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These are questions asked by Kitonum

Why does Maple 2015 solve this very simple system incorrectly?

solve({abs(a-b)=0, sqrt(2*b+c)=0, c^2-c+1/4=0});



With Maple 12 no problem:

solve({abs(a-b)=0, sqrt(2*b+c)=0, c^2-c+1/4=0});




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?

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

                 instead  of


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





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





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




What is the reason for this strange behavior of  simplify?

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.

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