Hi

Why Maple can't  calculate following definite double integral:

Error, (in simpl/Re) too many levels of recursion

The approximated midpoint intgration gives the value -0.4552861717e-1

The Legendre root nodes with Christoffle weights gives the value -0.4552311444e-1

Thanks

I have the following two questions/issues:

1.) It seems to me that in the Tetrads package, some tetrad is automatically calculated in terms of the metric. Is there any way to reverse the roles, i.e., to have the vierbein determine the metric?, as is anyway a more natural setup, I think. The point is that I would like to work with an arbitrary, non-fixed vierbein, and from it having the metric, Christoffel symbols, etc., calculated 'on the fly', and then ultimatively construct the socalled minimal spin connection from these quantities.

2.) Consider the following expressions:

Simplify(e_[a,mu ]*Christoffel[~mu,nu,rho]);
Simplify(e_[a,nu ]*Christoffel[mu,~nu,rho]);
Simplify(e_[a,rho]*Christoffel[mu,nu,~rho]);

As the Christoffel symbols do not transform as tensors, I find this notation unfortunate, as one cannot simply move the vierbein through a (partial) derivative. Conversion between world indices and Lorentz indices should, I think, only be performed for world indices of tensorial type.

if there a series of matrix,

current matrix and previous matrix has same value , then defined as pattern

and

then define x and y are the position of pattern , if Matrix([[777,x,x],[77,7,7],[2,y,y]]

then code auto exchange x and y become Matrix([[777,y,y],[77,7,7],[2,x,x]]

but this recognization need to observe manually, 

can this be automated for any kind of pattern , such as exchange or other operations of pattern?

can neural network or deep learning in maple code recognize the operations such as exchange part of row or flip or symmetric about axis or other need imaginable operations ?

Is there something wrong with dsolve?

ode := diff(y(x), x) = sqrt(2*32.2*y(x)):
ics := y(0) = 0:
dsolve({ics, ode});

maple output:   y(x) = 0

The answer should be

y(x) = 16.1 x^2

Wolfram got it

I tried using restart, with(DEtools), still no luck. Though I don't think its necessary to call with(DEtools) for this simple equation.

To make the problem simpler, use dsolve on  dy/dx = √y , y(0)=0.

ode := diff(y(x), x) = sqrt(y(x)):
ics := y(0) = 0:
dsolve({ics, ode});

maple returns  y(x) = 0, which is incorrect.  Should be y(x) = x^2/4

I uploaded the worksheet just in case 'its just me'.

diffeqseperable.mw

how can plot a graph of V(r) against E0,B0 and EO*B0;

given that V(r)=V0/b(a-exp**-eta*r/1-exp**-eta*r)-V1exp^-eta*r/(1-exp^-eta*r)+V2exp^-2eta*r/(1-exp^-eta*r)^2;

E0=q*rho(electron)*velocity(vs)/mu;

B0=h/2^2*omega^2/16

The problem and the error in the attached worksheet. 

https://www.maplesoft.com/support/help/errors/view.aspx?path=Error,%20(in%20DocumentTools:-GetProperty)%20input%20is%20ambiguous

Download MAPLE_PLEASE_HELP.mw

Hi there,

I have a function defined as:

U:=-[0.25*exp(1/2*epsilon*t)*(1/v^2-1+exp(epsilon*t))^(-0.5)]*sin(4*t)

which I am trying to plot on a 2D graph of axes (t,u(t)).

In the specific case I have epsilon=1/10 and v=2

When I try plot(U), maple returns the error message:

Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct

Could anybody help me out please?

Many thanks

I'm trying to solve a system of nonlinear differential equations. As a minimal working example, Maple is able to solve this just fine:

restart:

pde_sys :={diff(A(t1),t1)*cos(B(t1)) = 0, diff(A(t1),t1)*sin(B(t1)) = 0}:
solving_vars := {A(t1), B(t1)}:

dsolve(pde_sys, solving_vars);

This returns [{A(t1) = _C1}, {B(t1) = B(t1)}], as expected.

However, when simply adding an arbitrary dependence on a second variable, no solution is generated

restart:

pde_sys :={diff(A(t1,t2),t1)*cos(B(t1,t2)) = 0, diff(A(t1,t2),t1)*sin(B(t1,t2)) = 0}:
solving_vars := {A(t1,t2), B(t1,t2)}:

dsolve(pde_sys, solving_vars);

Of course, this has a solution: [{A(t1,t2) = _F1(t2)}, {B(t1) = B(t1,t2)}].

Using printlevel to debug, it seems the behavior diverges when dsolve attempts to call type/ODEtools/F(x). The univariate case correctly determines that A(t1) is of the type F(x); then, these functions are correctly passed to PDEtools/assign and execution continues nominally.

For the multivariate case, A(t1,t2) is not recognized as type F(x), so no functions are passed to PDEtools/assign and execution is dominated by null sets.

Is there something I'm missing here? Or is there another way to approach this problem?

Thanks!

How to linearize this equation by Taylor function?

or otherwise written:

sin(phi2)*sin(psi1(t))*lk*m1*(diff(psi1(t), t, t))+sin(phi2)*(diff(psi1(t), t))^2*cos(psi1(t))*lk*m1

Some one can help me?

Hi!

If i do something like this:

my_points := [[1, 2], [2, .9]];
plot(my_points, style = point)

It works ok. But then i try to take units in place:

my_scaled_points := [[1*Unit('kg'), 2*Unit('hour')], [21*Unit('kg'), 7*Unit('hour')]];
plot(my_scaled_points, style = point, useunits = [Unit('kg'), Unit('hour')])

..i got empty graph. How it can be fixed?

Thank you!

Is it possible to construct in Maple the following sequence of ascending fifths?:

3/2, 3^2/2^3, 3^3/2^4, 3^4/2^6, 3^5/2^7, 3^6/2^9, 3^7/2^11, 3^8/2^12 and so on. The result always more than 1 and less than 2.

Hello,

I'm quite new to Maple and as practise, I want to calculate some z-Transformations via the definition (sum).

sum(z^(-k),k=0..infinity) assuming abs(z)>1; this one works fine (after I added the convergence condition abs(z)>1.

sum(exp(a*k*Ta)*z^(-k),k=0..infinity) assuming abs(exp(a*Ta)*z^(-1))>1; doesn't work. But I if I change the convergence condition to a*Ta<ln(z), it is calculated correctly. Why does the first attempt not work? What is the correct way to tell maple the convergence condition?

Hi all

I would like to display 'Hello' or 'try again' to see the condition introduced is satisfied or not. 

if f(a) <0 then print( a, f(a));
display ('  Hello);
else
display( ' Tru again')

end if;

But this code does not work.

Thanks for any help.

Dear all

I solve an optimization problem ( minimization or maximization) using lagrangeMultiplier theorem 

The objective function is f:=(x,y,z) =x*y+y*z;

The constraints are: x*y=1  and y^2+z^2=1;

Using a numerical method I get the follwing point 

x = 1.41421356249703, y = .707106781124551, z = .707106781248575

How can I confirm that this point is a minumum or maximum

Maybe I must use Hessian matrix or something else.

Which condition must be introduced to know the type ( maximum or minumum) this point.

Many thanks for your help

I have a system of equation as

Hi all

I have a system of equation:

sys := [x+y, 2*x+y^2];

How can I convert the previous system to this function using maple

F:=(x,y)->(x+y,2*x^2+y^2);

then how can I compute the gradient of F.

Many thanks.