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Polynomials
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Sage 9.8.beta2 Reference Manual
  • Home - Polynomials
  • Constructors for polynomial rings
  • 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 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
    • Solution of polynomial systems using msolve
    • 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
    • Reconstruction of Algebraic Forms
  • 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
  • Fraction Field of Integral Domains
  • Fraction Field Elements
  • Univariate rational functions over prime fields
  • Ring of Laurent Polynomials
  • Elements of Laurent polynomial rings
  • MacMahon’s Partition Analysis Omega Operator
  • Infinite Polynomial Rings
  • Elements of Infinite Polynomial Rings
  • Symmetric Ideals of Infinite Polynomial Rings
  • Symmetric Reduction of Infinite Polynomials
  • Boolean Polynomials
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Classical Invariant Theory#

  • Classical Invariant Theory
    • AlgebraicForm
    • BinaryQuartic
    • BinaryQuintic
    • FormsBase
    • InvariantTheoryFactory
    • QuadraticForm
    • SeveralAlgebraicForms
    • TernaryCubic
    • TernaryQuadratic
    • TwoAlgebraicForms
    • TwoQuaternaryQuadratics
    • TwoTernaryQuadratics
    • transvectant()
  • Reconstruction of Algebraic Forms
    • binary_cubic_coefficients_from_invariants()
    • binary_quadratic_coefficients_from_invariants()
    • binary_quintic_coefficients_from_invariants()
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Classical Invariant Theory
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