GaussElimComputation — Gaussian elimination GB / submodule strategy over a field. More...

#include "relem.hpp"
#include "matrix.hpp"
#include "polyring.hpp"
#include "comp-gb.hpp"

Classes
struct	gm_elem
class	GaussElimComputation
	Gaussian elimination class. To be rewritten. More...

Detailed Description

GaussElimComputation — Gaussian elimination GB / submodule strategy over a field.

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

Declares GaussElimComputation, a GBComputation subclass that row-reduces a sparse matrix of generators to echelon form directly, plus the row-element struct gm_elem — a (f, fsyz) value/syzygy pair plus a cached nterms count and a next pointer. Rows are bucketed by lead component in parallel arrays gb_list[i] (the chosen pivot for component i) and reduce_list[i] (a linked list of pending rows with lead component i); on insert, the sparsest row (fewest nonzero terms) is promoted to gb_list[i] and any displaced pivot is pushed onto reduce_list[i]. After every generator is processed, the gb_list rows are a Groebner basis and the accumulated fsyz components form the matching syzygy module.

The strategy is the right call when the input is genuinely a linear-algebra problem in disguise — field-coefficient module presentations where Buchberger would just be performing the same row reductions with more overhead. The dispatcher in comp-gb.cpp selects this path automatically whenever the base ring of the input is a (non-polynomial) field; hermite.hpp is the analogous ZZ-coefficient algorithm.

See also: comp-gb.hpp; hermite.hpp

Definition in file gauss.hpp.

Classes

Detailed Description