Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

Могу ли я использовать Клен, чтобы найти конкретные решения, которые выражаются либо в начальных и эллиптических функций для систем обыкновенных дифференциальных уравнений. Например, вы можете получить в Maple решений (sub_Solve01, sub_Solve02) для систем, которые перечислены в файле?
exp01.mw

I have a system of pdes and solved numerically using pdsolve (numeric) command.

The system consists of four first order partial differentia equations.

for example u(x,t), R(x,t)....

what command should I give to the Maple and get the graph of u(x,t) at a specific point x_0?

For example, I need a plot for u(30,t).

Is it possible with the maple plot?

I really appreciate your help.

Thank you for reading this post. :)

 

So this is my minimal working code. Everything works, but I cannot get the arrow size fixed you can see the animation propperly. Adding wid=1/2 gives an error message.

Hi,

Is there a way to export worksheet to pdf format but not in A4 size since some lines are going beyond the page?


restart; with(Physics); with(Tetrads); with(PDETools)

0, "%1 is not a command in the %2 package", Tetrads, Physics

(1)

coords := zetabar, zeta, v, u

zetabar, zeta, v, u

(2)

X = [coords]

X = [zetabar, zeta, v, u]

(3)

ds2 := Physics:-`*`(Physics:-`*`(2, dzeta), dzetabar)+Physics:-`*`(Physics:-`*`(2, du), dv)+Physics:-`*`(Physics:-`*`(2, H(coords)), Physics:-`^`(du+Physics:-`*`(Ybar(coords), dzeta)+Physics:-`*`(Y(coords), dzetabar)-Physics:-`*`(Physics:-`*`(Y(coords), Ybar(coords)), dv), 2))

2*dzeta*dzetabar+2*du*dv+2*H(zetabar, zeta, v, u)*(du+Ybar(zetabar, zeta, v, u)*dzeta+Y(zetabar, zeta, v, u)*dzetabar-Y(zetabar, zeta, v, u)*Ybar(zetabar, zeta, v, u)*dv)^2

(4)

PDEtools:-declare(ds2)

Ybar(zetabar, zeta, v, u)*`will now be displayed as`*Ybar

(5)

vierbien := Matrix([[1, 0, -Ybar(coords), 0], [0, 1, -Y(coords), 0], [Physics:-`*`(H(coords), Y(coords)), Physics:-`*`(H(coords), Ybar(coords)), 1-Physics:-`*`(Physics:-`*`(H(coords), Y(coords)), Ybar(coords)), H(coords)], [Y(coords), Ybar(coords), -Physics:-`*`(Y(coords), Ybar(coords)), 1]])

vierbien := Matrix(4, 4, {(1, 1) = 1, (1, 2) = 0, (1, 3) = -Ybar(zetabar, Zeta, v, u), (1, 4) = 0, (2, 1) = 0, (2, 2) = 1, (2, 3) = -Y(zetabar, Zeta, v, u), (2, 4) = 0, (3, 1) = H(zetabar, Zeta, v, u)*Y(zetabar, Zeta, v, u), (3, 2) = H(zetabar, Zeta, v, u)*Ybar(zetabar, Zeta, v, u), (3, 3) = 1-H(zetabar, Zeta, v, u)*Y(zetabar, Zeta, v, u)*Ybar(zetabar, Zeta, v, u), (3, 4) = H(zetabar, Zeta, v, u), (4, 1) = Y(zetabar, Zeta, v, u), (4, 2) = Ybar(zetabar, Zeta, v, u), (4, 3) = -Y(zetabar, Zeta, v, u)*Ybar(zetabar, Zeta, v, u), (4, 4) = 1})

(6)

``

Physics:-Setup(coordinatesystem = (X = [zetabar, zeta, v, u]), metric = ds2, tetrad = vierbien, mathematicalnotation = true, automaticsimplification = true, signature = "+++-")

RicciT := proc (a, b) options operator, arrow; Physics:-SumOverRepeatedIndices(Ricci[mu, nu]*e_[a, `~mu`]*e_[b, `~nu`]) end proc

proc (a, b) options operator, arrow; Physics:-SumOverRepeatedIndices(Physics:-`*`(Physics:-`*`(Physics:-Ricci[mu, nu], Physics:-Tetrads:-e_[a, `~mu`]), Physics:-Tetrads:-e_[b, `~nu`])) end proc

(7)

SlashD := proc (f, a) options operator, arrow; Physics:-SumOverRepeatedIndices(Physics:-D_[mu](f)*e_[a, `~mu`]) end proc

proc (f, a) options operator, arrow; Physics:-SumOverRepeatedIndices(Physics:-`*`(Physics:-D_[mu](f), Physics:-Tetrads:-e_[a, `~mu`])) end proc

(8)

SlashD(H(X), 4) = H(X)[4]

(diff(H(X), zetabar))*Ybar(X)+(diff(H(X), zeta))*Y(X)+diff(H(X), v)-(diff(H(X), u))*Y(X)*Ybar(X) = H(X)[4]

(9)

Gamma := proc (a, b, c) options operator, arrow; -gamma_[a, b, c] end proc

proc (a, b, c) options operator, arrow; Physics:-`*`(Physics:-Tetrads:-gamma_[a, b, c], -1) end proc

(10)

Gamma(1, 4, 4) = 0

-(diff(Ybar(X), u))*Y(X)*Ybar(X)+Y(X)*(diff(Ybar(X), zeta))+Ybar(X)*(diff(Ybar(X), zetabar))+diff(Ybar(X), v) = 0

(11)

``

Gamma(2, 4, 4) = 0

-(diff(Y(X), u))*Y(X)*Ybar(X)+Y(X)*(diff(Y(X), zeta))+(diff(Y(X), zetabar))*Ybar(X)+diff(Y(X), v) = 0

(12)

``

Gamma(3, 4, 4) = 0

0 = 0

(13)

``

Gamma(4, 4, 4) = 0

0 = 0

(14)

Gamma(4, 1, 1) = 0

-(diff(Ybar(X), zeta))+(diff(Ybar(X), u))*Ybar(X) = 0

(15)

``

Gamma(4, 2, 2) = 0

-(diff(Y(X), zetabar))+(diff(Y(X), u))*Y(X) = 0

(16)

NULL

shearconditions := {-(diff(Y(X), zetabar))+(diff(Y(X), u))*Y(X) = 0, -(diff(Ybar(X), zeta))+(diff(Ybar(X), u))*Ybar(X) = 0, -(diff(Y(X), u))*Y(X)*Ybar(X)+Y(X)*(diff(Y(X), zeta))+(diff(Y(X), zetabar))*Ybar(X)+diff(Y(X), v) = 0, -(diff(Ybar(X), u))*Y(X)*Ybar(X)+Y(X)*(diff(Ybar(X), zeta))+Ybar(X)*(diff(Ybar(X), zetabar))+diff(Ybar(X), v) = 0}

{-(diff(Y(X), zetabar))+(diff(Y(X), u))*Y(X) = 0, -(diff(Ybar(X), zeta))+(diff(Ybar(X), u))*Ybar(X) = 0, -(diff(Y(X), u))*Y(X)*Ybar(X)+Y(X)*(diff(Y(X), zeta))+(diff(Y(X), zetabar))*Ybar(X)+diff(Y(X), v) = 0, -(diff(Ybar(X), u))*Y(X)*Ybar(X)+Y(X)*(diff(Ybar(X), zeta))+Ybar(X)*(diff(Ybar(X), zetabar))+diff(Ybar(X), v) = 0}

(17)

simplify(RicciT(1, 2), shearconditions) = 0

H(X)*(diff(diff(Y(X), zeta), zetabar))*Ybar(X)-H(X)*Ybar(X)*Y(X)*(diff(diff(Ybar(X), u), zetabar))-H(X)*Ybar(X)^2*(diff(diff(Y(X), u), zetabar))-H(X)*Y(X)^2*(diff(diff(Ybar(X), u), zeta))-2*H(X)*Y(X)*Ybar(X)*(diff(diff(Y(X), u), zeta))+H(X)*Y(X)^2*Ybar(X)*(diff(diff(Ybar(X), u), u))-H(X)*Y(X)*(diff(diff(Ybar(X), u), v))+H(X)*Y(X)*Ybar(X)^2*(diff(diff(Y(X), u), u))-H(X)*(diff(diff(Y(X), u), v))*Ybar(X)+H(X)*(diff(Ybar(X), zetabar))^2+(-3*H(X)*Y(X)*(diff(Ybar(X), u))-(diff(H(X), u))*Y(X)*Ybar(X)+(diff(H(X), zeta))*Y(X)+(diff(H(X), zetabar))*Ybar(X)+diff(H(X), v))*(diff(Ybar(X), zetabar))+H(X)*(diff(Y(X), zeta))^2+(-4*H(X)*(diff(Y(X), u))*Ybar(X)-(diff(H(X), u))*Y(X)*Ybar(X)+(diff(H(X), zeta))*Y(X)+(diff(H(X), zetabar))*Ybar(X)+diff(H(X), v))*(diff(Y(X), zeta))+2*H(X)*Y(X)^2*(diff(Ybar(X), u))^2-Y(X)*((diff(H(X), zetabar))*Ybar(X)+(diff(H(X), zeta))*Y(X)+diff(H(X), v)-(diff(H(X), u))*Y(X)*Ybar(X))*(diff(Ybar(X), u))+2*(H(X)*(diff(Y(X), u))*Ybar(X)+(1/2)*(diff(H(X), u))*Y(X)*Ybar(X)-(1/2)*(diff(H(X), zeta))*Y(X)-(1/2)*(diff(H(X), zetabar))*Ybar(X)-(1/2)*(diff(H(X), v)))*(diff(Y(X), u))*Ybar(X) = 0

(18)

0 = 0

0 = 0

(19)

The values in the paraenthesis  should substitute H[4]. This sequence works in Maple 18 but not in Maple 2015

 

NULL


Download Question_algsubs_3.27.15.mw

Write a Maple code that performs the Gaussian elimination for an nxn matrix, converting it to an upper triangular matrix. 

(Hint: you will need to use three for .. do loops.)

Hi

I'm trying to use the command: DocumentTools[Retrieve](path,label), but i recieve the message "unable to retrieve label reference" no mather what i do. When i use the GUI: Insert - reference and get the value it works fine, but in that way I can't assign the value to a variable in the document.

here is an example:

The document i want to retrieve a value from:

restart;

a := 5;

#a gets the label (1)

 

The document i want to retrieve the value to:

restart;
with(DocumentTools);

path := FileTools:-JoinPath(["test.mw"], base = worksheetdir); = "C:\Users\Nicolai\CloudStation\Nicolai\Skole stof\Sem 7\test.mw"

 

Retrieve(path, "());
Retrieve(path, "(1)");
Retrieve(path, "a");

#None of the above works

 

Is it even possible to do such thing?

with best regards

Nicolai

Hi,

I tried to use the Finance package and got:

with(Finance):
Warning, some commands in the Finance package may not work on this platform
Y := ItoProcess(1.0, mu, sigma, x, t);

Error, (in Finance:-ItoProcess) external linking: error loading external library finance.dll: The specified module could not be found.

 

Is it me or my pc that is causing this?

Thank you.

Murray

I want to translate my maple code with matrice multiplication  to C code. But the command  "Multiply" cannot be translated. So I want to edit the function translation by myself. I use "AddFunction" command to create a new function  "Multiply" and want to specify its corresponding C code.

 


f := proc ()
local x,y;
x := Matrix([[1, 2], [3, 4]]);
y := Matrix([[1,3],[4,2]]);
Multiply(x, y);
NULL;
end proc;

LanguageDefinition:-Define("NewC", extend = "C", AddFunction("Multiply", [Matrix,Matrix]::Matrix,
proc (X, Y)
local a,b;
a := 2;
b := convert(a, string);
Printer:-Print("Mmultiply(", X);
Printer:-Print(",", Y, ")"); Printer:-Print("\n");
Printer:-Print("from", b, "to");
Printer:-Print(",", Y, "do") end proc, numeric = double));
Translate(f, language = "NewC")

 

But when I run it, the "Multiply" function cannot be translated.  The result is:

 

Warning, type signature [CodeGeneration:-Names:-ArrayType(integer,CodeGeneration:-Names:-ArrayRanges(1 .. 2,1 .. 2),CodeGeneration:-Names:-ArrayOptions()), CodeGeneration:-Names:-ArrayType(integer,CodeGeneration:-Names:-ArrayRanges(1 .. 2,1 .. 2),CodeGeneration:-Names:-ArrayOptions())] for function Multiply is not recognized
void f (void)
{
  int x[2][2];
  int y[2][2];
  x[0][0] = 1;
  x[0][1] = 2;
  x[1][0] = 3;
  x[1][1] = 4;
  y[0][0] = 1;
  y[0][1] = 3;
  y[1][0] = 4;
  y[1][1] = 2;
  Multiply(x, y);
  ;
}

I don't know why "Multiply(x,y)" cannot be translated.

If I put two "Multiply(x, y)" in the procedure, like this:


f := proc ()
local x,y;

Multiply(x, y);
x := Matrix([[1, 2], [3, 4]]);
y := Matrix([[1,3],[4,2]]);
Multiply(x, y);
NULL;
end proc;

LanguageDefinition:-Define("NewC", extend = "C", AddFunction("Multiply", [Matrix,Matrix]::Matrix,
proc (X, Y)
local a;
a := 2;
b := convert(a, string);
Printer:-Print("Mmultiply(", X);
Printer:-Print(",", Y, ")"); Printer:-Print("\n");
Printer:-Print("from", b, "to");
Printer:-Print(",", Y, "do") end proc, numeric = double));
Translate(f, language = "NewC")

THe result is:

Warning, cannot resolve types, reassigning x's type
Warning, cannot resolve types, reassigning y's type
Error, (in CodeGeneration:-IssueError) type 'Matrix' cannot be translated to target language

I don't know why type 'Matrix' cannot be translated.

 

 

Maplesim 7.0(1) installer looks for Maple 18 installation.  Will Maplesim work with Maple 2015?

If not, what is the expected date of making both products compatible?

Regards,

G

integral.mw

 

Hi all, I want the best for you.

I really have confused with this bad integral (HeunB)which I've got it 2 weeks ago from a solution by Maple 17. I should solve this one to solve the derivative of this too.

 

Help me please, I attached the attribute file.

Regards.

Hi all,

 

It's been a while since I have used Maple. To be honest I haven't used it for over six years.

 

I am trying to solve simple differential equations, however I have many issues.

 

I am trying to simulate what author of this paper did 06421188.pdf

 

My file looks like this (Pendulum.mw)

 

Can someone help me to simulate this system? I simply can't remember how to do it.

 

Cheers,

Bart

Attached is a photo with the code I am working for.  

On the top is practice code with a simpler ODE to help with trouble shooting, on the bottom is the ODE I am working with.

I was hoping to gain insight about the _z1 symbol in the solution, I haven't been able to find much help on other threads.  I would like to know how I can go about working with it - if it is something on my end or if it is the nature of the equation I am working with.

 

Thank you for any help,

Josh

I have a nice procedure that is as follows, that explores the behaviour of a mapping in R^2.

InversePoincare := proc (v) options operator, arrow; v*Norm(v, 2)/(1-Norm(v, 2)^2) end proc

SphereVectorPlot := proc (T, radius, radiusIncrements, angleIncrements, lengthParam)
local listOfPairs;
listOfPairs := {seq(seq([[radius*r*cos(2*angle*Pi/angleIncrements)/radiusIncrements, radius*r*sin(2*angle*Pi/angleIncrements)/radiusIncrements], T(InversePoincare(`<,>`(radius*r*cos(2*angle*Pi/angleIncrements)/radiusIncrements, radius*r*sin(2*angle*Pi/angleIncrements)/radiusIncrements)))-InversePoincare(`<,>`(radius*r*cos(2*angle*Pi/angleIncrements)/radiusIncrements, radius*r*sin(2*angle*Pi/angleIncrements)/radiusIncrements))], r = 0 .. radiusIncrements), angle = 0 .. angleIncrements)};
if lengthParam = false then
 return arrow(listOfPairs, scaling = constrained, shape = arrow)
else
 return arrow(listOfPairs, length = lengthParam, scaling = constrained, shape = arrow)
end if
end proc

Essentially, we plot vectors v at location u. Since the vectors v in general vary wildly in magnitude, I would like to visualize the magnitude change by using color and/or transparency, preferably the latter. Is it possible to do so, and if so, how?

Hello everyone. I am trying to make a position time graph of a charged particle in an gravitational and electric field. This is just for an application of Maple to Lagrangian mechanics. I have set up my Lagrangian, did the Euler-Lagrange equation, and solved the differential equation. When I go to plot it, just the axes show up and I dont have a line. I have followed other examples of Lagrangian mechanics in Maple and its still not working. Here is the code for the odeplot:

Eq7:=dsolve({Eq6,initial},{q(t)},numeric,output=listprocedure)

odeplot(Eq7,t=0..10)

Eq6 is the Euler-Lagrange equation for my system, initial is the initial values, and q(t) is the position of the particle.

Any suggestions will help.

 

 

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