This should be a simple question. But sadly I couldn't figure it out on my own

:-(

I know how to get the multivariate Taylor series expansion of a function f of arguments X[1] and X[2], about zero, and to, say, the third order,

mtaylor( f(X[1],X[2]), [X[1],X[2]], 3 );

   f(0, 0) + D[1](f)(0, 0) X[1] + D[2](f)(0, 0) X[2]

        1       ...

why won't VectorCalculus[Jacobian] accept vectors?

... to prevent me from frying my system? or is it an unnecessary restriction?

Here's what I mean:

Fvec := Vector([x[1]*x[2],3*x[3]]);
Xvec := Vector([x[1],x[2]]);
Flst := [x[1]*x[2],3*x[3]];
Xlst := [x[1],x[2]];
VectorCalculus[Jacobian](Fvec,Xlst);
VectorCalculus[Jacobian](Flst,Xlst);
VectorCalculus[Jacobian](Flst,Xvec);

Error, invalid input: too many and/or wrong type...

I have two symbolic expressions which I think may be equal, one simpler than the other. I'm trying to use "is" to ascertain the equality. I tried things like:

is(expr1=expr2) assuming beta>0 and r>0 and d>0;

which returns false,

but this is what the difference between the two expressions looks like for constellations of parameters:

[okay, so here should appear the graph, but where do I store images and other files in the new mapleprimes?...

I would like to customize arrows of motion in a phase diagram. The system is the following, with critical point (1,1):

xdot := diff(x(t),t) = x(t)-y(t):
ydot := diff(y(t),t) = y(t)*(1-x(t)):

with phase diagram (the black line is the stable manifold of the system):

The command "simplify" fails to capture a fairly obvious simplification. Any way to make Maple see it?