Hi everyone,

I was trying to write a Maple sheet to calculate some perturbation theory expension as close to the "book notation" as possible. Lets for example consider a linearly perturbed harmonic oscillator with H = hω(n+1/2) and V = λ(a^†+a), this is one of the classical examples as it can be solved analytically by completing the square. In the Kato formulation (as used in the appended Maple worksheet), as well as in Rayleigh-Schrödinger perturbation theory one uses the projector onto the complement of the unperturbed state. I would like to do this by defining a projector in Maple. I've read the examples concerning projectors in Maple but it seems I have to use a rather ugly workaround by treating the states "below" the unperturbed state and the ones "above" separately. While this is a little annoying in one dimension it becomes a major nuisance in higher dimensions.

My question would be: How do I define the projector onto the complement of some state?

Cheers, Sören

Download kato_perturbation_theory.mw

Now that I got my units converted I have a new problem:

I have g/mol and g/cm^3, and the result is supposed to be per cm^3 too. So I would like to keep my grams as well as my  cm^3. However, Maple converts it all to kg and m^3!

That means I have to divide the final result by 10e6. No big deal, only that it looks strange on my worksheet (when I divide the units stay the same, so if I show that to someone they'll be amazed at the gigantic m^3 result number I got instead of just a few cm^3).

By the way, turing off the automatic unit cancellation (see link, my question a few days ago) does not change anything, the g->kg and cm^3->m^3 conversion take place as soon as I enter the values:

results in

and

gives

Hi guys,

im trying to solve the linear equation system:

Then, assigning the solutions:

Then, eliminating the RootOf's for variable a:

Unfortunately, a_explicit still contains RootOf's. How can I avoid this?

Thanks,

Martin

Hello Maple-Primers!

I am trying to evaluate a system at many different points.  I would like to include an interpolation function in this system, but have thusfar been unsuccessful.

Usually, I solve a system symbolically by using eliminate and unapply:

eq[1] := A = M^3;
eq[2] := C = A*2;
eq[3] := D = N+3;
eq[4] := B = piecewise(A = 0, 0,C);
eq[5] := E = B*D;
elimsol:=eliminate(convert(eq,list),[A,B,C,D,E])[1];

unappsol:=unapply(elimsol,[N,M]);

unappsol(1,2);
{A = 8, B = 16, C = 16, D = 4, E = 64} <--- great!

Now, I want to include an interpolation function in the system of equations.  They look like this (see worksheet for actual interpolation function):

B_interp := (W,T) -> CurveFitting:-ArrayInterpolation([FC_Map_W,FC_Map_T],FC_Map,Array(1 .. 1, 1 .. 1, 1 .. 2, [[[W, T]]]),method=linear);

eq[5] := E = B_interp(N,M);

Error, (in CurveFitting:-ArrayInterpolation) invalid input: coordinates of xvalues must be of type numeric <-- bad!

Anyone have any ideas?  I've tried to use polynomials, but I can't seem to get a fit close enough for my purposes.

Maple_2D_Interpolate_FC.mw

A (probably) stupid question that is driving me crazy: how can I expand in Taylor series the following potential function

f(r_):=Int(Int(Int(G(r_-r0_)-(x_-r0_)*rho(r_))))?

essentially the Green representation formula for a harmonic function f in the whole 3d space.

Thanks in advance!

solve([x + 3*y + 5*z = 0,
7*x + 9*y + 11*z = 0,
13*x + 15*y + 17*z = 0],[x,y]);

Hi guys,

I'm trying to find the solutions to a nonlinear equation system:

mysol := solve({J*a = m*g*l*st-m*l*(c*cp*st+d*sp*st), cx*ux = cMx*xd+(Mx+m)*c+m*l*(-cp*pd^2*st-cp*st*td^2-2*ct*pd*sp*td+a*cp*ct-b*sp*st), cy*uy = cMy*yd+(My+m)*d+m*l*(2*cp*ct*pd*td-pd^2*sp*st-sp*st*td^2+a*ct*sp+b*cp*st), (-M*l^2*st^2+J)*b = m*l*sqrt(d^2-2*d*ct+ct^2+c^2*ct^2+(c^2*sp^2-2*c*cp*d*sp+cp^2*d^2)*st^2)}, {a, b, c, d})

The solution contains various implicit solutions with RootOf's. When trying to evaluate them by typing

allvalues(mysol);,

the returned set of solutions is about 800.000 characters long, but unfortunately contains various "+ [...15295 terms...] +" elements, and thus not displaying the full solution. The limits on the precision tab in the maple options are all disabled.
Does anybody know how to display the full expression, although it gets very long?

Thank you in advance,

Martin

Hi everyone,

I'm running Maple 18 and MapleSim 6.4 on my macbook pro 13 " with retina display and the GUI is blurred like there is no smoothing or the antialiasing is not working properly. I tried to find something helpfull in the setting but with no luck.

Is there something I can do to fix this?

Thanks

Carlo

Here in this work and used as the main topic a short description of electrostatics and electrodynamics using the Explore to model the fundamental laws command.

 Corriente_Eléctrica.mw   (in spanish)

Atte.

L. Araujo C.

Hello,

       How long can I expect Maple17 to take to algebraically solve a system of 14 nonlinear equations that has approximately 40% nonlinearity in its terms? I am running it on the machine right now, but have no idea what to expect. As mentioned before, I'm new to Maple...

Here is my code:

restart; eq1 := A*z-B*a*z-V*a*q-W*(b+d)*a = 0; eq2 := W*(b+d)*a-V*b*q-(F*G+B+D)*b*z = 0; eq3 := V*a*q-W*c*(b+d)-(B+C+E)*c*z = 0; eq4 := V*b*q+W*(b+d)*c-(B+C+D+F)*d*z = 0; eq5 := G*F*b*z-V*q*e-(B+H)*e*z = 0; eq6 := H*e*z-V*q*f-(B+S)*f*z = 0; eq7 := S*f*z-V*q*g-B*g*z = 0; eq8 := V*q*g+S*s*z-(B+C+E)*h*z = 0; eq9 := F*d*z+V*q*e-(B+C+H+T)*t*z = 0; eq10 := H*t*z+V*q*f-(U+B+C+2*S)*s*z = 0; eq11 := T*t*z-(B+H+Y)*u*z = 0; eq12 := U*s*z-(B+S)*v*z+H*u*z-Y*H*v*z/(H+S) = 0; eq13 := g-c-d-t-s-h = 0; eq14 := z-a-b-c-d-e-f-g-h-s-t-u-v = 0; soln := solve({eq1, eq10, eq11, eq12, eq13, eq14, eq2, eq3, eq4, eq5, eq6, eq7, eq8, eq9}, {a, b, c, d, e, f, g, h, q, s, t, u, v, z});

Thanks.

Greetings,

       I am new to Maple and this forum. I would like to obtain a Jacobian of a system of 12 ODEs. What have I done wrongly with my code?

eq_1 := -B*a+A-V*(c+d+t+s+h)*a/(a+b+c+d+e+f+g+h+s+t+u+v)-W*(b+d)*a/(a+b+c+d+e+f+g+h+s+t+u+v);
eq_2 := W*(b+d)*a/(a+b+c+d+e+f+g+h+s+t+u+v)-V*(c+d+t+s+h)*b/(a+b+c+d+e+f+g+h+s+t+u+v)-(F*G+B+D)*b;
eq_3 := V*(c+d+t+s+h)*a/(a+b+c+d+e+f+g+h+s+t+u+v)-W*(b+d)*c/(a+b+c+d+e+f+g+h+s+t+u+v)-(B+E+C)*c;
eq_4 := V*(c+d+t+s+h)*b/(a+b+c+d+e+f+g+h+s+t+u+v)+W*(b+d)*c/(a+b+c+d+e+f+g+h+s+t+u+v)-(B+C+D+F)*d;
eq_5 := G*F*b-V*(c+d+t+s+h)*e/(a+b+c+d+e+f+g+h+s+t+u+v)-(B+H)*e;
eq_6 := H*e-V*(c+d+t+s+h)*f/(a+b+c+d+e+f+g+h+s+t+u+v)-(B+S)*f;
eq_7 := S*f-V*(c+d+t+s+h)*g/(a+b+c+d+e+f+g+h+s+t+u+v)-B*g;
eq_8 := V*(c+d+t+s+h)*g/(a+b+c+d+e+f+g+h+s+t+u+v)+S*s-(B+E+C)*h;
eq_9 := F*d+V*(c+d+t+s+h)*e/(a+b+c+d+e+f+g+h+s+t+u+v)-(B+C+H+T)*t;
eq_10 := H*t+V*(c+d+t+s+h)*f/(a+b+c+d+e+f+g+h+s+t+u+v)-(U+B+C+S+S)*s;
eq_11 := T*t+W*(b+d)*x/(a+b+c+d+e+f+g+h+s+t+u+v)-(B+H+Y)*u;
eq_12 := U*s-(B+S)*v+H*u-Y*H*v/(H+S);
with(linalg);
J := Jacobian([eq_1, eq_2, eq_3, eq_4, eq_5, eq_6, eq_7, eq_8, eq_9, eq_10, eq_11, eq_12], [a, b, c, d, e, f, g, h, s, t, u, v]);

I am getting the message: 

 Vector(4, {(1) = ` 12 x 12 `*Matrix, (2) = `Data Type: `*anything, (3) = `Storage: `*rectangular, (4) = `Order: `*Fortran_order})

Thanks!!

I have a rank 1 array M of 1000 values.

I want to apply a function f on each value of M and its location giving,

[f(1,M[1]), f(2,M[2]), ... , f(1000,M[1000])]

is it possible to get this using map or map2 or map[n] or maptype (without using seq since its slowing down computation).

inotherwords can i access the member location inside a map evaluation?

Hey,

I wish to find the zero crossing of the following eq. (with respect to x)

a is typically 1.729, b is 1.139 and c is 0.0688. Ploting the eq. and using the solve command result in two values (zero crossings) when replacing the constants by their respective values, but when I wish to have the solution with respect to the constants a, b and c the result is only for one of them. Any commands that can be helpful in this situation?

Thanks in advance.

Hello,

       I am new to this forum. I have typed the follwing code in Maple17:

restart; eq1 := A-B*a-V*a*q/z-W*(b+d)*a/z = 0; eq2 := W*(b+d)*a/z-V*b*q/z-(F*G+B+D)*b = 0; eq3 := V*a*q/z-W*c(b+d)/z-(B+C+E)*c = 0; eq4 := V*b*q/z+W*(b+d)*c/z-(B+C+D+F)*d = 0; eq5 := G*F*b-V*q*e/z-(B+H)*e = 0; eq6 := H*e-V*q*f/z-(B+S)*f = 0; eq7 := S*f-V*q*g/z-B*g = 0; eq8 := V*q*g/z+S*s-(B+C+E)*h = 0; eq9 := F*d+V*q*e/z-(B+C+H+T)*t = 0; eq10 := H*t+V*q*f/z-(U+B+C+2*S)*s = 0; eq11 := T*t+W*(b+d)*x/z-(B+H+Y)*u = 0; eq12 := U*s-(B+S)*v+H*u-Y*H*v/(H+S) = 0; eq13 := g-c-d-t-s-h = 0; eq14 := z-a-b-c-d-e-f-g-h-s-t-u-v = 0; soln := solve({eq1, eq10, eq11, eq12, eq13, eq14, eq2, eq3, eq4, eq5, eq6, eq7, eq8, eq9}, {a, b, c, d, e, f, g, h, q, s, t, u, v, z});

This is to symbolically solve a nonlinear system of (14) equations. But when I press Enter, it just returns the message "Ready". Shouldn't it say "Evaluating"?

I don't see anything syntactically wrong with my code...

Hello there!

There seems to be an issue with indexed variables and the instruction "DGsetup" of the differential geometry package when used with Maple 17. An error is returned to the effect that DGsetup is expecting independent variables to be unassigned names. This phenomenon does not occur with Maple 16!

Here is what I get:

> restart;
> with(DifferentialGeometry); with(Tools); with(Tensor); with(LinearAlgebra);

Executing the following command, I get an error with Maple 17 which does not occur with Maple 16!

> DGsetup([seq(x[i], i = 1 .. 4)], M, verbose);
Error, (in DifferentialGeometry:-DGsetup) expected 1st independent variable to be an unassigned name, received: x[1]

Is there any fix for this problem?

Kind regards
Freddy Baudine