Items tagged with transform

The piecewise plot below displays a sphere truncated by the plane z = 2 - y.

f := proc (x, y, z) options operator, arrow; piecewise(z <= 2-y, x^2+y^2+z^2-16, z-2+y) end proc; implicitplot3d(f, -4 .. 4, -4 .. 4, -4 .. 4, style = surface, numpoints = 50000);

The 3 transforms below when executed in display(T(sphere([0, 0, 0], 4, numpoints = 50000)), scaling = constrained) display the truncated sphere differently:

1) the truncating plane only partly conforms to the boundary of the truncated sphere

2) the truncated sphere is correct provided that the else condition coordinate is in the truncating plane and truncated sphere

3) the truncated sphere is correct but hollow


1) T := transform(proc (x, y, z) options operator, arrow; `if`(z <= 2-y, [x, y, z], [x, y, 2-y]) end proc)

2) T := transform(proc (x, y, z) options operator, arrow; `if`(z <= 2-y, [x, y, z], [0, 0, 2]) end proc)

3) T := transform(proc (x, y, z) options operator, arrow; `if`(z <= 2-y, [x, y, z], [`&+-`(sqrt(16-y^2-z^2)), y, 2-y]) end proc)

Please explain the different behavior of the three transforms.           



I am not sure how to find the Heaviside Laplace transform 







Thank you:)

Dear Community,

Would someone have a good and easy to understand/implement description of the Den Iseger algorithm for the numerical inversion of Laplace transform? Even better if someone would have a Maple script to do it, that would be superb.

Tx in advance,

best regards



To summarize, I have a variable ε = order(1),  which maple has assumed is a funtion ε(x,y,z) and so when I differentiate epsilon with respect to x (or y or z) I do not get 0. I get ε(or εy, εz). How do I ensure maple does not assume this?

More detail of my process:

I declare functions,

I have the function I want to transform,

Now I transform the variables to the new co-ordinate system. i.e. from (x,n,q) to (s,Y,z)


Good! - Everything correct so far. 

Now I want to linearise so i introduce x=x0+ε*x1; and the same for (Y,z), 


As you can see, epsilon has derivatives, which it should not. 

How I can avoid this? 

Thanks in advance - im well and truely stumped over this.

P.s. if the images do not show, the script can be found here: 


I have this list :

I would like to create this list automatically:


In other words, how can I remove the 3 characters "(t)" and replace it by "_"

Do you have ideas to do so ?

Thanks a lot for your help

f=x^2.  It's easy to compute the fouier transform. F(y)=fourier(f,x,y).

However, I want to do more. replace the variable y with a new formula g(z)=z^2.

I tried  "subs(y=g,F)". But failed. Need your help.


f := x^2



F := fourier(f, x, y)

-2*Pi*Dirac(2, y)


g := z^2



subs(y = g, F)

-2*Pi*Dirac(2, y) = z^2








I was wondering how to go about plotting a Fourier Tranform in Maple.

My assignment is to plot a simple harmonic equation as a Fourier transform, depicting amplitude against fequency.

I've been given: x'' + w^2 x = 0

And want to obtain both the f(x) = a0 sin(wt) + b0cos(wt) form, and a graph of the the amplitude (c^2 =a0^2 + b0^2) against frequency.

I know how to do this on paper but not in Maple, so any help with line commands and layout would be very much appreciated.



How evaluate system of two integral equation by laplace transform ?



L := laplace((1/2)*x^2+(1/2)*x^3+(1/12)*x^4 = int(u(t)*(-1+x-t)+v(t)*(1+x-t), t = 0 .. x), x, s);

(s^2+3*s+2)/s^5 = laplace(int(u(t)*(-1+x-t)+v(t)*(1+x-t), t = 0 .. x), x, s)


(3*s^2-s+2)/s^5 = laplace(int((1+x-t)*u(t)+(-1+x-t)*v(t), t = 0 .. x), x, s)





In Maple 15 it seems that plottools:-transform only accepts this form of conditional statement:  

`if`(conditional expression, true expression, false expression).

Is there any way to have plottools:-transform process more than one condition? Do later versions of Maple permit this?

Hi everyone,


Consider this maple 18 doc:


The code is regular code for Julia sets of the exponential.


To see how the Julia set behaves at infinity, I apply the transform mu(z)=1/z.


The plot3d command correctly plots the Julia set at an appropriate neighborhood of infinity, but:

1) Axes are not transformed

2) Saving as .eps produces an empty plot, sans the axes (plot is saved correctly, when not applying mu(z))


Is there any trick to force the axes to also show correctly with the transformed ranges?

Seems that this misalignment is bothering the .eps renderer, which probably plots the graph in twilight zone, given the false ranges of the untransformed axes.


Any ideas on how to force the saveas .eps to work in this case?


Many thanks,


Hallo everybody,

I just started to use maple and I think I need some help from more experienced users.
I would like to transform the stationary Navier Stokes equations to toroidal coordinates.

The definition of my coordinate system is as follows:
x = -r * cos(sigma)
y = cos(Theta) * ( R + r * sin(sigma) )
z = sin(Theta) * ( R + r * sin(sigma) )

I tried to define the coordinate system and transform each term of the equation:

div( rho * CC) = -grad(p) + div(Tau)

I can transform the pressure gradient. However, I get an error for the divergence of the tensors.
Could someone please give me a hint on how to get the divergences?


My code is printed below:

restart: with(plots): with(LinearAlgebra): with(VectorCalculus): with(linalg):

#torus defintion
x := -r*cos(sigma);
y := cos(Theta)*(R+r*sin(sigma));
z := sin(Theta)*(R+r*sin(sigma));
R := .35;
AddCoordinates(torus1[r, sigma, Theta], [cos(Theta)*(R+r*sin(sigma)), sin(Theta)*(R+r*sin(sigma)), -r*cos(sigma)]);
SetCoordinates(torus1[r, sigma, Theta]);

#pressure gradient
PressureGradient := Gradient(p(r, sigma, Theta, t));

#left hand side
c := vector(3, ([Cr, Ctheta, Cx])(r, sigma, Theta, t));
rhoCC := rho*multiply(c, transpose(c));
LHS := Divergence(rhoCC)

Hi all, 

I'm trying to implement the smithChart on Maple, but this error "Error, (in unknown) invalid transform: output is not 2 or 3 element" keeps popping up for some reason. I have no idea how to fix it. Can anyone help me with this? Here is the smithChart:


smithChart := proc(r)
  local i, a, b, c;
   a := PLOT(seq(plottools[arc]([-i*r/4, 0], i*r/4, 0..Pi),
                 i = 1..4),

  plottools[arc]([0, r/2], r/2,
  plottools[arc]([0,r], r, Pi..Pi+arcsin(15/17)),
  plottools[arc]([0, 2*r], 2*r,
  plottools[arc]([0,4*r], 4*r,

  b := plottools[transform]((x, y) -> [x-y])(a);
  c := plottools[line]([0,0], [-2*r, 0]):
  plots[display](a, b, c, axes = none, scaling = constrained, args[2..nargs]);
  end proc:

Error, (in unknown) invalid transform: output is not 2 or 3 elements

hello everyone. I have an undergradute project i'm currently working on and I'm stuck where I have to use the Differential Transforms Method to solve a problem with boundary conditions at infinity


Digits := 5;

F[0] := 0; F[1] := 0; F[2] := (1/2)*A; T[0] := 1; T[1] := B; M := 2; S := 1;

for k from 0 to 10 do F[k+3] := (2*(sum((r+1)*F[r+1]*(k+1-r)*F[k+1-r], r = 0 .. k))-T[k]-3*(sum((k+1-r)*(k+2-r)*F[r]*F[k+2-r], r = 0 .. k))-M*(k+1)*F[k+1])*factorial(k)/factorial(k+3);

T[k+2] := (-3*(sum((k+1-r)*F[r]*T[k+1-r], r = 0 .. k))-S*T[k])*factorial(k)/factorial(k+2)

end do; f := 0; t := 0;

for k from 0 to 10 do

f := f+F[k]*x^k;

t := t+T[k]*x^k end do;


but the problem is that i cant seem to evaluate

or higer diagonal pade-approximant. any help will be greatly appreciated. thank you.


I am trying to find the inverse fourier transform given a vector (of real) as input. I get the following error message:

Error, (in DiscreteTransforms:-InverseFourierTransform) entries of input data must all evaluate to complex floats, got '[.7644453211]'

I am unable to understand this message. I would much appreciate help to resolve this issue.


How can I access the Laplace Transform built-in package?

I want to try to modify it for something like this,

 int(f(t)*exp(-s*t), t=0..infinity);


 int(f(u*t)*exp(-s*t), t=0..infinity);

 or to

 int(f(u*t)*exp(-t), t=0..infinity);


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