RAZIN - Rigorous algebraic zero impeding numeration =====

For now, I offer

1. The fastest subroutine to calculate determinant of big matrice with big entries;
2. A subroutine to calculate HNF of a matrice whose determinant is small in absolute value;
3. PLU decomposition and inversion of a matrice modulo 2^64;
4. Inversion of an integer upper-triangular matrice with small determinant and positive diagonal;
5. Python binding to some methods of FLINT, called flint_sage;
6. A subroutine to count an integer matrice determinant.

See filelist.txt. For build instructions, see flint.binding/python.flint.sage.README.

My new algorithm to compute integer matrice determinant: fmpz_mat_det_hermitian_decomposition()

Small-det HNF: nmod_mat_HNF_nonsquare() and nmod_mat_HNF()

Mid-range target of the project is fast HNF computation with a new algorithm inspired by W.Stein double-determinant. Python wrapper is minimalistic and only contains functions required to reach the goal or to test/benchmark subroutines/algorithms.

The fastest in the open-source world subroutines to count big matrice determinant and small-det matrice Hermite form are a by-product.

FLINT and GMP data structures and subroutines are used.

If you find out that some subroutine of Razin produces bad result or crashes, your bug-report is welcome. If it includes the following data: sample code including input data, description of what happens, expected result (in case you think output is wrong). For instance, if you think that fmpz_mat_hermite_form() works incorrectly, provide

1. your code forming input matrice,
2. output matrice,
3. the correct output

FLINT

C numerical/matrice library with save-every-penny approach to arithmetic. Here

krisk0/razin

a research log and software package with quickest subroutines for integer linear algebra

NTL

C++ numerical/matrice library with gluttonous bigint constructor. Here

Captain Flint

fictional Caribbean adventurer (who said pirate?)

Stepan Razin

16??-1671, kozak, rebel leader (who said gangster?)