MaplePrimes Questions


Let a in ] 0, 1[  and  x real

Let  f := sin(x) / ( ( sin(a*x) )^a * ( sin((1-a)*x) )^(1-a) );

How can I find the limit of f as x goes to 0 ?
(limit, series, taylor don't work, wether I set or not assumptions on "a" [assume/assuming])

PS 1:  the limit is found once a numeric value is given to alpha

PS 2:  By simple calculations:
           sin(x) ~x  ;  sin(a*x) ~ ax  ; sin((1-a)*x) ~(1-a)x and thus
          ==>  f(x->0) ~ x / ( -a*x)^a * ((1-a)*x)^(1-a) )
                              = x / ( -a^a * (1-a)^(1-a) * x^(a+1-a)
                              = 1 /  ( -a^a * (1-a)^(1-a)  )

I am trying to solve system of coupled equations in maple, but when I execute it, maple gives a trivial answer. Here is the code:

                  d             i (p u1(x, t) + q u2(x, t))
           de1 := -- u1(x, t) = ---------------------------
                  dx                      lambda

> de2:=diff(u2(x,t),x)=(i/lambda)*(q*u1(x,t)-p*u2(x,t));

                  d             i (q u1(x, t) - p u2(x, t))
           de2 := -- u2(x, t) = ---------------------------
                  dx                      lambda

> de3 := diff(u1(x,t),t) = -(i*lambda/2)*u1(x,t)-q*u2(x,t);

      de3 := -- u1(x, t) = - 1/2 i lambda u1(x, t) - q u2(x, t)

> de4 := diff(u2(x,t),t) = 1/2*i*lambda*u2(x,t)+q*u1(x,t);

       de4 := -- u2(x, t) = 1/2 i lambda u2(x, t) + q u1(x, t)

> dsolve({de1,de2,de3,de4},{u1(x,t),u2(x,t)});

I have an equation

2*x + 3*x^3

would like to change to

x1 + x2 + x3*x4*x5 + x6*x7*x8 + x9*x10*x11


mathcad contains a command explicit all wich shows the equation with all the named variabels replaced with the numbers they repercent. can maple do something similar?



c:=a+b explicit all 5+10=15

i hope someone can point me in the right direction 



I have defined a function, F, as

F:=(s)->fouriersin(f(r), r, s)

I would now like to plot that function.

plot(F(s), s=0..3)

How can I do that? Calls to plot don't work, as the "s" in the fouriersin definition of the function get replaced by the value I'm trying to plot.





Is there any one can tell me why I get so many solutions there by use solve(f(x),{x,y},explicit)? There suppose to be only two solutions. Thanks in advance!


Can anyone tell me why this Maple phaseportrait command returns the error below ? Thanks in advance !


phaseportrait(-2*x*y, [x, y], x = -1.5 .. 1.5, {[0, -2], [0, -1], [0, 0], [0, 1], [0, 2], [0, 3]}, y = -1 .. 3);
Error, (in DEtools/phaseportrait) system must have same number of dependent variables as DE's.


The calculation of the jacobian matrix is not working.

Testes on windows, mac. worhksheet and document mode.

Maple 2017.





[`&x`, `*`, `+`, `-`, `.`, `<,>`, `<|>`, About, AddCoordinates, ArcLength, BasisFormat, Binormal, ConvertVector, CrossProduct, Curl, Curvature, D, Del, DirectionalDiff, Divergence, DotProduct, Flux, GetCoordinateParameters, GetCoordinates, GetNames, GetPVDescription, GetRootPoint, GetSpace, Gradient, Hessian, IsPositionVector, IsRootedVector, IsVectorField, Jacobian, Laplacian, LineInt, MapToBasis, Nabla, Norm, Normalize, PathInt, PlotPositionVector, PlotVector, PositionVector, PrincipalNormal, RadiusOfCurvature, RootedVector, ScalarPotential, SetCoordinateParameters, SetCoordinates, SpaceCurve, SurfaceInt, TNBFrame, TangentLine, TangentPlane, TangentVector, Torsion, Vector, VectorField, VectorPotential, VectorSpace, Wronskian, diff, eval, evalVF, int, limit, series]


Jacobian([rcos(t), rsin(t), r2t], [r, t])

Matrix(%id = 18446744078361292662)





There seems to be patterns for sin(10^-k) for rational k;

Here we have the "floats."

n sin(10^(-n-1/2))

1 0.03161750640

2 0.003162272390

3 0.0003162277607

4 0.00003162277660


Is it possible to create a vector, say

phi := Vector(2);
phi[1] := x[1]+2*x[2];
phi[2] := x[2]**2+x[1];

and then save it in a file that you can use in Matlab as a function handle?

I want to be able to create the phi vector in Maple but use it in Matlab.

Thanks for help!



Could the Maplesoft staff change the definition of the GammaDistribution in package Statistics?

In the all the papers or courses in the fiels of Probability or Statistics, the shape parameter is the first parameter of this distribution, while the scale (or "rate") parameter is the second.

From versions to versions the Maple definition of this distribution switches these parameters.
It's really a pain in the ass when you want to implement algorithms that use this distribution*

Thanks for your understanding

* for specialists, the Clayton copula uses as an ingredient a sample from Gamma(1/theta, 1) where theta is an adhoc parameter.
In Maple you must code s:=Sample(GammaDistribution(1, 1/theta)).

OK, you could reply me that once I know the trick it is the simplest thing at world to do the switch myself: nevertheless it's really boring, to say the least

1) start cmaple.exe;

2) type "proc(x, x);", and watch Maple die;

3) Request a refund from Maplesoft.

I am using command-line Maple cmaple.exe, I have been trying several hours to type the correct several characters to create a lambda function (anonymous function), but Maple's documentation is only for people using the GUI and gives no hint how to translate the right-arrow symbol into ASCII.

What is the secret, undocumented sequence of ASCII characters for defining an anonymous function via the command-line interface? (Why not document it in the user-manual, for those of who can't stand Maple's bad GUI?)

I have a maple code that has two output blocks giving a large number of numerical values for my experiment. I need these values to compare the output in both the code blocks and also to draw several figures using the data. On a single run of the program, a large number of values are obtained and then I manually copy them to excel sheet for further analysis. It takes a lot of my time to copy and paste the results on each run. I want to export the outputs of both the code blocks to a excel sheet. Any suggestion on this problem will be helpful to me. Thanks.

The link to my code is

I want the output in this format Book1.xlsx

Dear All,

I am having trouble with doing integration of a complex integrand with Maple 2016. The code is shown below. For simplicity, I have used a real function Psi00, but in general, it should be a complex function. Although I have assumed r to be real, in the final output, there is still an overhead bar on r^1/4. It is not recognized as real and is not multiplied on the r^5/4 factor to give r^3/2. May I ask you for help in solving this problem? Any of your help is highly appreciated!



assume(r, real); assume(phi, real);
Psi00 := exp(-(1/2)*r^2)/sqrt(Pi);
                             /  1  2\
                          exp|- - r |
                             \  2   /

int(int(conjugate(Psi00*r^(1/4))*Psi00*r^(1/4)*r, r = 0 .. infinity), phi = 0 .. 2*Pi);
    /   /             2 ______                          \\   
    |   |/   /  1  2\\   (1/4)  (5/4)                   ||   
    |   ||exp|- - r ||  r      r                        ||   
    |   |\   \  2   //                                  ||   
  2 |int|----------------------------, r = 0 .. infinity|| Pi
    \   \             Pi                                //   

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