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);

Hello,

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?

restart;

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.

Hi there,

I would like to have an operator (in this case, the natural logarithm) applied to a list/array of points defined as:

ydata := [0.572594976618e-1, 0.327865007249e-1, 0.280821589546e-1, 0.114365745192e-1, 0.578537931608e-2, 0.139154661062e-2, 0.641467839994e-3, 0.18013801847e-3];How can I apply Maple's ln() operator to the whole array (i.e. avoid to apply it to ydata [1], ydata [2], etc.)?

Thank you,

jon

Partial rectification for the Physics:-Simplify and Physics:-Library:-SortProducts procedures dealing with Fermi annihilation/creation operators

This post will be useful for physicists dealing with Fermi annihilation/creation operators. Physics Package provides plenty of powerful tools for quantum operators handling, however some of them often fail to render correct result. In particular incorrect behaviour with respect to Fermi annihilation/creation operators is observed for routines Simplify and SortProducts. In this post I present my procedures and which partially solve these issues.

Problems with Physics Package routines

Short explanation of custom routines and

Weak points

Final notes

Download FermiCreationAnnihilation.mw

Hello.I am trying to extract the terms that are a product of a commutative part and an operator part from the input expression. That is I am trying to extract a terms like a*A.B where A and B are quantum pperators. I am trying to do it by creating corresponding structured type:

restart; with(Physics); Physics[Setup](op = {A, B}, quiet);

`type/ProdComOp` := `&*`(commutative, specfunc(anything, Physics:-`*`)); z0 := u*A.B-A+k*B+B.A.B+g; z1 := z0+v*A.B.A;S1 := indets(z1, ProdComOp);

and all it is Ok. The result is But if

z2 := z0-v*A.B.A; S2 := indets(z2, ProdComOp);

then however I expected to receive the same as S1.How to handle the sign of the commutative part? Thank you.

Hello Dears

I have this equation

(Napla)^4 * F(x,y) + k^2 * (Napla)^2 * F(x,y)= 0, (1)

which may be written as a non-homgeneous Helmholtz equation as

(Napla)^2 * F(x,y) + k^2 * F(x,y)= g(x,y), (2)

where the function g(x,y) is a harmonic function and (Napla)^2 is the laplace's operator in two dimension.

Can Maple solve equation (1), it will be better. If not may be solve equation (2).

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