Maple 2016 Questions and Posts

These are Posts and Questions associated with the product, Maple 2016

Hi everybody,

Why f generates the error "... orthopoly is not a module or member"

f := proc(n)
   uses orthopoly;
   H(n,z);
end proc;

as g works correctly ?

g := proc(n)
   orthopoly:-H(n,z);
end proc;


Thanks in advance

How to calculate the following at point p=(xo,yo):

       n . del(u), u=u(x,y)

from the known function u, where n is the unit outward normal at p and the dot represents the dot product.

The objective is to create example PDE problems with Neumann BCs on irregular 2D domains.

Can someone help me to find graph of this type of solutions .

finalsol := exp(I*(-k*x+t*(k^2+2*rho^2-2*sigma^2)+theta))*rho*tanh(-2*k*rho*t+rho*x);

sol1 := eval(finalsol, [rho = .5, theta = .5, sigma = .5, k = .5]);

graph1 := plot3d(sol1, t = -5 .. 5, x = -5 .. 5, numpoints = 300, frames = 50, axes = framed, color = x, thickness = 5, axesfont = ["HELVETICA", "ROMAN", 24], labelfont = ["HELVETICA", "ROMAN", 24]);

ContPlot1 := contourplot(sol1, t = -20 .. 20, x = -20 .. 20, frames = 50, axes = framed, thickness = 5, numpoints = 300, a*xesfont = ["HELVETICA", "ROMAN", 24], labelfont = ["HELVETICA", "ROMAN", 24])

plot_solution.mw

 

Dear All

I want to plot A long rod with length L and its cross-section is a rectangle

Quadratic equation ax^2 + bx + c = 0. Coeff's long and ugly expressions in their own right, but I know that a is nonzero, that there is at least one real solution, and that I want the largest.

So, question: How do I get Maple to return the -b/2a PLUS sqrt((b/2a)^2-c/a) solution?

Hi,

This is a notional example

1/ I define a matrix through some procedure, for instance
p := k -> Matrix(3, 3, (i,j) -> i+j+k mod 3)

2/ Now I would like to animate the plot of matrices p(k) for successive values of k.
The red commend below doesn't work
N := 5:
plots[animate](Statistics[HeatMap], [ p(k) ], k=0..N, frames=N+1);


Could you please help me to fix this ?
TIA

Hi,
Can somebody explain me these strange results ?

 

restart:
with(Statistics):
X := RandomVariable(Normal(1.0, 1.0)):
S := Sample(X, 10):

# naively... but it's not what I was expecting for
#                maybe a misuse of the 'normalize=truefalse' option ????
Likelihood(Normal(1.0, 1.0), S);
       # a strange answer

# 2nd way
A := Likelihood(Normal(m, 1.0), S):
evalf(subs(m=1.0, A));
   # this is the good answer
   0.004387

# third way
Likelihood(Normal(1.0, 1.0), S, 'normalize=false');
   4.48e-7    # a wrong answer

 

Thanks for your enlightenment

Can we use this euler lagrange command for the system of pde's?

If we have a system without lagrangian then euler opertor is applied corresponding to three dependent variables.

so we have three equations but in this euler lagrange command no dependent variable is mentioned.   

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?

 

 

 

 

I would like to find which of my approximately 150 recorded worksheets reference the VariationalCalculus package.

Instead of tediously displaying these one at a time, is there a search mechanism that will list the names of all my worksheets containing the command with(VariationalCalculus)?

restart;
with(DEtools);
assume(r::real, a::real, b::real, upsilon::real, sigma::real, x::real, y::real, t > 0);
assume(sigma > 0); assume(-b^2-r+2 > 0);
V := -2*exp(I*(sqrt(-b^2-r+2)*x+b*y+r*t))*sqrt(1/sigma)*sech(-t*(-2*sqrt(-b^2-r+2)-2*b)-x-y):
pde[1] := I*(diff(V, t))+diff(V, x, x)+diff(V, y, y)+sigma*abs(V^2)*V = 0: evalc(pde[1]);

 

solution.mw

I am new to Maple and recently installed the software. Surprisingly, it attempt to load by bringing the splash screen and later open the interface but goes off without any error or warning. Can anyone help me out as I really need to use it?

Hi everyone again

This one is linked to my previous 2 question.

Essentially I am trying to use a procedure to reproduce the formula:

S(j) = (1 + sum(H_j*T_j,j=1..n))/(1 + sum(1/(H_j*T_j),j=1..n))

BigProc:= proc(H::list,T::list)
local Form, i;
Form:=[];
for i from 1 to nops(H) do
Form := [op(Form),(1 + [sum(H[1..i]*~T[1..i],i=1..5)])/~(1 + [sum(1/~(H[1..i]*~T[1..i]),i=1..5)])]
end do:
end proc:
MainProc([1,3,5],[3,6,8])

Error, (in sum) summation variable previously assigned, second argument evaluates to 1 = 1 .. 5
 

The actual answer should be (3, 396/25,22320/509)

ie 

S(1) = (1+ 3)/(1+(1/3)) = 3

S(2) = (1 +(3+18))/(1+1/3 + 1/18)) = 396/25

S(3) = (1 +(3+18+40))/(1+1/3 + 1/18 +1/40) = 22320/509

I feel like I am missing a few things to my procedure. Any help would be greatly appreciated!

Hi

This question may have been asked before but I cannot find it!

I am currently have 3 lists:

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

M:=[4,2,4,6,2]

R:= [5,3,2,1,4]

I would like to be able to come up with a way (I assume a procedure) where I can order L and M based on the numerical order of R. So in this case that would be:

R:=[1,2,3,4,5]

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

M:=[6,4,2,2,4]

I hope this makes sense? Any help would be greatly appreciated!

 

The uploaded worksheet animates a cam formed of two Archimedean spirals as the cam rotates, creating vertical motion in a circular cam follower.

DirectSearch is used to locate the centre of the follower, however I experience two problems with this use.

First: DirectSearch places the follower centre sometimes above and sometimes below the cam surface, seemingly at random.

Second: seemingly at random, DirectSearch produces completely wrong values for the follower centre unless its SolveEquations command is executed with the initialpoint values stated in the worksheet. I arrived at these by extensive trial and error.

Why does the first problem occur and is there a way to code SolveEquations to avoid it?

Is there a writeup anywhere which can guide me to correct initialpoint values for a particular SolveEquations attempt?

Archimedian_spiral_cam_follower.mw

3 4 5 6 7 8 9 Last Page 5 of 50