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Rouben Rostamian

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18 years, 274 days
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setoptions3d stopped working in Maple 20...

Rouben Rostamian 8259 Maple 2023
font setoptions3d
May 13 2023
1 2

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

> 

restart;
> 

kernelopts(version);

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

> 

with(plots):
> 

setoptions3d(font=[Times,roman,12]);
> 

arrow(<1,1,1>);

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

 

How to find a symbolic solution for this...

Rouben Rostamian 8259 Maple 2022
ode piecewise dsolve
April 15 2023
0 0

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

> 

restart;

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';

3

a

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

> 

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

Download ode-piecewise.mw

 

How to generate these combinations?...

Rouben Rostamian 8259 Maple
combinatorics combinat
March 25 2023
2 2

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.

> 

restart;

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:
> 

doit(a,b,1);

[[a], [b]]

> 

doit(p,q,3);

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

> 

doit(5,7,3);

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

Download mw.mw

How to define custom lighting?...

Rouben Rostamian 8259 Maple 2022
February 07 2023
1 4

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?

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

How many arguments does a proc take?...

Rouben Rostamian 8259 Maple 2022
parameters procedure
December 26 2022
2 3
 
> 

restart;
> 

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

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

> 

D[3](q);

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?

download number-of-arguments.mw

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