Thanks Patrick Hmm, but that's a shame, I find subscripts work will very well within loops where you have x[i] etc. I suppose x_||i would work, but it doesn't make for easily readable code. Is there a nicer alternative ? It seems bizarre that subscripts should be avoided altogether. :(

Sorry I'm still not sure that I fully understand this. I've figured out that Jacobian is being passed this as it's argument: [-O-O, O+a*O, b+O*O-c*O],[O, O, O] But it seems those Os are just some kind of internal representation that Maple uses for the name of things that have been "frozen". In the case of the third part of the first list b+O*O-c*O actually means (the frozen version of) b+x(t)*z(t)-c*z(t), and the third O in the second list actually means z(t), the point being that x(t) and z(t) treated as if they were "normal variables" x and z (ie just how we'd write it on pen and paper) . So inside the Jacobian routine, it just does the equivalent of diff(b+x*z-c*z,z) = x-c but since x(t) was "frozen" as x, frontend actually "thaws" x and outputs x(t)-c Am I right ? Thanks LR

Sorry I'm still not sure that I fully understand this. I've figured out that Jacobian is being passed this as it's argument: [-O-O, O+a*O, b+O*O-c*O],[O, O, O] But it seems those Os are just some kind of internal representation that Maple uses for the name of things that have been "frozen". In the case of the third part of the first list b+O*O-c*O actually means (the frozen version of) b+x(t)*z(t)-c*z(t), and the third O in the second list actually means z(t), the point being that x(t) and z(t) treated as if they were "normal variables" x and z (ie just how we'd write it on pen and paper) . So inside the Jacobian routine, it just does the equivalent of diff(b+x*z-c*z,z) = x-c but since x(t) was "frozen" as x, frontend actually "thaws" x and outputs x(t)-c Am I right ? Thanks LR

hmm, I see the issues, but....... "When Maple's too tied up and busy to abort the current computation, I will usually close the whole application (corner button on Maple's main window). This usually results in being queried about saving the open worksheet. That's fine." .......that's not fine for me, because more often than not I don't get the prompt to save the worksheet (maple becomes completely unresponsive to user input , though it's thrashing the CPU) and other times, when I do get the save prompt the result is a corrupt worksheet that when re-opens just appears blank. If I always got the save prompt and the worksheet saved correctly I'd be a very happy camper !

I was just giving a simple example. The main point of this is why can I sometimes interrupt it and other times not ? Even with the same code ! ?

Already putting it to good use !

I guess [x,y,z](t)] just shorthand for [x(t),y(t),z(t)] right ? Also, can you explain what the third parameter is doing : [{`*`,`+`,list}] "If the point p is supplied, the computed Jacobian will be evaluated at that point. The dimension of the point must equal the number of variables in v." http://www.maplesoft.com/support/help/AddOns/view.aspx?path=VectorCalculus/Jacobian Thanks !

I guess [x,y,z](t)] just shorthand for [x(t),y(t),z(t)] right ? Also, can you explain what the third parameter is doing : [{`*`,`+`,list}] "If the point p is supplied, the computed Jacobian will be evaluated at that point. The dimension of the point must equal the number of variables in v." http://www.maplesoft.com/support/help/AddOns/view.aspx?path=VectorCalculus/Jacobian Thanks !

My post above seems to have lost all it's new-line-carriage-return's. Why would that happen ? I'm sure it looked OK when I posted it earlier ! I'll try again: Here is the Rossler system, one of the simplest examples of 3 dimensional deterministic chaos (under certain conditions according to "params"). Thanks to Doug and Joe for various assists. Comments and critiques most welcome ! restart; interface(displayprecision=10): ross_x:=diff(x(t),t)=-y(t)-z(t): ross_y:=diff(y(t),t)=x(t)+a*y(t): ross_z:=diff(z(t),t)=b+x(t)*z(t)-c*z(t): rossler_sys:=ross_x,ross_y,ross_z; #Find fixed points: sol:=solve({rhs(ross_x)=0,rhs(ross_y)=0,rhs(ross_z)=0},{x(t),y(t),z(t)}): fp_sol:=solve({rhs(ross_x)=0,rhs(ross_y)=0,rhs(ross_z)=0},{x(t),y(t),z(t)}): params:={a=0.32,b=0.3,c=4.5}: fp_sol:=allvalues(eval(fp_sol,params)): fp1:=fp_sol[1];fp2:=fp_sol[2]; #Jacobian: J := frontend(Student:-VectorCalculus:-Jacobian, [map(rhs,[rossler_sys]), [x,y,z](t)], [{`*`,`+`,list},{}]); ev1:=LinearAlgebra[Eigenvalues](eval(J,fp1 union params)); ev2:=LinearAlgebra[Eigenvalues](eval(J,fp2 union params)); # now take a look at the orbits assign(params); DEtools[DEplot3d]({rossler_sys},{x(t),y(t),z(t)},t=50..200,[[x(0)=1,y(0)=1,z(0)=1]],scene=[x(t),y(t),z(t)],stepsize=0.05,thickness=1,linecolor=blue,orientation=[40,120]); #To do: #check eigenvectors #plot poincare return map #plot bifurcation diagram (vary b) #plot 2D or 1D orbits with differing IVPs

restart; VanDt:=proc(n) local M,i,j: M:=Matrix(n): for i from 1 to n do: for j from 1 to n do: M(i,j):=x[i]^(j-1): od: od: factor(LinearAlgebra[Determinant](M)); end proc: VanDt(10); I'm aware that this is a there are other (better) ways to compute this determinant, but I don't see why I have to kill the process to stop the evaluation !

SCR submitted. Thanks.

SCR submitted. Thanks.

Can anyone comment on this ?

What's an SCR and how do I submit one ? Thanks.

What's an SCR and how do I submit one ? Thanks.