## 19511 Reputation

14 years, 324 days

## Bug in Standard GUI Maple 2015...

In my  Standard GUI Maple 2015 (32 bit)  on Windows 8.1  plots[spacecurve]  command does not work:

plots[spacecurve]([cos(t), sin(t), t], t = 0 .. 2*Pi);

Can someone confirm this bug?

## Mixed number instead improper fraction...

Can we output a mixed number instead of  an improper fraction in Maple programmatically. For example

The expression  expr  the command  simplify  simplifies without any problems. Even certain automatic simplification is produced:

expr:=sqrt(4-sqrt(7))*sqrt(4+sqrt(7));

simplify(expr);

But if we slightly modify the expression, the simplification is not performed:

expr1:=sqrt(4-sqrt(6))*sqrt(4+sqrt(6));

simplify(expr1);

The last expression  expr1  succeed to simplify the only combination of commands:

expand(combine(expr1));

What is the reason for this strange behavior of  simplify?

## 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.

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