Hi guys. I tried to find Killing Vectors for Taub-NUT metrics but the maple gives an error.  Can someone explain what is wrong?

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

Can't seem to get Retrieve from DocumentTools to get any labels from any worksheet.  I just get an error saying unable to retrieve label reference.

with(DocumentTools):

Retrieve("c:/test/test/mw","L1") #sample test file named test.mw in directory test

Here's the same issue (unanswered) way back in 2015 https://www.mapleprimes.com/questions/203811-DocumentTools-Retrieve-Function-Returns

Maybe it's a Windows administrator issue?  Does it work for anyone else?

restart;

u1 := proc (x, y) options operator, arrow; 1-e^(a*x)*cos(2*Pi*y) end proc;
a := -.39323780;
evalf(int(int(u1(x, y)^2, y = -.5 .. 1.5), x = -.5 .. 1.5));
             1             /                  /          5 
  ------------------------ \0.000002034392421 \6.25000 10  
         (5898567/5000000)                                 
  ln(e) e                                                  

     (1966189/1250000)              6        (5898567/5000000)
    e                  + 1.966189 10  ln(e) e                 

                 5\\
     - 6.25000 10 //

I need help me , how can find this integral as simple number?

u1 := proc (x, y) options operator, arrow; 1-e^(a*x)*cos(2*`πy`) end proc;
u2 := proc (x, y) options operator, arrow; a*e^(a*x)*cos2*`πy` end proc;

norm(u2(x, y), 2)/norm(u1(x, y), 2);
Error, invalid input: norm expects its 1st argument, p, to be of type {Matrix, Vector, matrix, polynom, vector}, but received a*e^(a*x)*cos2*`πy`

Hi, I want to define A matrix (shown below) that has some definite products. These products have two arguments e.g. (k=1..N) and (k<>i) but product expects only one argument. What should I do?

I appreciate any help you can provide.

Hi,

How to import and manipulate different formulas of  Excel files in maple ?

See example in attachment

Thanks

Hi all

I wnat to produce following matrix P_{2r+1, 2r+1} in maple.

can any one help me please?

Error, (in dsolve/numeric/process_input) system must be entered as a set/list of expressions/equations
moadele_asli2.mw

solve does not show result!!

dtm.mw

can i have step by step procedure of the solution of the follwoing problem

sys[1] := [-(diff(u(x, t), t, t))-(diff(u(x, t), x, x))+u(x, t) = 2*exp(-t)*(x-(1/2)*x^2+(1/2)*t-1), u(x, 0) = x^2-2*x, u(x, 1) = u(x, 1/2)+((1/2)*x^2-x)*exp(-1)-((3/4)*x^2-(3/2)*x)*exp(-1/2), u(0, t) = 0, eval(diff(u(x, t), x), x = 1) = 0]

I am attempting to use the Gram-Schmidt process with Maple to show that the first six orthogonal polynomials which satisfy the following orthogonality condition:

$\int_0^1 (1-x)^{3/2} \phi_n(x) \phi_m(x) dx = h_{n} \delta_{nm}$   

can be expressed in the form:

\phi_0(x) = 1, \phi_1(x) = x − 2/7 , \phi_2(x) = x^2 − (8/11)x + 8/99 , \phi_3(x) = x^3 − (6/5)x^2 + (24/65)x − 16/715 , \phi_4(x) = x^4 − (32/19)x^3 + (288/323)x^2 − (256/1615)x + 128/20995 , \phi_5(x) = x^5 − (50/23)x^4 + (800/483)x^3 − (1600/3059)x^2 + (3200/52003)x − 256/156009.

At the same time I have to find the corresponding values for h_n, so for example, h_0 = 2/5 and h_1 = 8/441.  The polynomials which I obtain have to be combined with the Gaussian quadrature method to show that

$\int_0^1 (1-x)^{3/2} \phi_n(x) \phi_m(x) dx = h_{n} \delta_{nm} \approx \sum_{k=1}^4 c_k f(x_k)$

where x_k are the four roots of \phi_4(x)=0 such that x = [0.0524512, 0.256285, 0.548299, 0.827175]

and the 4 c_k coefficients are given by c = [0.121979, 0.168886, 0.0920439, 0.0170909].

I have learned about Gram-Schmidt orthogonalisation in a basic setting in linear algebra courses where a system of N linearly independent orthogonal vectors is constructed from a system of N linearly independent vectors, but unsure how to apply it to polynomials.  I am also vaguely familar with the idea of appoximating integrals with sets of orthogonal polynomials (Legendre, for example) but not exactly sure how this all works.

Hi, I'm very new to maple and I'm trying to solve  a system of ODEs but as of now it has taken over 5 hours to solve and is still evaluating. i feel as though I may have made some basic mistakes in the code which make the calculation much longer than it should be. I will try tyo explain the problem as well as I can

I'm trying to model a chemical reaction, and solve for the concentrations of two species involved in the reaction after a given time.

The rate of the reaction is given as: r=2900exp(-53300/RT)*Cno^0.62*Cnh3^-0.05;  where R is a constant, T is temperature and Cno and Cnh3 are the concentrations of NO and NH3 respectively. I am interested in solving for Cno and Cnh3 and getting an expression for each of them. I have tried to set up the system of ODEs as follows:

with(LinearAlgebra):

with(DEtools):

r := 2900*(exp(1)^(-53300/R*T)*CNO(t)^0.62*CNH3(t)^-0.05:

ode := diff(CNO(t), t) = -1* r: (negative because they are decaying with time)  

ode2 := diff(CNH3(t), t) = -1* r:

ics := CNO(1020) = 1.6, CNH3(1020) = 1.6; (sets up known initial conditions)

ode := subs(R = 8.314, T = 473, ode):

ode2 := subs(R = 8.314, T = 473, ode2):

sys_ode := (ode, ode2) :

dsolve([sys_ode, ics]);

I wonder if the problem has to do with the boundary conditions that I've set or not. Please help as I know I may have set it up very inefficiently which might be causing the problems. Thank you for your help

Using the Physics package (the newest updates for Maple 2016), I am trying to get a basic setup of fermions on a lattice. My lattice is indexed j=1,...,L for some length, L (I'm trying just for L=4 by hand). Using combinat and arraytools and lsit tools, I can generate my entire list of configurations from [0,0,0,..,0], [1,0,0,...,0], ..., [1,1,...,1]. I read through this https://www.mapleprimes.com/questions/151320-Creation-And-Annihilation-Operators# which should be even more general than my problem, but I'm not getting the anti-commutation relationships to work out properly. In that link, the original poster is putting the kets in by hand, I would like to generate them.

So I have this:

restart
with(Physics):
with(combinat):
with(LinearAlgebra):
with(ArrayTools):
with(ListTools):

Setup(mathematicalnotation=true):
Setup(quantumop={cre,ann}, algebrarules={%AntiCommutator(cre[j],ann[k])=I*KroneckerDelta[j,k],%AntiCommutator(cre[j],cre[k])=0, %AntiCommutator(ann[j],ann[k])=0})

and my algebra is defined. But if I try to compute AntiCommutator(ann[1],ann[1]) is doesn't evaluate it but computes AntiCommutator(cre[1],ann[2]) perfectly fine.

Okay. The algebra is defined, then I create my configurations by using a traingular array and then permutations (and some list/array tools to product vectors that look like [0,0,0,0],[0,0,0,1],...,[1,1,1,1])

Config_Gen := proc(Length)
global Configurations;
local fermionarray,n_n,V,Ln,i_i;
fermionarray:= Array(triangular[upper],1..Length+1,1..Length,fill=1);
for n_n from 1 to Length+1 do
V[n_n] := fermionarray(n_n,1..Length);
Ln[n_n] := permute(convert(V[n_n],list));
end do;
Configurations := Ln[1];
for i_i from 2 to Length+1 do
    Configurations := [op( Configurations), op(Ln[i_i] ) ];
#    Configurations := Reverse([op( Configurations), op(Ln[i_i] ) ]);
end do;
 print("Table of configuratons is", fermionarray);
 print("The table written as a set of vectors is", V);
 print("Permutations of generators is", Ln);
 print("Full list of Configurations is", Configurations);
end proc;

For Config_Gen(4) this makes the configurations perfectly fine. Then I need to translate these configurations into creation operators acting on the 0-particle vacuum:

for i_i from 1 to 2^4 do
Ket(psi,Configurations[i_i]):= product(cre[j_j]^Configurations[i_i][j_j],j_j = 1 .. 4)* Ket(psi,Vacuum);
nnn:= sum(Configurations[i_i][j_j],j_j=1..4) :
fff:=(-1)^(nnn*(nnn-1)/2):
Bra(psi,Configurations[i_i]):= fff* Bra(psi,Vacuum) * product(( ann[j_j] )^Configurations[i_i][j_j],j_j = 1 .. 4);
#[seq(ann,j=1..4)];
end do;
value(Simplify(Bra(psi,[1,1,0,1]) *Ket(psi,[1,1,0,1]) ));

Which generates the bras and kets. The factors of (-1) are chosen to give the correct bracket. A problem: For some reason, the product in Maple gives the same when I do Configurations[i_i][(4+1)-j_j].

Some other problems: When I go to evaluate AntiCommutator(ann[1],ann[2]) or more explicitly ann[1]*ann[2] + ann[2]*ann[1], the worksheet doesn't simplify. Is there a nice way to use the built in Annihilation and Creation operators of the physics package into the tensorproduct space on which I'd like to do calculations?

Hello,

Here is the code I used to generate the image:

densityplot(x,x=0..1,y=-0..0.1,colorstyle=HUE,style=patchnogrid,scaling=constrained,view=[0..1,0..0.1],axes=none);

Then, I exported the image in a eps format. When the file is displayed, white lines appear as a grid. The problem comes from Maple and not from the softwares used to visualize the image. I tried so many things to solve that but...

How to solve the problem?

Thank you.

Jaqr