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Rouben Rostamian

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19 years, 110 days
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These are questions asked by Rouben Rostamian

How to generate these combinations?...

Rouben Rostamian 8541 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 8541 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 8541 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

How to differentiate a vector-valued fun...

Rouben Rostamian 8541 Maple 2022
vector differentiation
December 26 2022
1 8

Given a vector-valued function z(u,v), I want to calculate the derivative of z with respect to its first argument by applying the D operator to it. I don't see how.  Any suggestions?

> 

restart;
> 

z := (u,v) -> < a(u,v), b(u,v) >;

proc (u, v) options operator, arrow; `<,>`(a(u, v), b(u, v)) end proc

Calculate the derivative of z with respect to its first argument:

> 

P := diff(z(u,v), u);

Vector(2, {(1) = diff(a(u, v), u), (2) = diff(b(u, v), u)})

Express P through the D operator:

> 

Q := convert(P, D);

Vector(2, {(1) = (D[1](a))(u, v), (2) = (D[1](b))(u, v)})

Question:  How do we obtain Q directly by applying the D operator to z

without the help of diff?  This one doesn't work:

> 

D[1](z)(u,v);
type(%, Vector);

(D[1](`<,>`))(a(u, v), b(u, v))*(D[1](a))(u, v)+(D[2](`<,>`))(a(u, v), b(u, v))*(D[1](b))(u, v)

false

Download diff.mw

Unexpected results from pdsolve...

Rouben Rostamian 8541 Maple 2022
pde pdsolve differential-equations
September 10 2022
2 2
> 

restart;
> 

pde := diff(u(x,t),t) + u(x,t)*diff(u(x,t),x) = 0;

diff(u(x, t), t)+u(x, t)*(diff(u(x, t), x)) = 0

These are all wrong:

> 

pdsolve({pde,u(x,0)=f(x)});
pdsolve({pde,u(x,0)=sin(x)});
pdsolve({pde,u(x,0)=erf(x)});

u(x, t) = 0

u(x, t) = 0

u(x, t) = 0

But these ones are correct:

> 

pdsolve({pde,u(x,0)=exp(x)});
pdsolve({pde,u(x,0)=x});

u(x, t) = LambertW(t*exp(x))/t

u(x, t) = x/(t+1)

Download mw.mw

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