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FreeAlgebra -- Type of a free algebra

Description

This is the type of a free algebra over a commutative ring R (i.e. a tensor algebra over R).

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.

The source of this document is in AssociativeAlgebras/doc.m2:492:0.