FreeAlgebra -- Type of a free algebra

i1 : A = QQ<|x,y|>

o1 = A

o1 : FreeAlgebra

Functions and methods returning a free algebra :

• freeAlgebra(Ring,BasicList) -- see freeAlgebra -- Create a FreeAlgebra

Methods that use a free algebra :

• derivation(FreeAlgebra,List) -- see Derivation -- Derivation defined on a noncommutative algebra
• derivation(FreeAlgebra,List,RingMap) -- see Derivation -- Derivation defined on a noncommutative algebra
• FreeAlgebra / Ideal -- Type of a noncommutative ring
• homogDual(FreeAlgebra) -- see homogDual -- Computes the dual of a pure homogeneous ideal
• ncHilbertSeries(FreeAlgebra) -- see ncHilbertSeries -- Computes the Hilbert series of a noncommutative ring
• oppositeRing(FreeAlgebra) -- see oppositeRing -- Creates the opposite ring of a noncommutative ring
• FreeAlgebra ** FreeAlgebra -- see qTensorProduct -- Define the (q-)commuting tensor product
• FreeAlgebra ** FreeAlgebraQuotient -- see qTensorProduct -- Define the (q-)commuting tensor product
• FreeAlgebraQuotient ** FreeAlgebra -- see qTensorProduct -- Define the (q-)commuting tensor product
• quadraticClosure(FreeAlgebra) -- see quadraticClosure -- Creates the subideal generated by quadratic elements of a given ideal
• toCommRing(FreeAlgebra) -- see toCommRing -- Compute the abelianization of a Ring and returns a Ring.

For the programmer

The object FreeAlgebra is a type, with ancestor classes EngineRing < Ring < Type < MutableHashTable < HashTable < Thing.