NCIdeal -- Type of a two-sided ideal in a noncommutative ring

Functions and methods returning an object of class NCIdeal :

• ideal(NCPolynomialRing) -- The defining ideal of an NCPolynomialRing
• ideal(NCQuotientRing) -- Defining ideal of an NCQuotientRing in its ambient ring

Methods that use an object of class NCIdeal :

• basis(ZZ,NCIdeal) -- Returns a basis of an NCIdeal in a particular degree.
• generators(NCIdeal) -- Returns the generators of an NCIdeal
• homogDual(NCIdeal) -- see homogDual -- Computes the dual of a pure homogeneous ideal
• isHomogeneous(NCIdeal) -- Determines whether the input defines a homogeneous object
• ncGroebnerBasis(NCIdeal) -- see ncGroebnerBasis -- Compute a noncommutative Groebner basis.
• NCIdeal + NCIdeal -- Sum of NCIdeals
• NCPolynomialRing / NCIdeal -- Construct a NCQuotientRing
• NCRingMap NCIdeal -- Apply a ring map to the generators of an ideal
• quadraticClosure(NCIdeal) -- see quadraticClosure -- Creates the subideal generated by quadratic elements of a given ideal
• ring(NCIdeal) -- Returns the ring of an NCIdeal or NCGroebnerBasis
• twoSidedNCGroebnerBasisBergman(NCIdeal) -- see twoSidedNCGroebnerBasisBergman -- Calls Bergman to compute a two sided noncommutative Groebner Basis.

For the programmer

The object NCIdeal is a type, with ancestor classes HashTable < Thing.