Sandbox
Finding radicals of arbitrary ideals in rings is hard! However, it's a doable task in polynomial rings, since they are Noetherian (all ideals are finitely generated)
Background
A quick introduction to radical ideals
A ring is a set, paired with two binary operations + and * such that ...
Implement PSL(2,3)
Since challenge to implement Galois field already have been many, I'm writing a challenge to implement a group of Lie type!
The ring \$\mathbb{Z}_3\$
The ring \$\mathbb{Z}_3\$ is the set \$\{0,1,2\}\$ with addition, negation, subtraction, and multiplication defined as modula...
Background
We define a circular step sequence of order \$n\$ as follows:
$$
a_1, a_2, \dots, a_n = \text{Permutation of } 1 \dots n \\
b_i = \min ( |a_{i+1} - a_i|, n-|a_{i+1} - a_i| ), 1 \le i < n \\
\text{Circular step sequence} \stackrel{\text{def}}{=} b_1, b_2, \dots, b_{n-1}
$$
Informally...0
A binary multiple of a positive integer k is a positive integer n such that n is written only with 0s and 1s in base 10. For example, 111111 is a binary multiple of 3.
It is easy to show that a positive integer has infinitely many binary multiples. See [here][blog] for a construction proof of on...
0
Background: I ran into numerous issues when presenting and running this King of the Hill challenge back in October: Write a bot to play Grid Game - I'm cooking up a new, similar challenge, but taking things a bit more slowly and preparing more thoroughly to try and pre-emptively solve the issues ...
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Introduction
You are an NSA undercover agent in a Middle-Eastern HR company, you just received a list of people with their jobs. Some are spies and you need to know who. Your mission, if you accept it, is to get what are people working in, and relate it to a list of job categories. Most dangerou...
