I have certainly zipped (using PKZIP under Windows) directories containing *.lib, *.ind, *.hdb and other types of files without any difficulty. Haven't tried *.mla yet. Note that if you create with march, you get to specify the size, so this gives you some control - see help under repositories or march.

I think the original question was about the diagonalizable nature of matrices, i.e., whether a similarity transform converts them to a diagonal matrix. Here again there is no correlation,

[1 0]
[0 0]

is trivially diagonalizable (because it is already diagonal) and has determinant zero, but

[0 1]
[0 0]

is not diagonalizable and still has determinant zero. Diagonalizability has more to do with whether there are missing eigenvectors. When the eigenvalues are all distinct, the matrix will be diagonalizable, but if some eigenvalues are equal then the matrix may be non-diagonalizable (or may be diagonalizable). Whether or not the degenerate (equal) eigenvalues are zero (determinant will then be zero) or not is not relevant to the question of diagonalizability. To check diagonalizability, one looks at the Jordan form to see if it is diagonal - see Maple's JordanForm.

Don't have a TI calculator, but maybe something like with(plots): animate( plot, [[sin,D(sin)], 0..x], x=0..2*Pi );

You can always do the taylor series and then convert theta to theta(t) afterwards with subs. If f is an expression with thetas and alphas in, then subs(theta=theta(t),alpha=alpha(t),f); I find myself doing this a lot. I work on various manipulations without the t, and then add them just before I solve the DEs.

An example of one of your DEs would help, and what output your are expecting. The following may be useful: f:=cos(theta)+sin(theta)+theta^2+theta*alpha; mtaylor(f,theta,2); gives 1+(1+alpha)*theta So all terms work the way you want except the theta*alpha, which you want to disappear. This works better: Student[MultivariateCalculus][TaylorApproximation](f,[theta,alpha]=[0,0],1); gives 1+theta It might be easier to think in terms of the Jacobian matrix if you have a system of DEs

If you plot plot(erf(ln(x)),x=0..10); you see that the function is negative and nice from 0..1, and indeed you can integrate this bit int(erf(ln(x)),x=0..1); gives -exp(1/4)+exp(1/4)*erf(1/2). From x=1 to infinity the function rises from zero and then asymptotically approaches 1. So the integral of this part must be infinity. Maple seems not to have an analytical answer for, say, the integral from 1 to 2, so here I guess you will have to be satisfied with a numerical answer (and therefore also for arbitrary a and b). Cheers, David.

This works for me (in Maple 10). evalc assumes real anyway so that part is redundant. Both evalc and evalc(Re()) work:

q:=(zks/(alphas+I*vs)*(exp(-I*times*vs)-exp(-I*times1*vs-alphas*tds))):
simplify(evalc(Re(q)));

gives

zks*(alphas*cos(times*vs)-alphas*exp(-alphas*tds)*cos(times1*vs)
 -vs*sin(times*vs)+vs*exp(-alphas*tds)*sin(times1*vs))/(alphas^2+vs^2)

asympt gives an asymptotic series, which tells how the function goes for large x. Can you be more specific about what you mean by "bound" here?

And yet a plot of Budaoy's sum gives answers out to about 2.3, and agrees with log(1+x)/(1+x) over this range.

> p1:=plot(sum((-1)^(i+1)*(Psi(i+1)+gamma)*x^i,
    i = 1 .. infinity),x=0..5,color=red):

> p2:=plot(log(1+x)/(1+x),x=0..5,color=blue):

> display(p2,p1);

There is no way to export the numbers directly from a plot. This is a non-trivial task. You need to generate the x,y values separately and then write them to a file. A lot will depend on what format etc you need them in your plotting program.

The DEplot command in the DETools package has more features than odeplot, including plots of different intial conditions.

solve(2*s^2 - 12*s + 16); returns the answers 4 and 2

Not sure really what you want to do, and your code fragment is not complete. Do h,l,i have values? The line g:=3*b*/w has a syntax error. Perhaps the complete code would be helpful. Do you still want to vary a, or something else; you mention v. If you just want to vary a in a loop it can be done like with(plots): plts:=NULL: for a from 0.4 to 1.8 by 0.2 do ... plts:=plts,plot( ... ): end do: display(plts);

You can use display to get all the plots statically displayed together. Animate (or display with insequence=true) can display them sequentially in an animation. For your case with static display use something like this

restart;with(plots):
Zin:=(a,b,c,d,e,f,omega)->a*sin(omega*b)+c+d+e+f;
display([seq(plot(Zin(1+0.2*i,1,0,0,0,0,omega),
        omega=0..2*Pi),i=0..3)]);

you can define operators with various properties (linearity, etc) and they can be non-commutative. Perhaps this is what you mean; see help for "define". But I don't think there would be much of the knowledge of matrices and vectors that you could build in (e.g. singular matrix times non-singular = singular).