May 30,2024 lrslib linux binaries v7.3 http://cgm.cs.mcgill.ca/~avis/C/lrs.html These binaries are intended for linux users with a fairly standard setup. 1. lrs uses limited multithreading and hybrid arithmetic is recommended for most small or medium size applications. Arithmetic is 64bit/128bit/GMP(using mini-gmp) 2. Timing and interrupts are not supported. 3. lrsgmp uses GMP(mini-gmp) arithmetic only and may be much slower. 4. lrsnash computes Nash equilibria of 2-person games 5. Input files should be plain text files, so be careful about preparing them on text editors that have hidden formatting features. vim.exe is supplied to produce plaintext inputs. 6. For the full package including full GMP support and the OpenMPI mplrs code download from https://cgm.cs.mcgill.ca/~avis/C/lrslib/archive/ ------------------------------------------------------------------------------------- Example 1: hello world % lrs cube.ine lrs:lrslib_v.7.3_2024.5.30(64bit,lrslong.h,hybrid_arithmetic) *Input taken from cube.ine cube *starting 3 threads V-representation begin ***** 4 rational 1 1 1 1 1 0 1 1 1 1 1 0 1 1 0 1 1 0 1 0 1 0 0 1 1 1 0 0 1 0 0 0 end *Totals: vertices=8 rays=0 bases=8 integer_vertices=8 max_vertex_depth=3 *lrs:lrslib_v.7.3_2024.5.30(64bit,lrslong.h,hybrid_arithmetic) *0.000u 0.000s 1120Kb 0 flts 0 swaps 0 blks-in 0 blks-out *Elapsed time: 0 seconds --------------------------------------------------------------------------- Example 2: Illustrates hybrid arithmetic % plrs mp5.ext lrs:lrslib_v.7.3_2024.5.30(64bit,lrslong.h,hybrid_arithmetic) *Input taken from mp5.ext mp5 *volume *starting 8 threads H-representation begin ***** 11 rational 0 0 0 0 0 0 0 0 1 -1 1 0 0 0 0 0 0 1 -1 0 0 1 *lrs:overflow possible: restarting with 128 bit arithmetic plrs.exe:lrslib_v.7.3_2023.12.7(128bit,lrslong.h,hybrid_arithmetic) *Input taken from lrs_restart9lVK7d mp5 *volume *starting 8 threads H-representation begin ***** 11 rational 0 0 0 0 0 0 0 0 1 -1 1 0 0 0 0 0 0 1 -1 0 0 1 0 0 -1 1 0 0 0 0 1 0 0 0 0 0 1 -1 0 0 0 0 0 1 2 0 -1 0 -1 0 0 0 0 -1 0 2 0 0 0 0 -1 0 -1 0 -1 0 0 0 0 0 0 1 0 1 0 -1 0 0 0 0 0 0 -1 1 0 1 0 0 0 0 0 0 0 0 -1 1 0 0 1 0 1 0 1 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 -1 1 1 2 -1 0 -1 0 0 -1 0 0 0 0 0 -1 0 1 0 0 1 0 0 0 0 2 -1 0 0 -1 0 0 -1 0 0 0 2 0 0 0 0 0 -1 -1 0 0 -1 0 0 1 1 0 0 0 0 -1 0 0 0 1 1 0 0 -1 0 0 0 0 0 0 0 0 0 0 1 -1 0 1 0 0 0 0 0 0 0 1 1 0 -1 0 0 0 0 -1 0 1 0 0 0 0 1 0 0 0 0 0 0 -1 0 1 0 1 0 0 1 0 0 1 0 0 -1 0 0 0 0 -1 1 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 -1 0 0 0 -1 1 0 0 0 0 0 1 0 1 0 -1 0 0 1 0 0 0 0 0 1 0 0 -1 0 0 1 0 0 0 0 0 1 0 -1 0 0 0 0 1 0 0 -1 0 0 1 0 0 1 0 0 0 0 0 1 0 1 0 0 0 0 -1 0 0 0 0 0 0 0 1 1 0 0 -1 2 0 0 0 0 0 0 0 -1 -1 -1 0 0 0 0 0 1 0 -1 0 1 0 2 0 0 0 0 -1 -1 0 -1 0 0 0 0 1 -1 0 0 0 0 1 0 0 0 1 -1 0 0 1 0 0 0 0 0 2 -1 -1 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 -1 2 0 0 -1 -1 0 0 0 0 0 -1 2 0 -1 -1 0 0 0 0 -1 0 0 end *Volume=4/1701 *Totals: facets=40 bases=14108 max_facet_depth=12 *lrs:lrslib_v.7.3_2024.5.30(128bit,lrslong.h,hybrid_arithmetic) *0.281u 0.109s 2276Kb 0 flts 0 swaps 0 blks-in 0 blks-out *Elapsed time: 0 seconds -------------------------------------------------------------- 3. Compute Nash Equilibria of game cgm-compute% lrsnash game *lrsnash:lrslib_v.7.3_2024.5.30(64bit,lrsgmp.h,mini-gmp) 2 1/3 2/3 4 1 2/3 1/3 0 2/3 2 2/3 1/3 3 1 0 1/3 2/3 8/3 2 1 0 3 1 0 0 1 4 *Number of equilibria found: 3 *Player 1: vertices=5 bases=5 pivots=8 *Player 2: vertices=3 bases=1 pivots=8 *lrsnash::lrslib_v.7.3_2024.5.30(64bit,lrsgmp.h,mini-gmp) *0.000u 0.003s 1664Kb 1 flts 0 swaps 544 blks-in 0 blks-out