## Lagrangian density...

Dear friends Is there any way (or any package,...) that can be used to find the density of the Lagrangian of a PDE. For example the nonlinear Schrodinger (NLS) equation has the form I*Diff(u,t)+1/2*Diff(u,x\$2)-abs(u)^2*u=0. This PDE may be considered as the Euler equation which follows from the Lagrangian with density L , L=I/2*(conjugate(u)*Diff(u,t)-u*diff(conjugate(u),t))-1/2*abs(u)^2-1/2*abs(u)^4. Now, could anybody please let me know about any way to find L from NLS? many thanks sayed

## Linear Programming...

Can anyone tell me how to input the following problem in maple?
Find the maximum value of C=3x+2y on the region determined by the constraints {3x+2y<=18, 0<=x and <=4, 0<=y<=5}

Any help will be greately appreciated. Thanks in advance<code>.

## how to solve this equation?...

this is the differential equation of second derivative. because i learn Maple not long. the equation name is 'eq5' > eq5:=D(D(x1))=(a1*fx1+a2*gx1)*D(x1)+(a1*fx2+a2*gx2)*D(x2)+(a1*fxt+a2*gxt); x1(t),in the file. if you interesting ,just download the file to help me to solve this problem. regards. View 1984_diff equ.mw on MapleNet or Download 1984_diff equ.mw
View file

## How to calculate symbolic formulas including matri...

I know the power of Maple for exact symbolic and numeric computing. With Maple, we can calculate symbolic formulas expressed with scalar values such as x, y, z, and so on. For example, ``` >> solve(x+z+1=0,x); x=-z-1 ``` However, I want to calculate formulas including matrices algebraically, too. I’ll show an example of my ideal result; ``` >> solve(A*x=b,x); x=A^-1*b or x=(A^T*A)^-1*A^T*b ``` In the example above, I assume A is a matrix, and x, b are vectors. “A^-1” means the inverse of the matrix A and “A^T” means the transpose of the matrix A. I want to keep “A” as a matrix and get a result like the equation which is often written in well-known textbooks of linear algebra.

## counting rotaions...

is there a way to count the full rotations of a curve around the axis (for example a spiral) any hints in the right direction would be appreciated. thank you

## Problem with document mode...

In document mode: 1) when i start a row with (math mode): 1+2 then press ctrl+= (and Maple intert the result 3) i can't continue writing on the same row 2) when i start a row with (math mode): 1/a then press ctrl+= (and Maple intert the result 1/a) i can continue writing on the same row why? Maple 10 last patch Thank you

## plotting dirac delta with maple...

Hello I´m trying to plot the fowllowing function using maple without success: f:=t->sum(Dirac(t-k*pi),k=1..20); it seems to be syntax right. Then when I try to plot it using plot (f(t),t=-10..10); I do get an error message: Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct Error, empty plot What is happening?

## Matrix Element Summation...

Here is my Problem. Im trying to do some calculations with matrices included. Suppose I have a Matrix A and one B. I wanna create a new Matrix call it C (diagonal) like this. c_ii = sum(a_ik^2 * b_kk, k = 1 .. n) I get an errormessage sayin: "Error, bad index into Matrix" How can i force Maple to evaluate the Matrixentries first before trying to sum them up. At least I think thats the problem. I tried to pack them into a function like (i,j) -> A[i,j] which didn't work either. Thanks for your help Michael

## Plotting Multi-Valued Functions in Maple 9...

Hello, I am trying to plot one value of a multi valued function in Maple 9. I am using the code below to try to plot I1 vs. Vin but it doesn't work. Suggestions appreciated. Thanks! -Joel > restart: > Digits := 16: > with(plots): > Is := 10^(-14): > Vt := 0.026: > M := 10: > Rl := 10e3: > R1 := 600: > R2 := 3e3: > soln := (Vin)-> 'fsolve({0 = -I1 + Is*exp((Vin - (I1*R1 + (I1 + I2)*R2))/Vt), 0 = -I2 + Is*exp((Vin - (I1 + I2)*R2)/Vt)}, {I1, I2})': > plot(rhs(soln(Vin)[1]), Vin = 1..2);

## What is wrong with this code?!...

I've read it again... and again... and again. It's a very simple calculator program, why is this not working? > with(Maplets[Elements]): > MapleCalculator:=Maplet > [ > ["Field 1", TextField['TF1'](10)] > , > ["Field 2", TextField['TF2'](10)] > , > [Button ("Calculate", Evaluate('TF3' =('TF1' + 'TF2'))] > , > ["Value: ", "TextField['TF3'](10)] > ]: > Maplets[Display](MapleCalculator); Error, `]` unexpected

## Whattype

Maple
Recently, working on Nested Verification, I took a look at the ` whattype` procedure. First, I couldn't find any use of local variables ` t1, t2, L, k1, k2` declared in it. That seems odd. Second, the order of types in it seems to be not exactly right. In particular, ` symbol` is located earlier than ` `module``. Also, some types are missing, ` record` for example. That leads to not recognizing modules and records,
```r := Record( 'a', 'b' ):
m := module() end:
whattype(r);
symbol
whattype(m);
symbol```
Similarly to the compact and efficient version of Nested Verification, I wrote a "compact and efficient" version of ` whattype`,

## Help with algorithm......

This is my first post here... My algorithm is about the 3x+1 problem. I want to test if some types of numbers have a stoping time. Until now i managed to do it by just testing one type of number each time... So i would like to automate the proccess... Here is an example: > k := 16 n + 3 > while modp(k, 2) = 0 or modp(k, 2) = 1 do if modp(k, 2) = 1 then k:= (3n+1)/2 elif modp(k,2)=0 then k:=k/2 end do k Well this example will produce k= 9n+2, which is smaller than the original 16n+3 so I know that numbers of the form 16n+3 have a finite stoping time...So it passes my test. If for example i start with k:=16n+7 i will get k=27n+3 which is bigger than 16n+7 so i do not know if this number has a stoping time... so it ''fails'' my test. I hope this is clear to you.

## Use interpolation to find missing data in my table...

I have a table of data that displays salaries for different jobs and how they have changed over the years. I figure that interpolation would be the best way to fill in the blanks, but im not sure of the correct syntax to accomplish this in maple, I tried using splines but i just couldnt find a suitable example in the help documentation. ``` YEAR| 1975| 1980| 1985| 1990| 1995 ---------------------------------- job1| 7843|11314| ??? |17820|21431 ---------------------------------- job2| 8388|12409| ??? |20694|28362 ---------------------------------- job3|12332|18075| ??? |31112|36980 ```