MaplePrimes Questions

Hi, I'm using Maple 2018 and I tried to run coding from https://www.maplesoft.com/applications/view.aspx?sid=4194&view=html

however, it said : unable to parse. I figured out that the problem maybe is in the if loop. though it seems perfectly fine, but it has some goto commands that i cannot search on maple website. does this mean that the goto cannot be used here and should be replaced? if yes, then how? 

i am still learning on how to use maple. any help would be much appreciated. thank you!

this is the coding for if loop:

 

label_7;

rv:=vector([p1(x1pt,x2pt),p2(x1pt,x2pt)]):

numgeval:=numgeval+1;

printf("%5d (%8.4f,%8.4f)",numIter,rv[1],rv[2]);

max:=n;

mg:=convert(sqrt(dotprod(rv,rv)),float);

printf("%12.4f",mg);

if(mg<tol or numIter>=max) then

goto(label_6);

else

numIter:=numIter+1;

fi;

v1:=x1pt+t*rv[1];

v2:=x2pt+t*rv[2];

newt:=evalf(subs({x1=v1,x2=v2},f1));

numfeval:=numfeval+1;

lam:=fsolve(diff(newt,t)=0,t,maxsols=1);

nv1:=evalf(subs({t=lam},v1));

nv2:=evalf(subs({t=lam},v2));

printf(" (%8.4f,%8.4f)%13.4f\n",x1pt,x2pt,lam);

x1pt:=nv1;

x2pt:=nv2;

goto(label_7);

label_6;

printf("\n\n-----------------------------------------");

printf("---------------------------------------------");

printf("\n\n Approximate Solution: ");

printf(" (%8.4f,%8.4f)\n",x1pt,x2pt);

Fvalue:=evalf(subs(x1=x1pt,x2=x2pt,f));

printf(" Maximum Functional Value: ");

printf("%21.4f",Fvalue);

printf("\n Number gradient evaluations:");

printf("%22d",numgeval);

printf("\n Number function evaluations:");

printf("%22d",numfeval);

printf("\n\n-----------------------------------------");

printf("---------------------------------------------");

end:

If q := [q1(t),q2(t),q3(t)];

and L=cos(q1(t))+sin(q2(t))+5*dq1 + 4*dq3

now I want to get the result of the following expression

d(dL/d dq1)/dt=?,

how can i write the expression?

In above expression dq1 is the derivative of q1(t), and dq3 is that of q3(t),

How do I solve (1/2)*n^2 +2n-1=O(n^2) in maple2018?Thank you

curry(`?[]`,f)([1]);
                                                  

I have plotted a 3d figure with MAPLE. How can I snap a point in 3d figure and  show  the coordinate value of snaped point ?It  can be  carried out  easily in MATLAB,but I  cann‘t  snap the point used  point probe tool in MAPLE ?

Given 2 inputs
m = integer
c = integer

where c ≤ m/2

and variables, a_i, b_i, a, b (all non-negative integers)
Here, m is the digit length of a number where a_i and b_i represent digits in a number writen in base b. a is simply b-1 and is used as another digit.

I am interested in generating specific permutations of a_1 ... a_c  a ... a  b_c ... b_1 where the total number of digits is m and the number of a's in the centre is m-2c.

The permutations I am interested in satisfy the condition. a_i is to the left of b_j for i ≤ j


examples for m=7:
c=1
a1,a,a,a,a,a,b1

c=2
a1,a2,a,a,a,b2,b1
a1,a2,a,a,a,b1,b2
a1,b1,a,a,a,a2,b2
a2,a1,a,a,a,b1,b2
a2,a1,a,a,a,b2,b1

c=3
a1,a2,a3,a,b3,b2,b1
...

c=4
n/a   2c > m

I would like a function L(m,c) that creates all valid permuatations of a_1 .. a_c b_1 .. b_c  (2n terms)


I met up with a lecturer at my university and we came up with this code. Unfortunately it is for mathematica as he doesn't use Maple. I feel there may be a more efficient way than to generate all permutations and then delete some.

thank you in advance for any help.

Ben

Hi,

with the Physics package, I want to represent a discrete two-dimensional Hilbert space in a direct-product basis.

I have looked at https://www.mapleprimes.com/posts/209099-Tensor-Product-Of-Quantum-State-Spaces but am not sure how to implement bracketrules.

Let's assume I have one-dimensional bases A and B that span a two-dimensional space C. A is of size Na and B is of size Nb. Consequently, C is of size Na * Nb.

If I understand it correclty, this can be done with

Setup(hilbertspaces = {{A, C}, {B, C}}, quantumbasisdimension = {A = 1 .. Na, B = 1 .. Nb, C = 1 .. Na*Nb}, quantumdiscretebasis = {A, B, C})

First question: Is this correct and if yes, why do I need to specify quantumbasisdimension for C?

Then, I want to define, using bracketrules, <A[i]| <B[j]| |Psi> = X[i,j],

where |Psi> lives in the full, two-dimensional space C and X is a matrix.

<B[j]|Psi> would be a state living in A and <A[i]||Psi> would be a state in B.

How do I define this?

bracketrules = {%Bracket(Bra(A, i)*Bra(B, j), Ket(C, t)) = X[i,j](t)}

gives me an error.

I found a way using the nested expression

bracketrules = {%Bracket(Bra(A, i), Ket(A, j)) = X[i,j], %Bracket(Bra(B, j), Ket(C)) = Ket(A, j)}

giving

Bracket(Bra(A, i), Bracket(Bra(B, j), Ket(C, t))) = X[i,j]

but this is error prone, clumsy and only works in one direction:

Bracket(Bra(B, j), Bracket(Bra(A, i), Ket(C)))

does not work. Of course, I could also specify rules for the reverse direction but this is quite an effort for higher-dimensional spaces (I have, e.g., 9-dimensional spaces in mind).

So how do I do this properly?

Please have a look at the attached example, where I also included time-dependence.

Thanks,

Henrik

 


 

-------``

First try

-------

restart; restart, with(Physics)

Setup(hilbertspaces = {{A, C}, {B, C}}, quantumbasisdimension = {A = 1 .. Na, B = 1 .. Nb, C = 1 .. Na*Nb}, quantumdiscretebasis = {A, B, C}, bracketrules = {%Bracket(Bra(A, i)*Bra(B, j), Ket(C, t)) = X[i, j](t)})

Error, (in Physics:-Setup) expected first argument in the Bracket defining a bracket rule to be a 'Bra'; received: Physics:-`*`(%Bra(A, i), %Bra(B, j))

 

 

---------

Second try

---------

 

restart; restart, with(Physics)

Setup(hilbertspaces = {{A, C}, {B, C}}, quantumbasisdimension = {A = 1 .. Na, B = 1 .. Nb, C = 1 .. Na*Nb}, quantumdiscretebasis = {A, B, C}, bracketrules = {%Bracket(Bra(A, i), Bra(B, j), Ket(C, t)) = X[i, j](t)})

[bracketrules = {%Bracket(%Bra(A, i), %Bra(B, j), %Ket(C, t)) = X[i, j](t)}, disjointedspaces = {{A, C}, {B, C}}, quantumbasisdimension = {A = 1 .. Na, B = 1 .. Nb, C = 1 .. Na*Nb}, quantumdiscretebasis = {A, B, C}]

(1)

Bracket(Bra(A, i), Bra(B, j), Ket(C, t))

Physics:-`*`(Physics:-Bra(A, i), Physics:-Bra(B, j), Physics:-Ket(C, t))

(2)

--------

Third try

--------

 

 

restart; restart, with(Physics)

Setup(hilbertspaces = {{A, C}, {B, C}}, quantumbasisdimension = {A = 1 .. Na, B = 1 .. Nb, C = 1 .. Na*Nb}, quantumdiscretebasis = {A, B, C}, bracketrules = {%Bracket(Bra(A, i), Ket(A, j, t)) = X[i, j](t), %Bracket(Bra(B, j), Ket(C, t)) = Ket(A, j, t)})

[bracketrules = {%Bracket(%Bra(A, i), %Ket(A, j, t)) = X[i, j](t), %Bracket(%Bra(B, j), %Ket(C, t)) = Physics:-Ket(A, j, t)}, disjointedspaces = {{A, C}, {B, C}}, quantumbasisdimension = {A = 1 .. Na, B = 1 .. Nb, C = 1 .. Na*Nb}, quantumdiscretebasis = {A, B, C}]

(3)

Bracket(Bra(A, i).Bra(B, j), Ket(C, t))

Physics:-`*`(Physics:-Bra(A, i), Physics:-Bra(B, j), Physics:-Ket(C, t))

(4)

Bracket(Bra(A, i), Bracket(Bra(B, j), Ket(C, t)))

X[i, j](t)

(5)

Bracket(Bra(B, j), Bracket(Bra(A, i), Ket(C, t)))

Error, (in Physics:-Bracket) expected a Bra and a Ket as a first and last arguments, or no Bra and no Ket when using the shortcut notation; received: Physics:-Bra(B,j), Physics:-Bracket(Physics:-Bra(A,i),Physics:-Ket(C,t))

 

``


 

Download twoD.mw

 

How do you create a variable name with a dot?  ie/ ini.param

I don't think it's possible without using single quotes ie `ini.param`.  The single quotes will always need to be used.

I have 3 lists of equal length:

A:=[1,1,1,1,1,2,2,2,2,2,3,3,3,3,3,4,4,4,4,4,5,5,5,5,5]
B:=[1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5,1,2,3,4,5]
C:=[5,2,7,9,1,6,2,8,4,6,2,1,5,8,3,5,2,9,6,6,3,2,1,6,4]

I would like to make a 3-D plot of C dependent on A and B (Ex. C(1,1)=5, C(1,2)=2.. C(5,5)=4).

 

What would be the best way to plot this? I have tried 'pointplot3d' which returns a decent result, but I would prefer a filled plot if possible.

hi

I want to mix two curve and have only one figure(I want to compare two curve in one plot domain )?

Thank you

plot.mw
 

h1 := solve(Vdc = 0.1500000000e-2*sqrt(2.53669508*10^8*u^3-6.06101011*10^8*u^2+3.46343435*10^8*u), u); plot([h1], Vdc = 0 .. 11.5, color = [magenta], thickness = 1); plot(Vector([0, 3.38, 5.21, 6.97, 8.4108, 10.099, 10.9232, 11.8091]), Vector([0, 0.760e-1, .1275, .1994, .2286, .3222, .3637, .999]), style = point, symbol = asterisk, color = "Blue")

 

 

``


 

Download plot.mw

 

 

Hi, fairly simple question,

I solve a simple equation:

solve(x^x = 4, allsolutions, explicit);

#(2*(I*Pi*_Z7+ln(2)))/LambertW(_Z9, 2*ln(2)+(2*I)*Pi*_Z7)

Maple  gave me solution with prefix _Z for integer values, but why  _Z9 must be exactly equal  Zero  to be correct ?.

If _Z9 is integer it can also take other values than zero ?

Thanks in advance.



More information see attached file:

Download Allsolution.mw

 

There is a builtin command "callback". It exists both in Maple 5 and today's Maple. There is no documentation on it. What is it? Why does it exist? Is there any code that uses it?

Hi, fairly simple question,
I've been using the physics package to calculate various different tensors but I can't see that I can calculate a cotton tensor for a given metric, is this included in the physics package? If so what is the calling sequence as I cannot find it. I understand I could use the differential geometry package but I do not want to as I don't know how to set up an arbitrary metric, thanks in advance.

Where can I find help with graphing on Maple?

Hi there,

I have difficulties in solving the first partial derivatives dw/db and dw/dvarphi of this equation with its constraint:

w := exp(exp(x*b)*(r-1)/(1+varphi*exp(x*b))) where ln(r) = varphi*(exp(x*b))(r-1)/(1+varphi*exp(x*b))-1

Please help.

Regards,

Sarni Berliana

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