8 years, 65 days

@epostma  (reply sent from my prof...

@epostma

Thanks for this precision.

@acer  Thank you acer, I will look...

@acer

Thank you acer, I will look to that closely when back home.

@acer  Thanks for the answer. I&#...

@acer

Will the compiler be included in the delivery ot will I have to download LLVM by myself?
In addition I've read here that 2019.2 seems to present some problems: what version do you recommend me to buy?

@acer  Just a question: I often me...

@acer

Just a question: I often meet situations wher simplify(MyExpression) doesn't work. In this cases I try symplify(expand(MyExpression))  and it sometimes works.
I always put this on some "natural", or "normal" difficulty so simplify an expression (the simplified expression may have different form depending on the person): why, do you consider, in the present case, the flaw of simplify merits a bug report?

@tomleslie Maybe you're right, ...

Maybe you're right, unfortunately I have no access to Maple for the week to come (this reply from my smartphone). As soon as it will be possible to test your reply I let you know. Be patient.

Thanks in the meantime

The problem is not well posed. Without ...

The problem is not well posed.

Without restriction on the diameters d[m] of the new balls every points in D = C \ B(X1, R1) meets your requirement if d[m] --> 0+.

More of this, as N --> +infinity the probability that any point of  radius < 1 meets the requirements goes to 1.
This because the ratio V / 2N of the volume of B(X1, R1)  to the volume of C goes uiformily to 0 as N increases
(V = pi^(N/2) * R1^N / Gamma(N/2+1)).

@acer Thanks (PS: it works in Maple 201...

@acer

Thanks (PS: it works in Maple 2018 too)

@acer  Letting a point free is a v...

@acer

Letting a point free is a very good idea to try understanding how the algorithm works: I'm going to execute your little code of yours.
You wrote " Visually the behavior "makes sense", but what is the precise characterization in words?": right the way Maple fills non simple polygons make sense, at least visually. As it is easy to fill simple polygons in a non ambiguous way (because their interior does exist), it's not the case for non simple polygons.
Other common methods are based on drawing (for instance horizontal) parallel lines and swithing between "coloring" and "non coloring"  as soon as these lines cut a side of the polygon.
But if you use this latter for the stellate pentagon
a := evalf(2*Pi/5):
p := [ seq([cos(a*k), sin(a*k)], k in [1, 3, 5, 2, 4]) ]
PLOT(POLYGONS(p));

then a central regular pentagon should be kept white as it is colored. Probably it is what the intuition suggests, but it doesn't help to understanf the coloring algorithm Maple uses.

I implemented different ways to color general polygons and none of them offer the same appearance than Maple's does.
But maybe it's a vain quest for the interior of a non simple polygon is not defined?

@ThU  Thank you. There are indeed ...

@ThU

Thank you.
There are indeed impressive new drawing options in Maple 2019.
For now on I have at best Maple 2018.

@Thomas Richard  Thank you Richard...

@Thomas Richard

Thank you Richard.

To answer your last phrase I'm working on a coupling between Maple and R to delegate the latter some specific calculations which would be too complex to recode in Maple. The R code generated in Maple is saved in a text file "MyFile.R"   that must me made executable before launching the command ssystem("..../bin/Rscript MyFile.R").

@Carl Love  You're right, I...

@Carl Love

You're right, I'd forgotten ths Welch's test and its "equivalent" number of degrees of freedom.
Consider my question as null and void

@Carl Love  I will rectify this as...

@Carl Love

I will rectify this as soon as I get home.

@Carl Love  Right, once I sent my ...

@Carl Love

Right, once I sent my answer, I realized that I should have mentioned that the constructor || makes the variable global (something that caused me serious problems the first time I used this in a procedure...)

@Thomas Richard