MaplePrimes Questions

Preliminaries: 

and 

I wrote a code for above. You can Download the code for Above:  

 

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

Now, we can calculate the Matrix  as follows  for k=2, M=3,

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


Question:  How can we find the Matrix  for ?

(If it is not possible to find the Matrix for any k and M,

can we find it for k=3, M=4? )

Before finding Matrix,   we must find to 

in terms of any of Psi_i,j    like

and others.

 

But how? :)
Update:

I found elements of Matrix 
NOW, How to create  Matrix A:=  by the elements in the_code.mw

J:=proc(j1,j2,j3,m1,m2,m3)
local i,f:
i:=max(0,j2-j3-m1,j1-j3+m2):
f:=min(j1+j2-j3,j1-m1,j2+m2):
if m1+m2+m3<>0 then:
0
elif j3>j1+j2 then:
# printf("Error. Does not satisfy the triangle relation");
0
elif j3<abs(j1-j2) then:
# printf("Error. Does not satisfy the triangle relation");
0
elif abs(m1)>j1 or abs(m2)>j2 or abs(m3)>j3 then:
0
else:
simplify(((-1)^(j1-j2-m3))*((((j1+j2-j3)!*(j1-j2+j3)!*(-j1+j2+j3)!*(j1+m1)!*(j1-m1)!*(j2+m2)!*(j2-m2)!*(j3+m3)!*(j3-m3)!)/(j1+j2+j3+1)!))^(1/2)*sum(((-1)^t)/((j1+j2-j3-t)!*(j1-m1-t)!*(j2+m2-t)!*(j3-j2+m1+t)!*(j3-j1-m2+t)!*t!),t=i..f));
end if;
end proc:

###### That is matrix which we want to find ###############
#psi_1aa.psi_1bb:=add(J(aa,bb,c,0,0,0)*J(aa,bb,c,0,0,0)*sqrt(2*(2*aa+1)*(2*bb+1)*(2*c+1))*psi(1,c),c=abs(aa-bb)..(aa+bb));
#psi_2aa.psi_2bb:=add(J(aa,bb,c,0,0,0)*J(aa,bb,c,0,0,0)*sqrt(2*(2*aa+1)*(2*bb+1)*(2*c+1))*psi(2,c),c=abs(aa-bb)..(aa+bb));
#Let A:= Psi.Transpose(Psi). So, it is matrix which we want to find.


aa:=0:bb:=0: 
A(1,1):=add(J(aa,bb,c,0,0,0)*J(aa,bb,c,0,0,0)*sqrt(2*(2*aa+1)*(2*bb+1)*(2*c+1))*psi(1,c),c=abs(aa-bb)..(aa+bb)); 
# it is element of A in first row and column or psi_10.psi_10
                               
aa:=1:bb:=0: 
A(2,1):=add(J(aa,bb,c,0,0,0)*J(aa,bb,c,0,0,0)*sqrt(2*(2*aa+1)*(2*bb+1)*(2*c+1))*psi(c),c=abs(aa-bb)..(aa+bb)); 
# it is element of A in second row and column or psi_11.psi_10 
#We can proceed so so for aa=0..M-1 and bb=0..M-1

#Similarly; Let's find psi_20.psi_20
A(M+1,1):=add(J(aa,bb,c,0,0,0)*J(aa,bb,c,0,0,0)*sqrt(2*(2*aa+1)*(2*bb+1)*(2*c+1))*psi(2,c),c=abs(aa-bb)..(aa+bb));
 # it is element of A in M+1 row and column or psi_20.psi_10

 

Best regards.

Hello,

Please , how can we plot two figures with different X-axis and the same Y-axis ?

Thank you

 


 

restart

``

Lambda := proc (z) options operator, arrow; int((z-u)*phi(u), u = 0 .. z) end proc

proc (z) options operator, arrow; int((z-u)*phi(u), u = 0 .. z) end proc

(1)

k := diff(Lambda(z), z)

int(phi(u), u = 0 .. z)

(2)

k

int(phi(u), u = 0 .. z)

(3)

m := subs(phi(z) = 1/2, k)

int(phi(u), u = 0 .. z)

(4)

``

``


 

Download dummy2.mw

Hi,

 

I'm trying to learn the dsolve command on Maple. I have a second order differential equation and two initial conditions to solve it.

I'm following maple help's procedure to solve it. But in the end i don't get my constants solved (which i do if i use Matlab i.e.)

What am i doing wrong?

restart;
ode := diff(Y(y), y, y) = 3*(1-(y/b)^2)*q/(4*k*b);
                                    /     2\  
                                    |    y |  
                                  3 |1 - --| q
                                    |     2|  
                  d  / d      \     \    b /  
                 --- |--- Y(y)| = ------------
                  dy \ dy     /      4 k b    
dsolve(ode);
                         2       4                
                    3 q y     q y                 
             Y(y) = ------ - ------- + _C1 y + _C2
                    8 b k        3                
                             16 b  k              
ics := Y(b) = Ts-Tb; (D(Y))(-b) = 0;
                         Y(b) = Ts - Tb
                          D(Y)(-b) = 0
dsolve({ics, ode});
                      2       4          
                 3 q y     q y           
          Y(y) = ------ - ------- + _C1 y
                 8 b k        3          
                          16 b  k        

               16 _C1 b k + 16 Tb k - 16 Ts k + 5 b q
             - --------------------------------------
                                16 k                 

or a screenshot:

 

 

 

 

I have a package that uses fsolve, a Maple function known (to me) to often fail when UseHardwareFloats is set to true. Since I set UseHardwareFloats:=true in my .mapleinit (for I want hardware performance when using floats) I set UseHardwareFloats:=deduced; in the ModuleLoad routine of this package. ModuleLoad executes as evidenced by a print statement in the routine that does in fact print, and within ModuleLoad, UseHardwareFloats is set to deduced. But at the worksheet level, UseHardwareFloats remains set to true.
 The only way I can set it is to set it explicitly in the sheet that calls the package. I tried various things, like putting it into the body of the module, using :-UseHardwareFloats, and so on. Nothing seems to work. While not a fatal issue it is bothersome & has had me run around with code not working several times.

Any hint would be appreciated.

Mac Dude

 

I am preparing a Slideshow with Maple 2018.2
I want to use a small laptop to do the presentation with MaplePlayer 2018.1 without purchasing and installing the hole stuff.

The presentation contains some 3d animated plots controlled by some DocumentTools,Components,Button components just
to start and stop the animations during my talk.

The Player dont appear to run (!!!)  the worksheet at startup, so the Plot components dont get an identity and the Button components dont get the Plot components identity neither to set their "play" property. As a consequence Button components appear useless.

Is there any mean to make this work?

Thanks.

@ecterrab 

To ensure the general accessibility of my Maple worksheets for Mathematics for Chemistry, I work with the classic interface.  When I tried to install first Maple 2018.1, when it became available, and then Maple 2018.2 when it became available, the output from use of either technical input in text lines, using function key F5, or simply from an executable input command or statement was corrupted.  I reported this behaviour but apparently the remedy has not yet been incorporated.  To avoid these problems, I had to delete Maple 2018.2 and to reinstall Maple 2018.0.  

     When I, in good faith, with that Maple 2018.0 reinstalled tried to install Maplesoft Physics Updates version 241, according to the encouragement of Edgardo Cheb-Terrab above, I discovered the same corruption in the output when I entered a procedure, for instance this one,

ft := proc(kk,ll,mm)
>      h^(-3/2)*int(int(int(expand(exp(-(2*Pi*I/h)*(sin(theta)*sin(Theta)*cos(Phi-phi)+cos(theta)*cos(Theta))*r*P)
>            *eval(psi,[k=kk,l=ll,m=mm])*r^2*sin(theta), trig),phi=0..2*Pi),theta=0..Pi),r=0..infinity);
> end proc;
  ft := proc(kk, ll, mm)
    1/h^(3/2)*int(int(int(expand(exp(-2*I*Pi*(in(theta)*sin(Theta)*cos(Phi - phi)+ cos(theta)*cos(Theta))*r*P/h)*eval(psi, [k = kk, l = ll,  m = mm])*r^2*sin(theta), trig), phi = 0 .. 2*Pi), theta = 0 .. Pi), r = 0 .. infinity)
end proc

namely that, instead of * in any location in the output that you can read above, there appears a large U.  Why is the testing by Dr. Cheb-Terrab and others connected with Maplesoft done in such a slipshod manner?  After all these years one should expect better control of quality than is evidently the case.  It seems that I must once again reinstall Maple 2018.0 to regain the full functionality of Maple 2018 without the deficiencies introduced in both the updates and the Physics package.  This condition is disgraceful and intolerable.

general_solution.mwI want to calculate the diff equations numerical solutions at z=500 with calling the integrals with limits -500..Z and i want the datefile of resualts

 

Hello,

I cannot find a solution for multiplying matrices containing vectors. I seems that matrix operations are not overloaded for accepting vectors. Here is a minimum example :

restart;
with(LinearAlgebra);
with(VectorCalculus);
A := Matrix([u, v]);
B := Transpose(A) . A;

# Entries of A are in fact vectors
u := `<,>`(u1, u2);
v := `<,>`(v1, v2);

# Here are the expected entries of matrix B

u . u;
v . v;
u . v;

# but entries cannot be calculated
simplify(B);

B := Transpose(A) . A;

Of course I can obtain the result if I construct the matrix A with the components of u and v but  my goal is to manipulate more concise expressions with vectors rather than components. May I find a solution in some other package ?

Would it be a complicated task to develop the missing operators or tell Maple to use the dot operator (for matrices and vector) when performing matrix multiplication ?

Thanks for your insights.

 K is a function by K(u,ux), and there is an equation K2,2=0,. It must be solved like K=K1(u)*ux+k2(u)

Is there any command to help me solve that kind of expression just in Jet space?

Dear users,

Can any one give a correct model statement (if what I have suggested is incorrect) for each one of the following in a module:

module() export eseq;  local lseq;  global gseq;  option optseq; 

 description dseq;  uses usesSequence;  statementSequence   end

My model statements:

export x1, y1;

# x1 and y1 are variables calculated here and sent to main document

 local a, b;  

# a and b are local constants are variables used here inside module only


global z1; 

# z1 is a constant or variable used all over the document can be read from and exported to main document and used in manipulation anywhere in the main document as well as inside the module.

option if x1 = .. else... end; 

 description dseq;

# Statements for self use and understanding the commands during execution

 usesSequence;

uses DocumentTools;

# Packages used in module like DocumentTools, Students Calculus

Statement Sequence

valid executable maple command  1

valid executable maple command  last

 

I want to understand the basic usage of  a module and procedure with a simple document.  

I am also confused over the following.


1) Is there any use of a module with zero statement (as given below) in it?

 module ()

end module

2) What is the major difference between module and procedure?

3) What is in module that is not possible in procedure?
I believe that procedure is like a function [for call from script(internally or eternally) or command window] in MATLAB and subroutine in FORTRAN or BASIC etc. What is module like in other programme siftwares?

Thanks for helping.

Ramakrishnan V


 

@tomleslie 

Dear Tom,

I need your help. I have a delay differential equation to solve and extract the value of the solution y(t) at a selected point of the independent variable t.  I am uploading a small sample code. 

Thanks.
 

dsys := {diff(y(t), t) = -y(t-1), y(0) = 2}; dsn := dsolve(dsys, numeric)

{diff(y(t), t) = -y(t-1), y(0) = 2}

(1)

 

 

``


 

Download delay-differential-equation.mw
 

dsys := {diff(y(t), t) = -y(t-1), y(0) = 2}; dsn := dsolve(dsys, numeric)

{diff(y(t), t) = -y(t-1), y(0) = 2}

(1)

 

 

``


 

Download delay-differential-equation.mw

 

Hi everyone: 

I want to obtain r1(t), V(t) , q(t) in terms of U0 and plot V(t) in terms of U0, how? 

eq1:= diff(r[1](t), t, t)+(.3293064114+209.6419478*U[0])*(diff(r[1](t), t))+569.4324330*r[1](t)-0.3123434112e-2*V(t) = -1.547206836*U[0]^2*q(t)
eq2:= 2.03*10^(-8)*(diff(V(t), t))+4.065040650*10^(-11)*V(t)+0.3123434112e-2*(diff(r[1](t), t)) = 0
eq3 := diff(q(t), t, t)+1047.197552*U[0]*(q(t)^2-1)*(diff(q(t), t))+1.096622713*10^6*U[0]^2*q(t) = -2822.855019*(diff(r[1](t), t, t))
ics:=r1(0)=0,D(r1)(0)=0,V(0)=0,q(0)=0,D(q)(0)=0;

Tnx...

Hi, everytimes I enter anythings, it turn out with Typesetting:-mparsed( bla1bla2, bla1bla2;"_noterminate")

example:

For an Array A, say, and some positive integer n, say, Maple interpretes A^n as raising each entry separately to the same power n. Without the Physics package loaded, A^n can also be written as A . A . ... . A (n times). But with the Physics package loaded, this equality is broken (at least in Maple 2017): If A is a 2D square Array, A . A all of a sudden is no longer equal to A^2, but rather to convert(A,Matrix)^2, i.e., to the square of the Array considered as a Matrix. The presence of the dot operator seems to make the Physics enviroment convert A to a Matrix. This seems to me to be a bug.

1 2 3 4 5 6 7 Last Page 3 of 1688