Example: Pair of linear programs
Profiles: OSCAR v1.5, OSCAR v1.6, OSCAR v1.7, OSCAR v1.8
Construct two linear programs over a number field and store them as a list.
Related Specification
Systems
Oscar.jl
Generate code (generate.jl) [ edit ]
using Oscar
P = dodecahedron()
F = coefficient_field(P)
a = gen(number_field(F))
LP1 = linear_program(P, F.([3, -2, 4]); k=2, convention=:min)
LP2 = linear_program(P, F.([-1, a - 2, a + 5]); k=2, convention=:min)
ov1 = optimal_value(LP1)
ov2 = optimal_value(LP2)
obj = [LP1, LP2]
save("data.mrdi", obj)
Data outputs
Profiles: 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": "Vector",
"params": {
"name": "LinearProgram",
"params": {
"field": "6f572036-b307-4c75-afeb-acab3fd6c7d5",
"pm_params": {
"name": "Dict",
"params": {
"key_params": "Symbol",
"AFFINE_HULL": {"name": "MatElem", "params": "8c219a81-f0c1-4fa6-8a99-9f7e99fd3572"},
"FACETS": {"name": "MatElem", "params": "455468de-b413-452f-a58b-dea7c3fcffc2"},
"_polymake_type": "String",
"GROUP": {
"name": "Tuple",
"params": [
{
"name": "Dict",
"params": {
"key_params": "Symbol",
"VERTICES_ACTION.GENERATORS": {"name": "Vector", "params": {"name": "Vector", "params": "Base.Int"}}
}
}
]
},
"LP": {
"name": "Tuple",
"params": [
{
"name": "Dict",
"params": {
"key_params": "Symbol",
"MINIMAL_FACE": {"name": "Set", "params": "Base.Int"},
"MINIMAL_VALUE": {
"name": "EmbeddedNumFieldElem",
"params": "6f572036-b307-4c75-afeb-acab3fd6c7d5"
},
"LINEAR_OBJECTIVE": {
"name": "Vector",
"params": {
"name": "EmbeddedNumFieldElem",
"params": "6f572036-b307-4c75-afeb-acab3fd6c7d5"
}
}
}
},
{
"name": "Dict",
"params": {
"key_params": "Symbol",
"MINIMAL_FACE": {"name": "Set", "params": "Base.Int"},
"MINIMAL_VALUE": {
"name": "EmbeddedNumFieldElem",
"params": "6f572036-b307-4c75-afeb-acab3fd6c7d5"
},
"LINEAR_OBJECTIVE": {
"name": "Vector",
"params": {
"name": "EmbeddedNumFieldElem",
"params": "6f572036-b307-4c75-afeb-acab3fd6c7d5"
}
}
}
}
]
},
"DUAL_GRAPH.ADJACENCY": "Graph{Undirected}",
"POINTED": "Bool",
"TRIANGULATION": {
"name": "Tuple",
"params": [
{
"name": "Dict",
"params": {
"key_params": "Symbol",
"FACETS": {"name": "Vector", "params": {"name": "Set", "params": "Base.Int"}}
}
}
]
},
"FEASIBLE": "Bool",
"CONE_DIM": "Base.Int",
"VERTICES": {"name": "MatElem", "params": "b637d82a-edca-4ff7-b9b5-14822e54f9bb"},
"N_VERTICES": "Base.Int",
"CONE_AMBIENT_DIM": "Base.Int",
"FAR_FACE": {"name": "Set", "params": "Base.Int"},
"COMBINATORIAL_DIM": "Base.Int",
"LINEALITY_SPACE": {"name": "MatElem", "params": "8c219a81-f0c1-4fa6-8a99-9f7e99fd3572"},
"VERTICES_IN_FACETS": "Polymake.IncidenceMatrixAllocated{Polymake.NonSymmetric}",
"CENTERED": "Bool",
"BOUNDED": "Bool",
"LINEALITY_DIM": "Base.Int",
"ESSENTIALLY_GENERIC": "Bool",
"GRAPH.ADJACENCY": "Graph{Undirected}"
}
}
}
}
},
"data": [
{
"feasible_region": {
"AFFINE_HULL": [],
"FACETS": [
[[["0", "1"], ["1", "1//2"]], [["0", "-1//2"], ["1", "-1//2"]], [["0", "-1"]], []],
[[["0", "1"], ["1", "1//2"]], [], [["0", "-1//2"], ["1", "-1//2"]], [["0", "-1"]]],
[[["0", "1"], ["1", "1//2"]], [], [["0", "-1//2"], ["1", "-1//2"]], [["0", "1"]]],
[[["0", "1"], ["1", "1//2"]], [["0", "1//2"], ["1", "1//2"]], [["0", "1"]], []],
[[["0", "3//4"], ["1", "1//4"]], [["0", "1//2"], ["1", "-1//2"]], [], [["0", "1"]]],
[[["0", "1"], ["1", "1//2"]], [["0", "1//2"], ["1", "1//2"]], [["0", "-1"]], []],
[[["0", "3//4"], ["1", "1//4"]], [["0", "1//2"], ["1", "-1//2"]], [], [["0", "-1"]]],
[[["0", "3//4"], ["1", "1//4"]], [["0", "-1//2"], ["1", "1//2"]], [], [["0", "-1"]]],
[[["0", "1"], ["1", "1//2"]], [], [["0", "1//2"], ["1", "1//2"]], [["0", "-1"]]],
[[["0", "3//4"], ["1", "1//4"]], [["0", "-1//2"], ["1", "1//2"]], [], [["0", "1"]]],
[[["0", "1"], ["1", "1//2"]], [["0", "-1//2"], ["1", "-1//2"]], [["0", "1"]], []],
[[["0", "1"], ["1", "1//2"]], [], [["0", "1//2"], ["1", "1//2"]], [["0", "1"]]]
],
"_polymake_type": "polytope::Polytope<OscarNumber>",
"GROUP": [
{
"VERTICES_ACTION.GENERATORS": [
[
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]
]
}
],
"LP": [
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"MINIMAL_VALUE": [["0", "-1//4"], ["1", "-9//4"]],
"LINEAR_OBJECTIVE": [[["0", "2"]], [["0", "3"]], [["0", "-2"]], [["0", "4"]]]
},
{
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}
],
"DUAL_GRAPH.ADJACENCY": {
"_ns": {"polymake": ["https://polymake.org", "4.15"]},
"data": [
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],
"_type": "common::GraphAdjacency<Undirected>"
},
"POINTED": "true",
"TRIANGULATION": [
{
"FACETS": [
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["4", "2", "3", "1"],
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["5", "6", "10", "3"],
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["7", "10", "9", "8"],
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["11", "10", "9", "12"],
["5", "10", "12", "8"],
["13", "9", "12", "8"],
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["13", "15", "16", "14"],
["13", "16", "9", "14"],
["15", "16", "14", "17"],
["15", "11", "14", "17"],
["13", "15", "16", "18"],
["15", "16", "18", "17"],
["15", "18", "17", "19"]
]
}
],
"FEASIBLE": "true",
"CONE_DIM": "4",
"VERTICES": [
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[[["0", "1"]], [["0", "-1//2"]], [["0", "3//4"], ["1", "1//4"]], []],
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],
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],
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[["0", "1//4"], ["1", "1//4"]],
[["0", "-1//4"], ["1", "-1//4"]]
],
[[["0", "1"]], [], [["0", "1//2"]], [["0", "3//4"], ["1", "1//4"]]],
[
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[["0", "-1//4"], ["1", "-1//4"]]
],
[[["0", "1"]], [], [["0", "1//2"]], [["0", "-3//4"], ["1", "-1//4"]]],
[[["0", "1"]], [["0", "3//4"], ["1", "1//4"]], [], [["0", "1//2"]]],
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[[["0", "1"]], [], [["0", "-1//2"]], [["0", "3//4"], ["1", "1//4"]]],
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[[["0", "1"]], [], [["0", "-1//2"]], [["0", "-3//4"], ["1", "-1//4"]]],
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],
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],
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"CONE_AMBIENT_DIM": "4",
"FAR_FACE": [],
"COMBINATORIAL_DIM": "3",
"LINEALITY_SPACE": [],
"VERTICES_IN_FACETS": {
"_ns": {"polymake": ["https://polymake.org", "4.15"]},
"data": [
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[0, 1, 2, 3, 5],
[0, 1, 4, 6, 7],
[10, 11, 15, 17, 19],
[4, 7, 9, 14, 16],
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[2, 5, 8, 12, 13],
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[8, 9, 13, 16, 18],
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{"cols": 20}
],
"_type": "common::IncidenceMatrix<NonSymmetric>"
},
"CENTERED": "true",
"BOUNDED": "true",
"LINEALITY_DIM": "0",
"ESSENTIALLY_GENERIC": "false",
"GRAPH.ADJACENCY": {
"_ns": {"polymake": ["https://polymake.org", "4.15"]},
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],
"_type": "common::GraphAdjacency<Undirected>"
}
},
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"lpcoeffs": [[["0", "2"]], [["0", "3"]], [["0", "-2"]], [["0", "4"]]]
},
{
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"FACETS": [
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[[["0", "1"], ["1", "1//2"]], [], [["0", "-1//2"], ["1", "-1//2"]], [["0", "-1"]]],
[[["0", "1"], ["1", "1//2"]], [], [["0", "-1//2"], ["1", "-1//2"]], [["0", "1"]]],
[[["0", "1"], ["1", "1//2"]], [["0", "1//2"], ["1", "1//2"]], [["0", "1"]], []],
[[["0", "3//4"], ["1", "1//4"]], [["0", "1//2"], ["1", "-1//2"]], [], [["0", "1"]]],
[[["0", "1"], ["1", "1//2"]], [["0", "1//2"], ["1", "1//2"]], [["0", "-1"]], []],
[[["0", "3//4"], ["1", "1//4"]], [["0", "1//2"], ["1", "-1//2"]], [], [["0", "-1"]]],
[[["0", "3//4"], ["1", "1//4"]], [["0", "-1//2"], ["1", "1//2"]], [], [["0", "-1"]]],
[[["0", "1"], ["1", "1//2"]], [], [["0", "1//2"], ["1", "1//2"]], [["0", "-1"]]],
[[["0", "3//4"], ["1", "1//4"]], [["0", "-1//2"], ["1", "1//2"]], [], [["0", "1"]]],
[[["0", "1"], ["1", "1//2"]], [["0", "-1//2"], ["1", "-1//2"]], [["0", "1"]], []],
[[["0", "1"], ["1", "1//2"]], [], [["0", "1//2"], ["1", "1//2"]], [["0", "1"]]]
],
"_polymake_type": "polytope::Polytope<OscarNumber>",
"GROUP": [
{
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[
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"3",
"2",
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"4",
"7",
"10",
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"8",
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],
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"10",
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"16",
"12",
"17",
"13",
"15",
"18",
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]
]
}
],
"LP": [
{
"MINIMAL_FACE": ["6"],
"MINIMAL_VALUE": [["0", "-1//4"], ["1", "-9//4"]],
"LINEAR_OBJECTIVE": [[["0", "2"]], [["0", "3"]], [["0", "-2"]], [["0", "4"]]]
},
{
"MINIMAL_FACE": ["14"],
"MINIMAL_VALUE": [["0", "-2"], ["1", "-5//2"]],
"LINEAR_OBJECTIVE": [[["0", "2"]], [["0", "-1"]], [["0", "-2"], ["1", "1"]], [["0", "5"], ["1", "1"]]]
}
],
"DUAL_GRAPH.ADJACENCY": {
"_type": "common::GraphAdjacency<Undirected>",
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[0, 2, 5, 6, 7],
[0, 1, 4, 5, 9],
[5, 7, 8, 9, 11],
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],
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},
"POINTED": "true",
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{
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["5", "7", "10", "8"],
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["13", "15", "11", "14"],
["13", "15", "16", "14"],
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["15", "16", "14", "17"],
["15", "11", "14", "17"],
["13", "15", "16", "18"],
["15", "16", "18", "17"],
["15", "18", "17", "19"]
]
}
],
"FEASIBLE": "true",
"CONE_DIM": "4",
"VERTICES": [
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[[["0", "1"]], [["0", "-1//2"]], [["0", "3//4"], ["1", "1//4"]], []],
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],
[
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[["0", "1//4"], ["1", "1//4"]]
],
[
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],
[[["0", "1"]], [], [["0", "1//2"]], [["0", "3//4"], ["1", "1//4"]]],
[
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[["0", "-1//4"], ["1", "-1//4"]]
],
[[["0", "1"]], [], [["0", "1//2"]], [["0", "-3//4"], ["1", "-1//4"]]],
[[["0", "1"]], [["0", "3//4"], ["1", "1//4"]], [], [["0", "1//2"]]],
[[["0", "1"]], [["0", "3//4"], ["1", "1//4"]], [], [["0", "-1//2"]]],
[[["0", "1"]], [["0", "-3//4"], ["1", "-1//4"]], [], [["0", "1//2"]]],
[[["0", "1"]], [["0", "-3//4"], ["1", "-1//4"]], [], [["0", "-1//2"]]],
[[["0", "1"]], [], [["0", "-1//2"]], [["0", "3//4"], ["1", "1//4"]]],
[
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[["0", "-1//4"], ["1", "-1//4"]],
[["0", "1//4"], ["1", "1//4"]]
],
[[["0", "1"]], [], [["0", "-1//2"]], [["0", "-3//4"], ["1", "-1//4"]]],
[
[["0", "1"]],
[["0", "-1//4"], ["1", "-1//4"]],
[["0", "-1//4"], ["1", "-1//4"]],
[["0", "1//4"], ["1", "1//4"]]
],
[
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[["0", "1//4"], ["1", "1//4"]],
[["0", "-1//4"], ["1", "-1//4"]],
[["0", "-1//4"], ["1", "-1//4"]]
],
[
[["0", "1"]],
[["0", "-1//4"], ["1", "-1//4"]],
[["0", "-1//4"], ["1", "-1//4"]],
[["0", "-1//4"], ["1", "-1//4"]]
],
[[["0", "1"]], [["0", "1//2"]], [["0", "-3//4"], ["1", "-1//4"]], []],
[[["0", "1"]], [["0", "-1//2"]], [["0", "-3//4"], ["1", "-1//4"]], []]
],
"N_VERTICES": "20",
"CONE_AMBIENT_DIM": "4",
"FAR_FACE": [],
"COMBINATORIAL_DIM": "3",
"LINEALITY_SPACE": [],
"VERTICES_IN_FACETS": {
"_ns": {"polymake": ["https://polymake.org", "4.15"]},
"data": [
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}This serialized output is equivalent for these profiles up to UUID renaming and recorded namespace version strings.
Profiles: OSCAR v1.8
Data file: data.mrdi
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