Markiyan Hirnyk

Markiyan Hirnyk
9 years, 185 days


These are questions asked by Markiyan Hirnyk

How to find the maximum natural number n s. t. the sum of its cubed digits is greater than or equal to n? Of course, with Maple. The same question for the sum of the  digits to k-th power. Here are my unsuccessful attempts:
1.Optimization:-Maximize(n, {n <= convert(map(c ->c^3, convert(n, base, 10)), `+`)}, assume = integer);

Error, invalid input: `convert/base` expects its 1st argument, n, to be of type {integer, list(integer)}, but received n


2. for n while n <= convert(map(c ->c^3, convert(n, base, 10)), `+`) do print(n) end do;

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of the cut-off sphere

Изображение

Изображение?

Of course, with Maple.

How to find (i. e. to evaluate) the positive root of the polynomial equation

mul(x+j, j = 0 .. 2015)=1?

The command

RootFinding:-NextZero(x-> mul(x+j, j = 0 .. 2015)-1 , 0);

outputs

                              FAIL
The same with Digits:=100.

of the improper integral of exp((1-x)/((1-x)^2+y^2)) over the unit disk x^2+y^2 <= 1 with Maple? For purists the function is assumed to be undefined at (1,0). It is not so difficult to verify that statement  by hand. It is not easy to prove that with Maple.

My try was

f := evalc(exp(Re(1/(1-x-I*y))));


VectorCalculus:-int(f, [x, y] = Circle(`<,>`(0, 0), 1), numeric);

and

evalf(Int(f, [y = -sqrt(-x^2+1) .. sqrt(-x^2+1), x = -1 .. 1]));
.

Edit. The formula for f.                  

PS.

 

 

 

How to find all nonisomorphic undirected graphs with 5 vertexes? Of course, with Maple.

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