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Hi,

I open a new subject about Fredholm Integral equation. My code work correctly.

But, I need some modification to get a nice display of the matrix found using
MatA,Vectb := GenerateMatrix(convert(sys3,list),Sol_phi);

such as Sol_phi is my solution that I want to find.

I introduced two function alpha1 and alpha2 in the code  see Equation (9) can I write all the coeficient of my matrix using the two function alpha[1] and alpha[2], it's better to see and read the matrix form.

 

Fred.mw

Hi guys!

 

I want to do a fractalzoom into the mandelbrot fractal. The basic idea was to produce all single plot pictures, and then display/animate the zoom by iterate through the list. But I cant find a solution that really works. Any help would be very appreciated :)

 

So where am I? A single picture is made like this: (Sorry math tool didnt take it)

 

plot3d(0, -2 .. 1, -1.5 .. 1.5, orientation = [-90, 0], grid = [250, 250], style = patchnogrid, color = mandelbrot, lightmodel = None):

As u can see, I use the colorfunc property to color the plane. The mandelbrot procedure evalueates how many iterations are needed to go beyond 2 (> 2).

I cant post pictures, so heres the code if u want to reproduce some:

mandelbrot := proc (x, y)

local c, z, iterationCount, position, iterations;

z := 0; iterations := 0; iterationCount := 35;

position := Complex(x, y);

c := evalf(position);

while iterations < iterationCount do

    if 2 <= abs(z) then return iterations;

    else z := z^2+c; iterations := iterations+1;

    end if

od;

return iterations

end:

 

As you can see i get a list of PLOT3D structures, each with different axis sizes or views. The problem now is when i use the straightforward way:

display(plots, insequence=true);

the animated frames get smaller and smaller, because the frame is set to the same size as the first frame. 

Do you have any idea how I can make the axis somewhat dynamic, or do you see a better approach?

 

Here's the rest of the code to produce the effect. Its nearly hardcoded, because its still in experimental phase, sorry for that :P

The test does the following: Start with window -2 .. 1, -1.5 .. 1.5 and with linear interpolation zoom in to the window -0.82 .. -0.7, -0.2 .. -0.08.

 v is used to store the view explicitely, is explained afterwards

 

steps := 3:

d1 := (2-0.82)/steps:

d2 := (1+0.7)/steps:

d3 := (1.5-0.2)/steps:

d4 := (1.5+0.08)/steps:

l := Array(1 .. 4):

v := Array(1 .. 4):

for i from 0 to steps do

    v(i+1) := [d1*i-2 .. -d2*i+1, -1.5+d3*i .. 1.5-d4*i, 0 .. 0];

    l(i+1) := plot3d(0, d1*i-2 .. -d2*i+1, -1.5+d3*i .. 1.5-d4*i, orientation = [-90, 0], grid = [100, 100], style = patchnogrid, color = mandelbrot, lightmodel = None);

od:

 

display a single picture:

display(l(4));

 

create the animation:

ll := convert(l, list):

display(ll, insequence = true);

 

Another approach:

I tried to explicitely give the view as argument:

display(l(i), view = v(i)), v(i) stored in previous render loop. This works, but then the question to resolve is how to draw each frame into the same plot figure and not creating a new plot window for each one?

 

Now you should have all informations, any help is very welcome!

Thanks in advance,

Cheers,

geischtli

Hi,

thank for any  help.

I need you help to make a movies ( animation)  according to the index k=1..10.  k is used in Vect_T[k], vector of time to make an animation of the true solution, and it's also used in Matrix(M[..,..,k]), h

True solution:ow can I make a seq of plots for different value of k. 

 

plot3d(True_solution(x,y,Vect_T[k]),x=0..a,y=0..b,axes=boxed,grid= [11,11]);

Analytic solution

plots:-matrixplot(Matrix(M[..,..,k]),axes=boxed,tickmarks= [[1="0", 2=" ", 3=" ", 4=" ", 5=".4", 6=" ", 7=" 0.6", 8=" ", 9=".8", 10=" ", 11="1"],[1="0", 2=" ", 3=" ", 4=" ", 5=".4", 6=" ", 7=" 0.6", 8=" ", 9=".8", 10=" ", 11="1"],default],labels=[x,y,u],axes = boxed);

I tried, this:

S:=seq(plots:-matrixplot(Matrix(M[..,..,i]),labels=[x,y,u],axes = boxed),i=1..10):
plots:-display(S);
 But I get only one figure.

 also,

I tried

BoxTrue:=Null;
for k from 1 to 10 do
BoxTrue:=BoxTrue, plot3d(True_solution(x,y,Vector_time[k]),x=0..a,y=0..b,axes=boxed,grid= [11,11]): od:
display(BoxTrue, insequence=true);
also, no display

 

Dear all;

 

I need a help in this question.

u(x,y,t) my solution of PDE. x,y space, and t=time.

In the case without t. .i.e. u(x,y). Here is a visualization of the lattice u(x_i,y_j). i=1..3, anf j=1..3.  Please try this example, it's working. 

my question, if i would like to add a third variable t, i.e.  and get u(x_i,y_j,t_k)  on each points. I would like to show the lattice in (x,y) plan for each t_k. I Think I will get many parallel lattice. 

Please can some one, modify this code to get the parallel lattice. Thanks.


with(LinearAlgebra):
with(plots):
with(PDEtools):
interface(rtablesize=20):

Here,


L := 'L':
N := 'N':
g := 'g':
Z := i -> -L+2*L/(N+1)*i;
x[0] = Z(0),x[N+1] = Z(N+1),y[0] = Z(0),y[N+1] = Z(N+1);

 

N := 4;
L := 1;
r := L/(N+1)/4;
ngon := (n,x,y,r,phi) -> [seq([x+r*cos(2*Pi*i/n+phi), y+r*sin(2*Pi*i/n+phi)], i = 1 .. n)]:
p[1] := display([seq(polygonplot(ngon(4,Z(0),Z(j),r,Pi/2),color=magenta),j=0..N+1),

seq(polygonplot(ngon(4,Z(N+1),Z(j),r,Pi/2),color=magenta),j=0..N+1),

seq(polygonplot(ngon(4,Z(i),Z(0),r,0),color=magenta),i=1..N),

seq(polygonplot(ngon(4,Z(i),Z(N+1),r,0),color=magenta),i=1..N),

seq(seq(polygonplot(ngon(20,Z(i),Z(j),r,0),color=white),i=1..N),j=1..N),

textplot([seq(seq([Z(i+0.1),Z(j),typeset(u[i,j])],i=0..N+1),j=0..N+1)],align={above,right})],view=[Z(-1)..Z(N+2),Z(-1)..Z(N+2)],tickmarks=[[seq(Z(i)=typeset(x[i]=evalf[2](Z(i))),i=0..N+1)],[seq(Z(i)=typeset(y[i]=evalf[2](Z(i))),i=0..N+1)]],

axes=boxed,scaling=constrained,labels=[``,``]):
p[1];

 

 

 

 

 

 

Hi

worksheet output doesnt display the eigenvalues of a 19X19 matrix. Just gives in the form Root of(...). when datatype is indicated as anything other than complex(sflot) it gives error "unable to store". solution is required in compact mathematical expression form (may involve square roots etc). Please help.

Thanks

I am trying to display a graph where there is a rotating square. My code is 

   for k to 30 do

RotSquare := Trans(1.5, 1.5).HomRot(k*Pi/15).Trans(-1.5, -1.5).HomSquare;

graph[k] := plot(Transpose(<RotSquare[1], RotSquare[2]>), x = -3..3, y = -3..3):

od:

display(seq(graph[k], k = 1..30), insequence = true);

with HomRot being 

HomRot := theta ->((cos(theta), sin(theta), 0)(-sin(theta), cos(theta), 0) (0 0 1))

However, when I run this code, my output is 

display(PLOT(...), PLOT(...), PLOT(...), PLOT(...), PLOT(...), PLOT(...), PLOT(...), PLOT(...), PLOT(...), PLOT(...), PLOT(...), PLOT(...), PLOT(...), PLOT(...), PLOT(...), PLOT(...), PLOT(...), PLOT(...), PLOT(...), PLOT(...), PLOT(...), PLOT(...), PLOT(...), PLOT(...), PLOT(...), PLOT(...), PLOT(...), PLOT(...), PLOT(...), insequence = true)

and I'm not sure what I am doing wrong. Help would be greatly appreciated

I'm taking calculus and my professor introduced us to maple software. The professor asked us to plot the families of curves for this orthogonal equation:

dy/dx = (x^2) - (2y^2) - C = 0

This is what I had so far:

 

restart;

with(DEtools):

with(plots):

 

Function:=unapply(simplify(x^2-2y^2-C),(x,y)):

'Function'(x,y) = Function(x,y);

plotFunction:=C->implicitplot(eval(F(x,y),a=C),x=-5..5,y=5..5,scaling=constrained):

plot1:=display(seq(plotFunction(a),a=-5..5)):

display(plot1);

 

This is only display one family. How do I code for it plot the other families?

(The graph should look like curves converging from left, top and right sides toward to the origin of the axes)

Please help.

Hello,

 

I don't seem to be able to create an array of plot with two rows, where the first one is a sigle animation and the second rwo is two animations in the same plot. For example I would the first row of the array to display

H := animate(plot3d, [x-k*y+1, x=-10..10, y=-10..10], k=-10..0, frames=4):

display([H]);

end the second row to display

P := animate(plot, [sin(x+t), x=-Pi..Pi], t=-Pi..Pi, frames=8):
Q := animate(plot, [cos(x+t), x=-Pi..Pi], t=-Pi..Pi, frames=8):


display([P, Q]);


Any ideas?

I'd like to bind a symbol to some expression, but display the expression analytically before evaluating, and show the value on the same line (not new line).

Something like:

restart;
a:=10: b:=3:
f:='a+b^2';`=`,f;

But this display the expression and its numerical value on 2 lines. I'd like to get this output:

      f:=a+b^2 ,`=`,19  

This is just so I can see the expression before it is evaluated, and its numerical value on same line. Or if there is a better way do this. I tried using print, but could not get the assignment to work then.

 

Hi,

 

I am trying to plot union of regions in Maple 15. Each region is formed by a set of inequalities. I can see from online such a feature is available in Maple 17.

The code is:

> with(plots);

> I1 := inequal({x < 1, y < 1}, x = 0 .. 2, y = 0 .. 2, optionsfeasible = [color = "Brown", thickness = 2]);

> I2 := inequal({y > 1, x < 1}, x = 0 .. 2, y = 0 .. 2, optionsfeasible = [color = "Yellow", thickness = 2]);

> display(I1);      ---> This is working 

>display(I2);      ---> This is also working

>display({I1,I2});  ---> Not working.

The above is also attached in the worksheet.

Is there any other way to plot the two region. I am new to Maple. Please suggest me the alternative in Maple 15.

 

Thanks!

 

Hello my friends

I have a problem in displaying the mesh grid in my plot3d graphs in maple 17. For instance, I when I type:

plot3d(x^2-y^2, x = -1 .. 1, y = -1 .. 1)

The graph has no mesh grid on it. I mean I am not seeing the black lines on the 3d surface. Can anyone help me to display the mesh grid please? Thanks. 

Hello everyone,

 

I'm having some trouble overlaying a set of complex plots. I follow the usual procedure 'display(p0,p1)' I only get p1...

 

If i try with plots the display command works fine, here's the piece of code I'm trying to get working (r is defined elswhere as function of x and phi):

i := 0;

p := Array(0 .. 10);

for x from 0 by .2 to 2

do p[i] := complexplot(r, phi = -(1/2)*Pi .. (1/2)*Pi);

i := i+1

end do;

display(p[1], p[10]);

 

Any hints?

 

Cheers,

Felipe

Hi, the display function in the simplex package gives us a nice breakdown of the form Ax<=b, but how do we extract the individual elements, i.e. the matrix A and vectors x and b? Normal indexing into the expression doesn't work, i.e. if for some set of constraints of the form 2x+3y<=21 we enter

res:=display(constraintSet);

this gives us a nice expression, but res[1] etc. doesn't work as we might hope (i.e. by returning the matrix A).

 

Is it possible to display each element of a sequence on a new line?

The default behaviour, obviously, is to display each element on the same line separated by commas, and wrapping to a new line as required by screen space. This is somewhat unsightly when the elements of the sequence contain long equations or expressions, and impacts readability because the commas don't stand out as effective separators between elements.

For example:

B := b=2;

C := c=3;

A := B,C;

>A

b=2, c=3

 

Is there a way to display each element on a new line?

For example:

>A

b=2,

c=3

 

Is there another data type or a simple expression that could achieve this effect?

Hi all,

I designed the animation and wanted to display it automatically in the embedded component. Instead of animation toolbar, is it possible to control animation through commands? How do I do that?

 Thanks.

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