Commutative Algebra
Gröbner Bases
Buchberger’s algorithm and Gröbner basis configuration.
Polynomial Ring Ideal Operations
Ideal creation, operations, varieties, and multiplicities.
Local Polynomial Rings
Element orders, creation, Gröbner bases, and ideal operations.
Affine Algebras
Affine algebra creation, operations, and maps.
Modules over Multivariate Rings
Module creation, order, embedded components, and homomorphisms.
Invariant Theory
Invariant rings, group actions, and permutation/matrix invariants.
Differential Rings
Differential rings and the Galois theory of linear differential equations.