## Special operators in Maple...

Below I wanted Maple to calculate the 4. degree Taylorpolynomium of a function f around x = 7. As shown below, Maple delivers a polynomial, but not a function definition. In other words one cannot have the polynomial evaluated at a specific value. The reason for this is obvious: The value 3 of x is passed to the command, implying 3 = 7 is a parameter to the command: Therefore the error message. I solved the problem by using the unapply command, but this operation is a bit tedious. I think I remember there is another more simple operator to make the same happen in Maple. I hope someone can remind me of that one!

Regards,

Erik

## Declare a multilinear operator as real valued...

I'm trying to define some multilinear forms to study differential geometry. What I need is only symbolic. My intention is symplify computations involving multilinear forms.

For example, to create an symbolic inner product "g" I used the command "define" like in this post:

http://www.mapleprimes.com/questions/203480-Define-And-Use-Abstract-Linear-Operator

So I tipped:

define(g, orderless, multilinear);

My doubt is: how can I declare that g(x,y) is always scalar?

With it I would simplify things like g(g(z,w)*x,y) = g(z,w)*g(x,y)

In my case, specifically, I type:

v:=(X,Y,Z)->g(Y,Z)*X-g(X,Z)*Y;

r:=(X,Y,Z,W)->g(v(X,Y,Z),W)-g(Y,T)*g(v(X,T,Z),W)+g(X,T)*g(v(Y,T,Z),W);

expand(r(X,Y,Z,W));

and the result is:

g(W,g(Y,Z)*X)-g(W,g(X,Z)*Y)-g(T,Y)*g(W,g(T,Z)*X)+g(T,Y)*g(W,g(X,Z)*T)+g(T,X)*g(W,g(T,Z)*Y)-g(T,X)*g(W,g(Y,Z)*T)

But I would enjoy that it were:

g(Y,Z)*g(W,X)-g(X,Z)*g(W,Y)-g(T,Z)*g(T,Y)*g(W,X)+g(X,Z)*g(T,Y)*g(W,T)+g(T,Z)*g(T,X)*g(W,Y)-g(Y,Z)*g(T,X)*g(W,T)

Is there a way to declare that g(x,y) is always scalar?

Thanks.

## Functional operator within a proc...

Hello

It has been years since I last used maple so I apologize if my question makes no sense and my code is outdated (and wrong!).

I need to write a function (proc) that uses a functional operator inside.  Something like

test:=proc()

local f,vars, func, aux, res;

f:=arg[1]; # a list

vars:=arg[2]: # a list

aux:=op(vars):

func:=aux -> f:  # a function from () to []

res:=func(op(func(aux))):

return(res):

end:

This is the basic idea of the proc.  If f:=[y, y*z-x, -15*x*y-x*z-x] and vars:=[x,y,z], the function of a function does not return as it supposes to.  Please tell me what I am doing wrong and how to improve and update the code.

many thanks

Ed

## How to deal with operator with both differential a...

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  D2+4u+uxD-1 multiply with D3+uD+ux,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?

## How to use seq to make a sequence of functions?...

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?

## Problem with KelvinBei function...

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??

## Reccurence relation between two operators ...

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

## Problem with differential operator...

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

maple2.mw

 (1)

 (2)

 (3)

 (4)

 (5)

 (6)

 (7)

 (8)

 (9)

## Function from dsolve result?...

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

For example, dsolve() outputs:

u(t) = u0ea t

then I would like to create function:

u := t → u0ea t

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

## How do I use result of dsolve?...

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

## How can I get result of real part?...

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?...

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);

## Function of (x,y,y') ?...

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

## How to define a symbolic Expectation Operator?...

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!