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Example: Linear program

Profiles: OSCAR v1.0, OSCAR v1.1, OSCAR v1.2, OSCAR v1.3, OSCAR v1.4, OSCAR v1.5, OSCAR v1.6, OSCAR v1.7, OSCAR v1.8

We take the matrix

$$ A:= \left( \begin{array}{ccc} 31 & 24 & 78\\ 63 & 17 & 35\\ 99 & 19 & 34 \end{array} \right) $$

with entries in the rational numbers $\mathbb{Q}$.

Now we take the following two vector with entries in $\mathbb{Q}$:

$$ b := (12, 51, 23)\ \mbox{ and }\ w := (64449, 26552, 73367). $$

Now find $x\in\mathbb{Q}^3$ such that $A\cdot x\ge -b$ and $\langle x,w\rangle$ becomes minimal.

Systems

CPLEX

Generate code (generate.sh) [ edit ]

update me

Data outputs

Profiles: default

Data file: data.lp

MINIMIZE
  obj: +64449 x1 +26552 x2 +73367 x3
Subject To
  ie0: +31 x1 +24 x2 +78 x3 >= -12
  ie1: +63 x1 +17 x2 +35 x3 >= -51
  ie2: +99 x1 +19 x2 +34 x3 >= -23
BOUNDS
  x1 free
  x2 free
  x3 free
END

Oscar.jl

Generate code (generate.jl) [ edit ]

using Oscar
A = matrix(QQ,[31 24 78; 63 17 35; 99 19 34]);
b = [12, 51, 23]
P = polyhedron(-A, b)
println(vertices(P))
w = [64449, 26552, 73367]
LP = linear_program(P,w;k=0,convention = :min)
println(optimal_value(LP))
save("data.mrdi", LP)

Data outputs

Profiles: OSCAR v1.0, OSCAR v1.1, OSCAR v1.2, OSCAR v1.3, OSCAR v1.4, OSCAR v1.5, OSCAR v1.6, OSCAR v1.7

Data file: data.mrdi

{
  "_ns": {"Oscar": ["https://github.com/oscar-system/Oscar.jl", "1.7.0"]},
  "_type": {"name": "LinearProgram", "params": {"_type": "QQField"}},
  "data": {
    "feasible_region": {
      "COMBINATORIAL_DIM": 3,
      "_info": {
        "credits": {
          "ppl": "  The Parma Polyhedra Library ([[wiki:external_software#PPL]]): A C++ library for convex polyhedra\n  and other numerical abstractions.\n  http://www.cs.unipr.it/ppl/\n",
          "cdd": "\nCopyright by Komei Fukuda.\nhttps://people.inf.ethz.ch/fukudak/cdd_home/\n"
        }
      },
      "_vertex_indices": [4],
      "FULL_DIM": true,
      "N_VERTICES": 4,
      "LINEALITY_DIM": 0,
      "_type": "polytope::Polytope<Rational>",
      "AFFINE_HULL": [{"cols": 4}],
      "EQUATIONS": [{"cols": 4}],
      "FEASIBLE": true,
      "VERTICES": [
        ["0", "1", "-3829/486", "985/486"],
        ["0", "-1", "3334/333", "-1787/666"],
        ["0", "1", "-441/29", "162/29"],
        ["1", "7248/2951", "-236125/8853", "62650/8853"]
      ],
      "_ns": {"polymake": ["https://polymake.org", "4.15"]},
      "CONE_AMBIENT_DIM": 4,
      "INEQUALITIES": [
        ["12", "31", "24", "78"],
        ["51", "63", "17", "35"],
        ["23", "99", "19", "34"],
        ["1", "0", "0", "0"]
      ],
      "LP": [
        {
          "MINIMAL_VERTEX": ["1", "7248/2951", "-236125/8853", "62650/8853"],
          "MINIMAL_VALUE": "-30698",
          "LINEAR_OBJECTIVE": ["0", "64449", "26552", "73367"],
          "_attrs": {"convention": {"attachment": true}},
          "convention": "min",
          "_id": "unnamed#0"
        }
      ],
      "POINTED": true,
      "BOUNDED": false,
      "_attrs": {"_vertex_indices": {"_type": "Vector<Int>", "attachment": true}},
      "FAR_FACE": [0, 1, 2],
      "CONE_DIM": 4,
      "LINEALITY_SPACE": [{"cols": 4}]
    },
    "convention": "min",
    "lpcoeffs": {
      "_ns": {"polymake": ["https://polymake.org", "4.15"]},
      "data": ["0", "64449", "26552", "73367"],
      "_type": "common::Vector<Rational>"
    }
  }
}

This serialized output is equivalent for these profiles up to UUID renaming and recorded namespace version strings.

cdd

Generate code (generate.sh) [ edit ]

scdd data.ine

Data outputs

Profiles: default

Data file: data.ine

H-representation
begin
3 4 rational
12 31 24 78
51 63 17 35
23 99 19 34
end
minimize
0 64449 26552 73367

polymake

Generate code (generate.pl) [ edit ]

use strict;
use warnings;
use application "polytope";
my $A = new Matrix<Rational>([[31,24,78],[63,17,35],[99,19,34]]);
my $b = new Vector<Rational>([12, 51, 23]);
my $w = new Vector<Rational>([64449, 26552, 73367]);

my $P = new Polytope(INEQUALITIES=>($b|$A));
my $lp = $P->LP(LINEAR_OBJECTIVE=>zero_vector(1)|$w);

save_data($P, "data.json");

Data outputs

Profiles: default

Data file: data.json

{
  "LP": [{"LINEAR_OBJECTIVE": ["0", "64449", "26552", "73367"], "_id": "unnamed#0"}],
  "_id": "data.json",
  "INEQUALITIES": [
    ["12", "31", "24", "78"],
    ["51", "63", "17", "35"],
    ["23", "99", "19", "34"],
    ["1", "0", "0", "0"]
  ],
  "_type": "polytope::Polytope<Rational>",
  "CONE_AMBIENT_DIM": 4,
  "_ns": {"polymake": ["https://polymake.org", "4.14"]}
}