dmat-lu-qq.hpp File Reference

DMatLinAlg<M2::ARingQQ> — rational dense LU routed through FLINT fmpq_mat / fmpz_mat. More...

#include "dmat-qq-interface-flint.hpp"

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Classes
class	DMatLinAlg< M2::ARingQQ >
	Specialisation of DMatLinAlg for ARingQQ dense matrices, routing every linear-algebra query (rank, determinant, kernel, inverse, solve) through FLINT's fmpq_mat_* routines. More...

Detailed Description

DMatLinAlg<M2::ARingQQ> — rational dense LU routed through FLINT fmpq_mat / fmpz_mat.

Note

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

Specialises DMatLinAlg for the rational aring ARingQQ. Each operation copies the input through FlintQQMat (dmat-qq-interface-flint.hpp) so a FLINT fmpq_mat_t is available without disturbing the M2 matrix, then dispatches: rank clears denominators via fmpq_mat_get_fmpz_mat_rowwise and falls into fmpz_mat_rank; kernel (null-space) follows the same denominator-clearing pattern and finishes with fmpz_mat_nullspace; inverse goes through fmpz_mat_inv on the cleared matrix and scales back to fmpq; and determinant and solveInvertible stay in rationals via fmpq_mat_det and fmpq_mat_solve_dixon directly.

matrixPLU is the exception: an in-source comment notes fmpz_mat_fflu does not return a true LU factorisation, so the specialisation builds a generic DMatLUinPlace<ARingQQ> locally and uses LUUtil<ARingQQ>::setUpperLower to split. solve(B, X) handles the non-square / rank-deficient case by concatenateMatrices<Mat> of [A | B], calling fmpq_mat_rref, and reading the solution out of the column-rank profile via the static findColumnRankProfileFromLU.

See also

dmat-lu.hpp

dmat-qq-interface-flint.hpp

aring-qq.hpp

Definition in file dmat-lu-qq.hpp.