Rouben Rostamian

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These are questions asked by Rouben Rostamian

This code fails in Maple 2023.  It used to work in earlier versions.  Did I miss something in the release notes?



`Maple 2023.0, X86 64 LINUX, Mar 06 2023, Build ID 1689885`




Error, (in plottools:-rotate) invalid arguments for 3-D transformation


I can derive a symbolic solution by hand for the following ODE, but cannot get Maple to do it for me.  Any tricks?


Velocity field, -infinity < x and x < infinity,  t > 0.

v := (x,t) -> piecewise(x <= -t, 0, x < t, 1 - 1/2*(1 - x/t));

v := proc (x, t) options operator, arrow; piecewise(x <= -t, 0, x < t, 1/2+(1/2)*x/t) end proc

Position x(t):

de := diff(x(t),t) = v(x(t),t);

de := diff(x(t), t) = piecewise(x(t) <= -t, 0, x(t) < t, 1/2+x(t)/(2*t))

Initial condition, assuming a > 0

ic := x(0) = -a;

x(0) = -a

Symbolic solution, calculated by hand:

x__exact := t -> piecewise(t < a, -a, t - 2*sqrt(t)*sqrt(a));

x__exact := proc (t) options operator, arrow; piecewise(t < a, -a, t-2*sqrt(t)*sqrt(a)) end proc

Verify exact solution by comparing it against the numeric solution for some a > 0:

a := 3;  # any a>0 should do
dsol := dsolve({de,ic}, numeric):
plots:-odeplot(dsol, t=0..5);   # dsolve solution
plot(x__exact(t), t=0..5);      # symbolic solution (calculated by hand)
a := 'a';



Can Maple's dsolve find the exact solution?  This one returns empty in Maple 2022:

dsolve({de, ic}) assuming a > 0, t > 0;



I expect that there must exist a Maple proc that does the equivalent of the following but I couldn't find it.  Can it be in the combinat package?

And if there isn't one, can the following be improved?  It seems to be horribly inefficient to me, although efficiency is not a major concern for me right now since I need it only for small values of n.


Proc produces all lists of length n consisting of the

two distinct symbols a and b.

doit := proc(a, b, n::posint)
        local p := 1, L := [ [a], [b] ];
        for p from 1 to n-1 do
                 L := [ map( x -> [a,op(x)], L)[], map( x -> [b,op(x)], L)[] ];
        end do:
        return L;
end proc:


[[a], [b]]


[[p, p, p], [p, p, q], [p, q, p], [p, q, q], [q, p, p], [q, p, q], [q, q, p], [q, q, q]]


[[5, 5, 5], [5, 5, 7], [5, 7, 5], [5, 7, 7], [7, 5, 5], [7, 5, 7], [7, 7, 5], [7, 7, 7]]


I have been unable to add a directed light source to my plot3d drawings.  Perhaps I am misreading the documentation.  In the following experiment, I attempt to shine a red light from the direction (phi,theta) but changing the values of phi and theta don't seem to change the scene's lighting.  Can you change the lighting in your Maple?

Explore(display(sphere(), style=surface, color=yellow, light=[phi,theta,1,0,0]),
	phi=0..Pi, theta=0..Pi);



q := (u,v) -> u^2 + v^2;

proc (u, v) options operator, arrow; v^2+u^2 end proc


Error, (in D/procedure) index out of range: function takes only 2 arguments

Question: How does D know that q takes two arguments?

In general, if I pass q to another proc, how can I find out, within
that proc, that q takes only two arguments?


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