Items tagged with jacobian jacobian Tagged Items Feed

Hi all,

For research purposes, I have symbolic matrices of dimentions up to 100 x 50 (and above) with certain number of parameters. Then giving random value to those paramters, I want the numerical rank of the matrices.

Maple 17 does not seem to work well with symbolic ranks, where expentials are involved.

And more to it, both

Student[MultivariateCalculus][Jacobian]

and

VectorCalculus[Jacobian]

does not seem to work. ...

MAPLE Users,

Suppose I have a set of points in some N-dimensional space.  I would like to obtain a simple polynomial that

best fits the data.  I do not know in advance the form of the function, but a simple function that does not overfit

the data would probably be OK.  By "simple" I mean the smallest degree with or without cross-terms that gives a

decent fit.  My data set will typically be an external comma or tab separated text file.

I have a 2D ode system. Let the interior equilibrium points be x1 & y1. It is easy to get the Jacobian matrix with the code

> with(linalg);
> with(DEtools);
> J := jacobian([H, K], [x, y]);

where H & K are the RHS of odes. But I need the higher order terms by transforming x=x1+u, 

y=y1+v in matrix notation. Please give me the code. 

restart:

with(LinearAlgebra):
with(ArrayTools):


k:=4;
pA:=<seq(p[a,i],i=2..(k+1))>;
pB:=<seq(p[b,i],i=2..(k+1))>;
pA+pB;

with(VectorCalculus):

pA:=<seq(p[a,i],i=2..(k+1))>;
pB:=<seq(p[b,i],i=2..(k+1))>;
pA+pB;

Hi all,

After I loaded the package with(VectorCalculus), the output of vectors changed to a different one.

Is there any real "difference" when...

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...