Is there a fast algorithm to reduce systems of linear inequalities?

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Daniel R. Page

What is your metric for "fast". Time complexity or experimental results? That may help researchers answer your question.

Klaus Scheicher

I mean time complexity.

Adil AL-Rammahi

you can it by the elementary row operations (Gauss) . you find this in linear algebra. it is working on equations . you can used it in inequalities.

@Peter Breuer. Yes. Reducing all redundant inequalities. I have thousands of inequalities but only up to ten variables.

Silvano Dal Zilio

You may want to take a look at Avis, Fukuda, Picozzi, "On canonical representations of convex polyhedra" (2002); not sure if it fits our case though.

Also, your problem as a simple solution if you only have inequations of the from x - y \leq cst (systems of difference constraints). In this case the problem is known to be polynomial.