IML - Integer Matrix Library
IML - Integer Matrix Library. IML is a free library of C source code which implements algorithms for computing exact solutions to dense systems of linear equations over the integers. IML is designed to be compiled with a CBLAS library (e.g., ATLAS/BLAS) and the GMP bignum library. Written in portable C, IML can be used on both 32-bit and 64-bit machines. It can be called from C++. Currently, IML provides the following functionality: Nonsingular rational system solving: compute the unique rational solution X to the system AX=B, where A and B are integer matrices, A nonsingular. Compute the right nullspace of an integer matrix. Certified linear system solving: compute a minimal denominator solution x to a system Ax=b, where b is an integer vector and A is an integer matrix with arbitrary shape and rank profile. In addition, IML provides some low level routines for a variety of mod p matrix operations: computing the row-echelon form, determinant, rank profile, and inverse of a mod p matrix. These mod p routines are not general purpose; they require that p satisfy some preconditions based on the dimension of the input matrix (usually p should be prime and should be no more than about 20 bits long).
This software is also referenced in ORMS.
This software is also referenced in ORMS.
Keywords for this software
References in zbMATH (referenced in 14 articles )
Showing results 1 to 14 of 14.
Sorted by year (- Fu, Norie; Shibuta, Takafumi: An algebraic algorithm for solving parametric integer programs (2018)
- Dixon, Lance J.; Drummond, James; Harrington, Thomas; McLeod, Andrew J.; Papathanasiou, Georgios; Spradlin, Marcus: Heptagons from the Steinmann cluster bootstrap (2017)
- Monniaux, David: A survey of satisfiability modulo theory (2016)
- Fu, Norie; Shibuta, Takafumi: An algorithm for solving parametric integer program (2015)
- Berthomieu, Jérémy; Lebreton, Romain: Relaxed $p$-adic Hensel lifting for algebraic systems (2012)
- Chen, Liang; Monagan, Michael: Algorithms for solving linear systems over cyclotomic fields (2010)
- Guffin, Josh; Katz, Sheldon: Deformed quantum cohomology and (0,2) mirror symmetry (2010)
- Jacobson, Michael J. jun.; Scheidler, Renate; Stein, Andreas: Cryptographic aspects of real hyperelliptic curves (2010)
- Steffy, Daniel E.: Exact solutions to linear systems of equations using output sensitive lifting (2010)
- Stehlé, Damien: Floating-point LLL: Theoretical and practical aspects (2010)
- Villard, Gilles: Some recent progress in exact linear algebra and related questions (2007)
- Dumas, Jean-Guillaume; Urbańska, Anna: An introspective algorithm for the integer determinant (2006)
- Chen, Zhuliang; Storjohann, Arne: A BLAS based C library for exact linear algebra on integer matrices (2005)
- Storjohann, Arne: The shifted number system for fast linear algebra on integer matrices (2005)