HermiteComputation — Hermite normal form over ZZ, the ZZ-analogue of GaussElimComputation. More...

#include "relem.hpp"
#include "matrix.hpp"
#include "polyring.hpp"
#include "comp-gb.hpp"
#include "ZZ.hpp"
#include <vector>

Classes
struct	hm_elem
class	HermiteComputation
	Slow Hermite normal form computation over ZZ. Replace. More...

Detailed Description

HermiteComputation — Hermite normal form over ZZ, the ZZ-analogue of GaussElimComputation.

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

Declares HermiteComputation, a GBComputation subclass that reduces a sparse matrix of generators over ZZ to a Hermite normal form: each row has a distinct lead component, and the above-pivot entries in that column are reduced against the pivot in absolute value via globalZZ->remainderAndQuotient. Rows live as an intrusive list of hm_elem structs — a gm_elem cousin with an explicit cached mpz_t lead so pivot comparisons do not have to re-walk f (the class even carries its own merge / sort over hm_elem* lists). Each elimination step is an extended-GCD (Bezout) update of the pivot followed by a reduction of the remaining rows — a structure that preserves integrality where the field-coefficient GaussElimComputation could not.

The dispatcher in comp-gb.cpp picks this path automatically when a GB is requested with the base ring globalZZ, i.e. for any submodule of ZZ^n. The header notes the implementation is "slow, replace" — a candidate for a future-perf rewrite.

See also: gauss.hpp; comp-gb.hpp; LLL.hpp

Definition in file hermite.hpp.

Classes

Detailed Description