MaplePrimes Questions

Hi everyone:

How can I convert the following phrase (eq) into the phrase in the photo?

eq:= -w*z^2/(2*E*MI*alpha^2)+w*H*sinh(alpha*H)*cosh(alpha*z)/(alpha^3*E*MI*cosh(alpha*H))-w*H*sinh(alpha*H)/(alpha^3*E*MI*cosh(alpha*H))+w*cosh(alpha*z)/(alpha^4*E*MI*cosh(alpha*H))-w/(alpha^4*E*MI*cosh(alpha*H))+w*H*z/(E*MI*alpha^2)-w*H*sinh(alpha*z)/(E*MI*alpha^3):

the phrase in the photo:

tnx...

I want to write a proc, say f, that takes an single argument Z, as in
f := proc(Z::?) ...
where the only acceptable Z values are pairs [x,y], where x and y are selected from the set {a,b,c,d}. The entries a,b,c,d of that set are prescribed symbolic constants. 

Thus, the following are legal calls to f:
f([a,a]), f([a,b]), f([d,c])
but these are illegal:
f([a]), f([a,b,c]), f([a,x])

I don't know what to put for the "::?" in the proc's definition in order to enforce those constraints.  Any ideas?

Extra: In fact, I would prefer to ban the f([a,a]) option as well (no repeated symbols) but that's of secondary importance since it is easy to inspect and handle that within the proc's body.

Hello. I am a student who has been given access to Maple through my school. Normally, the program works just fine and without any problems. But today I tried to do a linear regression which did not work as it used to do. Though, the exponential (ExpReg) and the potential (PowReg) regression still works normally.

Here is a picture of what the error looks like:

As shown on the picture, I use a special extension called the 'Gym-pakke' which we use in my high school. As far as I know, this extension is created for Danish high schools?

Another thing that I had like to emphasize, is that the linear regression still works whenever I copy-paste the command from a previous document - a document from before the issue began. But I am tired of having to copy-paste every time I have to do a linear regression.

Please help me solve this problem, thanks! :)

Hi there!

I am trying to save the coefficients of a polynomial in a list to work with them in a rather complicated procedure. It is about representing a polynomial via a set of orthogonal polynomials phi_n which change depending on the input. For example, phi_s*phi_0=1*phi_s, so the coefficient of phi_s is 1 and the rest is 0. I save this as a[s][0][s]:=1. In this procedure, however, the coefficient of phi_{s+1} or phi_{s+10} might come up, and I have not declared them as 0, so the procedure stops whenever something like a[s][0][s+2] or a[s][0][s+10] appears. I could work with polynomials I guess, saving x^s for the result of

phi_s*phi_0 and working with coeff (x^s,n), which would indeed return 0 if n is not s instead of aborting the entire procedure, however, to me, it's not quite beautiful coding to encrypt the needed coefficients in another polynomial instead of just extracting them into a list. Is there a way to tell Maple that anything unspecified, a[s][j][x], shall just be 0?
 
Thank you in advance, Daniel
 
 

I did two attempts with different ideas
 

 

restart;

Task (a) A list of numbers in Maple :

L:=[1,2,3,4,5];

[1, 2, 3, 4, 5]

(1)

 

In general summing up numbers sum(a, i = k .. n) = sum(a_i, i = 1 .. 5) and sum(a_i, i = 1 .. 5) = a1+a2+a3+a4+a5

underscript? ..i like to write a with underscore n : how to that

#S:={seq(L[i],i=1..5)};

#L:= [seq(L[i],i=1..5)];

For summing up numbers in a list of L i can use a ...

Sumlist := proc (L,N):  

Sumlist:=proc(L,N)

   a:=1;

   for i from 1 to N do

      a:=seq(L[i],i=1..5);

   end do;

end proc:

 

Warning, (in Sumlist) `a` is implicitly declared local

 

Warning, (in Sumlist) `i` is implicitly declared local

 

L:=[1,2,3,4,5];

[1, 2, 3, 4, 5]

(2)

N:=3;

3

(3)

Sumlist(L,N);

1, 2, 3, 4, 5

(4)

 

And now to sum the number sequenze  from the procedure?

 

restart;

Sumlist:=proc(L,N)

   a:=1;

   for i from 1 to N do

      a:=seq(L[i],i=1..5);
      #sum(a, i=1..5); # for this probably a second do loop nested ?

   end do;

end proc:

 

Warning, (in Sumlist) `a` is implicitly declared local

 

Warning, (in Sumlist) `i` is implicitly declared local

 

L:=[1,2,3,4,5];

[1, 2, 3, 4, 5]

(5)

N:=3;

3

(6)

Sumlist(L,N);

1, 2, 3, 4, 5

(7)

 

 

 

 

========================================================================

Also possible by? : a1 = 1, a2=a1+1, a3=a2+1, etc

restart;

 

Sumlist:=proc(L,N)

   a:=1;

   for i from 1 to N do

      a:=L[i]+1;

   end do;

end proc:

 

Warning, (in Sumlist) `a` is implicitly declared local

 

Warning, (in Sumlist) `i` is implicitly declared local

 

L:=[1,2,3,4,5];

[1, 2, 3, 4, 5]

(8)

N:=2;

2

(9)

Sumlist(L,N);

3

(10)

L[1];

1

(11)

 

Try some things out, but summing up list ?


 

Download betounes_ex_set_2_task_5.mw

 

restart;
a := 10;
ff := proc()

       ##local a,b;

        b := a + 10:  #### implicit local

         return b:

        end proc:
ff();

output: 20

restart;

a := 10:
ff := proc()

       ##local a,b;

        b := a + 10:   #### implicit local

        a:=b:

        return b:

        end proc:
ff();

output: a+10

expected: 20

Please explain the reason

 

How can I create an even function, g, in Maple? I want Maple to give g(x) - g(-x) as 0.

Good day sirs, I write a system of DAE but giving me this code "(The use of global variables in numerical ODE problems is deprecated, and will be removed in a future release. Use the 'parameters' argument instead (see ?dsolve,numeric,parameters)". The code is attached below.

Thanking you in anticipating for your help.

Help!!!!.mw

Hello, I was given the problem "Set N:=100. (i) Form four lists L[1], L[3], L[5], L[7] where L[r] contains all primes 2< p < N such that p mod 8 = r ." and came up with the following code:

N := 100;
List1 := [];
List3 := [];
List5 := [];
List7 := [];
for p from 2 to N do
    if isprime(p) and p mod 8 = 1 then List1 := [op(List1), p]; end if;
    if isprime(p) and p mod 8 = 3 then
        List3 := [op(List3), p];
    end if;
    if isprime(p) and p mod 8 = 5 then
        List5 := [op(List5), p];
    end if;
    if isprime(p) and p mod 8 = 7 then
        List7 := [op(List7), p];
    end if;
end do;
List1;
List3;
List5;
List7;
 

this gave me the answer I wanted, however using the above code I have to answer this second question: 

In the notation of Problem 1, make a procedure with input = arbitrary  positive integer N and output = the list [nops(L[1]), nops(L[3]), nops(L[5]), nops(L[7])]. Do some experiments to see for which (if any) r, L[r] is largest. 

I am unsure of how to create a procedure out of the code I already have. I created this: 
 

restart;
F := proc(n)

local N, p, List1, List3, List5, List7;

List1 := [];

List3 := [];

List5 := [];

List7 := [];

for p from N do

if isprime(p) and p mod 8 = 1 then List1 := [op(List1), p]; end if;

if isprime(p) and p mod 8 = 3 then List3 := [op(List3), p]; end if;

if isprime(p) and p mod 8 = 5 then List5 := [op(List5), p]; end if;

if isprime(p) and p mod 8 = 7 then List7 := [op(List7), p]; end if;

return [nops(List1), nops(List3), nops(List5), nops(List7)];

end do;

end proc;

 

however, when I input F(100) or any other value of N, I am receiving the error message "Error, (in F) initial value in for loop must be numeric or character"

 

Any ideas on how to improve my program to get the output I desire?

thank you 

 

 

 


 

restart;

with(PDEtools):

with(plot):

Error, invalid input: with expects its 1st argument, pname, to be of type {`module`, package}, but received plot

 

A1:=Matrix([[phi,(chi),conjugate(phi),conjugate(chi)],
          [chi,(phi),conjugate(chi),conjugate(phi)],
          [lambda*phi,-(lambda)*(chi),
           conjugate(lambda)*conjugate(phi),-conjugate(lambda)*conjugate(chi)],
          [lambda*chi,-(lambda)*(phi),
           conjugate(lambda)*conjugate(chi),-conjugate(lambda)*conjugate(phi)]]);

A1 := Matrix(4, 4, {(1, 1) = phi, (1, 2) = chi, (1, 3) = conjugate(phi), (1, 4) = conjugate(chi), (2, 1) = chi, (2, 2) = phi, (2, 3) = conjugate(chi), (2, 4) = conjugate(phi), (3, 1) = lambda*phi, (3, 2) = -lambda*chi, (3, 3) = conjugate(lambda)*conjugate(phi), (3, 4) = -conjugate(lambda)*conjugate(chi), (4, 1) = lambda*chi, (4, 2) = -lambda*phi, (4, 3) = conjugate(lambda)*conjugate(chi), (4, 4) = -conjugate(lambda)*conjugate(phi)})

(1)

d1 := LinearAlgebra:-Determinant(A1):

d1; length(%);

conjugate(lambda)^2*conjugate(phi)^2*chi^2-conjugate(lambda)^2*conjugate(phi)^2*phi^2-conjugate(lambda)^2*conjugate(chi)^2*chi^2+conjugate(lambda)^2*conjugate(chi)^2*phi^2+2*conjugate(lambda)*conjugate(phi)^2*chi^2*lambda+2*conjugate(lambda)*conjugate(phi)^2*lambda*phi^2-8*conjugate(lambda)*conjugate(phi)*conjugate(chi)*chi*lambda*phi+2*conjugate(lambda)*conjugate(chi)^2*chi^2*lambda+2*conjugate(lambda)*conjugate(chi)^2*lambda*phi^2+conjugate(phi)^2*chi^2*lambda^2-conjugate(phi)^2*lambda^2*phi^2-conjugate(chi)^2*chi^2*lambda^2+conjugate(chi)^2*lambda^2*phi^2

 

705

(2)

den:=simplify(d1,size); length(%);

-(-(conjugate(chi)-conjugate(phi))*(chi+phi)*conjugate(lambda)+lambda*(conjugate(chi)+conjugate(phi))*(chi-phi))*(-(conjugate(chi)+conjugate(phi))*(chi-phi)*conjugate(lambda)+lambda*(conjugate(chi)-conjugate(phi))*(chi+phi))

 

333

(3)

 

con1:=phi=exp(I*lambda*(x-t/(4*lambda^2)-w^2)):con2:=chi=exp(-I*lambda*(x-t/(4*lambda^2)-w^2)):

 

den1:=simplify(dsubs({con1,con2},den));

4*conjugate(lambda)^2*cos((1/4)*(4*w^2*lambda^2-4*x*lambda^2+conjugate((4*lambda^2*w^2-4*lambda^2*x+t)/lambda)*lambda+t)/lambda)^2-4*conjugate(lambda)^2*cos((1/4)*(-4*w^2*lambda^2+4*x*lambda^2+conjugate((4*lambda^2*w^2-4*lambda^2*x+t)/lambda)*lambda-t)/lambda)^2+8*conjugate(lambda)*cos((1/4)*(4*w^2*lambda^2-4*x*lambda^2+conjugate((4*lambda^2*w^2-4*lambda^2*x+t)/lambda)*lambda+t)/lambda)^2*lambda+8*conjugate(lambda)*cos((1/4)*(-4*w^2*lambda^2+4*x*lambda^2+conjugate((4*lambda^2*w^2-4*lambda^2*x+t)/lambda)*lambda-t)/lambda)^2*lambda+4*cos((1/4)*(4*w^2*lambda^2-4*x*lambda^2+conjugate((4*lambda^2*w^2-4*lambda^2*x+t)/lambda)*lambda+t)/lambda)^2*lambda^2-4*cos((1/4)*(-4*w^2*lambda^2+4*x*lambda^2+conjugate((4*lambda^2*w^2-4*lambda^2*x+t)/lambda)*lambda-t)/lambda)^2*lambda^2-16*conjugate(lambda)*lambda

(4)

plot3d(subs(Re(lambda)=1, Im(lambda)=.2, w=1, rhs(den1)),x=-6..6, t=-6..6)

Warning, inserted missing semicolon at end of statement

 

Error, invalid input: rhs received 4*conjugate(lambda)^2*cos((1/4)*(4*w^2*lambda^2-4*x*lambda^2+conjugate((4*lambda^2*w^2-4*lambda^2*x+t)/lambda)*lambda+t)/lambda)^2-4*conjugate(lambda)^2*cos((1/4)*(-4*w^2*lambda^2+4*x*lambda^2+conjugate((4*lambda^2*w^2-4*lambda^2*x+t)/lambda)*lambda-t)/lambda)^2+8*conjugate(lambda)*cos((1/4)*(4*w^2*lambda^2-4*x*lambda^2+conjugate((4*lambda^2*w^2-4*lambda^2*x+t)/lambda)*lambda+t)/lambda)^2*lambda+8*conjugate(lambda)*cos((1/4)*(-4*w^2*lambda^2+4*x*lambda^2+conjugate((4*lambda^2*w^2-4*lambda^2*x+t)/lambda)*lambda-t)/lambda)^2*lambda+4*cos((1/4)*(4*w^2*lambda^2-4*x*lambda^2+conjugate((4*lambda^2*w^2-4*lambda^2*...

 

NULL

``

 

``


 

Download 23May(1).mw

Seems to make no difference with or without RETURN() for the procedure ?

 

vraag_op_forum_gesteld_over_boek_vb_binomium.mw

 

For to know what each graph is standing for in the plot legenda

Could not yet get it  in y , y' , y '' , to 5th derative 

Better is perhaps to have vertical table with the names and function expression together , but that could be difficult betounes_ex_set_task_4def.mw  

 

f := x -> exp(-x)*sin(x); intvx:= 0..3;
f := proc (x) options operator, arrow; exp(-x)*sin(x) end proc
intvx := 0 .. 3

 

And this one below ( i prefer this one ) , but got in worksheet now the one above
Probably a option issue ?

 

 

f := x -> exp(-x)*sin(x); intvx:= 0..3;

proc (x) options operator, arrow; exp(-x)*sin(x) end proc


 

2 determinants equal, solve for the unknowns in one determinant/Linear Algebra

Hi guys, thank you for reading my question.

A is one determinant "Matrix(2, 3, [[1, 2, 3], [3, 1, 2]])".B is" Matrix(2, 3, [[1, x, 3], [y, 1, z]])"

I wrote 2 matrice in the maple

As I try to solve the unknowns,I wrote:

A:= B, solve(x, y, z) It doesn't work

I switch another phrase,

A = B;solve(B:x,y,z)    It doesn't work as well

Could you help me with it ?

Thank you

 

 

Dear All.

Please kindly help to correct the attached code on discretization of fourth order PDE using method of line.
Thank you and kind regards.

restart

``

``

Discretization of parabolic equation with method of line

diff(u(x, t), t) = -2*(diff(diff(u(x, t), x), x))-(diff(diff(diff(diff(u(x, t), x), x), x), x))-u(x, t)*(diff(u(x, t), x))

u(x, t)

u(x, t)

u(x, 0) = 0.3e-1*sin(x)

8

``

``

``

Convert the BC to finite difference

(1/2)*(u[m+1](t)-u[m-1](t))/h

(u[m-1](t)-2*u[m](t)+u[m+1](t))/h^2

(u[m-2](t)-4*u[m-1](t)+6*u[m](t)-4*u[m+1](t)+u[m+2](t))/h^4

````

Convert the governing equation to finite difference form

Error, invalid input: diff received 2*h, which is not valid for its 2nd argument

Error, invalid input: diff received 2*h, which is not valid for its 2nd argument

Error, invalid input: LinearAlgebra:-GenerateMatrix expects its 1st argument, eqns, to be of type ({list, set})({`=`, algebraic}), but received eqs

A

``


 

Download Discretization_of_PDE_Order_4.mw

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