## 20369 Reputation

16 years, 30 days

## The problem for Maple funs...

Recently, in one of the old book on programming came across the following problem: to place on the chessboard 5 queens so that each free field was attacked by at least one queen. This problem is called the problem of the dominant queens. I have not seen the implementation of this task in Maple. Naturally to solve this problem for an arbitrary board N by N. I have 2 variants to solve the problem, but I am not going to to present them yet, so that everyone can enjoy the independent decision. Especially the interesting case is the case of the board 6 by 6, when the solution is unique (certainly up to symmetry).

Of course, it is interesting for each board  N by N to find the minimum number of queens that satisfy the above condition. It seems that for arbitrary board  N by N the exact value of this number is not known. I do not know any other way of solving the problem as a brute force method.

## Bug in VectorCalculus:-int...

Maple 16

In Maple 16  (obviously, the result must be positive):

VectorCalculus:-int(x+y, [x, y] = Sector(Ellipse((1/4)*x^2+(1/9)*y^2-1), 0, (1/2)*Pi));

-2

Probably, this error occurs only in the latest versions, as in Maple 12 the output is correct. It would be interesting to know the reason for this behavior.

## Can Maple to prove...

properties of operations on sets?

Example:

is((A minus B) intersect (A minus C) = A minus (B union C)) assuming A::set, B::set, C::set;

FAIL

## Strange behavior of plots[contourplot]...

Contour lines must be ordinary circles. In fact, we get:

plots[contourplot](1/(x^2+y^2), x=-1..1, y=-1..1);

If we use the additional options, the result is even worse:

plots[contourplot](1/(x^2+y^2), x=-1..1,y=-1..1, numpoints=10000);

## Vectors of lists...

restart;

Vector([a, b]);  <a, b>;  # Identical results

a:=[1, 2]:  b:=[3, 4]:

Vector([a, b]), <a, b>;   # Different results. Why?

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