*((x_1-y_1)^2+(x_2-y_2)^2+(x_3-y_3)^2)*(x_3-y_3)^4)+(-(D[1](u))((-x_1*y_3+x_3*y_1+x_2-y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2-x_1+y_1)/(x_3-y_3), (-x_1*y_3+x_3*y_1-x_2+y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2+x_1-y_1)/(x_3-y_3))/(x_3-y_3)+(D[2](u))((-x_1*y_3+x_3*y_1+x_2-y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2-x_1+y_1)/(x_3-y_3), (-x_1*y_3+x_3*y_1-x_2+y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2+x_1-y_1)/(x_3-y_3))*x_3/(x_3-y_3)+(D[3](u))((-x_1*y_3+x_3*y_1+x_2-y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2-x_1+y_1)/(x_3-y_3), (-x_1*y_3+x_3*y_1-x_2+y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2+x_1-y_1)/(x_3-y_3))/(x_3-y_3)+(D[4](u))((-x_1*y_3+x_3*y_1+x_2-y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2-x_1+y_1)/(x_3-y_3), (-x_1*y_3+x_3*y_1-x_2+y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2+x_1-y_1)/(x_3-y_3))*x_3/(x_3-y_3))*(x_1-y_1)/(((x_1-y_1)^2/(x_3-y_3)^2+(x_2-y_2)^2/(x_3-y_3)^2+1)^(1/2)*((x_1-y_1)^2+(x_2-y_2)^2+(x_3-y_3)^2)*(x_3-y_3)^2)-u((-x_1*y_3+x_3*y_1+x_2-y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2-x_1+y_1)/(x_3-y_3), (-x_1*y_3+x_3*y_1-x_2+y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2+x_1-y_1)/(x_3-y_3))*(x_1-y_1)*(-2*x_2+2*y_2)/(((x_1-y_1)^2/(x_3-y_3)^2+(x_2-y_2)^2/(x_3-y_3)^2+1)^(1/2)*((x_1-y_1)^2+(x_2-y_2)^2+(x_3-y_3)^2)^2*(x_3-y_3)^2)-(-(D[1](u))((-x_1*y_3+x_3*y_1+x_2-y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2-x_1+y_1)/(x_3-y_3), (-x_1*y_3+x_3*y_1-x_2+y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2+x_1-y_1)/(x_3-y_3))*y_3/(x_3-y_3)-(D[2](u))((-x_1*y_3+x_3*y_1+x_2-y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2-x_1+y_1)/(x_3-y_3), (-x_1*y_3+x_3*y_1-x_2+y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2+x_1-y_1)/(x_3-y_3))/(x_3-y_3)-(D[3](u))((-x_1*y_3+x_3*y_1+x_2-y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2-x_1+y_1)/(x_3-y_3), (-x_1*y_3+x_3*y_1-x_2+y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2+x_1-y_1)/(x_3-y_3))*y_3/(x_3-y_3)+(D[4](u))((-x_1*y_3+x_3*y_1+x_2-y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2-x_1+y_1)/(x_3-y_3), (-x_1*y_3+x_3*y_1-x_2+y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2+x_1-y_1)/(x_3-y_3))/(x_3-y_3))*(x_2-y_2)/(((x_1-y_1)^2/(x_3-y_3)^2+(x_2-y_2)^2/(x_3-y_3)^2+1)^(1/2)*((x_1-y_1)^2+(x_2-y_2)^2+(x_3-y_3)^2)*(x_3-y_3)^2)+((x_1-y_1)^2/(x_3-y_3)^2+(x_2-y_2)^2/(x_3-y_3)^2+1)^(1/2)*(-(-(D[1, 1](u))((-x_1*y_3+x_3*y_1+x_2-y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2-x_1+y_1)/(x_3-y_3), (-x_1*y_3+x_3*y_1-x_2+y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2+x_1-y_1)/(x_3-y_3))/(x_3-y_3)+(D[1, 2](u))((-x_1*y_3+x_3*y_1+x_2-y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2-x_1+y_1)/(x_3-y_3), (-x_1*y_3+x_3*y_1-x_2+y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2+x_1-y_1)/(x_3-y_3))*x_3/(x_3-y_3)+(D[1, 3](u))((-x_1*y_3+x_3*y_1+x_2-y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2-x_1+y_1)/(x_3-y_3), (-x_1*y_3+x_3*y_1-x_2+y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2+x_1-y_1)/(x_3-y_3))/(x_3-y_3)+(D[1, 4](u))((-x_1*y_3+x_3*y_1+x_2-y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2-x_1+y_1)/(x_3-y_3), (-x_1*y_3+x_3*y_1-x_2+y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2+x_1-y_1)/(x_3-y_3))*x_3/(x_3-y_3))*y_3/(x_3-y_3)-(-(D[1, 2](u))((-x_1*y_3+x_3*y_1+x_2-y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2-x_1+y_1)/(x_3-y_3), (-x_1*y_3+x_3*y_1-x_2+y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2+x_1-y_1)/(x_3-y_3))/(x_3-y_3)+(D[2, 2](u))((-x_1*y_3+x_3*y_1+x_2-y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2-x_1+y_1)/(x_3-y_3), (-x_1*y_3+x_3*y_1-x_2+y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2+x_1-y_1)/(x_3-y_3))*x_3/(x_3-y_3)+(D[2, 3](u))((-x_1*y_3+x_3*y_1+x_2-y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2-x_1+y_1)/(x_3-y_3), (-x_1*y_3+x_3*y_1-x_2+y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2+x_1-y_1)/(x_3-y_3))/(x_3-y_3)+(D[2, 4](u))((-x_1*y_3+x_3*y_1+x_2-y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2-x_1+y_1)/(x_3-y_3), (-x_1*y_3+x_3*y_1-x_2+y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2+x_1-y_1)/(x_3-y_3))*x_3/(x_3-y_3))/(x_3-y_3)-(-(D[1, 3](u))((-x_1*y_3+x_3*y_1+x_2-y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2-x_1+y_1)/(x_3-y_3), (-x_1*y_3+x_3*y_1-x_2+y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2+x_1-y_1)/(x_3-y_3))/(x_3-y_3)+(D[2, 3](u))((-x_1*y_3+x_3*y_1+x_2-y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2-x_1+y_1)/(x_3-y_3), (-x_1*y_3+x_3*y_1-x_2+y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2+x_1-y_1)/(x_3-y_3))*x_3/(x_3-y_3)+(D[3, 3](u))((-x_1*y_3+x_3*y_1+x_2-y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2-x_1+y_1)/(x_3-y_3), (-x_1*y_3+x_3*y_1-x_2+y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2+x_1-y_1)/(x_3-y_3))/(x_3-y_3)+(D[3, 4](u))((-x_1*y_3+x_3*y_1+x_2-y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2-x_1+y_1)/(x_3-y_3), (-x_1*y_3+x_3*y_1-x_2+y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2+x_1-y_1)/(x_3-y_3))*x_3/(x_3-y_3))*y_3/(x_3-y_3)+(-(D[1, 4](u))((-x_1*y_3+x_3*y_1+x_2-y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2-x_1+y_1)/(x_3-y_3), (-x_1*y_3+x_3*y_1-x_2+y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2+x_1-y_1)/(x_3-y_3))/(x_3-y_3)+(D[2, 4](u))((-x_1*y_3+x_3*y_1+x_2-y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2-x_1+y_1)/(x_3-y_3), (-x_1*y_3+x_3*y_1-x_2+y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2+x_1-y_1)/(x_3-y_3))*x_3/(x_3-y_3)+(D[3, 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(-x_2*y_3+x_3*y_2+x_1-y_1)/(x_3-y_3))*x_3/(x_3-y_3)+(D[2, 3](u))((-x_1*y_3+x_3*y_1+x_2-y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2-x_1+y_1)/(x_3-y_3), (-x_1*y_3+x_3*y_1-x_2+y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2+x_1-y_1)/(x_3-y_3))/(x_3-y_3)+(D[3, 3](u))((-x_1*y_3+x_3*y_1+x_2-y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2-x_1+y_1)/(x_3-y_3), (-x_1*y_3+x_3*y_1-x_2+y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2+x_1-y_1)/(x_3-y_3))*x_3/(x_3-y_3)-(D[3, 4](u))((-x_1*y_3+x_3*y_1+x_2-y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2-x_1+y_1)/(x_3-y_3), (-x_1*y_3+x_3*y_1-x_2+y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2+x_1-y_1)/(x_3-y_3))/(x_3-y_3))/(x_3-y_3)-((D[1, 4](u))((-x_1*y_3+x_3*y_1+x_2-y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2-x_1+y_1)/(x_3-y_3), (-x_1*y_3+x_3*y_1-x_2+y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2+x_1-y_1)/(x_3-y_3))*x_3/(x_3-y_3)+(D[2, 4](u))((-x_1*y_3+x_3*y_1+x_2-y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2-x_1+y_1)/(x_3-y_3), (-x_1*y_3+x_3*y_1-x_2+y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2+x_1-y_1)/(x_3-y_3))/(x_3-y_3)+(D[3, 4](u))((-x_1*y_3+x_3*y_1+x_2-y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2-x_1+y_1)/(x_3-y_3), (-x_1*y_3+x_3*y_1-x_2+y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2+x_1-y_1)/(x_3-y_3))*x_3/(x_3-y_3)-(D[4, 4](u))((-x_1*y_3+x_3*y_1+x_2-y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2-x_1+y_1)/(x_3-y_3), (-x_1*y_3+x_3*y_1-x_2+y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2+x_1-y_1)/(x_3-y_3))/(x_3-y_3))*y_3/(x_3-y_3))/((x_1-y_1)^2+(x_2-y_2)^2+(x_3-y_3)^2)-((x_1-y_1)^2/(x_3-y_3)^2+(x_2-y_2)^2/(x_3-y_3)^2+1)^(1/2)*((D[1](u))((-x_1*y_3+x_3*y_1+x_2-y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2-x_1+y_1)/(x_3-y_3), (-x_1*y_3+x_3*y_1-x_2+y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2+x_1-y_1)/(x_3-y_3))/(x_3-y_3)-(D[2](u))((-x_1*y_3+x_3*y_1+x_2-y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2-x_1+y_1)/(x_3-y_3), (-x_1*y_3+x_3*y_1-x_2+y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2+x_1-y_1)/(x_3-y_3))*y_3/(x_3-y_3)-(D[3](u))((-x_1*y_3+x_3*y_1+x_2-y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2-x_1+y_1)/(x_3-y_3), (-x_1*y_3+x_3*y_1-x_2+y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2+x_1-y_1)/(x_3-y_3))/(x_3-y_3)-(D[4](u))((-x_1*y_3+x_3*y_1+x_2-y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2-x_1+y_1)/(x_3-y_3), (-x_1*y_3+x_3*y_1-x_2+y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2+x_1-y_1)/(x_3-y_3))*y_3/(x_3-y_3))*(-2*x_1+2*y_1)/((x_1-y_1)^2+(x_2-y_2)^2+(x_3-y_3)^2)^2+u((-x_1*y_3+x_3*y_1+x_2-y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2-x_1+y_1)/(x_3-y_3), (-x_1*y_3+x_3*y_1-x_2+y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2+x_1-y_1)/(x_3-y_3))*(2*x_2-2*y_2)*(x_1-y_1)/(((x_1-y_1)^2/(x_3-y_3)^2+(x_2-y_2)^2/(x_3-y_3)^2+1)^(1/2)*((x_1-y_1)^2+(x_2-y_2)^2+(x_3-y_3)^2)^2*(x_3-y_3)^2)-((x_1-y_1)^2/(x_3-y_3)^2+(x_2-y_2)^2/(x_3-y_3)^2+1)^(1/2)*((D[1](u))((-x_1*y_3+x_3*y_1+x_2-y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2-x_1+y_1)/(x_3-y_3), (-x_1*y_3+x_3*y_1-x_2+y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2+x_1-y_1)/(x_3-y_3))*x_3/(x_3-y_3)+(D[2](u))((-x_1*y_3+x_3*y_1+x_2-y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2-x_1+y_1)/(x_3-y_3), (-x_1*y_3+x_3*y_1-x_2+y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2+x_1-y_1)/(x_3-y_3))/(x_3-y_3)+(D[3](u))((-x_1*y_3+x_3*y_1+x_2-y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2-x_1+y_1)/(x_3-y_3), (-x_1*y_3+x_3*y_1-x_2+y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2+x_1-y_1)/(x_3-y_3))*x_3/(x_3-y_3)-(D[4](u))((-x_1*y_3+x_3*y_1+x_2-y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2-x_1+y_1)/(x_3-y_3), (-x_1*y_3+x_3*y_1-x_2+y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2+x_1-y_1)/(x_3-y_3))/(x_3-y_3))*(2*x_2-2*y_2)/((x_1-y_1)^2+(x_2-y_2)^2+(x_3-y_3)^2)^2+2*((x_1-y_1)^2/(x_3-y_3)^2+(x_2-y_2)^2/(x_3-y_3)^2+1)^(1/2)*u((-x_1*y_3+x_3*y_1+x_2-y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2-x_1+y_1)/(x_3-y_3), (-x_1*y_3+x_3*y_1-x_2+y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2+x_1-y_1)/(x_3-y_3))*(2*x_2-2*y_2)*(-2*x_1+2*y_1)/((x_1-y_1)^2+(x_2-y_2)^2+(x_3-y_3)^2)^3

 

false

(1)

``

``

 

Download ultrhyperbolic_pde.mw

v := (((x_1-y_1)/(x_3-y_3))^2+((x_2-y_2)/(x_3-y_3))^2+1)^(1/2)*u((-x_1*y_3+x_3*y_1+x_2-y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2-x_1+y_1)/(x_3-y_3), (-x_1*y_3+x_3*y_1-x_2+y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2+x_1-y_1)/(x_3-y_3)); 1; diff(diff(v/((x_1-y_1)^2+(x_2-y_2)^2+(x_3-y_3)^2), x_1), y_2); 1; diff(diff(v/((x_1-y_1)^2+(x_2-y_2)^2+(x_3-y_3)^2), x_2), y_1); 1; evalb(diff(diff(v/((x_1-y_1)^2+(x_2-y_2)^2+(x_3-y_3)^2), x_1), y_2) = diff(diff(v/((x_1-y_1)^2+(x_2-y_2)^2+(x_3-y_3)^2), x_2), y_1))

((x_1-y_1)^2/(x_3-y_3)^2+(x_2-y_2)^2/(x_3-y_3)^2+1)^(1/2)*u((-x_1*y_3+x_3*y_1+x_2-y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2-x_1+y_1)/(x_3-y_3), (-x_1*y_3+x_3*y_1-x_2+y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2+x_1-y_1)/(x_3-y_3))

 

u((-x_1*y_3+x_3*y_1+x_2-y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2-x_1+y_1)/(x_3-y_3), (-x_1*y_3+x_3*y_1-x_2+y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2+x_1-y_1)/(x_3-y_3))*(x_1-y_1)*(x_2-y_2)/(((x_1-y_1)^2/(x_3-y_3)^2+(x_2-y_2)^2/(x_3-y_3)^2+1)^(3/2)*((x_1-y_1)^2+(x_2-y_2)^2+(x_3-y_3)^2)*(x_3-y_3)^4)+(-(D[1](u))((-x_1*y_3+x_3*y_1+x_2-y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2-x_1+y_1)/(x_3-y_3), (-x_1*y_3+x_3*y_1-x_2+y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2+x_1-y_1)/(x_3-y_3))/(x_3-y_3)+(D[2](u))((-x_1*y_3+x_3*y_1+x_2-y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2-x_1+y_1)/(x_3-y_3), (-x_1*y_3+x_3*y_1-x_2+y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2+x_1-y_1)/(x_3-y_3))*x_3/(x_3-y_3)+(D[3](u))((-x_1*y_3+x_3*y_1+x_2-y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2-x_1+y_1)/(x_3-y_3), (-x_1*y_3+x_3*y_1-x_2+y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2+x_1-y_1)/(x_3-y_3))/(x_3-y_3)+(D[4](u))((-x_1*y_3+x_3*y_1+x_2-y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2-x_1+y_1)/(x_3-y_3), (-x_1*y_3+x_3*y_1-x_2+y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2+x_1-y_1)/(x_3-y_3))*x_3/(x_3-y_3))*(x_1-y_1)/(((x_1-y_1)^2/(x_3-y_3)^2+(x_2-y_2)^2/(x_3-y_3)^2+1)^(1/2)*((x_1-y_1)^2+(x_2-y_2)^2+(x_3-y_3)^2)*(x_3-y_3)^2)-u((-x_1*y_3+x_3*y_1+x_2-y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2-x_1+y_1)/(x_3-y_3), (-x_1*y_3+x_3*y_1-x_2+y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2+x_1-y_1)/(x_3-y_3))*(x_1-y_1)*(-2*x_2+2*y_2)/(((x_1-y_1)^2/(x_3-y_3)^2+(x_2-y_2)^2/(x_3-y_3)^2+1)^(1/2)*((x_1-y_1)^2+(x_2-y_2)^2+(x_3-y_3)^2)^2*(x_3-y_3)^2)-(-(D[1](u))((-x_1*y_3+x_3*y_1+x_2-y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2-x_1+y_1)/(x_3-y_3), (-x_1*y_3+x_3*y_1-x_2+y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2+x_1-y_1)/(x_3-y_3))*y_3/(x_3-y_3)-(D[2](u))((-x_1*y_3+x_3*y_1+x_2-y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2-x_1+y_1)/(x_3-y_3), (-x_1*y_3+x_3*y_1-x_2+y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2+x_1-y_1)/(x_3-y_3))/(x_3-y_3)-(D[3](u))((-x_1*y_3+x_3*y_1+x_2-y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2-x_1+y_1)/(x_3-y_3), (-x_1*y_3+x_3*y_1-x_2+y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2+x_1-y_1)/(x_3-y_3))*y_3/(x_3-y_3)+(D[4](u))((-x_1*y_3+x_3*y_1+x_2-y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2-x_1+y_1)/(x_3-y_3), (-x_1*y_3+x_3*y_1-x_2+y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2+x_1-y_1)/(x_3-y_3))/(x_3-y_3))*(x_2-y_2)/(((x_1-y_1)^2/(x_3-y_3)^2+(x_2-y_2)^2/(x_3-y_3)^2+1)^(1/2)*((x_1-y_1)^2+(x_2-y_2)^2+(x_3-y_3)^2)*(x_3-y_3)^2)+((x_1-y_1)^2/(x_3-y_3)^2+(x_2-y_2)^2/(x_3-y_3)^2+1)^(1/2)*(-(-(D[1, 1](u))((-x_1*y_3+x_3*y_1+x_2-y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2-x_1+y_1)/(x_3-y_3), (-x_1*y_3+x_3*y_1-x_2+y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2+x_1-y_1)/(x_3-y_3))/(x_3-y_3)+(D[1, 2](u))((-x_1*y_3+x_3*y_1+x_2-y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2-x_1+y_1)/(x_3-y_3), (-x_1*y_3+x_3*y_1-x_2+y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2+x_1-y_1)/(x_3-y_3))*x_3/(x_3-y_3)+(D[1, 3](u))((-x_1*y_3+x_3*y_1+x_2-y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2-x_1+y_1)/(x_3-y_3), (-x_1*y_3+x_3*y_1-x_2+y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2+x_1-y_1)/(x_3-y_3))/(x_3-y_3)+(D[1, 4](u))((-x_1*y_3+x_3*y_1+x_2-y_2)/(x_3-y_3), 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(-x_2*y_3+x_3*y_2+x_1-y_1)/(x_3-y_3))/(x_3-y_3)+(D[2, 3](u))((-x_1*y_3+x_3*y_1+x_2-y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2-x_1+y_1)/(x_3-y_3), (-x_1*y_3+x_3*y_1-x_2+y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2+x_1-y_1)/(x_3-y_3))*x_3/(x_3-y_3)+(D[3, 3](u))((-x_1*y_3+x_3*y_1+x_2-y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2-x_1+y_1)/(x_3-y_3), (-x_1*y_3+x_3*y_1-x_2+y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2+x_1-y_1)/(x_3-y_3))/(x_3-y_3)+(D[3, 4](u))((-x_1*y_3+x_3*y_1+x_2-y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2-x_1+y_1)/(x_3-y_3), (-x_1*y_3+x_3*y_1-x_2+y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2+x_1-y_1)/(x_3-y_3))*x_3/(x_3-y_3))*y_3/(x_3-y_3)+(-(D[1, 4](u))((-x_1*y_3+x_3*y_1+x_2-y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2-x_1+y_1)/(x_3-y_3), (-x_1*y_3+x_3*y_1-x_2+y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2+x_1-y_1)/(x_3-y_3))/(x_3-y_3)+(D[2, 4](u))((-x_1*y_3+x_3*y_1+x_2-y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2-x_1+y_1)/(x_3-y_3), (-x_1*y_3+x_3*y_1-x_2+y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2+x_1-y_1)/(x_3-y_3))*x_3/(x_3-y_3)+(D[3, 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(-x_2*y_3+x_3*y_2-x_1+y_1)/(x_3-y_3), (-x_1*y_3+x_3*y_1-x_2+y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2+x_1-y_1)/(x_3-y_3))*y_3/(x_3-y_3))*(-2*x_1+2*y_1)/((x_1-y_1)^2+(x_2-y_2)^2+(x_3-y_3)^2)^2+u((-x_1*y_3+x_3*y_1+x_2-y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2-x_1+y_1)/(x_3-y_3), (-x_1*y_3+x_3*y_1-x_2+y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2+x_1-y_1)/(x_3-y_3))*(2*x_2-2*y_2)*(x_1-y_1)/(((x_1-y_1)^2/(x_3-y_3)^2+(x_2-y_2)^2/(x_3-y_3)^2+1)^(1/2)*((x_1-y_1)^2+(x_2-y_2)^2+(x_3-y_3)^2)^2*(x_3-y_3)^2)-((x_1-y_1)^2/(x_3-y_3)^2+(x_2-y_2)^2/(x_3-y_3)^2+1)^(1/2)*((D[1](u))((-x_1*y_3+x_3*y_1+x_2-y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2-x_1+y_1)/(x_3-y_3), (-x_1*y_3+x_3*y_1-x_2+y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2+x_1-y_1)/(x_3-y_3))*x_3/(x_3-y_3)+(D[2](u))((-x_1*y_3+x_3*y_1+x_2-y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2-x_1+y_1)/(x_3-y_3), (-x_1*y_3+x_3*y_1-x_2+y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2+x_1-y_1)/(x_3-y_3))/(x_3-y_3)+(D[3](u))((-x_1*y_3+x_3*y_1+x_2-y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2-x_1+y_1)/(x_3-y_3), (-x_1*y_3+x_3*y_1-x_2+y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2+x_1-y_1)/(x_3-y_3))*x_3/(x_3-y_3)-(D[4](u))((-x_1*y_3+x_3*y_1+x_2-y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2-x_1+y_1)/(x_3-y_3), (-x_1*y_3+x_3*y_1-x_2+y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2+x_1-y_1)/(x_3-y_3))/(x_3-y_3))*(2*x_2-2*y_2)/((x_1-y_1)^2+(x_2-y_2)^2+(x_3-y_3)^2)^2+2*((x_1-y_1)^2/(x_3-y_3)^2+(x_2-y_2)^2/(x_3-y_3)^2+1)^(1/2)*u((-x_1*y_3+x_3*y_1+x_2-y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2-x_1+y_1)/(x_3-y_3), (-x_1*y_3+x_3*y_1-x_2+y_2)/(x_3-y_3), (-x_2*y_3+x_3*y_2+x_1-y_1)/(x_3-y_3))*(2*x_2-2*y_2)*(-2*x_1+2*y_1)/((x_1-y_1)^2+(x_2-y_2)^2+(x_3-y_3)^2)^3

 

false

(1)

``

``

 

Download ultrhyperbolic_pde.mw

As part of a project, I am numerically estimating the roots of many large polynomials. Occasionally, "fsolve" fails with strange errors related to "fsolve/refine2". Searches for these error messages have turned up nothing.

I've inluded the code below that causes the error on Maple 18.02. I apologize for the polynomial in question being so long, it's the shortest example I have. The error it generates is:

    Error, (in fsolve/refine2) invalid input: evalf expects its 2nd argument, n, to be of type posint, but received undefined

Is this a bug? Or am I missing some fsolve option to prevent this? Note that it only happens when the "complex" flag is used.

=========

P := 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fsolve(P,complex);

I would like to get some sort of table (maybe also a plot) that shows me the effect on the function if I change a variable.

For example, I have f(x,y,z)=x+yz

Now I would like to get a list with the results for f if I run z from, say, -10 to +10.

Is it also possible to do this with all variables at the same time?

Hi,

I am trying to solve a set of ode which depends on some parameters like A0,0,  A1,0, A1,1, B0,0,  B1,0, B1,1, C0,0 and so on. Here is some part of my code:

 

restart;

sigma := 1; X := proc (m) if m <= 1 then 0 elif 2 <= m then 1 end if end proc;

lambda := proc (m, k) if k <= m and 0 <= k then 1 else 0 end if end proc;

Typesetting:-Settings(functionassign = false);

for m from 0  to 4 do    

for k  from 4 by -1 to 0 do  

A[m,k](r) :=diff(f[m,k](r),r$2)+((k+1)*(k+2))/(r^(2))*(lambda(m,k+2)*f[m,k+2](r)-f[m,k](r)):  

T[m,k]:=(k+1)*(lambda(m,k+1)*A[m,k+1](r) -lambda(m,k-1)*A[m,k-1](r)):      

S[m,k]:=(k+1)*(lambda(m,k+1)*f[m,k+1]( r)-lambda(m,k-1)*f[m,k-1](r)):               # There are also C[m,k], B[m,k] and E[m,k] definitions similar to A[m,k],T[m,k] and S[m,k]

Q[m, k] := r^(4-sigma)*E[m, k]-2*lambda(m, k+2)*(k+1)*(k+2)*(r^2*(diff(f[m, k+2](r), `$`(r, 2)))-2*r*(diff(f[m, k+2](r), r)))-(k+1)*(k+2)*(k+4)*((k+3)*lambda(m, k+4)*f[m, k+4](r)-(2*(k+1))*lambda(m, k+2)*f[m, k+2](r));

ode[m, k] := r^4*(diff(f[m, k](r), `$`(r, 4)))-(k+1)*(k+2)*(2*r^2*(diff(f[m, k](r), `$`(r, 2)))-4*r*(diff(f[m, k](r), r))-(k-1)*(k+4)*f[m, k](r)) = Q[m, k];

soln[m, k] := rhs(dsolve(ode[m, k], f[m, k](r)))

 

After obtaining the solution, there are some additional parts in my code to find the coefficients of odes. The code is just working fine until m=3. When m=3, I am getting this error:

Error, (in solve) cannot solve expressions with Int(-(1/282240)*r*(3*(h . R)^2*(Int((6720*ln(r)*h*r^6-22176*ln(r)*h*r^5-50400*ln(r)*r^6-2814*h*r^6+33600*r^7+18144*ln(r)*h*r^4+90720*ln(r)*r^5+8238*h*r^5-95520*r^6+2352*h*ln(r)*r^3-7974*h*r^4+57780*r^5-2880*ln(r)*h*r^2-14400*ln(r)*r^3-2443*h*r^3+2100*r^4+6108*h*r^2+5340*r^3-1115*h-3300*r)/r^6, r))-4480*_C1), r) for _C1

I think the problem is due to declaration of f[m,k](r) values for the set of odes. For example, before solving ode[3,3], the code declares a value for f[3,3](r) which includes some integral definition in ode[3,3] although i want to find the solution for f[3,3](r). 

To illustrate,

ode[1,1]=r^4*(diff(f[1, 1](r), r, r, r, r))-12*r^2*(diff(f[1, 1](r), r, r))+24*r*(diff(f[1, 1](r), r)) = -Typesetting[delayDotProduct](r, h . R, true)*((2*(diff(f[0, 0](r), r))-4*f[0, 0](r)/r)*(diff(f[0, 0](r), r, r)-2*f[0, 0](r)/r^2)-(2*(-3/4-1/(4*r^2)+r))*A[0, 0]+(2*(diff(f[0, 0](r), r, r, r)+4*f[0, 0](r)/r^3-2*(diff(f[0, 0](r), r))/r^2))*f[0, 0](r))

soln[m, k] := rhs(dsolve(ode[m, k], f[m, k](r)))

 

where I already know the definition of f[0,0](r)=-(3/4)*r+1/(4*r)+(1/2)*r^2   and A[0,0]=1/(2*r^3)+1+(2*((3/4)*r-1/(4*r)-(1/2)*r^2))/r^2 

So, ode[1,1] can be solved with respect to f[1,1](r).

I would be glad for any comments. 

Here is my code.

 test.mw

Int(exp(t), t= 0 ..x) +1 is just a way to write exp(x), use value(%).

ff:= x -> evalf(Int(exp(t), t= 0 .. x, method = _d01ajc) + 1) does
the same, but in a numerical way.

Now consider that as a differential equation, to be solved numerically:

de:=D(f)(x) = f(x);
dsolve({%, f(0)=1});
                         f(x) = exp(x)


ff:= x -> evalf(Int(exp(t), t= 0 .. x, method = _d01ajc) + 1);

D(f)(x) = ff(x);
sol:=dsolve({%, f(0)=1}, numeric);

  Warning, The use of global variables in numerical ODE problems is deprecated,
  and will be removed in a future release. Use the 'parameters' argument instead
  (see ?dsolve,numeric,parameters)

sol(1);

  Error, (in sol) parameter 't' must be assigned a numeric value before
  obtaining a solution

Question: how to write it down correctly?

I have been here before...  My head is full of cotton, as usual.

 

f := proc (t) 2*t^3+9*t^2-60*t+1 end proc;
deq:=diff(f(t),t);
df := t->deq;  ## this is most likely one of my problems.
plot(df(t),t=-10..10);
isneg := x -> if is(df(x) < 0) then df(x) else 0 end if;  ## and, another??
plot(isneg(t),t=-10..10);
Plt1:=plot(isneg(t),t=-10..10);
plots:-display(Plt1);
isneg(0.12017234);

The if statement is not fully evauated.

I am missing something.  What?

Tom Dean

Hi dear friends

How do I improve my ability to manipulate code?

Thanks

_________________________________________________________________________________________

 

restart:

Digits := 30: m := 20: p0 := 8.: g := -0.3: nu := 0.3: a := 1:


w := sum(b[n]*r^(1.02*n), n = 1 .. m):


ODE := r^3*(g*r+a)^3*(diff(w, r, r, r, r))+2*(diff(w, r, r, r))*r^2*(4*g*r+a)*(g*r+a)^2+(diff(w, r, r))*r*(3*g^3*nu*r^3+P*a^3*r^2+6*a*g^2*nu*r^2+11*g^3*r^3+3*a^2*g*nu*r+15*a*g^2*r^2+3*a^2*g*r-a^3)+(diff(w, r))*(6*g^3*nu*r^3+P*a^3*r^2+6*a*g^2*nu*r^2-2*g^3*r^3-3*a*g^2*r^2+a^3):


for P from p0 by 0.1e-1 to p0+1 do
W := simplify(subs(solve({seq(evalf(subs(r = j/(m+2), ODE)), j = 2 .. m-1), subs(r = 1, diff(w, r))}, {seq(b[j], j = 1 .. m)}), w/b[m])):
F := (int(((diff(W, `$`(r, 2))+(diff(W, r))/r)^2-(2*(1-nu))*(diff(W, `$`(r, 2)))*(diff(W, r))/r)*r*(1+g*r/a)^3, r = 0 .. a))/(int((diff(W, r))^2*r, r = 0 .. a)):
delta[trunc(100*(P-p0))] := abs(F-P) end do:


plot(W, r = 0 .. a);


Min := min(seq(delta[j], j = 0 .. 100)):


for j from 0 to 100 do if delta[j] = Min then print(p0+j/(100.)) else  end if end do;

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