simplify(series(sin(g(x)),x=0,4));

sin(g(0)) + cos(g(0))*D(g)(0)*x + (-1/2*sin(g(0))*D(g)(0)^2 + 1/2*cos(g(0))*(D@@2)(g)(0))*x^2 + (1/6*(-D(g)(0)^3 + (D@@3)(g)(0))*cos(g(0)) - 1/2*sin(g(0))*(D@@2)(g)(0)*D(g)(0))*x^3 + :-O(1)*x^4

and I'd like to give the various values for g to evaluate the series. That is, I know g and it's derivatives at 0.

When plotting a sequence S, plot(S) a series of horizontal lines are plotted. Is there a way to plot a "time series" without having to reconstruct S, e.g., "seq([i,S[i]],i=1..numelems(S))" and plot that? Seems like a lot of work just to make a simple plot.

RandomMatrix(n, 1);

does not seem too work with Vectors of dimension d in elementwise multiplication ;/ Even though it is an nx1 matrix = an n vector.

This seems like a limitation maple!

RandomVector(n);

Does seem to work with Matrix and Vector.

Matrix(5,1)*~Vector(5);

Both have the same dimensions and should be possible to multiply them pointwise!

I was playing around with some of the maple examples(specifically the knots) and all the plots seem difficult to visualize in 3D... well, more difficult than they should.

In some cases the plots look more like projections and 2D because the graphical representation does seem to project in to the depth of the screen in a natural way.

Mainly it happens when rotating when some of the curve's appear to stay in front due to the highlighting and size issues.

I'm not sure exactly what the problem is but I imagine it definitely can be improved. It may be simply that there are no other depth cues in the plot to make things more real.

1. I'd like anti-aliased edges. The edges of the plot are hard and not correct coloring wise(do not fade like in real life).

2. Some type of depth perspective where the size changes with depth in to the screen in a meaningful way.

3. Proper coloring of this. Maple seems to handle the lighting correctly but it is far too weak to give the impresson of depth

I think maple essentially does all this(except probably AA, although there is probably a setting somewhere) but it seems they are not properly tweaked for maximum realism. I played with the lighting and projection and it seems to help a little but not much.

Any ideas on how to improve this? Ideally something that doesn't have to be set every plot.

add(q[k],k=1..5)

I'd like to be able to display a general result such as

q_1 + q_2 + ... + q_n

ideally maple would do all the special stuff for me, e.g., somehow I could do

add(q[k],k=1..2..n)

but I can't even seem to get a nice output manually that doesn't involve a lot of printing code.