Polynomials

Polynomial Rings

• Constructors for polynomial rings

Univariate Polynomials

• Univariate Polynomials and Polynomial Rings
  • Univariate Polynomial Rings
  • Ring homomorphisms from a polynomial ring to another ring
  • Univariate Polynomial Base Class
  • Univariate Polynomials over domains and fields
  • Univariate Polynomials over GF(2) via NTL’s GF2X.
  • Univariate polynomials over number fields.
  • Dense univariate polynomials over \(\ZZ\), implemented using FLINT.
  • Dense univariate polynomials over \(\ZZ\), implemented using NTL.
  • Univariate polynomials over \(\QQ\) implemented via FLINT
  • Dense univariate polynomials over \(\ZZ/n\ZZ\), implemented using FLINT.
  • Dense univariate polynomials over \(\ZZ/n\ZZ\), implemented using NTL.
  • Dense univariate polynomials over \(\RR\), implemented using MPFR
  • Polynomial Interfaces to Singular
  • Base class for generic \(p\)-adic polynomials
  • p-adic Capped Relative Dense Polynomials
  • p-adic Flat Polynomials
  • Univariate Polynomials over GF(p^e) via NTL’s ZZ_pEX.
  • Isolate Real Roots of Real Polynomials
  • Isolate Complex Roots of Polynomials
  • Refine polynomial roots using Newton–Raphson
  • Ideals in Univariate Polynomial Rings.
  • Quotients of Univariate Polynomial Rings
  • Elements of Quotients of Univariate Polynomial Rings
  • Polynomial Compilers
  • Polynomial multiplication by Kronecker substitution
• Generic Convolution
• Fast calculation of cyclotomic polynomials

Multivariate Polynomials

• Multivariate Polynomials and Polynomial Rings
  • Term orders
  • Base class for multivariate polynomial rings
  • Base class for elements of multivariate polynomial rings
  • Multivariate Polynomial Rings over Generic Rings
  • Generic Multivariate Polynomials
  • Ideals in multivariate polynomial rings.
  • Polynomial Sequences
  • Multivariate Polynomials via libSINGULAR
  • Direct low-level access to SINGULAR’s Groebner basis engine via libSINGULAR.
  • PolyDict engine for generic multivariate polynomial rings
  • Compute Hilbert series of monomial ideals
  • Class to flatten polynomial rings over polynomial ring
  • Monomials
• Classical Invariant Theory
  • Classical Invariant Theory
• Educational Versions of Groebner Basis Related Algorithms
  • Educational versions of Groebner basis algorithms
  • Educational versions of Groebner basis algorithms: triangular factorization
  • Educational version of the \(d\)-Groebner basis algorithm over PIDs

Skew Polynomials

• Univariate Skew Polynomials
• Constructor for skew polynomial rings
• Skew Univariate Polynomial Rings

Rational Functions

• Fraction Field of Integral Domains
• Fraction Field Elements
• Univariate rational functions over prime fields

Laurent Polynomials

• Ring of Laurent Polynomials
• Elements of Laurent polynomial rings
• MacMahon’s Partition Analysis Omega Operator

Infinite Polynomial Rings

• Infinite Polynomial Rings.
• Elements of Infinite Polynomial Rings
• Symmetric Ideals of Infinite Polynomial Rings
• Symmetric Reduction of Infinite Polynomials

Boolean Polynomials

• Boolean Polynomials

Noncommutative Polynomials

• Noncommutative Polynomials via libSINGULAR/Plural

Indices and Tables

• Index
• Module Index
• Search Page