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.

References in zbMATH (referenced in 16 articles )

Showing results 1 to 16 of 16.
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  1. Hemelsoet, Nicolas; Voorhaar, Rik: A computer algorithm for the BGG resolution (2021)
  2. Gleixner, Ambros; Steffy, Daniel E.: Linear programming using limited-precision oracles (2020)
  3. Fu, Norie; Shibuta, Takafumi: An algebraic algorithm for solving parametric integer programs (2018)
  4. Dixon, Lance J.; Drummond, James; Harrington, Thomas; McLeod, Andrew J.; Papathanasiou, Georgios; Spradlin, Marcus: Heptagons from the Steinmann cluster bootstrap (2017)
  5. Monniaux, David: A survey of satisfiability modulo theory (2016)
  6. Fu, Norie; Shibuta, Takafumi: An algorithm for solving parametric integer program (2015)
  7. Berthomieu, Jérémy; Lebreton, Romain: Relaxed (p)-adic Hensel lifting for algebraic systems (2012)
  8. Chen, Liang; Monagan, Michael: Algorithms for solving linear systems over cyclotomic fields (2010)
  9. Guffin, Josh; Katz, Sheldon: Deformed quantum cohomology and (0,2) mirror symmetry (2010)
  10. Jacobson, Michael J. jun.; Scheidler, Renate; Stein, Andreas: Cryptographic aspects of real hyperelliptic curves (2010)
  11. Steffy, Daniel E.: Exact solutions to linear systems of equations using output sensitive lifting (2010)
  12. Stehlé, Damien: Floating-point LLL: Theoretical and practical aspects (2010)
  13. Villard, Gilles: Some recent progress in exact linear algebra and related questions (2007)
  14. Dumas, Jean-Guillaume; Urbańska, Anna: An introspective algorithm for the integer determinant (2006)
  15. Chen, Zhuliang; Storjohann, Arne: A BLAS based C library for exact linear algebra on integer matrices (2005)
  16. Storjohann, Arne: The shifted number system for fast linear algebra on integer matrices (2005)