Anonymous user
Sturmian word: Difference between revisions
described the problem
imported>CosmiaNebula (Sturmian word) |
imported>CosmiaNebula (described the problem) |
||
Line 5:
The Sturmian word can be computed thus as an algorithm:
* If x > 1, then it is the inverse of the Sturmian word for (1/x). So we have reduced to the case of <math>0 < x
* Iterate over <math>floor(1x), floor(2x), floor(3x), \dots </math>
* If <math>kx </math> is an integer, then the program terminates. Else, if <math>floor((k-1)x) = floor(kx)</math>, then the program outputs 0, else, it outputs 10.
The problem:
* Given a positive rational number <math>\frac mn</math>, specified by two positive integers <math>m, n</math>, output its entire Sturmian word.
* Given a quadratic real number <math>\frac{\sqrt{a} + m}{n}</math>, specified by three positive integers <math>a, m, n </math>, where <math>a</math> is not a perfect square, output the first <math>k</math> letters of its Sturmian word when given a positive number <math>k</math>.
Stretch goal: calculate the Sturmian word for other kinds of definable real numbers, such as cubic roots.
| |||