Questions tagged [abstract-algebra]
Abstract algebra is the study of algebraic structures, including groups, rings, fields, vector spaces, and the like.
75 questions
8 votes
4 answers
576 views
Find a primitive polynomial
Objective Given a prime number \$p\$ and an integer \$n \geq 2\$, find a degree-\$n\$ primitive polynomial modulo \$p\$. Mathematical explanation When we perform "modular arithmetic" over ...
- 7,371
13 votes
9 answers
865 views
Output the symmetric inverse semigroup
The symmetric inverse semigroup is a very important object in the study of semigroups, for a number of reasons, but most obviously due to the Wagner-Preston theorem. In brief, for any set \$X\$, the ...
- 50.9k
7 votes
1 answer
355 views
Solving the high school algebra problem
We learned many identities involving addition, multiplication and exponentiation in highschool, for example: $$ \begin{aligned} (a+b)c &= ac + bc \\ (a b)^c &= a^c b^c \\ (a^b)^c &= a^{bc} ...
- 805
6 votes
2 answers
381 views
Count the symmetries
Find the order (size) of the symmetry group of a finite set of integer points in d-dimensional space. Input You will be given the coordinates of a finite set of points in d-dimensional space, in any ...
- 2,072
16 votes
2 answers
684 views
Construct this point
Given a constructible point \$(x, y) \in \mathbb R^2\$, output the steps required to construct \$(x, y)\$ Constructing a point Consider the following "construction" of a point \$(\alpha, \...
- 50.9k
14 votes
1 answer
339 views
Construct the Constructability sequence
Consider compass-and-straightedge construction, where you can construct new points from existing ones by examining intersections of straight lines and circles constructed with one of the following two ...
- 50.9k
12 votes
18 answers
691 views
Normal Subgroups of \$S_4\$
Objective Given a permutation of 4 distinct items, classify the permutation by the normal subgroup(s) it belongs. Input/Output Format You gotta choose the followings as the hyperparameters for your ...
- 7,371
9 votes
8 answers
558 views
Count the ways to transform
A rigid transformation of a square array is a mapping from square arrays of a certain size to square arrays of the same size, which rearranges the elements of the array such that the distance to each ...
- 103k