This tutorial is probably also available as a Jupyter notebook in the demo folder in the polymake source and on github.
Different versions of this tutorial: latest release, release 4.13, release 4.12, release 4.11, release 4.10, release 4.9, release 4.8, release 4.7, release 4.6, release 4.5, release 4.4, release 4.3, release 4.2, release 4.1, release 4.0, release 3.6, nightly master
polymake file format and the polyDB
Polymake Data Files
JSON File Format
With release 4.0 polymake adopts a new file format for its data files. In the new version all data is now serialized to JSON instead of XML.
polymake can still read files in XML format.
> $p = new Polytope(POINTS=>[[1,0,0],[1,1,0],[1,0,1]]); > print JSON->new->pretty->encode(Core::Serializer::serialize($p)); { "_type" : "polytope::Polytope<Rational>", "CONE_AMBIENT_DIM" : 3, "_id" : "p", "POINTS" : [ [ "1", "0", "0" ], [ "1", "1", "0" ], [ "1", "0", "1" ] ], "_ns" : { "polymake" : [ "https://polymake.org", "4.10" ] } }
JSON is a pretty simple format. Entries in a JSON object are either
- number: no distinction between float and int
- string
- boolean: true/false
- array: comma separated list of elements in square brackets
- object: comma separeted key-value pairs in curly brackets. associative array
- null
Polymake stores
- perl builtin numbers a number
- vectors, matrices as array
- tuples as object
- Integer/Rartional as string
- Bool as boolean
- big objects as objects (with properties as keys)
Type information that cannot be infered from the rule base (sparse, attachment) is stored in an separate key-value pair.
There are only a few meta tags left in a data file:
- _id: name
- _ns: mark it as a polymake file
- _info: credits and description
- _type: big object type
- _attrs: additional attributes for properties, marks e.g. attachments, non-standard types (e.g. sparse)
- _ext: extensions
- _load: further applications needed to read data file
- _polyDB: database information, if object is retrieved from db
Object Arrays
You can now use standard perl arrays to store a list of objects.
> $cube = cube(2); > $simplex = simplex(2); > $array = [ $cube, $simplex ]; > print JSON->new->pretty->encode(Core::Serializer::serialize($array)); { "_ns" : { "polymake" : [ "https://polymake.org", "4.10" ] }, "data" : [ { "CONE_DIM" : 3, "FACETS" : [ { "0" : "1", "1" : "1" }, { "0" : "1", "1" : "-1" }, { "0" : "1", "2" : "1" }, { "0" : "1", "2" : "-1" }, { "cols" : 3 } ], "BOUNDED" : true, "_attrs" : { "FACETS" : { "_type" : "SparseMatrix<Rational, NonSymmetric>" } }, "_type" : "polytope::Polytope<Rational>", "AFFINE_HULL" : [ { "cols" : 3 } ], "VERTICES_IN_FACETS" : [ [ 0, 2 ], [ 1, 3 ], [ 0, 1 ], [ 2, 3 ], { "cols" : 4 } ], "_info" : { "description" : "cube of dimension 2\n" }, "_id" : "cube", "CONE_AMBIENT_DIM" : 3 }, { "CONE_AMBIENT_DIM" : 3, "_info" : { "description" : "standard simplex of dimension 2\n" }, "BOUNDED" : true, "_attrs" : { "VERTICES" : { "_type" : "SparseMatrix<Rational, NonSymmetric>" } }, "_type" : "polytope::Polytope<Rational>", "CENTERED" : false, "N_VERTICES" : 3, "SIMPLICIALITY" : 2, "_id" : "simplex", "FEASIBLE" : true, "CONE_DIM" : 3, "POINTED" : true, "VERTICES" : [ { "0" : "1" }, { "0" : "1", "1" : "1" }, { "0" : "1", "2" : "1" }, { "cols" : 3 } ] } ], "_type" : null }
Background: JSON Schemata
> $p = new Polytope(VERTICES=>[[1,0,0],[1,1,0],[1,0,1]]); > $p->N_VERTICES; > $schema = create_restrictive_schema($p); > print JSON->new->pretty->encode($schema->source); { "additionalProperties" : false, "required" : [ "_ns", "_type", "VERTICES", "CONE_AMBIENT_DIM", "N_VERTICES" ], "type" : "object", "$schema" : "http://json-schema.org/draft-07/schema#", "definitions" : { "common-Vector-Rational" : { "items" : { "$ref" : "#/definitions/common-Rational" }, "type" : "array" }, "common-Rational" : { "type" : "string", "pattern" : "^-?(\\d+(/\\d+)?|inf)$" }, "common-Int" : { "type" : "integer" }, "common-Matrix-Rational-NonSymmetric" : { "type" : "array", "items" : { "oneOf" : [ { "$ref" : "#/definitions/common-Vector-Rational" }, { "additionalProperties" : false, "required" : [ "cols" ], "properties" : { "cols" : { "type" : "integer", "minimum" : 0 } }, "type" : "object" } ] } } }, "properties" : { "_canonical" : { "type" : "boolean" }, "CONE_AMBIENT_DIM" : { "$ref" : "#/definitions/common-Int" }, "_load" : { "items" : { "type" : "string" }, "type" : "array" }, "_id" : { "$ref" : "https://polymake.org/schemas/data.json#/definitions/obj_id" }, "_info" : { "$ref" : "https://polymake.org/schemas/data.json#/definitions/obj_info" }, "N_VERTICES" : { "$ref" : "#/definitions/common-Int" }, "_type" : { "const" : "polytope::Polytope<Rational>" }, "VERTICES" : { "$ref" : "#/definitions/common-Matrix-Rational-NonSymmetric" }, "_ns" : { "additionalProperties" : false, "properties" : { "polymake" : { "additionalItems" : false, "items" : [ { "const" : "https://polymake.org" }, { "const" : "4.10" } ], "type" : "array" } }, "type" : "object" } } } > print $schema->validate(Core::Serializer::serialize($p)); true
We can use a schema to modify a data file so that it validates against the schema
> $q = new Polytope(VERTICES=>[[1,0,0],[1,1,0],[1,0,1],[1,1,1]]); > print JSON->new->pretty->encode(Core::Serializer::serialize($q)); { "VERTICES" : [ [ "1", "0", "0" ], [ "1", "1", "0" ], [ "1", "0", "1" ], [ "1", "1", "1" ] ], "CONE_AMBIENT_DIM" : 3, "_id" : "q", "_type" : "polytope::Polytope<Rational>", "_ns" : { "polymake" : [ "https://polymake.org", "4.10" ] } } > print JSON->new->pretty->encode(Core::Serializer::serialize($q, { schema => $schema } )); { "N_VERTICES" : 4, "_ns" : { "polymake" : [ "https://polymake.org", "4.10" ] }, "_type" : "polytope::Polytope<Rational>", "VERTICES" : [ [ "1", "0", "0" ], [ "1", "1", "0" ], [ "1", "0", "1" ], [ "1", "1", "1" ] ], "_id" : "q", "CONE_AMBIENT_DIM" : 3 } > help "prescribe_property_types"; core/objects/Schema/methods/prescribe_property_types: prescribe_property_types(properties; ... ) Change the stored data type for properties in a restrictive schema Selected properties will be coerced to a different type when the object is stored in a data file or in PolyDB using this schema. Note: This function does not try to verify that the properties can be serialized as the given type or will be successfully deserialized when reading the object from a file or retrieving it from a database. It's solely in the users responsibility to choose a compatible and convertible data type. Arguments: Any __properties__ list of pairs PROPERTY_NAME => type A property in a subobject is written in dotted path notation: "NAME1.NAME2.NAME3..." Types can be specified by name in a string or as a typeof expression or as a type of an exsiting data object. Specifying undef or "default" will enforce storing the properties in their original form, as declared in the rulebase. This operation might be useful e.g. to update the schema after a data mode change. Examples: *) Require FACETS to be stored as a sparse matrix > $schema->prescribe_property_types(FACETS => typeof SparseMatrix<Rational>); *) Require F_VECTOR and F2_VECTOR to be stored with simple integer entries > $schema->prescribe_property_types(F_VECTOR => "Vector<Int>", F2_VECTOR => "Matrix<Int>"); *) Require VERTICES to be stored as declared in the rules, that is, as a dense matrix > $schema->prescribe_property_types(VERTICES => "default");
We can change the type of VERTICES in our schema:
> $schema->prescribe_property_types(VERTICES => typeof SparseMatrix<Rational>); > print JSON->new->pretty->encode(Core::Serializer::serialize($q, { schema => $schema } )); { "CONE_AMBIENT_DIM" : 3, "_id" : "q", "N_VERTICES" : 4, "VERTICES" : [ { "0" : "1" }, { "0" : "1", "1" : "1" }, { "0" : "1", "2" : "1" }, [ "1", "1", "1" ], { "cols" : 3 } ], "_attrs" : { "VERTICES" : { "_type" : "SparseMatrix<Rational, NonSymmetric>" } }, "_type" : "polytope::Polytope<Rational>", "_ns" : { "polymake" : [ "https://polymake.org", "4.10" ] } }
We can also create a schema for a complete big object type
> $full_schema=create_permissive_schema(typeof graph::Graph); > print JSON->new->pretty->encode($full_schema->source); { "allOf" : [ { "properties" : { "_type" : { "const" : "graph::Graph<Undirected>" } } }, { "$ref" : "https://polymake.org/schemas/data.json#/definitions/top_level" }, { "$ref" : "#/definitions/graph-Graph-Undirected" } ], "$schema" : "http://json-schema.org/draft-07/schema#", "definitions" : { "common-Float" : { "type" : [ "number", "string" ], "pattern" : "^-?[Ii]nf$" }, "common-HashMap-Int-Rational" : { "type" : "object", "patternProperties" : { "^-?\\d+$" : { "$ref" : "#/definitions/common-Rational" } }, "additionalProperties" : false }, "common-IncidenceMatrix-NonSymmetric" : { "type" : "array", "items" : { "oneOf" : [ { "$ref" : "#/definitions/common-Set-Int" }, { "type" : "object", "properties" : { "cols" : { "type" : "integer", "minimum" : 0 } }, "additionalProperties" : false, "required" : [ "cols" ] } ] } }, "common-Array-String" : { "type" : "array", "items" : { "$ref" : "#/definitions/common-String" } }, "common-SparseVector-Float" : { "additionalProperties" : false, "properties" : { "_dim" : { "minimum" : 0, "type" : "integer" } }, "type" : [ "array", "object" ], "items" : { "$ref" : "#/definitions/common-Float" }, "patternProperties" : { "^\\d+$" : { "$ref" : "#/definitions/common-Float" } } }, "common-Set-Set-Int" : { "items" : { "$ref" : "#/definitions/common-Set-Int" }, "type" : "array" }, "common-Rational" : { "pattern" : "^-?(\\d+(/\\d+)?|inf)$", "type" : "string" }, "common-GraphAdjacency-Undirected" : { "items" : { "$ref" : "#/definitions/common-Set-Int" }, "type" : [ "array", "object" ], "patternProperties" : { "^\\d+$" : { "$ref" : "#/definitions/common-Set-Int" } }, "properties" : { "_dim" : { "minimum" : 0, "type" : "integer" } }, "additionalProperties" : false }, "common-Bool" : { "type" : "boolean" }, "common-UniPolynomial-Rational-Int" : { "$ref" : "#/definitions/common-Serialized-UniPolynomial-Rational-Int" }, "common-Set-Int" : { "type" : "array", "items" : { "$ref" : "#/definitions/common-Int" }, "uniqueItems" : true }, "graph-Graph-Undirected" : { "allOf" : [ { "$ref" : "https://polymake.org/schemas/data.json#/definitions/big_obj" }, { "properties" : { "NodePerm" : false, "BICONNECTED_COMPONENTS" : { "anyOf" : [ { "type" : "null" }, { "$ref" : "#/definitions/common-IncidenceMatrix-NonSymmetric" } ] }, "NodePerm.pure" : false, "SIGNATURE" : { "anyOf" : [ { "type" : "null" }, { "$ref" : "#/definitions/common-Int" } ] }, "MAX_CLIQUES" : { "anyOf" : [ { "type" : "null" }, { "$ref" : "#/definitions/common-Set-Set-Int" } ] }, "AVERAGE_DEGREE" : { "anyOf" : [ { "type" : "null" }, { "$ref" : "#/definitions/common-Rational" } ] }, "DEGREE_SEQUENCE" : { "anyOf" : [ { "type" : "null" }, { "$ref" : "#/definitions/common-Map-Int-Int" } ] }, "CHARACTERISTIC_POLYNOMIAL" : { "anyOf" : [ { "type" : "null" }, { "$ref" : "#/definitions/common-UniPolynomial-Rational-Int" } ] }, "ADJACENCY" : { "anyOf" : [ { "type" : "null" }, { "$ref" : "#/definitions/common-GraphAdjacency-Undirected" } ] }, "NODE_DEGREES" : { "anyOf" : [ { "type" : "null" }, { "$ref" : "#/definitions/common-Array-Int" } ] }, "CONNECTIVITY" : { "anyOf" : [ { "type" : "null" }, { "$ref" : "#/definitions/common-Int" } ] }, "DIAMETER" : { "anyOf" : [ { "type" : "null" }, { "$ref" : "#/definitions/common-Int" } ] }, "N_EDGES" : { "anyOf" : [ { "type" : "null" }, { "$ref" : "#/definitions/common-Int" } ] }, "BIPARTITE" : { "anyOf" : [ { "type" : "null" }, { "$ref" : "#/definitions/common-Bool" } ] }, "SIGNED_INCIDENCE_MATRIX" : { "anyOf" : [ { "type" : "null" }, { "$ref" : "#/definitions/common-SparseMatrix-Int-NonSymmetric" } ] }, "N_CONNECTED_COMPONENTS" : { "anyOf" : [ { "type" : "null" }, { "$ref" : "#/definitions/common-Int" } ] }, "CONNECTED" : { "anyOf" : [ { "type" : "null" }, { "$ref" : "#/definitions/common-Bool" } ] }, "CONNECTED_COMPONENTS" : { "anyOf" : [ { "type" : "null" }, { "$ref" : "#/definitions/common-IncidenceMatrix-NonSymmetric" } ] }, "NODE_LABELS" : { "anyOf" : [ { "type" : "null" }, { "$ref" : "#/definitions/common-Array-String" } ] }, "TRIANGLE_FREE" : { "anyOf" : [ { "type" : "null" }, { "$ref" : "#/definitions/common-Bool" } ] }, "N_NODES" : { "anyOf" : [ { "type" : "null" }, { "$ref" : "#/definitions/common-Int" } ] } } }, { "anyOf" : [ { "properties" : { "_attrs" : { "properties" : { "EIGENVALUES_LAPLACIAN" : { "properties" : { "_type" : false } } } }, "EIGENVALUES_LAPLACIAN" : { "anyOf" : [ { "type" : "null" }, { "$ref" : "#/definitions/common-Vector-Float" } ] } } }, { "properties" : { "_attrs" : { "properties" : { "EIGENVALUES_LAPLACIAN" : { "properties" : { "_type" : { "const" : "SparseVector<Float>" } } } } }, "EIGENVALUES_LAPLACIAN" : { "$ref" : "#/definitions/common-SparseVector-Float" } } } ] } ] }, "common-Serialized-UniPolynomial-Rational-Int" : { "minItems" : 1, "additionalItems" : false, "items" : [ { "$ref" : "#/definitions/common-HashMap-Int-Rational" } ], "type" : "array" }, "common-Int" : { "type" : "integer" }, "common-Vector-Float" : { "type" : "array", "items" : { "$ref" : "#/definitions/common-Float" } }, "common-String" : { "type" : "string" }, "common-SparseMatrix-Int-NonSymmetric" : { "type" : "array", "items" : { "oneOf" : [ { "$ref" : "#/definitions/common-SparseVector-Int" }, { "type" : "object", "properties" : { "cols" : { "type" : "integer", "minimum" : 0 } }, "additionalProperties" : false, "required" : [ "cols" ] } ] } }, "common-SparseVector-Int" : { "type" : [ "array", "object" ], "items" : { "$ref" : "#/definitions/common-Int" }, "patternProperties" : { "^\\d+$" : { "$ref" : "#/definitions/common-Int" } }, "properties" : { "_dim" : { "type" : "integer", "minimum" : 0 } }, "additionalProperties" : false }, "common-Map-Int-Int" : { "additionalProperties" : false, "patternProperties" : { "^-?\\d+$" : { "$ref" : "#/definitions/common-Int" } }, "type" : "object" }, "common-Array-Int" : { "items" : { "$ref" : "#/definitions/common-Int" }, "type" : "array" } }, "title" : "polymake data objects of type graph::Graph<Undirected>" } > $m=graph::petersen(); > print $full_schema->validate(Core::Serializer::serialize($m)); true
PolyDB
General Information
Database for mathematical objects. Intended for data related to the projects within OSCAR.
Database is independent of particular software package, but information necessary for in-/output to a software can be stored alongside.
Currently accessible via web (still at an experimental stage) and via polymake.
A database connection is established by calling the function polyDB:
> $pdb_default=polyDB();
Get info
> $pdb_default->info(); =============== available polydb collections =============== SECTION: Manifolds This database contains combinatorial manifolds COLLECTION: DIM2_3 This is a collection of combinatorial 2- and 3-manifolds with up to 10 vertices given as triangulations and calculcated by Frank Lutz found at: http://page.math.tu-berlin.de/~lutz/stellar/mixed.html. SECTION: Matroids This database contains various classes of matroids. COLLECTION: SelfDual Collection of identically self-dual matroids of rank 2 to 5, based on the computational results in the paper ''Self-dual matroids from canonical curves'' by Geiger, Hashimoto, Sturmfels and Vlad. COLLECTION: Small Collection of small matroids based on the census by Yoshitake Matsumoto, Sonoko Moriyama, Hiroshi Imai, David Bremner. SECTION: Polytopes A collection of families of polytopes SECTION: Polytopes.Combinatorial This database contains various classes of combinatorial polytopes. COLLECTION: 01Polytopes 0/1-Polytopes up to combinatorial equivalence COLLECTION: CombinatorialTypes Combinatorial types of polytopes of small dimension and number of vertices COLLECTION: FacesBirkhoffPolytope Combinatorial types of faces up to dimension 8 of a Birkhoff polytope in any dimension COLLECTION: SmallSpheresDim4 Combinatorial 3-spheres with up to 9 vertices SECTION: Polytopes.Geometric This database contains various classes of geometric polytopes. COLLECTION: 01Polytopes 0/1-Polytopes up to rotation and reflection SECTION: Polytopes.Lattice This database contains various classes of lattice polytopes. COLLECTION: 01Polytopes 0/1-Polytopes up to lattice equivalence COLLECTION: ExceptionalMaximalHollow Exceptional maximal hollow lattice polytopes up to dimension 3 COLLECTION: FewLatticePoints3D 3-dimensional lattice polytopes of width at least 2 and few lattice points. COLLECTION: NonSpanning3D Non-spanning 3-dimensional lattice polytopes of width at least 2 and at most 200 lattice points. COLLECTION: Panoptigons Non-hyperelliptic Panoptigons of lattice diameter at least 3 COLLECTION: Reflexive Reflexive Polytopes in dimension 4 COLLECTION: SmallVolume Lattice Polytopes with low volume COLLECTION: SmoothReflexive Smooth reflexive polytopes in dimensions 1 to 9 with splitting data SECTION: Polytopes.Combinatorial This database contains various classes of combinatorial polytopes. COLLECTION: 01Polytopes 0/1-Polytopes up to combinatorial equivalence COLLECTION: CombinatorialTypes Combinatorial types of polytopes of small dimension and number of vertices COLLECTION: FacesBirkhoffPolytope Combinatorial types of faces up to dimension 8 of a Birkhoff polytope in any dimension COLLECTION: SmallSpheresDim4 Combinatorial 3-spheres with up to 9 vertices SECTION: Polytopes.Geometric This database contains various classes of geometric polytopes. COLLECTION: 01Polytopes 0/1-Polytopes up to rotation and reflection SECTION: Polytopes.Lattice This database contains various classes of lattice polytopes. COLLECTION: 01Polytopes 0/1-Polytopes up to lattice equivalence COLLECTION: ExceptionalMaximalHollow Exceptional maximal hollow lattice polytopes up to dimension 3 COLLECTION: FewLatticePoints3D 3-dimensional lattice polytopes of width at least 2 and few lattice points. COLLECTION: NonSpanning3D Non-spanning 3-dimensional lattice polytopes of width at least 2 and at most 200 lattice points. COLLECTION: Panoptigons Non-hyperelliptic Panoptigons of lattice diameter at least 3 COLLECTION: Reflexive Reflexive Polytopes in dimension 4 COLLECTION: SmallVolume Lattice Polytopes with low volume COLLECTION: SmoothReflexive Smooth reflexive polytopes in dimensions 1 to 9 with splitting data SECTION: Tropical This database contains tropical objects. COLLECTION: Cubics Regular unimodular triangulations of the triple tetrahedron and their motifs. COLLECTION: Polytropes Representatives for all combinatorial tropical types of full-dimensional polytropes in TP3. COLLECTION: QuarticCurves Regular unimodular triangulations of the fourth dilation of the standard 2-dimensional simplex and their dual deformation motifs. COLLECTION: SchlaefliFan Regular unimodular triangulations of the triple tetrahedron and their motifs. COLLECTION: TOM All known non-realisable tropical oriented matroids with parameters n=6, d=3 or n=d=4.
For individual collections we can get more detailed information:
- level 1: short description (default if no collection is given),
- level 2: description,
- level 3: description, authors, maintainers,
- level 4: full info
- level 5: full info and list of recommended search fields, if defined in info (default if collection is given)
> $pdb_default->info(section=>"Polytopes.Combinatorial", collection=>"CombinatorialTypes", info_level=>4); =============== available polydb collections =============== SECTION: Polytopes.Combinatorial This database contains various classes of combinatorial polytopes. COLLECTION: CombinatorialTypes Combinatorial types of polytopes of small dimension and number of vertices, see [[http://www-imai.is.s.u-tokyo.ac.jp/~hmiyata/oriented_matroids/index.html]] Author(s): Hiroyuki Miyata, University of Tokyo, Bunkyo-ku, Tokyo, Japan, hmiyata@is.s.u-tokyo.ac.jp Sonoko Moriyama, Tokuyama laboratory, System Information Sciences, Graduate School of Information Sciences, Tohoku University, moriso@dais.is.tohoku.ac.jp Komei Fukuda, Theory of Combinatorial Algorithms, Department of Mathematics, ETHZ, fukuda@math.ethz.ch Contributor(s): Constantin Fischer, TU Berlin, cfischer@mailbox.tu-berlin.de Maintainer(s): Constantin Fischer, TU Berlin, cfischer@mailbox.tu-berlin.de Online Resources: Classification of Oriented Matroids: http://www-imai.is.s.u-tokyo.ac.jp/~hmiyata/oriented_matroids/index.html
Reading Data from polymake
Simple reading
> $coll_default=$pdb_default->get_collection("Polytopes.Lattice.SmoothReflexive"); > $a=$coll_default->find({"DIM"=>3});
This returns a cursor over the data.
> print $a->has_next; true > $p=$a->next; > print $p->F_VECTOR; 8 12 6 > while ( $p = $a->next ) { > print $p->F_VECTOR, "\n"; > } 6 9 5 10 15 7 12 18 8 10 15 7 8 12 6 8 12 6 10 15 7 10 15 7 12 18 8 8 12 6 8 12 6 8 12 6 6 9 5 6 9 5 8 12 6 6 9 5 4 6 4
Objects from the database know where they come from
> $a=$coll_default->find({"DIM"=>3}); > $p=$a->next; > $info=$p->get_attachment("_polyDB"); > foreach (keys %$info) { print $_, ": ", $info->{$_}, "\n"; }; id: F.3D.0000 uri: http://polymake.org/polytopes/paffenholz/www/fano.html section: Polytopes.Lattice collection: SmoothReflexive version: 2.1 app: polytope database: LatticePolytopes tag: object creation_date: 2019-08-01 type: polytope::Polytope<Rational>
Queries
> $cur=$coll_default->find({"DIM"=>3, "N_VERTICES" => 8});
A query usually returns a cursor over all matching results.
> while ( $p = $cur->next ) { > print "(", $p->DIM, ", ", $p->N_VERTICES, ") "; > } (3, 8) (3, 8) (3, 8) (3, 8) (3, 8) (3, 8) (3, 8)
The cursor keeps its position, so to return to the first result we need to reset the cursor.
> $cur=$coll_default->find({"DIM"=>3, "N_VERTICES" => 8}); > while ( $p = $cur->next ) { > print "(", $p->DIM, ", ", $p->N_VERTICES, ") "; > } (3, 8) (3, 8) (3, 8) (3, 8) (3, 8) (3, 8) (3, 8)
We can collect all results into an array.
> $a=$coll_default->find({"DIM"=>3, "N_VERTICES" => 8})->all; > print scalar(@$a); 7
We can ask for ranges:
> $a=$coll_default->find({"DIM" => { '$lt' => 4}})->all; > print scalar(@$a); 25 > foreach (@$a) { > print $_->F_VECTOR, "\n"; > } 2 3 3 4 4 4 4 5 5 6 6 8 12 6 6 9 5 10 15 7 12 18 8 10 15 7 8 12 6 8 12 6 10 15 7 10 15 7 12 18 8 8 12 6 8 12 6 8 12 6 6 9 5 6 9 5 8 12 6 6 9 5 4 6 4
Boolean operations are possible:
> $a=$coll_default->find({'$or' => [{ 'DIM' => 2}, { 'DIM' => 4}]})->all; > foreach (@$a) { > print $_->F_VECTOR, "\n"; > } 3 3 4 4 4 4 5 5 6 6 11 22 18 7 8 16 14 6 17 34 25 8 13 26 20 7 15 30 23 8 18 36 27 9 15 30 23 8 16 32 24 8 12 24 19 7 12 24 19 7 15 30 23 8 16 32 24 8 16 32 24 8 12 24 19 7 16 32 24 8 16 32 24 8 16 32 24 8 13 26 20 7 12 24 19 7 12 24 19 7 9 18 15 6 21 42 30 9 17 34 25 8 17 34 25 8 23 46 32 9 30 60 40 10 13 26 20 7 17 34 25 8 15 30 23 8 18 36 27 9 16 32 24 8 15 30 23 8 12 24 19 7 17 34 25 8 21 42 30 9 21 42 30 9 18 36 26 8 24 48 33 9 18 36 26 8 17 34 25 8 16 32 24 8 13 26 20 7 13 26 20 7 12 24 19 7 15 30 23 8 12 24 19 7 9 18 15 6 20 40 29 9 24 48 34 10 20 40 29 9 16 32 24 8 16 32 24 8 20 40 29 9 20 40 29 9 24 48 34 10 20 40 29 9 24 48 34 10 20 40 29 9 20 40 29 9 16 32 24 8 20 40 29 9 24 48 34 10 20 40 29 9 21 42 30 9 20 40 29 9 24 48 34 10 24 48 34 10 20 40 29 9 20 40 29 9 16 32 24 8 16 32 24 8 16 32 24 8 16 32 24 8 12 24 19 7 25 50 35 10 30 60 41 11 36 72 48 12 20 40 29 9 24 48 34 10 20 40 29 9 16 32 24 8 16 32 24 8 16 32 24 8 20 40 29 9 16 32 24 8 12 24 19 7 17 34 25 8 16 32 24 8 16 32 24 8 16 32 24 8 16 32 24 8 20 40 29 9 16 32 24 8 12 24 19 7 15 30 23 8 18 36 27 9 15 30 23 8 20 40 29 9 24 48 34 10 18 36 27 9 15 30 23 8 15 30 23 8 16 32 24 8 11 22 18 7 11 22 18 7 12 24 19 7 12 24 19 7 12 24 19 7 13 26 20 7 16 32 24 8 16 32 24 8 12 24 19 7 12 24 19 7 12 24 19 7 8 16 14 6 8 16 14 6 12 24 19 7 9 18 15 6 16 32 24 8 12 24 19 7 8 16 14 6 8 16 14 6 9 18 15 6 5 10 10 5 > $a=$coll_default->find({'$and' => [{ 'DIM' => 2}, { 'N_VERTICES' => 4}]})->all; > foreach (@$a) { > print $_->F_VECTOR, "\n"; > } 4 4 4 4
Type matters
> $a=$coll_default->find({'LATTICE_VOLUME' => "8"})->all; > print scalar(@$a); 0 > $a=$coll_default->find({'LATTICE_VOLUME' => 8})->all; > print scalar(@$a); 2
Creating and filling new collections
Some preparations for a test database
> $PolyDB::default::db_host="db-test-server"; > $PolyDB::default::useSSL = 0; > $pdb_local_admin = polyDB(user=>"admin", password=>"admin"); > $pdb_local_admin->client->create_default_user_and_role();
We initiate a new collection. MongoDB is lazy, so what this function actually does is just creating access permisssions. The collection is only created when the first document is inserted.
> $pdb_local_admin->new_collection(collection=>"Polytopes.01Polytopes");
We insert an info document for the section. This can only be done by database admins. A documentation entry is necessary, otherwise the section is not listed by the info()-function.
> $section_doc=load_json("files/json_and_polydb/polydb_meta/Polytopes/Polytopes.2.1.json"); > print JSON->new->pretty->encode($section_doc); { "description" : "A collection of families of polytopes", "short_description" : "A collection of families of polytopes", "polydb_version" : "2.1", "maintainer" : { "name" : "Andreas Paffenholz", "affiliation" : "TU Darmstadt", "email" : "paffenholz@opt.tu-darmstadt.de" }, "section" : [ "Polytopes" ], "sectionDepth" : 1 } > $pdb_local_admin->set_section_doc("Polytopes", $section_doc);
From now on we can hand over the administration of the collection to a user that has admin permissions just on this collection, not the whole database. We create a new one, we could also extend an existing user.
> $pdb_local_admin->create_user("workshop", "workshop", admin_collections=>["Polytopes.01Polytopes"]); > print $pdb_local_admin->user_exists("workshop"); true
Now we can connect as the newly created user with admin rights on the new collection.
> $pdb_local = polyDB(user=>"workshop", password=>"workshop"); > $coll_local = $pdb_local->get_collection("Polytopes.01Polytopes");
We first set the documentation for the collection. Again, without a documentation entry the collection is not listed by the info() command.
> $collection_doc=load_json("files/json_and_polydb/polydb_meta/Polytopes/01Polytopes/Polytopes.01Polytopes.2.1.json"); > print JSON->new->pretty->encode($collection_doc); { "collection" : "01Polytopes", "section" : [ "Polytopes" ], "contributor" : [ { "affiliation" : "TU Darmstadt", "name" : "Andreas Paffenholz", "email" : "paffenholz@opt.tu-darmstadt.de" } ], "polydb_version" : "2.1", "maintainer" : [ { "email" : "paffenholz@opt.tu-darmstadt.de", "affiliation" : "TU Darmstadt", "name" : "Andreas Paffenholz" } ], "author" : [ { "name" : "Oswin Aichholzer" } ], "_id" : "Polytopes.01Polytopes.2.1", "short_description" : "0/1-Polytopes up to rotation and reflection", "description" : "0/1-Polytopes up to rotation and reflection" } > $coll_local->set_doc($collection_doc);
We need to insert two further documents before we can insert data:
- a schema
- an info document with some meta information on the collection. The second needs the id of the schema, so the schema must be inserted first.
We create a schema from a polymake object.
> $a = load_data("files/json_and_polydb/data/geometric_01.pdata"); > print join " ", $a->[0]->list_properties; CONE_AMBIENT_DIM VERTICES > $p=$a->[0]; > $p->provide("VERTICES","FACETS","F_VECTOR","SIMPLE","SIMPLICIAL"); > print join " ", $p->list_properties; CONE_AMBIENT_DIM VERTICES FEASIBLE N_VERTICES POINTED BOUNDED FAR_FACE AFFINE_HULL CONE_DIM LINEALITY_DIM LINEALITY_SPACE COMBINATORIAL_DIM SIMPLICITY SIMPLICIALITY SIMPLE SIMPLICIAL FACETS N_FACETS F_VECTOR > $schema=create_restrictive_schema($p); > print JSON->new->pretty->encode($schema->source); { "required" : [ "_ns", "_type", "CONE_AMBIENT_DIM", "VERTICES", "FEASIBLE", "N_VERTICES", "POINTED", "BOUNDED", "FAR_FACE", "AFFINE_HULL", "CONE_DIM", "LINEALITY_DIM", "LINEALITY_SPACE", "COMBINATORIAL_DIM", "SIMPLICITY", "SIMPLICIALITY", "SIMPLE", "SIMPLICIAL", "FACETS", "N_FACETS", "F_VECTOR" ], "additionalProperties" : false, "$schema" : "http://json-schema.org/draft-07/schema#", "type" : "object", "definitions" : { "common-Rational" : { "type" : "string", "pattern" : "^-?(\\d+(/\\d+)?|inf)$" }, "common-Matrix-Rational-NonSymmetric" : { "type" : "array", "items" : { "oneOf" : [ { "$ref" : "#/definitions/common-Vector-Rational" }, { "properties" : { "cols" : { "type" : "integer", "minimum" : 0 } }, "additionalProperties" : false, "required" : [ "cols" ], "type" : "object" } ] } }, "common-Bool" : { "type" : "boolean" }, "common-Vector-Integer" : { "type" : "array", "items" : { "$ref" : "#/definitions/common-Integer" } }, "common-Integer" : { "type" : "string", "pattern" : "^-?(\\d+|inf)$" }, "common-Vector-Rational" : { "type" : "array", "items" : { "$ref" : "#/definitions/common-Rational" } }, "common-Set-Int" : { "uniqueItems" : true, "type" : "array", "items" : { "$ref" : "#/definitions/common-Int" } }, "common-Int" : { "type" : "integer" } }, "properties" : { "LINEALITY_DIM" : { "$ref" : "#/definitions/common-Int" }, "SIMPLICIAL" : { "$ref" : "#/definitions/common-Bool" }, "_load" : { "items" : { "type" : "string" }, "type" : "array" }, "CONE_AMBIENT_DIM" : { "$ref" : "#/definitions/common-Int" }, "_info" : { "$ref" : "https://polymake.org/schemas/data.json#/definitions/obj_info" }, "SIMPLICITY" : { "$ref" : "#/definitions/common-Int" }, "F_VECTOR" : { "$ref" : "#/definitions/common-Vector-Integer" }, "LINEALITY_SPACE" : { "$ref" : "#/definitions/common-Matrix-Rational-NonSymmetric" }, "N_FACETS" : { "$ref" : "#/definitions/common-Int" }, "_type" : { "const" : "polytope::Polytope<Rational>" }, "BOUNDED" : { "$ref" : "#/definitions/common-Bool" }, "COMBINATORIAL_DIM" : { "$ref" : "#/definitions/common-Int" }, "SIMPLICIALITY" : { "$ref" : "#/definitions/common-Int" }, "AFFINE_HULL" : { "$ref" : "#/definitions/common-Matrix-Rational-NonSymmetric" }, "FAR_FACE" : { "$ref" : "#/definitions/common-Set-Int" }, "N_VERTICES" : { "$ref" : "#/definitions/common-Int" }, "FEASIBLE" : { "$ref" : "#/definitions/common-Bool" }, "_canonical" : { "type" : "boolean" }, "_id" : { "$ref" : "https://polymake.org/schemas/data.json#/definitions/obj_id" }, "SIMPLE" : { "$ref" : "#/definitions/common-Bool" }, "CONE_DIM" : { "$ref" : "#/definitions/common-Int" }, "_ns" : { "additionalProperties" : false, "properties" : { "polymake" : { "type" : "array", "items" : [ { "const" : "https://polymake.org" }, { "const" : "4.10" } ], "additionalItems" : false } }, "type" : "object" }, "FACETS" : { "$ref" : "#/definitions/common-Matrix-Rational-NonSymmetric" }, "VERTICES" : { "$ref" : "#/definitions/common-Matrix-Rational-NonSymmetric" }, "POINTED" : { "$ref" : "#/definitions/common-Bool" } } } > $coll_local->set_schema($schema->source);
Now we can insert the info document.
> $info_doc=load_json("files/json_and_polydb/polydb_meta/Polytopes/01Polytopes/info.2.1.json"); > print JSON->new->pretty->encode($info_doc); { "_id" : "info.2.1", "description" : "0/1 Polytopes", "maintainer" : "Andreas Paffenholz", "polydb_version" : "2.1", "creator" : "Oswin Aichholzer", "contributor" : "Andreas Paffenholz", "uri" : "https://polymake.org", "section" : [ "Polytopes" ], "packages" : { "polymake" : { "version" : "3.4", "type" : "polytope::Polytope<Rational>" } }, "collection" : "01Polytopes" } > $coll_local->set_info($info_doc, "schema.2.1");
Now the new collection is fully prepared and is listed with info():
> $pdb_local->info(); =============== available polydb collections =============== SECTION: Polytopes A collection of families of polytopes COLLECTION: 01Polytopes 0/1-Polytopes up to rotation and reflection
We can now insert our data.
> $coll_local->insert_many($a); > print $coll_local->count({}); 14 > $b=$coll_local->find({})->all; > print scalar(@$b); 14 > $p=$coll_local->find_one({}); > print join " ", $p->list_properties; CONE_DIM FACETS VERTICES POINTED AFFINE_HULL COMBINATORIAL_DIM SIMPLICIALITY N_VERTICES FAR_FACE FEASIBLE SIMPLE F_VECTOR LINEALITY_SPACE N_FACETS BOUNDED LINEALITY_DIM SIMPLICIAL CONE_AMBIENT_DIM SIMPLICITY > $coll_local->remove_one($p->name); > print $coll_local->count({}); 13