We all know that Maple has bugs. But any CAS has.
It would be nice if Maple solves the bugs faster and maintains a list of known bugs and their status.
In your other thread (about Probability) the bugs are clear.
Here, ProbabilityFunction(X, 1.1) = 0 is OK: 1.1 is not in the sample (within current precision). Note that X is not supposed to take only integer values (unlike Geometric). The situation is not perfect but acceptable in my opinion (as long as it is documented).

I don't see any bug.

ProbabilityFunction(Geometric(p), t);
is defined clearly as piecewise(t < 0, 0, p*(1-p)^t)  for 0 < p <=1,  t::integer.
The fact that it returns values instead of an error when t is not integer should not be a problem, and it is easier then to work with floats (no need for round). [Think of n! for noninteger n].

max( maximize(a-b,x=0..1), maximize(b-a,x=0..1) );
convert(%, radical);

@Markiyan Hirnyk 

But it's not complicated. If alpha is algebraic and a[k] are its conjugates (k=1..n) considered by Norm, then the conjugates of x - alpha are x - a[k].
So,  mul(x - a[k], k=1..n)  = Norm(x - alpha) = the minimal polynomial of alpha.

@Markiyan Hirnyk 

f1 is an algebraic number (or element) over the field Q(z).
The conjugates of f1 are the roots of the minimal polynomial; ==> the mentioned expression of the minimal polynomial.

@Markiyan Hirnyk 

If alpha is an algebraic number (over a field)  expressed with RootOfs then

evala( Norm(x - alpha) )

is the minimal polynomial for alpha (by definition).
See ?evala,Norm

@Markiyan Hirnyk 

z>1 was considered implicitly because the ode was considered in an interval containing z=2 and z=3, corresponding to x=1 and x=2.
So, all we need to know is that the hypergeometric function
hypergeom([1/3, 2/3], [3/2], w)
exists (and is C^2) for w<=0.

I prefer to work in cartesian coordonates

restart;
with(plots):with(plottools):
f:=r^2 *cos(theta)+r*sin(theta):
r1:= 0.3+0.1*cos(theta):
r2:= 0.5+0.1*cos(theta):
p:=densityplot(f, theta=0..2*Pi, r=r1..r2,  
colorstyle = HUE, style = patchnogrid):
T:=transform( (u,v) -> [v*cos(u),v*sin(u)]):
display(T(p));

@arman 

When coords=polar, the axes are cartesian.
Why don't you plot directly in cartesian coordinates? Simply use x=r*cos(t), y=r*sin(t).
P.S. Your image is missing.

 

@one man 

Try this simple one which is obvious by hand:

x1^4 + x2^4 + x3^4 - 1 = 0, x3 = 0.

You must be careful with the numbering (0..n) and the fact that in matices indices start at 1.
You should also check the formulae in wiki. Note that the wiki formulae for TSP are completely wrong (they talk there about index 0 which does not exist) and I had to correct them before coding.

Happy New Year!

Thank you for the answer.
So, the reason for opposite orders will remain a mistery.

Happy New Year! (actually also for all the mapleprimes members).

V.A.

@Markiyan Hirnyk 

I don't think that sort could be useful for an answer.
I'd like to know whether there is a consistent/logical rendering order for the objects in display.
The CURVES seem to be on top of POLYGONS and the orders differ.
When using transparency e.g., the order is important.
 

@torabi 

I suspect that the system has no solution (even after trying some other initial conditions).
Unfortunately it is hard to prove that this is the case and even harder to find an existence theorem for such a system. Sorry.
(If the system came from a concrete problem, you should try anoher approach).

@Rouben Rostamian  

Thank you Rouben, I'll keep these worksheets in my "special" collection.
In order to solve the memory problem for animation, one may use Explore. This way a single frame is present in memory but now the animation speed depends on  the computer speed.

anim := proc(tau, lambda, T)
  local R := 6;  # orbit's radius
      display([
      sphere([0,0,0], 1, style=surface, color="Orange"),
      tubeplot([R*cos(t), R*sin(t), 0], t=0..2*Pi, radius=0.04, color=red, style=surface),
      translate(globe(tau, lambda, T), R*cos(T), R*sin(T), 0)],
      view=[-R-1..R+1,-R-1..R+1,-1..1],
      scaling=constrained, lightmodel=light4, axes=none, orientation=[-144,65,0]
    )
end proc:
Explore(anim(tau,lambda,T),
parameters=[[tau=0..2*Pi,animate=false,shown=true], [lambda=0..2*Pi,animate=false,shown=true], [T=0..2*Pi,animate=true]],
initialvalues=[tau=Pi/6,lambda=Pi/4], loop, size=[1000,1000], numframes=240, autorun);