I got a double sum as a solution to heat equation in 2d. How do I plot that för different time values? 

I can't get the right syntax for add, op

Hello everyone

I am new in mapple software and i am facing some proplem to tackle  Laplace equation and Poisson equation. I want to find out the potential psi given in two equations 

I want to solve following equ with finite difference method in order to find potential psi .In the second equation  n = concentration of electrons  ,p= concentration of holes and C= additional concentration ,q is electronic charge .

Can anyone suggeset how I can solve this type of partial differential equation with numerical method (FDM) in mapple?

Can we use this euler lagrange command for the system of pde's?

If we have a system without lagrangian then euler opertor is applied corresponding to three dependent variables.

so we have three equations but in this euler lagrange command no dependent variable is mentioned.   

When I right-click on a Matrix, the cursor rotates, but the context menu does not open at all (in Maple 2017, in document mode, in Win 10).
Any suggestions - Anyone else with this problem?

Just like the title described, I have encountered an error when I use the command "expand". Actually, I just follow the example, but it doesn't work. Please help me or tell me how can I solve it in other commands.

restart;
alias(epsilon = e, omega = w, omega[0] = w0, t[1] = t1, t[2] = t2); e := proc (t1, t2) options operator, arrow; e end proc; w0 := proc (t1, t2) options operator, arrow; w0 end proc; a := proc (t1, t2) options operator, arrow; a end proc; f := proc (t1, t2) options operator, arrow; f end proc; mu := proc (t1, t2) options operator, arrow; mu end proc;
ode := (D@@2)(u)+2*mu*e*D(u)+w0^2*u+e*w0^2*u^3-e*f*cos(omega*t) = 0;
                                               2  
     @@(D, 2)(u) + 2 mu epsilon D(u) + omega[0]  u

                          2  3                             
        + epsilon omega[0]  u  - epsilon f cos(omega t) = 0
e_oredr := 1;
ode := simplify(subs(D = sum('e^(i-1)*D[i]', 'i' = 1 .. e_oredr+1), ode), {e^(e_oredr+1) = 0});
 / 3         2                                                 
 \u  omega[0]  + 2 (epsilon D[2] + D[1])(u) mu - cos(omega t) f

                  \                   2                   
    + 2 D[1, 2](u)/ epsilon + omega[0]  u + D[1, 1](u) = 0
simplify(collect(%, e), {e^(e_oredr+1) = 0});

u := sum('v[i]*e^i', 'i' = 0 .. e_oredr);
                      epsilon v[1] + v[0]
ode := simplify(collect(ode, e), {e^2 = 0});
for i from 0 to e_oredr do eq[i] := coeff(lhs(ode), e, i) = 0 end do;
                       2                         
               omega[0]  v[0] + D[1, 1](v[0]) = 0
       3         2           2                       
   v[0]  omega[0]  + omega[0]  v[1] + 2 D[1](v[0]) mu

      - cos(omega t) f + 2 D[1, 2](v[0]) + D[1, 1](v[1]) = 0
remove(has, lhs(eq[1]), cos); convert(%(t1, t2), diff);
eq[1] := %-convert(f*cos(sigma*t2+t1*w0), 'exp');

v[0] := A(t2)*cos(w0*t1+B(t2)); convert(%, 'exp'); v[0] := unapply(%, t1, t2);
                         /1                             
       (t1, t2) -> A(t2) |- exp(I (omega[0] t1 + B(t2)))
                         \2                             

            1                              \
          + - exp(-I (omega[0] t1 + B(t2)))|
            2                              /

expand(eq[1]);
Error, (in property/ConvertProperty) invalid input: PropRange uses a 2nd argument, b, which is missing
collect(%, exp(I*w0*t1));
Error, (in collect) invalid 1st argument proc (t1, t2) options operator, arrow; A(t2)*((1/2)*exp(I*(w0*t1+B(t2)))+(1/2)*exp(-I*(w0*t1+B(t2)))) end proc
coeff(%, exp(I*w0*t1));
map(proc (x) options operator, arrow; x*exp(-I*B(t2)) end proc, %);
combine(%, 'exp');
subs(I*B(t2) = I*sigma*t2-I*C(t2), B(t2) = sigma*t2-C(t2), %);
conds := combine(%, 'exp');
                               0

With this feature, it requires the worksheet from which to import a result from executing it from the worksheet with the Run worksheet command to have section titles as Input  and Calculation respectively.

This is a really helpful feature, but what i need is to "fetch" the content from a number of worksheets in a folder from a specified particular section name, for a number of different section names.

P1 : x + 2y - z = 1

P2 : 2x + 4y - z = 0

formula is s = |d1-d2|/||n|| 

d1 = 1 d2 = 0 i assume , n = (1 + 2 -1) (P1 pretty much) 

So I end up getting 1/(1+4+(-1))²

1/ √6 , and its the correct answer 

but I can't figure out how to do this properly in maple, does anyone here know how to? (not sure if i even used the formula correctly to get the correct answer by hand)

sorry for a poorly written question I am in a  rush.

I worked on a document about 2 hours ago. And now when I try to open it, it is empty. I saved it in MapleCloud, and I have had it saved before. So today I opnened the saved file from MapleCloud, but now it is gone. How can I get it back!!? It happend to two of my most important files..

PDE := diff(u(x, y), x, x)+diff(u(x, y), y, y)-6*x*y*(1-y)-2*x^3 = 0; BCsx := u(xL, y) = 0, u(xU, y) = y*(1-y); BCsy := u(x, yL) = 0, u(x, yU) = 0; solPDE := pdsolve({BCsx, BCsy, PDE}, u(x, y)); exactSol := unapply(rhs(%), x, y)

how i can write these boundary conditions for dsolve?

(diff(u(r), r))^(n-1)*(diff(r*(diff(u(r), r)), r))/r    be [finite] at r =0

and  u(0) = finite?

Thanks..

Hello!

I can't seem to figure out how to use the Physics package within a procedure. In particular, I can't get tensors to be recognized within the body of the proc.

As an example, here's a short program that works correctly when not in a procedure:

with(Physics):
Coordinates(X,quiet):
d_[mu](X[~mu]);
# Returns 4; Correct

However, placing this code inside a proc causes the tensor X to not be recognized as a tensor:

Test := proc()
  uses Physics:

  Coordinates(X,quiet):
  d_[mu](X[~mu]);
end proc:
Test();
# Returns 0; Wrong

Apparently, Physics:-Coordinates still defines the tensor X (as can be checked by calling Physics:-Define()). However, the derivative d_[mu] (X[~mu]) seems to be treating X as a standard symbol. Any idea how I would go about correcting this?

Thanks!

I am sure that this is a common enough problem. I want to show what commands I'm using to make an output in a maple worksheet in a latex document that i can include in a report.

So far I've got the export feature to work:

(here is an example mapleworksheet, texfile and a corresponding LatexProducedPDF),

but i can't see how to get it to include the commands that create the output.

Hello!

I want to use abstract linear operators between Lie algebras. I have the problem shown in the following short code:

with(LinearAlgebra): with(DifferentialGeometry): with(LieAlgebras):
LAr:=LieAlgebraData([ [e1,e2]=e3],[e1,e2,e3],LA);
DGsetup(LAr);
define(lin,linear);
lin(-e3);
lin(-LieBracket(e1,e2));
lin(LieBracket(e2,e1));

As you see, the minus "-" does not come out of the argument of lin() in the last line. What is going wrong?

Thanks!

-------------------------------------

Later on, I realized that the linear operator has nothing to do with the issue. The problem lies in the fact that the output of "LieBracket(e2,e1)" is "_DG([["vector", LA, []], [[[3], -1]]])" , where the latter "-1" refers to the coeffiecient. For some reason, this coefficient is not handled in the way I would expect. For example, the following two lines:

LieBracket(e2,e1)+LieBracket(e1,e2);
_DG([["vector", LA, []], [[[3], 1]]])+_DG([["vector", LA, []], [[[3], -1]]]);

give both as an output "e3+-e3" instead of "0", while both the lines

LieBracket(e2,e1) + LieBracket(e2,e1);
_DG([["vector", LA, []], [[[3], -1]]])+_DG([["vector", LA, []], [[[3], -1]]]);

give the output "2-e3" (which I interpret as "2(-e3)" ).

I don't understand what I am doing wrong.

I have PDE i trying to solve the equation using series.

pdsolve(diff(u(x, y), x, x)+diff(u(x, y), y, y) = Pi, series, order = 2);

Give me: "Error, (in DifferentialAlgebra:-RosenfeldGroebner) unexpected occurrence of the non-rational constants {Pi} in the given input" ?

pdsolve(diff(u(x, y), x, x)+diff(u(x, y), y, y) =gamma, series, order = 2);#gamma = 0.5772156649,Gives ERROR ?

If I  change instead of Pi is e or exp(1) works fine.

pdsolve(diff(u(x, y), x, x)+diff(u(x, y), y, y) = exp(1), series, order = 2);#OK.

It's a bug, design or  something else ?

How can one calculate isogeny of elliptic curves over finite fields in maple ?