Hi Edgardo/Others, 

I'm not sure if any more development work is being done on the physics package or not. But I've gotten back to playing around with the great tetrad package you've developed. 

Specfically, I'm calculating spin connections for various metrics. I've run into a few troubles, and have written a simple example showing some calculations that don't match my expectations. 

This is by no means urgent, and if you are no longer developing the package, you can ignore this post. 

Hopefully you can follow the code, I've commented on the issues I have, summary:

1. Checking the tetrads match the minkowski metric when contracted with the curved metric. 

2. I build a tensor Gamma_mu (represents spin connection for a covariant derivative) which contains non-commuting gamma matricies (ideally dirac gamma's). I then try and contract this tensor with another non commutating tensor (dirac gamma matrix) using SumOverRepeatedIndices(). Unless I'm mistaken, this function doesn't preserve the anticommuting nature of the tensor components. 

Cheers. 

Correcting_-_Tetrads.mw

Can we rotate 3d text in Maple like this shown here?

http://mathematica.stackexchange.com/questions/25065/rotating-3d-text

Let us consider the definite integral

J:=int(abs(x-(-x^5+1)^(1/5)), x = 0 .. 1);

Maple fails with it, Mathematica 10.1 finds it in terms of  special functions. Let us look at the integrand:
plot(x-(-x^5+1)^(1/5), x = 0 .. 1);

We see the expression under the modulus changes its sign at the unique point of RealRange(0,1). Therefore

solve(x-(-x^5+1)^(1/5));

Then

J:= int(-x+(-x^5+1)^(1/5), x = 0 .. (1/2)*2^(4/5))+int(x-(-x^5+1)^(1/5), x = (1/2)*2^(4/5) .. 1);

which outputs a complicated expression

(1/8)*2^(4/5)*(4*hypergeom([-1/5, 1/5], [6/5], 1/2)-2^(4/5))+(1/2)*2^(4/5)*((1/2)*2^(1/5)-(1/4)*2^(4/5))-(1/25)*Pi*csc((1/5)*Pi)*(-(25/2)*sin((1/5)*Pi)*GAMMA(4/5)*2^(4/5)*hypergeom([-1/5, 1/5], [6/5], 1/2)/Pi+(5/4)*sec((3/10)*Pi)*cos((1/10)*Pi)*2^(3/5)*Pi^(1/2)*csc((3/10)*Pi)/GAMMA(7/10))/GAMMA(4/5).

At the same time we have

int(abs(x-(-x^5+1)^(1/5)), x = 0 .. 1, numeric);

                          0.5000000000

How to obtain 1/2 symbolically?

I am trying to integrate product of exp(t+s) and a piecewise polynomial but the result can not be read and not usefull. also I used numerical integration function "Quadrature" but the result did not change.

error.mwerror.mw

guys ,

in a differential equation i want to expand its variable, but i  have some problem with it for exponential term :jadid.mw

thanks guys

 Let M be a matrix with polynomial array f_i's such that any array is in K[a_1,..,a_m][x_1,..,x_n] where a=a_1,,,a_m are sequence of parameters and x=x_1,..,x_n are sequense of variables. Now, I want to extract the coefficients of  f_i that are in K[a_1,a_2,..,a_m]. For example if how can I extract the matrix coefficint ?

Please note that a,b,c,d are parameters and x,y are variables.

Hi, I'm having a problem regarding this equation:
                                                           sum(v(i), i = 1 .. 28)

where, v is a Data Table created under the Components Tab with 28 Rows, and 1 Column.

I keep on getting an error of: 

                                                     Error, unsupported type of index, i

I didn't use or declare 'i' in any part of the program.

Thank you for your help! 

Let's say I have something like

p1:=((a+b+c)*t + (a^2 + b^2)*t^3)*(c^3a^b + a*b)*t^2 + (1/(b^2 + a^3)) + b + 1/c^7)*t^7 = 0;

or something complicated like that.

Would it be possible to print the polynomail up to say order 3?

I want to be able to print

collect(expand(p1),t) up to order 3 and see the resulting coefficients

In the following worksheet, I can evaluate , but not . As a result, I can't use any value that depends on  (or any ), for example, the graph is incomplete. How can I get Maple to evaluate ?

All told, S(i) fails for i in [0..31], i = 115,116, and 221. S(i) succeeds for all other i < 3500.

Download test.mw

How to express sin(-(1/6)*Pi+(1/2)*arccos(1/3)) in radicals with Maple? The use of the applyrule command is not desired. Here is one of  my tries:
>convert(expand(sin(-(1/6)*Pi+(1/2)*arccos(1/3))), radical);
-(1/2)*cos((1/2)*arccos(1/3))+(1/2)*sqrt(3)*sin((1/2)*arccos(1/3))

Hi guys,

I'm studying a system of six differential equations. Given the fact that the system cannot be solved symbolically, I've tried the numeric procedure, and it works. I proceeded like this :

soleqd:=dsolve(sysd2,numeric,var);

then i checked if maple could calculate the solutions for given values of t. It works for t=0, t=0.5, t=1,t=2,...,t=5. The solutions are all real numbers.

But when i try to draw a graphic representation of the solutions, it doesn't work. I do :

ff1:=t->subs(soleqd(t),u[1](t));
gg1:=t->subs(soleqd(t),nu[1](t));

Then :

plot(['ff1(t)','gg1(t)',t=0..5],u[1]=0...1,nu[1]=0...1);

(The square brackets are indices)

Now maple answers that it is "unable to evaluate the function to numeric values in the region". I went to the help page but no solution seems to work. I can't figure it out by myself. Does anybody notice something wrong with my code ?

Thank you for your time,

Best regards,

Louis

The model of fixed-bed adsorption column

Fluid phase:

PDE:= diff(U(x, tau),tau)+ psi*Theta*diff(U(x, tau),x)-(1/Pe)*psi*Theta*diff(U(x, tau),$(x, 2))=-3*psi*xi*(U(x, tau)-Q/K);

IBC:={U(x, 0) = 0,U(0, tau) = 1+(1/Pe)*(D[1](U))(0, tau),(D[1](U))(1, tau)=0};

Particle:

PDE:= diff(Q(r, tau), tau) = diff(Q(r, tau), $(r, 2))+(2/r)*diff(Q(r, tau),r);

IBC:={Q(r, 0) = 0,(D[1](Q))(0, tau) = 0,(1/K)*(D[1](Q))(1, tau)=xi*(U-Q(1, tau)/K)};

Pe:=0.01:

psi:=6780:

Theta:=3.0:

xi:=10000:

I will really appreciate your help. Thanks in anticipation.

Hi guys,

I'm trying to draw a phase portrait based on a system of differential equations, but executing the DEplot command gives me the response in the title. 

The command I entered is this one :

DEplot(sysdif,[u(t),nu(t)],t=0..50,{[u(0)=0.831,nu(0)=0.7]},linecolor=red,numpoints=1000, thickness=1, u=0.5...1, nu=0.6...1, color=black);

the system of equation is this one :

eqd1 := diff(u(t), t) = u(t)*[-gamma + (rho)/(mu - nu(t)) - delta*u(t) + pii - (tau)/(alpha + epsilon*exp(-beta*((omega-u(t))/(kappa-u(t)))))] ;
eqd2 := diff(nu(t), t) = nu(t)*[(omega-u(t))/(kappa-u(t)) - (tau)/(alpha+epsilon*exp(-beta*((omega-u(t))/(kappa-u(t)))))] ;

the model is calibrated. I understand that maple cannot store a kind of number but even changing the parameters won't help. I've been looking for people with same error message but using solutions provided by forum members don't work. Before getting that error message i did have the one with "vars must be declared as a list ..." so I did :

u:='u' ;

nu:='nu';

but now I have the error  "unable to store  '[HFloat(0.005711776872341132)]' when datatype=float[8]".

Does anybody have an idea of the solution to my problem ?

Thanks for your time,

best regards,

Louis

I'm just using it this way:

with(QDifferenceEquations):
QPochhammer(-1,5,10)

Error, (in QDifferenceEquations:-QPochhammer) wrong type of arguments

Am I doing something terribly wrong???

Hi,

     I'm trying to numerically solve a PDE in Maple for different boundary conditions, however I'm having trouble even getting Maple to numerically solve it for simple boundary conditions.

I have cylindrical coordinates, r, z, theta, and I treat r = r(z, theta) for convenience to plot my solution surface. The initial coundary condition is that at z = epsilon (z = 0 is singular) , r = constant and of course r is periodic in theta. This is just a circle, and the analytical solution is know to be a half-sphere  r = sqrt(R^2 - z^2). I entered my initial boundary conditions into Maple, but it doesn't like the periodic one

IBC := { r(epsilon, theta) = R - epsilon__r,
              r(z, 0) = r(z, 2*Pi) };

pdsolve(
  PDE,
  IBC,
  numeric,
  indepvars = [z, theta],
  time = z,
  range = 0..2*Pi);
Error, (in pdsolve/numeric/par_hyp) Incorrect number of boundary conditions, expected 2, got 1

I'm not sure how to make this work, and then generalize it to more arbitrary intial slices r(epsilon, theta) = f(theta).

Here's the attached worksheet, ForMaplePrimesSUbmission.mw

Any help is appreciated,

Thanks