Hello,

I am using Maple Physics for symbolic tensor computations. However, I fail to simplify quite a simple expression.

Consider the following code:

    with(Physics):with(Library):

    Setup(spacetimeindices = lowercaselatin):

    Define(F[a]);

    read "example2.txt"; 

    Simplify(%);

Here is a file with expression: example2.txt.

The expression in the example2.txt is equal to zero. The following steps allow to obtain this result: expand, contract Kronecker deltas and metric tensors and collect similar terms. This also can be verified using another software (Cadabra, Mathematica xAct, etc.). As one can see, the result of Maple Simplify(%) contains terms like -462661905780*F[k]*F[~k] - 5856479820*F[m]*F[~m] which can be futher simplified, but Maple does not do this (even when I invoke Simplify(%) several times).

What is the right sequence of manipulations needed to obtain zero?

I use the latest Physics package (39.2, updated on November 30).

Thanks,

Dmitry.

Hello,

For some days, i no longer manage to open MapleSIM.

In fact, after double clicking on the shortcut, the software seems to be launched.

However, i can't open MapleSim on my screen. It seems that MapleSIM is only visible on the taskbars.

Maybe I have changed an option on my windows7.

I don't know.

Has somebody got a idea to help me ? so as to open my application normally ?

I attached a copy of my screen where you can see MapleSIM only in the taskbars.

 

Thank you for your help.

I created a interactice slider and graph (Parabolas_In_Vertex_.mw)and want to have a title to display the actual equation being graphed. where graph of is, I would like it to say "graph of . with a being the value of the slider. I have inserted a title and put the following code in, but it does not work:

display( [

'title' = typeset( "Graph of ", y = %Slider*x^2),
'titlefont' = ["Times New Roman", 'BOLD', 14]]
);

This was put in the edit click action of the title. Any help would be great. I have looked everywhere and can't seem to find the answer. I can send you my file if you would like to look at it.  

how to find lie group or finite group or symmetry group of one differential equation or system of differential equations

Let a convex polygon, for example Q:=polygon([[0,2],[1,4],[4,4],[5,1],[3,0]]), be given.
How to find the disk of the biggest radius which is contained in Q?
How to find the disk of the smallest radius which contains Q? Of course, with Maple.

restart;

Lfh := proc(numoflevel, h, fx, var)

if numoflevel = 1 then

        hello := 0;

        for i from 1 to nops(var) do

                hello := hello + diff(h[i], var[i])*fx[i];

        od;

        return hello;

else

        hello := 0;

        for i from 1 to nops(var) do

                hello := hello + diff(Lfh(numoflevel-1, h, fx, var), var[i])*fx[i];

        od;

        return hello;

end if;

end proc:

f:=[x3-x2^3,-x2,x1^2-x3];

g:=[0,-1,1];

h:=[x1,0,0];

variables := [x1,x2,x3];

Lf1h := Lfh(1,h,f,variables);

Lgf1h := Lfh(1,[seq(Lf1h,n=1..nops(variables))],g,variables);

Lf2h := Lfh(2,h,f,variables);

Lgf2h := Lfh(1,[seq(Lf2h,n=1..nops(variables))],g,variables);

Lf3h := Lfh(3,h,f,variables);

Lgf3h := Lfh(1,[seq(Lf3h,n=1..nops(variables))],g,variables);

i doubt that my book example is wrong

it said relative rank is 2, but i can not find any zero when Lgf3h

if i continue to Lgf4h, Lgf5h, Lgf6h...etc, still no zero what does it mean?

Example

Diff(x1,t) = x2^2,
Diff(x2,t) = u,
y = x1

result in

Diff(y,t$2)-4*u^2*Diff(y,t) = 0
2*u*x2 - Diff(y,t^2) = 0
x1 - y = 0

is it possible a general and generic method to apply some steps on system below

Diff(u1, t) = u1*u2-u1*u3,
Diff(u2, t) = -u1*u2+u2*u3-(1/2)*(conjugate(u2-u3)*(u1*u2-u1*u3)+conjugate(u1)*(-u1*u2+u2*u3)-conjugate(u1)*(u1*u3-u2*u3))/conjugate(u1),
Diff(u3, t) = u1*u3-u2*u3+(1/2)*(conjugate(u2-u3)*(u1*u2-u1*u3)+conjugate(u1)*(-u1*u2+u2*u3)-conjugate(u1)*(u1*u3-u2*u3))/conjugate(u1),
y = u1

I often have problem with evalf function for exaple:

Maybe you have suggest for me, how solve this problem?

Hello,

Assume a periodic signal that is the sum of four sinusoidal signals, all with different frequency and phase. The fundamental frequency has phase=0, so at t=0 its value is 0 (a zero crossing point). I need to find the influence of the other frequency components on the zero crossing point in [seconds] as an analytical expression. I made the Maple script below to find out, but get a RootOf result. How can I solve this?

Thanks for your help!

Download 20131130_Zero_crossi.mw

I am using maple (version 12) for the first time.  I want equations of x and y ( in terms of a) from these two given equations. The equations I got are very complex, how to simplify these equations?

Equation#1 is:

Equation#2 is:

From Equation#1, i find "y"

  

Now i put y in Equation#2

and from that euation, i can get x

but these equations are very complex..

I simply want to find the equations of x and y..
How to simplify it?

I define a func

f(x,y):=piecewise(x=0 and y=0,139 ,x=1 and y=0,144,x=2 and y=0,149,x=3 and y=0,155,x=4 and y=0,155,x=5 and y=0,155,x=6 and y=0,155,x=7 and y=0,155,x=0 and y=1,144,x=1 and y=1,151,x=2 and y=1,153,x=3 and y=1,156,x=4 and y=1,159,x=5 and y=1,159,x=6 and y=1,159,x=7 and y=1,159,x=0 and y=2,150,x=1 and y=2,155,x=2 and y=2,160,x=3 and y=2,163,x=4 and y=2,158,x=5 and y=2,156,x=6 and y=2,156,x=7 and y=2,156,x=0 and y=3,159,x=1 and y=3,161,x=2 and y=3,162,x=3 and y=3,160,x=4 and y=3,160,x=5 and y=3,159,x=6 and y=3,159,x=7 and y=3,159,x=0 and y=4,159,x=1 and y=4,160,x=2 and y=4,161,x=3 and y=4,162,x=4 and y=4,162,x=5 and y=4,155,x=6 and y=4,155,x=7 and y=4,155,x=0 and y=5,161,x=1 and y=5,161,x=2 and y=5,161,x=3 and y=5,161,x=4 and y=5,160,x=5 and y=5,157,x=6 and y=5,157,x=7 and y=5,157,x=0 and y=6,162,x=1 and y=6,162,x=2 and y=6,161,x=3 and y=6,163,x=4 and y=6,162,x=5 and y=6,157,x=6 and y=6,157,x=7 and y=6,157,x=0 and y=7,162,x=1 and y=7,162,x=2 and y=7,161,x=3 and y=7,161,x=4 and y=7,163,x=5 and y=7,158,x=6 and y=7,158,x=7 and y=7,158)

It is really a chore . By the way , is there more concise way to definition of the same effet as this ? 

then I type:

sum(f(0, y), y = 0 .. 7) 

Maple just respond me a 0 

why ?

How can I expand the mutivariate taylor series of the functions below about the point (x,y)

f(h*a[2]+x, h*a[2]*k[1]+y);

 and

f(h*a[3]+x, y+h(a[3]-b[32])*k[1]+h*b[32]*k[2]);

Hello, everyone. I'm sorry for bed view. Can i solve the system of equations in maple which above this text. I had inputted the system in Maple, but there is mistake: 

Error, (in dsolve/numeric/process_input) input system must be an ODE system, got independent variables {t, tau, Q(tau)}.

Code:

eq :=

diff(x(t), t) = -y(t)-z(t)-(diff(x(Q(tau)), tau))*((diff(x(Q(tau)), tau))*(-y(t)-z(t))+(diff(y(Q(tau)), tau))*(x(t)+a*y(t))+(diff(z(Q(tau)), tau))*(b-z(t)*(x(t)-c)))/((diff(x(Q(tau)), tau))^2+(diff(y(Q(tau)), tau))^2+(diff(z(Q(tau)), tau))^2)+eps_x*q(t),

diff(y(t), t) = x(t)+a*y(t)-(diff(y(Q(tau)), tau))*((diff(x(Q(tau)), tau))*(-y(t)-z(t))+(diff(y(Q(tau)), tau))*(x(t)+a*y(t))+(diff(z(Q(tau)), tau))*(b-z(t)*(x(t)-c)))/((diff(x(Q(tau)), tau))^2+(diff(y(Q(tau)), tau))^2+(diff(z(Q(tau)), tau))^2)+eps_y*q(t),

diff(z(t), t) = b+z(t)*(x(t)-c)-(diff(z(Q(tau)), tau))*((diff(x(Q(tau)), tau))*(-y(t)-z(t))+(diff(y(Q(tau)), tau))*(x(t)+a*y(t))+(diff(z(Q(tau)), tau))*(b-z(t)*(x(t)-c)))/((diff(x(Q(tau)), tau))^2+(diff(y(Q(tau)), tau))^2+(diff(z(Q(tau)), tau))^2)+eps_z*q(t),

diff(q(t), t) = ax*(-y(t)-z(t)-(diff(x(Q(tau)), tau))*((diff(x(Q(tau)), tau))*(-y(t)-z(t))+(diff(y(Q(tau)), tau))*(x(t)+a*y(t))+(diff(z(Q(tau)), tau))*(b-z(t)*(x(t)-c)))/((diff(x(Q(tau)), tau))^2+(diff(y(Q(tau)), tau))^2+(diff(z(Q(tau)), tau))^2))+ay*(x(t)+a*y(t)-(diff(y(Q(tau)), tau))*((diff(x(Q(tau)), tau))*(-y(t)-z(t))+(diff(y(Q(tau)), tau))*(x(t)+a*y(t))+(diff(z(Q(tau)), tau))*(b-z(t)*(x(t)-c)))/((diff(x(Q(tau)), tau))^2+(diff(y(Q(tau)), tau))^2+(diff(z(Q(tau)), tau))^2))+az*(b+z(t)*(x(t)-c)-(diff(z(Q(tau)), tau))*((diff(x(Q(tau)), tau))*(-y(t)-z(t))+(diff(y(Q(tau)), tau))*(x(t)+a*y(t))+(diff(z(Q(tau)), tau))*(b-z(t)*(x(t)-c)))/((diff(x(Q(tau)), tau))^2+(diff(y(Q(tau)), tau))^2+(diff(z(Q(tau)), tau))^2))+beta*q(t):

cond := x(0) = 0, y(0) = 0, z(0) = 1, q(0) = 0:
F := dsolve({cond, eq}, [x(t), y(t), z(t), q(t)], numeric).

What program (Maple,Matlab,mathcad...) can solve, if Maple can't.

Thank's.

Hello everyone

Here is my problem: I have a procedure depending on a variable and a parameter, let's say F(x,a). I have another procedure that gives me a specific value for x depending on the parameter a, let's say X1(a). I would like to make a list of values of F(X1(a),a) for different values of a. So the list would go F(X1(a1),a1), F(X1(a2),a2), and so on. Here is what I tried

xlist:=[seq(X1(i),i=1..10)]:

flist:=[seq(F(xlist,i),i=1..10)]:

but it doesn't work.

Another thing I tried was

Matrix([seq(eval(map(evalf@F(xlist,i),xlist),i=1..10)]):

Also doesn't work. Not with evalhf either. I can do it for specific values of xlist by choosing xlist[i] inside F, but that's it. If I leave i unspecified it can't do it.

Thanks for the help

Dear All,

I would like to perform a numerical integration of the following. Please let me know the method.

The integration consits of one variable essentially. Since the symbolic integration is not possibl and hence I have to do it numerically.

Appreciate you reply. Thanks