Sections

• Introduction
• Monomial Orders
• Creation of Polynomial Rings and Creation of Polynomials
• Structure Operations
• Element Operations
• Greatest Common Divisors
• Polynomials over the Integers
• Factorization
• Resultant and Discriminant
• Creation of Ideals and Computation of Gröbner Bases
• Basic Operations on Ideals
• Computation of Varieties
• Elimination
• Changing Coefficient Ring
• Changing Monomial Order
• Variable Extension of Ideals
• Homogenization of Ideals
• Extension and Contraction of Ideals
• Dimension of Ideals
• Radical and Primary Decomposition of Ideals
• Graded Polynomial Rings
• Hilbert Series and Hilbert Polynomial
• Hilbert-driven Gröbner Basis Construction
• Syzygy Modules
• Affine Algebras (Quotient rings)
• Maps between Polynomial Rings
• Symmetric Polynomials
• Functions for Polynomial Algebra and Module Generators