Maple 18 Questions and Posts

These are Posts and Questions associated with the product, Maple 18

I am trying to solve system linear partial differential equations using command "pdsolve". I am surprised to see that the solution given by this command is not satisfying the system, instead, an additional constraint is obtained for an arbitrary function, is there something about "pdsolve" I am missing? 


 

with(PDEtools):

DepVars := [f(x, y, t, u)]

[f(x, y, t, u)]

(1)

Sys := {diff(f(x, y, t, u), u, t)-(diff(f(x, y, t, u), x, y)) = 0, diff(f(x, y, t, u), u, u) = 0, diff(f(x, y, t, u), u, y) = 0, diff(f(x, y, t, u), x, u) = 0, diff(f(x, y, t, u), x, x) = 0, diff(f(x, y, t, u), y, y, y) = 0}

{diff(diff(f(x, y, t, u), t), u)-(diff(diff(f(x, y, t, u), x), y)) = 0, diff(diff(diff(f(x, y, t, u), y), y), y) = 0, diff(diff(f(x, y, t, u), u), u) = 0, diff(diff(f(x, y, t, u), u), x) = 0, diff(diff(f(x, y, t, u), u), y) = 0, diff(diff(f(x, y, t, u), x), x) = 0}

(2)

pdsolve(Sys)

{f(x, y, t, u) = (_F3(t)*y+_F4(t))*x+(_F3(t)+_C1)*u+(1/2)*_F7(t)*y^2+_F8(t)*y+_F9(t)}

(3)

f := proc (x, y, t, u) options operator, arrow; (_F3(t)*y+_F4(t))*x+(_F3(t)+_C1)*u+(1/2)*_F7(t)*y^2+_F8(t)*y+_F9(t) end proc

proc (x, y, t, u) options operator, arrow; (_F3(t)*y+_F4(t))*x+(_F3(t)+_C1)*u+(1/2)*_F7(t)*y^2+_F8(t)*y+_F9(t) end proc

(4)

Sys

{0 = 0, diff(_F3(t), t)-_F3(t) = 0}

(5)

``


 

Download pdsolve_command.mw

I can not understand why the following statement works perfectly:
with (plots);
P1: = plot (f (x), x = xmin .. xmax, y = ymin .. ymax, color = "green");
P2: = plot (orddir, x = xmin .. xmax, y = ymin .. ymax, color = "blue");

Plots [display] (plottools [line] ([ascf, ymin], [ascf, 10]), color = red;
Plot ([5, y, y = 0 .. 10]);
P3: = implicit plot (x = ascf, x = xmin .. xmax, y = ymin .. ymax, color = red, linestyle = 3, thickness = 2);
P4: = plot (points, x = xmin .. xmax, y = ymin .. ymax, style = point, symbol = circle, symbolsize = 20, color = "black");
P5: = plot (h, x = xmin .. xmax, y = ymin .. ymax, color = "yellow");
Display ({p1, p2, p3, p4, p5}, axes = normal, scaling = unconstrained, title = "Parallel, vertice, focus, direction and axis of symmetry", gridlines = true);

While in the following
Points: = [F, V, A, B];
with (plots):
P1: = plot (f (x), x = xmin .. xmax, y = ymin .. ymax, color = "green");
P2: = plot (yd, x = xmin .. xmax, y = ymin .. ymax, color = "blue");
P3: = implicitplot (x = xv, x = xmin .. xmax, y = ymin .. ymax, color = red, linestyle = 3, thickness = 2);
P4: = plot (points, x = xmin .. xmax, y = ymin .. ymax, style = point, symbol = circle, symbolsize = 20, color = "black");

Do (% Plot0 = display ({p1, p2, p3, p4}, axes = normal, scaling = unconstrained, title = "Parallel, vertices, focus, direction and axis of symmetry", gridlines = true));

P4 does not print anything. In thanking you for the kind attention, I cordially greet you. Carmine Marotta ..

This worksheet is designed to develop engineering exercises with Maple applications. You should know the theory before using these applications. It is designed to solve problems faster. I hope you use something that is fully developed with embedded components.

In Spanish

Vector_Force.mw

Lenin Araujo Castillo

Ambassador Of Maple

 

 

Hello all,

So far I have been unable to find this question anywhere, but I apologize if it is a duplicate. I'm trying to evaluate the integral of sechq(x), where q is a positive integer. Mathematica is able to tell me the result (a hypergeometric function), but for some reason, Maple seems not to be able to compute this integral, it just gives me back the integral. A higher info-level on the 'int' function reveals a line that says 'Risch d.e. has no solution', but I'm not sure if that has anything to do with my problem. Any suggestions or tips on how to get an answer out of Maple would be greatly appreciated!

Hello!

I am working with the Maple 18.02 version. I just want want to perform a basic polynomial expansion using the command "expand" and it does not respond as it should according to what Maple Programming Help says it would. For example:

Maple Programming Help says:

I get:

.

Also, one sees that this isn't even true, as x(x+2) + 1 = x^2 +2x +1, which is not equal to x^2 + 3x +2.

Moreover, maple tells me it is equal..:

What is going on here? I woul like to get the full expanded form (without factors). Also, this is obviously not true, or maybe Maple means something else by x(x+2) +1...

Thank you!

I have a Maple code which generates a matrix, saves it to a .txt file and this is then read in to a C++ program. I have hit a snag with these matrices, in that they are generating absolutely enourmous .txt files. I need to get to a 5000*5000 matrix yet a 200*200 is generating a 100MB file.

The matrix elements contain a lot of algebraic terms which I would like to keep general as these are defined in the C++ code. They also contain hypergeometric functions which in the example below I have left unsimplified (although they are simplified before reaching C++). I have tried various operations/combinations to simplify, but the file sizes still come out very large.

From previous experience expanding the expressions and then simplifying allows Maple to "do more" with it, but it does not seem to work in this instance. I have tried map(options,expr), simplify(expr,options), combine(expr,options), convert (expr,options) etc... The script attached only contains a small example 10*10 matrix on its own without the code which generates it due to the size of the code. What is the best way to simplify these matrices to generate the smallest .txt file?

Large_Matrix.mw

Any help is appreciated.


-Yeti
 

Hello,

To check my arguments in a procedure I need something like

myproc := proc(M :: Matrix(square, rational)

                       , N :: Matrix(shape=triangular[lower, unit], datatype = rational
                       , O :: Matrix(shape = square, dimension = 5

               )

end proc;

How does that work in Maple? What is the correct Syntax? I tried many different things that doesn't fit.

Hi,

I started using Maple recently. The output sometime is not simplified like that in the attached picture. How can I simplify such expressions?

Hello,

I am trying to write a procedure to see, which (di)-graphs are isomorphic (here represented by there 3*3 adjecency-matrices). When I try the procedure for all 3*3-matrices with entries in {0,1} (there are 512 of them), I get the following error:
"Error, (in GraphTheory:-IsIsomorphic) invalid subscript selector"

Can you possibly say, what I am doing wrong? My code is the following:

getIso3 := proc(liste)
  local i,k,M1,c,d:
  c := 0:
  M1 := [[liste[1]]]:
  for i from 2 to numelems(liste) do
    for k from 1 to numelems(M1) do
        if IsIsomorphic(Digraph([a,b,c], liste[i]),Digraph([a,b,c],M1[k][1])) then
          M1[k] := [op(M1[k]), liste[i]]:
          c := 1:
        end if:
    end do:
    if c=0 then
      M1 := [op(M1), [liste[i]]]:
    else
      c := 0:
    end if:   end do: 
  return(M1):
end proc:

 

My input is a list (JJ) of 512 3*3 matrices constructed the following way :

all9Perm := proc(list)
  local P,i,m,n,A:
  P := list:
  for i from 0 to 9 do
    m:= i:  n:= 9-i:
    A := combinat:-permute([1$n, 0$m]):
    P := [op(P), op(1..numelems(A),A)]:
  od:
  return(P):
end proc:
K := []:
L := all9Perm(K):
listoflistsToListofmatrices := proc(liste)
  local M,i:
  M := []:
  for i from 1 to numelems(liste) do
      M := [op(M), Matrix([
          [ liste[i][1] , liste[i][2] , liste[i][3] ],
          [ liste[i][4] , liste[i][5] , liste[i][6] ],
          [ liste[i][7] , liste[i][8] , liste[i][9] ]])
          ]:
  end do:
  return(M):
end proc:
JJ := listoflistsToListofmatrices(L):

 

When I run this procedure on some of the 512 matrices it does work, but it crashes somewhere around matrix 350. I have try so split the list of the 512 matrices, and I am able to run the procedure on these splits, but this is very inconvenient :-)

I hope you can help me. Also if this can be done in an easier way - I am new to programming and recieve help with a smile.

Yours, Tomas.

Hi,

I want to fit a curve to the function that you can see in the picture "maple4.png" (in the appendix) to determine two parameters. This works in Maple 2.
Unfortunately Maple 18 shows me an error. Can you help me with this problem?
 
 
 
 
 
Best regards

 

 

Hi I am getting this message while soliving my first order non-linear initial value problem.

please share me your thoughts

ode := dsolve({diff(y(x), x)-2*(diff(y(x), x))^3 = -2*x+2, y(0) = 1}, type = numeric, range = 0 .. .24);
Error, (in DEtools/convertsys) unable to convert to an explicit first-order system

Abbas

 

Hi everybody

In the attached file, when I run the code an error appears while calculating "omegaL1" parameter. The dimensions of the matrices are correct but the source of error is unknown to me. Can anyone help me?

Thanks in advance

R2_Link_2D.mw 

This must have a simple answer but I have been unable to figure it out after many attempts. 

I am trying to create a Clifford algebra, and then use the results in the multiplication table "MT". The multiplication table elements are correct as displayed, but I don't know how to access the results in the table (i.e. the products of the basis elements).  For example, trying to access the table results as matrix elements like MT[2,3] doesn't work, presumably because it is not a matrix. In other words, I need a matrix that contains the same information as the multiplication table.

DGsetup([x, y, z], M);
I12 := Matrix([[-1, 0, 0], [0, -1, 0], [0, 0, -1]]);
AD3b := AlgebraLibraryData("Clifford(3)", Cl3Q, quadraticform = I12);
DGsetup(AD3b, '[e0, e1, e2, e3, e12, e13, e23, e123]', '[omega]');
MT := MultiplicationTable(Cl3Q, "AlgebraTable");

 

Hi everyone, i am using Maple 18 and i have a problem in converting a equation to a nice polynomial form (a cubic equation with a form of A*x^3+B*x^2+C*x+D), can anyone please help me on the command? Thanks in advance.

My equation is "  d := s*x*(E*K*q-K*r+K*sigma[1]+r*x)*(1-x*(E*K*q-K*r+K*sigma[1]+r*x)/(K*sigma[2]*L))/(K*sigma[2])+sigma[1]*x-x*(E*K*q-K*r+K*sigma[1]+r*x)/K  " or for simplicity is

 

Can someone please teach me on the command? Really appreciate the help!

Hello, thanks for read me

I don't know why my code don't work, I'm trying to calculate the magnitude of a complex vector but I get a error in the next image you can view it, 

 

Can someone help me? thank you

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