gbring.hpp File Reference

GBRing and gbvector — the GB-tuned polynomial-ring view used by classical Buchberger code. More...

#include <M2/math-include.h>
#include "engine-includes.hpp"
#include <iostream>
#include <string>
#include "buffer.hpp"
#include "monoid.hpp"
#include "newdelete.hpp"
#include "ringelem.hpp"
#include "skew.hpp"
#include "style.hpp"

Go to the source code of this file.

Classes
struct	gbvector
struct	POLY
	Pairs a gbvector with its evolving syzygy gbvector. More...
class	GBRing
	Polynomial-ring view tuned for the inner loop of classical Buchberger Groebner-basis computations. More...
class	GBRingPoly
	GBRing specialisation for ordinary commutative polynomial rings. More...
class	GBRingWeyl
	GBRing specialisation for Weyl algebras over a field. More...
class	GBRingWeylZZ
	GBRingWeyl specialisation for Weyl algebras over ZZ. More...
class	GBRingSkew
	GBRing specialisation for skew-commutative (exterior-like) polynomial rings. More...
class	GBRingSolvable
	GBRing specialisation for solvable polynomial algebras (PBW-style non-commutative rings whose relations have the form x_j * x_i = c_ij * x_i * x_j + lower-order terms). More...
class	gbvectorHeap

Typedefs
typedef int *	monomial

Functions
template<typename container, typename fcn>
void	displayElements (std::string header, GBRing *R, container a, fcn f)

Detailed Description

GBRing and gbvector — the GB-tuned polynomial-ring view used by classical Buchberger code.

Note

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

gbvector is the value type: a singly-linked list of { gbvector *next; ring_elem coeff; int Computations; int monom[1]; } nodes, with the flexible-array monom[1] trailing whatever variable-length encoding the monoid uses. POLY { gbvector *f; gbvector *fsyz; } pairs the polynomial with its evolving syzygy. GBRing is the matching ring view: it inherits from our_new_delete, holds the coefficient ring and monoid, and exposes the core polynomial-arithmetic primitives the GB inner loop needs — in particular gbvector_add_to (general-coefficient addition) and its gbvector_add_to_zzp specialisation for prime-field hot paths. Concrete subclasses (GBRingPoly, GBRingSkew, GBRingWeyl, GBRingWeylZZ, GBRingSolvable) cover the cross of ring flavour and coefficient kind; the in-source comment block enumerates the full Schreyer-encoded / KK vs ZZ / quotient axes.

Compared with polyring.hpp's PolynomialRing, this view trades the opaque ring_elem for an explicit linked-list representation that makes head/tail decomposition cheap and lets the companion gbvectorHeap accumulator absorb the many summands of a GB reduction without quadratic merge cost. A GBRing is constructed once per GB computation from a PolynomialRing and torn down at the end.

See also

polyring.hpp

comp-gb.hpp

gb-default.hpp

Definition in file gbring.hpp.