...but to answer your original question, one way is to make a function (proc) that takes a Vector, and use seq

seq.mw

Profiling the code shows nearly all of the time is spent on the solve line, so changing to map or eval won't help you. I'm guessing changing to fsolve or something from the RootFinding package is the next step

Roots_with_map.mw

As @Preben Alsholm and others have shown, you can get numerical values of sigma as a function of lambda, k and Q.

But you can get an explicit formula for lambda in terms of sigma, which enables plotting sigma vs lambda for fixed k and Q, and may be useful for further manipulations. A lot depends on what you what to do and what are expected ranges of lambda, sigma, k and Q

Real_root.mw

evalc converts to real and imaginary part: evalc(exp(I*x))

It can execute in about a minute on my machine for n=25 if you compile it. You need to set up the Vector outside the procedure and then it will be updated on exit. I didn't check the output or try to follow the algorithm, so hope it has worked correctly.

Mobius.mw

[Edit: I got it further down from about a minute to 20 seconds by redoing the algorithm - the worksheet runs through my logic and several rounds of improvements and compares with the Matrix. Possibly could be improved slightly more.

Hadamard_and_BooleMobius_Transforms.mw

I still got sporadic integer overflow errors - maybe a memory or garbage collection from too many 2^25 x 2^25 matrices.

]

Interesting. Trying DEtools:-dalembertsol(ode,y(x)); returns the empty set, suggesting Maple doesn't really think it is d'Alembert. However, for other equations that odeadvisor doesn't classify as dalembert, such as ode2:=diff(y(x),x)=y(x)^2, dalembertsol(ode2,y(x)) does return a parametric solution.

Since there might be lots of ways to transform to dalembert, I'm guessing that odeadvisor's result is more of a hint, and it doesn't try that hard to check it, but dalembertsol does.

seq(fracdiff(v(t), t,alpha),alpha=-1..1.5,0.5);

gives (1/2)*t^2, .7522527780*t^(3/2), 0., 1.128379167*t^(1/2), 0., 0.

So the ones that are zero are just running along the x-axis and are hard to see.

Click on the plot, and then there will be some controls for the animaton - such as PLAY, Single/continuous cycle etc

Nice worksheet. Some initial thoughts. I guess that a tangent plane can be defined for a point on a surface, and the normal from a pedal point to that plane is well-defined, so the set of all such points where the normal meets the tangent plane can be a pedal surface. The sphere for a point at the centre would be the same sphere, and I think that for any solid of revolution, the pedal surface would be the solid of revolution generated by rotating the pedal curve.

If it is mainly for display then

lprint('fadc_vmon(vmon)'=fadc_vmon(vmon));

gives

fadc_vmon(vmon) = 1638.400000*vmon+200.

For digits to display see the tools -> options -> precision menu.

Note also Maple can convert to various computer languages - see the CodeGeneration package.

Like this? (Not sure what DeltaW is) [Edit: work calculated at end]
 

Download Thermo.mw

The equation has only one solution:  x=1/e. Implicit plot expects an equation in two variables, such as x+y=3.

Edit: if you really wanted the whole vertical line you can get it, but I would usually use a parametric plot for this.
 

Download implicitplot.mw

You can use any font on your system. I don't really understand all the different Computer Modern fonts, but they seem to work. [Edit: Thanks to @acer the update. Image below is from export as .pdf ]

>  P1 := plot(x^2): P2 := plot(x^2,            axesfont=[cmr12,roman,16],            labelfont=[cmr16,roman,24]): >  plots:-display(Array([ P1, P2 ]));

Download Latexfonts.mw

Download Pencil3.mw

With some values of M and R and selected initial condition you can get a numeric solution with

dsolve(eval(sys,{M=2,R=1}) union {y(0)=2},y(r),numeric);

If you try the intial condition y(0)=1, you get the message that there is a singularity and it will work only with two initial values. This is probably why you can't get a series solution about r=0. But perhaps that's not what you want? it should be a start