Markiyan Hirnyk

Markiyan Hirnyk
10 years, 85 days


These are questions asked by Markiyan Hirnyk

How to solve the inequality

,

assuming a::real ?

Of course, with Maple. I'd like to demonstrate the difficulties, solving

>solve(log[2*abs(x-a)](abs(x+a)+abs(x-a)) < 1, x) assuming a > 0, a < 1/2

.

The correct answer under the above restrictions is

{x  > 0, x  <  a} union {a  <  x, x <  a + 1/2} union { -infinity < x, x < a - 1/2}.

This is a problem from Lviv math school olympiad '2016.

 

 

Here is my unsuccessful try

>restart; plots:-contourplot(exp(2*x/(x^2+y^2)), x = -2 .. 2, y = -2 .. 2,
grid = [100, 100], coloring = [blue, red], contours = [.1, .3, .5, 1, 2]);

Nonzero complex numbers a, b, and c are such that every pair of the polynomials ( in x )
a*x^11+b*x^4+c, b*x^11+c*x^4+a, c*x^11+a*x^4+b has a common root. How to prove or disprove with Maple that all the three polynomials have a common root? I am aware of the resultant command in Maple.

How to realize the Cantor staircase function in Maple? Mathematica has it.

I'd like to stress the three desired properties:

(i) The virtual Cantor function can be evaluated to arbitrary numerical precision.

(ii) For certain arguments, this function automatically evaluates to exact values.

(iii) Mathematical function, suitable for both symbolic and numeric manipulation.

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