I'm trying to find lypunov exponent for this  system of ODEs. I know I need to take the Jacobian but not sure if it's possible the way it's currently defined. If anyone could provide insight it would be much appreciated.

Eqns:= diff(omega(t),t)=-(G*MSat*beta^(2)*(xH(t)*sin(theta(t))-yH(t)* cos(theta(t)))*(xH(t)*cos(theta(t))+yH(t)*sin(theta(t))))/((xH(t)^(2)+yH(t)^(2))^(2.5)),diff(theta(t),t)=omega(t), diff(xH(t),t)=vxH(t),diff(vxH(t),t)=-(G*M*xH(t))/((xH(t)^(2)+yH(t)^(2))^(1.5)),diff(yH(t),t)=vyH(t),diff(vyH(t),t)=-(G*M*yH(t))/((xH(t)^(2)+yH(t)^(2))^(1.5)): ;

ICs := omega(0) = omega0, theta(0) = theta0, xH(0) = a*(1+e), yH(0) = 0, vxH(0) = 0, vyH(0) = sqrt(G*M*(1-e)/(a*(1+e)));

I want the exponent for omega, I  procedure that takes some initial conditions, changing just w0, and computes the long term value of omega. This plots a sort of bifurcation diagram. I'd like an estimate of the exponent to compare what I see. 

thanks for the help

ft

Variable exists but is not shown when using save/read with extension .m

My example maple code is

 

a:=b^2:

save a, "test1.m"

restart:

read "test1.m"

a;

after the read command, I can access the variable, but it is not shown under "Variables".

This lead to some confusion when debugging the worksheet. Can I change this somehow?

Using the input type file format is not a solution, since then reading takes forever for complicated expressions.

Further, in the read command documentation it says "This functionality is not intended for end users" for saving the file as .m. What does that mean?

I am a Mathematica user trying to make the switch to Maple, so first of all I apologise if I am making a stupid mistake here. The complete script is attached below.

I have the following line in my script:

    b := Trace(map(diff, HermitianTranspose(W), coords[1]) . map(diff, W, coords[1]))

W is a matrix defined earlier in the script. I can provide the context if it would help but I'm not sure if it's relevant to the issue I'm having. The problem is that

    simplify(b) assuming real, r>0

gives a vastly different result to

    simplify(Trace(map(diff, HermitianTranspose(W), coords[1]) . map(diff, W, coords[1]))) assuming real, r>0

How can this be? What can I do to make Maple simplify the expression correctly?

conifold_metric.mw

hello guys,

i have a system of autonomous equations which i want to plot its 3D phase space with directional field,

i have some problem with it :dy.mw , and i dont know how to command for add some directional field for 3D phase space .

thank you guys

I do not know! I am a novice in maple as well as in graph theory. I attach a doc in which i attempted to learn what is network. It seems alright with maple as it gives as what it understands as horizontal and vertical network. I do not expect a horizontal line as horizontal network and vertical line as vertical network, in which case a horizontal line with nodes 1 and 2 will be vertical network if  draw it vertically. The maple, in my opinion ( i am not a maple man) gives the answer in a vertical pattern, rightly so for clarity and space constraint.

I am sorry if i am confusing.  The document in my attempt to know more may give you also more insight. Thanks.

Download MyAttempt.mwMyAttempt.mw

When I use the option assume = nonnegint or integervariables = {...} in Optimization[Minimize], or Optimization[LPSolve] I've got the message "kernel connection lost'. 

Thie even happens when I use the simple example from the Maple help:

with(Optimization):
LPSolve(2*x+5*y,{3*x-y=1,x-y<=5},assume={nonnegative,integer});

It says; mserver.exe has stopped working. 

What's wrong? 

How can I compute F from G according to the following text? (I implemented this but I need a more efficient implementation.)

Given a set G of polynomials which are a subset of k[U, X] and a monomial order with U << X, we want to comput set F from G s.t.

1. F is subset of G and for any two distinct f1, f2 in F , neither lpp (f1) is a multiple of lpp (f2) nor lpp (f2) is a multiple of lpp (f1).

2. for every polynomial g in G, there is some polynomial f in F such that lpp (g) is a multiple of
lpp (f ), i.e. ⟨lpp (F )⟩ = ⟨lpp (G)⟩,

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

It is worth nothing that F is not unique.

Example:  Let us consider G = {ax^2 − y, ay^2 − 1, ax − 1, (a + 1)x − y, (a + 1)y − a} ⊂ Q[a, x, y], with the lexicographic order on terms with a < y < x.

Then F = {ax − 1, (a + 1)y − a} and F ′ = {(a + 1)x − y, (a + 1)y − a} are both considered set.

please not that K[U,X] is a parametric polynomial ring (U is e sequence of parameters and X is a sequence of variables).

lpp(f) is leading monomial of f w.r.t. variables X. For example lpp(a*x^2+b*y)= x^2.

In Maple 2015.1 we have

restart;

solve([sin(2*x)/cos(x+3*Pi/2)=1,  x>-4*Pi, x<-5*Pi/2], x, allsolutions, explicit);

solve([sin(2*x)/cos(x+3*Pi/2)=1, x>0, x<2*Pi], x, allsolutions, explicit);

In the first example, the error message is not clear (actually there exists a unique root  x=-11*Pi/3), in the second example, one root  (x=5*Pi/3) is lost.

I've got this huge chunk of code which leads to an optimiazation at the very last line (Bestangles:=minimize(maximize()-minimize))). This minization is taking a very long time (havent solved it yet) and I would very much like to reduce that time. As I've understood maple does optimization by differentiating and then finding all extremes and comparing. Would this mean that since I minimize and optimize within a minimization command, it differentiates a ton of times? And if this is the case, can I somehow do the differentiation beforehand, since it is the same function being differentiate all the time? Or is there some other way I can improve the code? 
Thanks alot!

Heres the full code:

Download wrong_answers.mwwrong_answers.mwwrong_answers.mw

Ramakrishnan V

rukmini_ramki@hotmail.com

hello everyone

can any one tell me what is this anti reduction method. In the paper of serdal palmuk,the link is given bellow

http://www.hindawi.com/journals/mpe/2009/202307/

in this paper question #4 is first solved by anti reduction method for  exact solution.

but i dont understand this method,

if anybody know this then please also tell me how to solve this,

and in the next  (6 & 7 ) examples "in the pourus media equation" they first find its particular exact solution.i also dont understand this,so please tell me

actually i know how to solve ODE to find its exact solution but  i dont know how we find exact solutions of partial differtial equations,

so please help me to solve this problem

thanks

How to find the integral
,

assuming k and n  integer?
It is known (McCrea W. H., Whipple F. J. W.Random paths in two and three dimensions, Proc. Roy. Soc. Edinburgh. 1940. V. 60. P. 281–298) that

G(n,n)=2/Pi*sum(1/(2*k-1),k=1..n).

The general case is reduced to the case k=n.
This is not a creature of pure reason: the one appears in electric circuits
(see M. Skopenkov, A. Paharev, A. Ustinov, Through resistor net, Mat. pros. Issue 18 (2014), 33-65, in Russian, http://www.mccme.ru/free-books/matpros/pdf/mp-18.pdf).
I found G(8,8) = 182144/(45045*Pi) in 657.797 s and G(9,9) = 3186538/(765765*Pi) in 4157.687 s on my comp by

restart; s := time():(1/2)*VectorCalculus:-int((1-cos(9*Pi*x)*cos(9*Pi*y))/(sin((1/2)*Pi*x)^2+sin((1/2)*Pi*y)^2), [x, y] = Rectangle(0 .. 1, 0 .. 1)); time()-s;
Mathematica 10.3.0 does G(9,9) in 250.391 s on my comp.

Hello,

I have a question about poincare sections. I have this piece of code i need to analyse and I want to use a poincare section in order to so. How could I do it? I am interested in theta and omega. Any help is greatly appreciated! Thank you in advance!

Kind regards,

Gambia Man

Download New_Poincare_section.mw

http://www.maplesoft.com/support/help/Maple/view.aspx?path=Physics/.

i see bra and ket expression are so beautiful,

however,

how do real valued eigenvectors involve in calculation of bra and ket style computation?

Download Bryson_sesson1_p6.mw