Hi all,

I have recentry constructed Fourier amplitude and Fouier Power graphs which are plotted against the frequency of the oscillations, like the picture below.

I would like to change the frequency scale along the x axis into a period scale in order to Fourier analyse future ODE systems in  terms of period rather than frequency.

But I unsure how to manipulate my code to do so.

Any help would be much apreciated, and the Maple file that I am using is attached.

Thanks in advance!

Fourier_with_Period.mw

Hi, I'm having trouble with print doing strange things:

a:=1235
                1235

b:=751
                751


p:=1601
                1601

print(The solution `to` a^x = b (`mod ` p) is x = 1323)

                              1601 The solution to (1235^x) = 751 mod is x = 1323


Why has the 1601 gone to the beginning, and how do I make it go to the correct place?

Also is it possible to remove the brackets from around 1235^x?

And is it possible to make the brackets (that I have put in) go around the `mod` p?

EDIT:

If I do: print(The solution `to` a^x = b (`mod ` ,p) is x = 1323)

I get:  The solution to (1235^x) = 751 (mod, 1601) is x = 1323

So is there a way to just remove the comma on the output?


Thanks.

Hello,

In my code, I need to use 2 packages :
- with(LinearAlgebra)
- with(ListTools)

Problem :
It seems that the package with(ListTools) creates some troubles/ conflicts when I use some functions of the LinearAlgebra package such as DotProduct.

Here a small example to illustrate my issue

with(LinearAlgebra):
with(Student[MultivariateCalculus]):
with(plots):
with(MathML):
DotProduct(<0,0,l>, <0,0,l>, conjugate = false);

--> This code works

with(LinearAlgebra):
with(Student[MultivariateCalculus]):
with(plots):
with(MathML):
with(ListTools):
DotProduct(<0,0,l>, <0,0,l>, conjugate = false);

--> This code doesn't work

I try to replace the line with the DotProduct by the following line but it still doesn't work

with(LinearAlgebra):-DotProduct(<0,0,l>, <0,0,l>, conjugate = false));

How can I do to use in my code both packages (LinearAlgebra and ListTools) ?

Thanks a lot for your help

Hello :-),

How can I differentiate the follwing function:

Cq = Cao*k1*t / [(1+k1*t)*(1+k2*t)]

If want to find the maximum:

dCq/dt = 0

I can solve if of course by hand. The solution is t=1/sqrt(k1*k2)

I tried it with maple, but I got a strange result (see picture). How can I use maple to get the right result?

Thank you very much!

Consider the following lines:

eqs := {x - a*y,y - a*x};
sol := solve(eqs,y);

In general, sol will be NULL, but if a²=1 then the equations can be solved. How can such side relations be implemented in connection with solving?

PS: The above example is of course a grossly simplified one.

Note added: Perhaps it would be prudent to mention that the variable 'a' above is intended to be a symbolic place holder for some operator acting on some functions x,y, and having square equal to the identity map; it is not simply some algebraic number. The equations should thus be solved for x,y using a²=1, without having assigned anything to 'a' itself. For the simple example above, this can be done using the function eliminate, as suggested by Axel Vogt, but for more complicated cases, its success seems quite unlikely: for one thing, how can one determine, by looking at the set of equations, which variables can or should be eliminated?

I am using maple 13 to get the result of the einstein field equations,

with(tensor)

...

Estn := Einstein(metric, RICCI, RS);

displayGR(Einstein, Estn);

How can I put the result on an array element, so I can use it later on?

The following integral appears in the recent SEEMOUS 2016 competition:
Int( arctan(x) * ln(1+1/x^2), x = 0..infinity );

Maple 2015 can compute it, but with a little help.
What about Maple 2016?

How can I get maple to express the end result more compact/dense. Like for example in the picture, why can the program not just sum up all the fractions and everything in one number?

 when send email to technical support of maple?

i would like to encrypt email content with maple public key in gmail

Magnet lattices for particle accelerators (the sequence of focusing and bending magnets and drift sections making up a beam line) are often designed numerically using computer codes like MAD that model each beam-line element using either a matrix description or numeric integration, or some other algorithm. The Lattice package for Maple—recently published in Maplesoft's Application Center—allows modelling such beam lines using the full algebraic power of Maple. In this way, analytic solutions to beam-optics problems can be found in order to establish feasibility of certain solutions or study parameter dependencies. Beam lines are constructed in an intuitive way from standard beam-optical elements (drifts, bends, quadrupoles etc.) using Maple's object-oriented features, in particular Records which represent individual elements or whole beam lines. These Records hold properties like the first-order transport matrices, element length and some other properties plus, for beam lines, the elements the line is composed of. Operations like finding matched Twiss (beam-envelope) functions and dispersion are implemented and the results can be plotted. The Lattice package knows about beam matrices and can track such matrices as well as particles in a beam. The tracking function (map) is implemented separately from the first-order matrices thus allowing nonlinear or even scattering simulations; at present sextupole elements, compensating-wire elements and scattering-foil elements take advantage of this feature. Standard textbook problems are programmed and solved easily, and more complicated ones are readily solved as well €”within the limits set by Maple's capabilities, memory and computing time. Many investigations are possible by using standard Maple operations on the relevant properties of the beam lines defined. An interesting possibility is, e.g., using Maple's mtaylor command to truncate the transfer map of a beam line to a desired order, making it a more manageable function.

The package can output a beam-line description in MAD8 format for further refinement of the solution, cross-checking the results and possibly more detailed tracking.

Developed initially for my own use I have found the package useful for a number of accelerator design problems, teaching at the US Particle Accelerator School as well as in modelling beam lines for experiments I have been involved in. Presently at Version 1.0 the package still has limits; esp. the higher-order descriptions are not yet as complete as desirable. Yet already many practical design problems can be tackled in great detail. The package is backwards compatible to Maple 15. It can be found in the Application center together with help database files (old and new style) and a Users Guide.

An example showing the flavor of working with the package is attached (FODO_example.mw). It analyzes a FODO cell, the basic cell used in many ring accelerators.

Uli Wienands, aka Mac Dude

Hi, I need help finding the index of a given element in a list?

Say I have A:=[2,4,6,8,10,12], I want something that can do something like this:

index(A,6) 
                      3

EDIT:

Thanks, and sorry if my questions are trivial but I'm (clearly) not great with maple.

Now say I had two lists:

A:=[5,10,15,20,25,30,35,40,45,50]

B:=[7,14,21,28,35,42]

How would I get maple to return the index of the first element in list B that matches an element in list A, and the index of said element in list A? 


So something (remotely) like:

FirstMatch(B,A)
                        B[5], A[7]

(So I'm not looking for the first case of A[i]=B[i]. I just want i, j where A[i]=B[j])

Hello,

So I want to create an image of the cusp catastrophe that looks like this 

but instead I have been getting this image where the discontinuity is plotted out to infinity

I have tried to split up the surfaces on either side of this but I haven't been able to display both on the same plot whilst using implicitplot3d. 
This is the line of code for the image, there't not much too it
"
with(plots);

implicitplot3d(x^4+x^2*z+x*y, x = -7 .. 7, y = -50 .. 50, z = -10 .. 5, axes = boxed, style = surfacecontour, grid = [60, 60, 60], orientation = [180, 8, 175], 'transparency' = .1);
"
If anyone could help or point me in the right direction that would be great.
Cheers,
Darryl A.M.

using the code generator assistant I entered the following function

p := proc (z::(float[8]))

local a::integer, accm::(float[8]), k::integer, k1::(float[8]), c;
c := Array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], order = C_order, datatype = float[8]);
k1 := 1;
c[1] := evalf(sqrt(2*Pi));
a := 12;
for k to a-1 do c[k+1] := evalf(exp(a-k)*(a-k)^(k-1/2)/k1); k1 := -k1*k end do;
accm := c[1];
for k to a-1 do accm := accm+evalf(c[k+1]/(z+k)) end do;
accm := accm*evalf(exp(-z-a)*(z+a)^(z+1/2));
return accm/z
end proc

the code-generated julia code follows

function input(z)
c = [0,0,0,0,0,0,0,0,0,0,0,0]
k1 = 1
c[0] = (sqrt(2 * pi))
a = 12
for k = 1:a - 1
c[k] = (exp(a - k) * (a - k) ^ (k - 1//2) / k1)
k1 = -k1 * k
accm = c[0]
for k = 1:a - 1
accm = accm + (c[k] / (z + k))
accm = accm * (exp(-z - a) * (z + a) ^ (z + 1//2))
return(accm / z)
end

two things are wrong

1: no end after loop end

2: array index starts at 0, it should be 1 and of course the array references should reflect that

btw, it would be nice to be able to enter code tags like [code] code here [/code]

Hello everyone.  Let n be a positive number; I seek how to write the matrix Z\in M_{2^n,n} that is defined as follows:

for every i,j, Z_{ij}\in \{-1,1\}.

When I consider the 2^n rows of Z, I want to find ALL the possible sequences of length n with the entries +-1. A toy example, when n=2, is Z=\begin{pmatrix}1&1\\1&-1\\-1&1\\-1&-1\end{pmatrix}.

Thanks in advance;

The method of solving underdetermined systems of equations, and universal method for calculating link mechanisms. It is based on the Draghilev’s method for solving systems of nonlinear equations. 
When calculating link mechanisms we can use geometrical relationships to produce their mathematical models without specifying the “input link”. The new method allows us to specify the “input link”, any link of mechanism.

Example.
Three-bar mechanism.  The system of equations linkages in this mechanism is as follows:

f1 := x1^2+(x2+1)^2+(x3-.5)^2-R^2;
f2 := x1-.5*x2+.5*x3;
f3 := (x1-x4)^2+(x2-x5)^2+(x3-x6)^2-19;
f4 := sin(x4)-x5;
f5 := sin(2*x4)-x6;

Coordinates green point x'i', i = 1..3, the coordinates of red point x'i', i = 4..6.
Set of x0'i', i = 1..6 searched arbitrarily, is the solution of the system of equations and is the initial point for the solution of the ODE system. The solution of ODE system is the solution of system of equations linkages for concrete assembly linkage.
Two texts of the program for one mechanism. In one case, the “input link” is the red-green, other case the “input link” is the green-blue.
After the calculation trajectories of points, we can always find the values of other variables, for example, the angles.
Animation displays the kinematics of the mechanism.
MECAN_3_GR_P_bar.mw 
MECAN_3_Red_P_bar.mw

(if to use another color instead of color = "Niagara Dark Orchid", the version of Maple <17)

Method_Mechan_PDF.pdf