## How to plot Fourier transform?...

Hi,

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.

Thanks

## Why are different answers produced?...

PrimesQuestion.mw

Please let me know if this link correctly accesses my worksheet. If not, I will copy its contents into this question.

Which ODE in the worksheet, if any, provides the correct answer?

 >
 >
 >
 >
 (1)
 >
 (2)
 >
 >
 (3)
 >
 >
 (4)
 >

## Gauge indices in Physics Package...

Hi,

I'm trying to work out whether or not Maple will be able to help me out with some algebra involving lots of indices, but I can't seem to work out how the gauge indices features work in the Physics package. For example I would like to define a gauge field carrying an SU(3) index and a spacetime index. The SU(3) index should run from 1 to 8 and the spacetime index from 1 to 5. I think I have worked out how it works with spacetime indices but I can't seem to find any documentation on the gauge indices.

Is there are a way to set the "dimension" of the gauge index, like we can set the space time dimension?

Cheers

Hi,

I would need to get access to the values of euler angles defining the orientation of a 3D plot.

I generate the 3D plot with a given orientation, then the user is allowed to rotate it with mouse orbit. How can I get the values of the new euler angles to use them in further computations?

In the plot/structure I cannot find any data concerned with orientation...

Thank you.

Marco

## Quality of implicit plot...

Hi,

I am trying to solve an equation and plot it as an implicit plot, I would like to increase the number of points in the plot calculation but it seems that there is a limit for it, I chose 10^8 and for a bigger values I get an memorry error from Maple. Is there anyway I can solve this problem?

This is just for an example:

implicitplot(subs({values = ...}), function), for a given values, numpoints=10^8)

Regards,

Baharm31

Is there a simple way to see wich packages that I have loaded, without being forced to see thru the entire document?

## How to differentiate w.r.t expression?...

I'd like to differentiate  3*(r/sqrt(a))+ (r/sqrt(a))^2  w.r.t  r/sqrt(a) and obtain

3 + 2* (r/sqrt(a))

in otherwords, treat (r/sqrt(a)) as a single variable. This is what I tried:

restart;
v:=r/sqrt(a);    #the single expression to differentiate w.r.t
p:=x->x^2+3*x;
expr:=Diff(p(v),v);
algsubs(v=x,expr);
algsubs(x=v,value(%));

The problem is that when doing x^2 and x is r/sqrt(a), then it become r^2/a and it does not remain (r/sqrt(a))^2, so now the algsubs does not "see" it. I get as final answer

ofcourse, one can now try to simplify the above to the required form, maybe using assumptions or by dividing by sqrt(a) the numerator and denominator of the first term above to get  3+2*(r/sqrt(a)) but this is all requires extra work and can be hard depending on the result.

is there a better way to do the above so it works in general? The problem is in the function p, I need a way to tell Maple now to simplify it somehow. In Mathematica, I can do this like this:

Clear[p, x, r, a]
p[x_] := x^2 + 3*x;
v = r/Sqrt[a];
With[{v = x}, Inactive[D][p[v], v]];
Activate[%];
% /. x -> v

## The dchange command returns zero...

Hello Maple primers

I am trying to do a coordinate transformation which involves a number of partial derivatives. I turned to the PDETools[dchange] to accomplish this but it will just return 0 when run through.

The problem is as such. First two functions are defined which contain a lot of "stuff". Then the forward and reverse transformations are defined between the coordinates; and finally the transformation is done.

del_1:=Diff(Y,r1,r1)+2/r1*(Diff(Y,r1)) + Diff(Y,r2,r2)+2/r2*(Diff(Y,r2))+2*(Diff(Y,r3,r3))+4/r3*(Diff(Y,r3))+((r1^2-r2^2+r3^2)/(r1*r3))*(Diff(Y,r1,r3))+(r2^2-r1^2+r3^2)/(r2*r3)*(Diff(Y,r2,r3)):

del_2:=Diff(Y,r1,r1)+2/r1*(Diff(Y,r1))+(r1^2-r2^2+r3^2)/(r1*r3)*Diff(Y,r1,r3)+Diff(Y,r2,r2)+2/r2*(Diff(Y,r2))+(-r1^2+r2^2+r3^2)/(r2*r3)*(Diff(Y,r2,r3))+4/r3*(Diff(Y,r3))+2*(Diff(Y,r3,r3)):

#Forward transformation

R1:=0.5*(v)+0.25*(w):
R2:=0.5*(u)+0.25*(w):
R3:=0.5*(u)+0.5*(v):

tr:={r1=R1,r2=R2,r3=R3}:

#Reverse transformation
rR1:=(-r1+r2+r3):
rR2:=(r1-r2+r3):
rR3:=2*(r1+r2-r3):

rtr:={u=rR1,v=rR2,w=rR3}:
nv:={u,v,w}:
AA:=simplify(del_1+del_2);
PDEtools[dchange](tr,AA,nv,rtr);

This will return zero. Is there something obvious I am missing here? I have used the dchange tool before in a similar manner and it has worked without issue.

## Finding a numerical solution to system of equation...

I have a system of equations in several variables and I just need one numerical solution of it, I tryed to use fsolve of Maple but it always show me some errors or gives back the command as the output.

aaghulu := {-6-4*y-x-(1+y)*x+sqrt((4*(1+y))*(2+x)*(4+2*y+x)+(-(1+y)*x+2+x)^2), (2*(4+2*y+x))*(1+y)-(1+y)*x+2+x+sqrt((4*(1+y))*(2+x)*(4+2*y+x)+(-(1+y)*x+2+x)^2)-(2+y)*(-(1+y)*x+2+x+sqrt((4*(1+y))*(2+x)*(4+2*y+x)+(-(1+y)*x+2+x)^2))};

fsolve(aaghulu, {x, y}, maxsols = 1);

I will be happy if someone guide me how to do these kinds of things using Maple.

## How to copy execution group?...

Using worksheet, in 2015. I have an execution group, such as

>....code
....
...

>... another execution group

And want to copy all the code from the first group, using the mouse. Is there another way, other than having to move the mouse by hand and select all the code in order to copy it?  In Mathematica, I can right-click on the cell edge, and select copy. This copies the cell to the buffer, then one can paste the code somewhere else. In Maple, I could not duplicate this behaviour which is annoying when one wants to copy large amount of code.

I found that if I put the code in a "code edit region", ie., do insert->code edit region, then right-click inside the small window of the code edit region, the copy is enabled, so I can copy the whole region without manually select it first.

But this does not work outside the code edit region.

## `assuming` not working for functions...

This is a stripped down example of something I've been doing. Basically I'm building matrices which I then, using unapply, convert into functions of some variables of t.
.... but found that simplify seems to often not work as i'd wish.

restart:
mm:=Matrix([[cos(sqrt(g__1^2)*t), (-I*g__1*sin(sqrt(g__1^2)*t))*(1/sqrt(g__1^2))], [(-I*g__1*sin(sqrt(g__1^2)*t))*(1/sqrt(g__1^2)) ,cos(sqrt(g__1^2)*t)]]);

#great - simplifies as i'd expect:
simplify(mm) assuming g__1::positive;

Do the same thing but when matrix is a function of t
mmFun:=unapply(mm, t);

#the function works - gives what i'd expect
mmFun(3); mmFun(t);

#but now the simplification does not work - why the g__1 in the argument of cos does not get properly simplified?
simplify(mmFun(t)) assuming g__1::positive;

Any ideas if this is a bug? I'm using maple 2015.2 on linux 64-bit.

here is the worksheet: simplify_issue.mw

thanks

EDIT:

as a side note once can sometimes overcome this with mapping simplify  as in :

map(simplify, resultMatrix ) assuming g__1::positive;

but this is not optimal, and sometimes does not work when i first multiply the matrix by say a vector.

## How to produce that approximation?...

Hi all

Assume that we have folowings:

Assume that we devide [0,1] to N subintervals and in each subinterval we have:

Also we want to approximate arbitrary function x(t) with following manner:

How can we produce these basic polynomials?

Ph.D Candidate

Applied Mathematics Department

## How to form equation of specific kind?...

Hello,

I would like to create a function from an equation.
I have define 4 functions u[1](t), ..., u[4](t).
From these 4 functions, I would like to define 4 equations. I would like to obtain this result:
Equ[1]:=u[1](t)=L/2*cos(w*t+phi[1])
Equ[2]:=u[2](t)=L/2*cos(w*t+phi[2])
Equ[3]:=u[3](t)=L/2*cos(w*t+phi[3])
Equ[4]:=u[4](t)=L/2*cos(w*t+phi[4])

My code is the following:

for i to 4
do
u[i]:=unapply(L/2*cos(w*t+phi[i]),t);
Equ[i]:='u[i](t)'=u[i](t);
end do;

These lines are not working because the left member is not incremented (u[i](t) stays at each iteration u[i](t))

Generally, how can I transform a function to an equation ?
And, in this specific case, how can I obtain the four equations mentioned above ?

Thanks a lot for your help.

## Certain vertical lines ...

Hello,

I would like to plot a vertical line each time my function is null and is increasing.

Here an extract of my code:

v:=unapply(H*sin(w*t),t);
L:=0.080;
H:=0.020;
Vf:=0.3;
w:=10;
fsolve(v(t)=0,t=0.5..2);
zeros:=Roots(v(t),t=0.5..2);

vdot:=unapply(diff(v(t),t),t);
map(vdot,zeros);
LignesVerticales=implicitplot(x=To complete, colour=yellow,linestyle=3, thickness=2):

With Roots function, I could obtain the zero-crossings.

With the derative of the functions, I could obtain a vector which gives me when the derivative is positive or not.

I would like now to obtain the list of the zero-crossing values which are increasing but I have difficulties to obtain it.

By list manipulation, it should be easy to do.

May you help to plot obtain this list so that I can plot the desired vertical lines?

## All solutions of equation...

Hello,

I would like to obtain all the solutions of a equation.

Here an extract of my code:

v:=unapply(H*sin(w*t),t);
L:=0.080;
H:=0.020;
Vf:=0.3;
w:=10;
fsolve(v(t)=0,t=0.5..2);

How can I do to obtain all the solutions of the equation in the wanted interval ?

I'm not fixed to use fsolve function.