Abstract Algebra

An abstract algebra cli written in Rust.

Listing Group Elements

To list the elements in a group, use abstract-algebra group <group_id> --elements.

$ abstract-algebra group S3 --elements
Elements of S3:
[order 6] {(0, 1, 2), (0, 2, 1), (2, 0, 1), (2, 1, 0), (1, 2, 0), (1, 0, 2)}

Conjugacy classes

Use abstract-algebra group <group_id> --conjugacy-classes to list the conjugacy classes of a group.

$ abstract-algebra group A4 --conjugacy-classes
Conjugacy classes of A4:
[1 element] {(0, 1, 2, 3)}
[4 elements] {(0, 3, 1, 2), (1, 2, 0, 3), (3, 0, 2, 1), (2, 1, 3, 0)}
[4 elements] {(0, 2, 3, 1), (2, 0, 1, 3), (1, 3, 2, 0), (3, 1, 0, 2)}
[3 elements] {(2, 3, 0, 1), (1, 0, 3, 2), (3, 2, 1, 0)}

You can also use abstract-algebra group <group_id> --center to list the members of trivial conjugacy classes.

Supported Groups

• Alternating groups A<n>
• Symmetric groups S<n>
• Cyclic groups Z<n>
• Dihedral groups of order 2n D<n>
• Quaternion group Q8

Upcoming Features

• Direct product of groups
• Formatting permutations with cycle notation