A FreeAlgebra modulo a two-sided ideal carried by an embedded NCGroebner. More...

#include "NCAlgebras/FreeAlgebra.hpp"
#include "NCAlgebras/FreeMonoid.hpp"
#include "NCAlgebras/NCGroebner.hpp"
#include "Polynomial.hpp"
#include "newdelete.hpp"
#include "ringelem.hpp"
#include <vector>

Classes
class	FreeAlgebraQuotient
	Quotient of a FreeAlgebra by a Groebner basis up to a fixed degree bound. More...
class	FreeAlgebraQuotientElement
	Owned Poly value paired with its FreeAlgebraQuotient*, providing operator-overloaded arithmetic for debugging / scripting. More...

Detailed Description

A FreeAlgebra modulo a two-sided ideal carried by an embedded NCGroebner.

Note: AI-generated documentation. Verify against the source before relying on it.

Declares the non-commutative analogue of PolyRingQuotient (the commutative quotient ring lives in polyquotient.hpp; the PolyQuotient name in polyring.hpp is just a stale forward declaration). The class holds a reference to its ambient FreeAlgebra together with an NCGroebner mGroebner that owns the stored Gröbner basis of the defining ideal (the word-table / suffix-tree indices for divisor lookup also live inside NCGroebner — in-source comments here confirm the lookup tables were "placed in NCGroebner object"). The constructor takes a precomputed ConstPolyList& GB plus a maxdeg cap. normalizeInPlace, mult, power, and the other arithmetic entries compute in the ambient algebra and then reduce modulo the GB via the embedded NCGroebner. The full Ring-like surface is implemented here even though the class does not inherit from Ring; M2FreeAlgebraQuotient wraps it to provide the engine-wide Ring facade.

The companion FreeAlgebraQuotientElement at the bottom of the header is a lightweight RAII handle around one Poly (calls init/clear on construction/destruction) with overloaded + / - / * / ^ / ==, exposed for unit tests and interactive debugging. A two-sided GB in a free algebra is in general infinite, so maxdeg is how the engine keeps the computation finite at the cost of incomplete reduction past that degree.

See also: FreeAlgebra.hpp; FreeMonoid.hpp; NCGroebner.hpp; Polynomial.hpp; M2FreeAlgebraQuotient.hpp; polyquotient.hpp

Definition in file FreeAlgebraQuotient.hpp.

Classes

Detailed Description