In my study, I often need to verify that two operator is symmetric i.e. [P,Q]=PQ-QP=0, where A and D are operator polynomial such like D^{2}+4u+u_{x}D^{-1 }multiply with D^{3}+uD+u_{x},where D is differential operator.

I tried to use the Ore_package which can easily deal with the operator polynomial without integral(i.e. D^{-1} term), so in my case , how to deal with operator with both differential and integral?

When using seq function below in the second call, it does not generate a sequence of functions with 'a' being 1, 2, and 3, and I had expected.

First seq function call is just to show that it works without the function "x ->" wrapping.

I could of couse use unapply as in the third call, but I had expected the second call to work.

Am I doing anything wrong, or is this a Maple bug?

Hello,

I need to crate a function to be evaluated in a range of values, and this function i would to use in other expression, example:

cel1 "seq(i,i=0.001..2,0.001)"

cel2 "A:=&1";cel1

cel3 "f:=x->diff(KelvinBei(0,x),x)"

cel4 ""B:=map(x->f(x),[A])"

This is ok with a lot of function but with diff(KelvinBei(0,x),x) in cel4 show this error "Error,(in f) invalid input:.1e-2, which is not valid for its 2nd argument.

Why??? How can I do??

Hi

Hope a nice day for all

restart;

# *% define the product of between two operators, and q real number a*%b = q*b*%a+1;

# First I would like to give a simple for a^n*%b;# and a*%b^n;

them deduce a general for

b^n*%a^k*%b^N*%a^K-q^(k*N-n*K)*b^N*%a^K*%b^n*%a^k;

where n, k and k greater than 1 and n geater than k

Simplification.mw

Thanks for your help

hi.please see attached file below and help me.one problem is apply differential operator on matrix and then caclute 3D integral?

maple2.mw

Error, invalid derivative

Error, Got internal error in Typesetting:-Parse : "invalid subscript selector"

Warning, computation interrupted

Download maple2.mw

How do I create a function from dsolve() result?

For example, dsolve() outputs:

u(t) = u_{0}e^{a t}

then I would like to create function:

u := t → u_{0}e^{a t}

but I want to do it using dsolve() output, not typing it manually. Thanks.

Hi !

I have trouble to do this stuff :

i am solving an ODE and i would like to use the result as a function.

example :

>>ode := diff(f(x), x) = 2*x+6; d --- f(x) = 2 x + 6 dx >>init := f(0) = 12; f(0) = 12>>dsolve({init, ode}); f(x) = x + 6 x + 12

Here everything works fine...

but now i want to define g(x) = f(x)*exp(x) ...

but i can't use g(x) after :

like :

>> g := x -> f(x)*exp(x) ; x -> f(x) exp(x)g(2); f(2) exp(2)f(2); f(2)

How can i do that please ??

Thanks,

Corentin

Hi all!

as shown below, how can get a result without 'R':

p_com(z,t):=Re(exp(I*omega*t-I*k*(lambda[r]+I*lambda[i])*z)) assuming omega::real,t::real,k::real,lambda[r]::real,lambda[i]::real,z::real

Thanks very much!

How to evaluate The Abel integral has the form I can not compute this

> restart;

> f := proc (x) options operator, arrow; (4/3)*x^(3/2) end proc; k := proc (x, t) options operator, arrow; 1/sqrt(x-t) end proc;

> int((4/3)*t^(3/2)/sqrt(x-t), t = 0 .. x);

Thank you :)

> restart;> f := proc (x) options operator, arrow; (4/3)*x^(3/2) end proc; k := proc (x, t) options operator, arrow; 1/sqrt(x-t) end proc;> int((4/3)*t^(3/2)/sqrt(x-t), t = 0 .. x);

I am trying to get W(x,y,y')=y*y'/x

I am trying

omega:=(x, y(x), (diff(y(x),x)))-> (y(x)*(diff(y(x), x))/x);

but get

Error, invalid parameter; functional operators require their parameters to be of type symbol or (symbol::type)

Can anyone help me out?

thank you

Hello, i am recently doing a lot of my (really simple) equation manipulations with Maple and would like to include an expectation operator E( ) in my symbolic equations. As maple threads E() as a function, differentiating is not very convenient, as i have to replace all D(E) ... manually. I tried defining some properties of E() via the define() function, but when trying to set the behavior of d E(f(x))/dx I am not sure how to use (diff()=result) in the define() function. Any help or ideas are greatly appreciated!

In the following, the diff operator calcuates the derivative correctly, but the D operator doesn't. A bug?

f := x -> a[1][2]*x; # the double index on a[][] is intended

diff(f(x), x);

D(f)(x);

Here is a worksheet containing the commands above in case you want to try it yourself: mw.mw

Its a well known fact that the spherical harmonics are eigenfunctions of the Laplace operator on the unit sphere with eigenvalues -l(l+1). Its used all over the place in QM for example. However maple does not seem to have this.

Try it, you might be surprised. Its going to be a mess. How do you deal with it, to simplify it to the known form -l(l+1)r^{-2}Y_{lm}??

I have a nice family of functions of the form:

W:=(p,n,mu,w)->sum(w[k] * (n-k)^{p *} mu^{(n-k)},k=1..n)

which can be evaluated for different p's using the operator mu*diff(...,mu)

The recursion begins with p=0 and proceeds using mu*diff(W(p,n,mu,w),mu) = W(p+1,n,mu,w).

Can anybody implement this procedure in Maple

Thank you

Is it possible to define and use an abstract linear operator L which is a function of y(x) and z(x)?

For example, Maple should be able to recognise that L(y(x),z(x)) = L(z(x),y(x)) and simplify expressions such as

L(c*y(x),d*z(x)) = c*d*L(y(x),z(x)) where c and d are constants or numbers.

It should also be able to expand things like L(c*y1(x)+d*y2(x),e*z1(x)+f*z2(x)).

Thanks.

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