- Introduction
- Creation Functions
- Creation of Structures
- Print Options
- Creation of Elements
- P . 1 : RngUPol, RngInt -> RngPolElt
- elt< P | a0, ..., ad > : RngUPol, RngElt, ..., RngElt -> RngUPolElt
- P ! s : RngUPol, RngElt -> RngPolElt
- Polynomial(Q) : [ RngElt ] -> RngUPolElt
- Polynomial(R, Q) : Rng, [ RngElt] -> RngUPolElt
- Polynomial(R, f) : Rng, RngUPolElt -> RngUPolElt
- Example RngPol_Polynomials (H24E2)
- Structure Operations
- Element Operations
- Parent and Category
- Arithmetic Operators
- Equality and Membership
- Predicates on Ring Elements
- Coefficients and Terms
- Degree
- Roots
- Roots(p) : RngUPolElt -> [ < RngElt, RngIntElt> ]
- Roots(p, S) : RngUPolElt -> [ < RngElt, RngIntElt> ]
- HasRoot(p) : RngUPolElt -> BoolElt, RngElt
- HasRoot(p, S) : RngUPolElt, Rng -> BoolElt, RngElt
- SmallRoots(p, N, X) : RngUPolElt, RngElt, RngElt -> [RngElt]
- Example RngPol_SmallRootsUsage (H24E5)
- SetVerbose("SmallRoots", v) : MonStgElt, RngIntElt ->
- Derivative, Integral
- Evaluation, Interpolation
- Decomposition
- Quotient and Remainder
- Quotrem(f, g) : RngUPolElt, RngUPolElt -> RngUPolElt, RngUPolElt
- f div g : RngUPolElt, RngUPolElt -> RngUPolElt
- IsDivisibleBy(f, g) : RngUPolElt, RngUPolElt -> BoolElt, RngUPolElt
- ExactQuotient(f, g) : RngUPolElt, RngUPolElt -> RngUPolElt
- f mod g : RngUPolElt, RngUPolElt -> RngUPolElt
- Valuation(f, g) : RngUPolElt, RngUPolElt -> RngIntElt
- Reductum(f) : RngUPolElt -> RngUPolElt
- PseudoRemainder(f, g) : RngUPolElt, RngUPolElt -> RngUPolElt
- EuclideanNorm(p) : RngUPol -> RngIntElt
- Modular Arithmetic
- Other Operations
- Common Divisors and Common Multiples
- Polynomials over the Integers
- Polynomials over Finite Fields
- Factorization
- Factorization and Irreducibility
- Factorization(f) : RngUPolElt -> [ < RngUPolElt, RngIntElt >], RngElt
- HasPolynomialFactorization(R) : Rng -> BoolElt
- SetVerbose("PolyFact", v) : MonStgElt, RngIntElt ->
- FactorisationToPolynomial(f) : [Tup] -> BoolElt
- Example RngPol_SwinnertonDyerPolynomial (H24E7)
- SquarefreeFactorization(f) : RngUPolElt -> [ <RngUPolElt, RngIntElt> ]
- DistinctDegreeFactorization(f) : RngUPolElt -> [ <RngIntElt, RngUPolElt> ]
- EqualDegreeFactorization(f, d, g) : RngUPolElt, RngIntElt, RngUPolElt -> [ RngUPolElt ]
- IsIrreducible(f) : RngUPolElt -> BoolElt
- IsSeparable(f) : RngUPolElt -> BoolElt
- QMatrix(f) : RngUPolElt -> AlgMatElt
- Resultant and Discriminant
- Hensel Lifting
- Ideals and Quotient Rings
- Special Families of Polynomials
- Bibliography
V2.28, 13 July 2023