det.hpp File Reference

Determinants and minors of Matrix values via Bareiss, cofactor, or dynamic-programming strategies. More...

#include "matrix.hpp"
#include "matrix-con.hpp"
#include <utility>
#include <vector>
#include <map>
#include <algorithm>

Go to the source code of this file.

Classes
class	DetComputation
	Computation of minors of a matrix. More...

Variables
const int	DET_BAREISS = 0
const int	DET_COFACTOR = 1
const int	DET_DYNAMIC = 2

Detailed Description

Determinants and minors of Matrix values via Bareiss, cofactor, or dynamic-programming strategies.

Note

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

Declares DetComputation and the three integer strategy constants the caller selects between: DET_BAREISS, DET_COFACTOR, and DET_DYNAMIC. Bareiss is the fraction-free Gaussian variant — requires the coefficient ring to be a domain (the in-source comment annotates it "fraction free, DOMAINS only") and keeps the intermediate pivots integral by carrying the previous pivot through the divisions. Cofactor is a straight recursive Laplace expansion along the last row of each submatrix, skipping zero entries; it is the natural fallback over rings where Bareiss division does not apply (inexact fields, quotient rings). Dynamic is the memoised variant: it caches submatrix minors in nested std::maps keyed by row/column index sets so that minor-list queries of many sizes share work. The user-facing det / minors functions defined in m2/multilin.m2 map their Strategy => option onto these three constants.

Entry points operate on a Matrix and return either a RingElement (the determinant of a square submatrix) or a Matrix collecting minors (or an exterior power when the do_exterior flag is set).

See also

matrix.hpp

matrix-con.hpp

Definition in file det.hpp.