restart:local D:
with(plots):
with(plottools):

a := 7;
b := a/2;
NULL;

r := b/2;
c := 2*sqrt(10)*r;
A := [c/2, c/2];
B := [c/2, -1/2*c];
C := [-c/2, (-c)/2];
D := [-c/2, c/2];
f := (x, y) -> x^2/a^2 + y^2/b^2 = 1;
Ell1 := rotate(implicitplot(f(x, y), x = -9 .. 9, y = -6 .. 6, color = blue), Pi/4);

g := (x, y) -> x^2/b^2 + y^2/a^2 = 1;
Ell2 := rotate(implicitplot(g(x, y), x = -10 .. 10, y = -10 .. 10, color = blue), Pi/4);

quadri := plot([A, B, C, D, A], x = -6 .. 6, y = -6 .. 6, filled = true, color = red, transparency = 0.7);
Cir1 := disk([c/2 - r, -c/2 + r], r, color = blue);
Cir2 := disk([-c/2 + r, -c/2 + r], r, color = blue);
Cir3 := disk([-c/2 + r, c/2 - r], r, color = blue);
Cir4 := disk([c/2 - r, c/2 - r], r, color = blue);
display([quadri, Ell1, Ell2, Cir1, Cir2, Cir3, Cir4], scaling = constrained, axes = normal);
how to find the equations of ellipses in order to fit them to discs and whiten the interior of ellipses ? Thank you.

Is it possible to solve the mixed PDEs below using the method of lines or any other numerical scheme?

B.C:

theta(0,t) = theta(d,t) = 0

v(0,t) = v(d,t) = 0

I.C: theta(z,0) = \thetab*sin(pi/2)*z,  v(z,0) =0 at t =0  for both the initial conditions, where thetab = 0.0001 

% parameters.

K3 = 7.5*10^(-12);

eta2 = 0.1361;

alpha2 = -0.1104;

gamma1 = 0.1093;

d = 0.0002;

xi = 0.1; 

Note: xi is the controlling parameter. For instance, we can plot theta and v for different values of xi.

I tried matlab but no standard scheme to solve the problem because of the partial^2 theta/partial d partial t term. It would have been possible to use pdepe in Matlab if not for the mixed derivative. Please any help.

Thank you

I have a set of equations gathered in a vector. The number of equations varies each time. Here in this example it is 4. How you suggest so solve them with fsolve? I tried to use seq but faced error.

Download SoalNewton.mw

According to Wikipedia

"In computing, a programming language reference or language reference manual is
part of the documentation associated with most mainstream programming languages. It is
written for users and developers, and describes the basic elements of the language and how
to use them in a program. For a command-based language, for example, this will include details
of every available command and of the syntax for using it.

The reference manual is usually separate and distinct from a more detailed
 programming language specification meant for implementors of the language rather than those who simply use it to accomplish some processing task."

And no, Maple's Programming guide is not a Language reference manual. This is a guide to how to program in Maple. But it is not reference manual for the language itself. i.e. description of the Language itself.

Examples of Language reference manuals are

C

Original C++ 

Python

Ada

Fortran 77

and so on.

Why is there no LRM for Maple? Should there be one? I find Maple semantics sometime confusing, and many times I find how things work by trial and error. Having a reference to look at will be good. 

I know for a language as large as Maple, this is not easy to do. But it will good for Maplesoft to invest into making one.

Dear All,

I have a question about "fraddiff" command to compute the fractional derivative of a function.
I need to produce  a procedure to manually compute Caputo fractional derivative of a function, instead of using "fracdiff", as the following:

Frac_C:=proc()
description "Frac_C(function,lower bound, variable (upper bound), order of differentiation)";
a:=args[2];
x:=args[3];
alpha:=args[4];
f:=unapply(args[1],args[3]);
m:=ceil(alpha);
return 1/GAMMA(m-alpha)*int((x-tau)^(m-alpha-1)*diff(f(tau),tau$m),tau=a..x);
end proc;

when I call the above procedure, as Frac_C(x^(3.4),0,x,3/4), Maple is not able to calculate the integral defined in the Caputo fractional derivative. However, I saw the pre-defined Maple command, namely fracdiff, is able to do.
Where is the trouble?
can anyone help me?

It is worth mentioning that I can calculate the fractional derivative of a functional by procedure "Frac_C()" when I try to use it at the given x as the following which is not desirable for me.
evalf(subs(x=2,Frac_C(x^(3.4),0,x,3/4)));
evalf(subs(x=2,fracdiff(x^(3.4),x,3/4)));

Best wishes

t is removed from gamma(t)

Download arg_removed.mw

If i matrix of order

m1 cross n1

and 

other of order

m2 cross n2

and say n1 >n2 

The function change(A,B) and make the matrices of order m1 cross n1 and m2 cross n1 by appending zero columns to the other where n2 is the smaller one to make it n1=n2

Download a.mw

The question is in the picture.

y(x) is the result of the last calculation. How do I apply diff to the last result?

Thanks!

Can pacemaker and corosync work with maple?

How to setup pacemaker and Corosync to maple work in Amazon EC2?

i had only one installed License in linux

how to make it work in clusters ?

what is the difference with supercomputing in Amazon ?

which consulting company in Hong Kong can help to use supercomputing in Amazon in my case ? I would like to run batch of batch total 100 script running maple in one instance , but total numbers need to run around 60 years. Any consultant to calculate and setup this supercomputing or pacemaker to make calculations into one day or a few days ? 

Suppose their are two matrices A and B say

A has dimension  n1   rows  and m columns

B has dimension n2 rows and m columns

I need to find if any two rows of A are same as that of B  or not

How many are same.

If they are same in some rows which row of A is same as which row of B 

Function     checkrowsuniquie(A,B)

I want the resulting shape of the 3D matrix M (ٍExcel file) to be placed in below grids codes.
The range of x and y is between 0 and 1 and the range of z is 1/1 e-4 to 1/1 e-10.

PlotTest.xlsx

Download eeeeeee.mw

Dear all,

I would like to simplify the expression a*f(x)=0 with a>0.

It is expected to give f(x)=0, but maple still returns a*f(x)=0

I have tried this

assume(a>0)

simplify(a*f(x)=0)

It gives

a~ f(x)=0, not f(x)=0 

Thanks!

Dear Mapler

I want to find all real and complex solutions to the following equation. then calculate the omega based on these values and finally select the present the omega with the smallest imaginary part.

with(SignalProcessing):

n:=8;

kk:=FFT(GenerateJaehne(n,1));

#params:= [p,    s, nu,   rho, h,    sigma, C1[1], C1[2], C2[1], C2[2], k1,  k2,  m1[1], m1[2], m2[1], m2[2] ]
 params:= [1e-7, 0, 1e-6, 1e3, 1e-2, 0,     5e-4,  5e-4,  5e-4,  5e-4,  1.4, 1.4, 1+I,   1+I,   1-I,   1-I   ]:

for i from 1 to n do
    x:=kk[i]:
    mm[i]:=[solve(
             eval(
                  ( (x*h)*( (y*h)*sinh((x*h))*cosh((y*h))-(x*h)*cosh((x*h))*sinh((y*h)))*(1+s*(x*h)^2)
                    +p*(-4*(x*h)^2*(y*h)*((x*h)^2+(y*h)^2)+(y*h)*((y*h)^4+2*(x*h)^2*(y*h)^2+5*(x*h)^4)*cosh((x*h))*cosh((y*h))
                    -(x*h)*((y*h)^4+6*(x*h)^2*(y*h)^2+(x*h)^4)*sinh((x*h))*sinh((y*h))))
                  /((x*h)^2*(y*h)*cosh((y*h)))
                 , [p=params[1], s=params[2], h=params[5] ]), y
            , AllSolutions=true)]:
    print(kk[i]);
    print(mm[i]);
    for j from 1 to nops(mm[i]) do
        omega[i][j]:=eval(-I*nu*((x*h)^2-mm[i][j]^2), [nu=params[3],h=params[5]]);
        print(omega[i][j]);
    od:
    print(`======`);
od:

Given two terms in expression of type  `+` where the first is rational and the second is not, I wanted to combine both under on common denominator to obtain one term (not `+` any more).

I expected that combine will do that.

restart;
expr:=A/B+C;
combine(expr);

But the above leaves the original expression as is. Ofcourse I can just do

numer(expr)/denom(expr);

Here is screen shot

My question is why combine does not do that automatically? For reference, Mathematica command Together is the equivalent to Maple combine and this is what it does

Which is what one would expect to happen. 

I am just trying to understand the logic why Maple's combine did not work as one would expect. That is all. I looked at help and tried different option to combine, but non worked.

Is there  a specific type name for vectors in Physics[Vectors]?  Specifically, Let's say we want to write a proc whose argument is expected to be a (Physics) Vector, as in  these (trivial) demos:

with(Physics[Vectors]);

f := proc(a_::???)
    return a_ . a_;
end proc:

g := proc(a_::???, b_::???)
    return a_ &x b_;
end proc:

What do we put in place of "???".