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Manuscript Title: A program for solving systems of homogeneous linear inequalities.
Authors: K.S. Kolbig, F. Schwarz
Program title: LIHOIN
Catalogue identifier: ACZH_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 17(1979)375
Programming language: Fortran.
Computer: CDC 7600.
Operating system: CDC SCOPE.
RAM: 721K words
Word size: 60
Keywords: General purpose, Linear inequalities, Expansion fourier, Positive function, Polyhedral cone, Matrix, Scattering amplitude, Unitarity.
Classification: 4.8.

Nature of problem:
The unitarity condition for physical scattering amplitudes implies the positivity of the imaginary parts of the partial waves. In an explicit construction of amplitudes this leads to inequality constraints for certain expansions.

Solution method:
The Motzkin-Burger rules are used to obtain iteratively the solution polyhedral cone of a system of homogeneous linear inequalities.

It is assumed that the matrix of the system is of rank N, the number of unknowns. Similar to ill-conditioned systems of linear equations, a system of inequalities may also be ill-conditioned, and the program may fail in such cases. Note also that the number of intermediate vectors can become very large, and that some systems are inconsistent.