6443

Reputation

25

Badges

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 n2. for n while n <= convert(map(c ->c^3, convert(n, base, 10)), `+`) do print(n) end do; 1 2 3 4 5 6 7 8 9

of the cut-off sphere

?

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 FAILThe 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.

You must be logged into your Facebook account in order to share via Facebook.

Click the button below to share this on Google+. A new window will open.

You must be logged in to your Twitter account in order to share. Click the button below to login (a new window will open.)

Please log-in to your MaplePrimes account.

Wrong Email/Password. Please try again.