Table of Contents

Introduction to polyDB

This tutorial explains how to access the polyDB database from within polymake using the extension polyDB. It comes bundled with polymake, so there is no need to install extra software, except for the MongoDB.pm perl package. (This tutorial is for polymake version 4 and later. The old version is here, but this needs also an old version of the database). If you encounter any errors or problems concerning polyDB or the extension, please don't hesitate to ask in the forum.

The polymake extension is not necessary to use the data. You can access the data also

Software developers can also include access to polyDB using any of the many MongoDB interfaces and use the data directly in their programs. The few structural assumptions made in the database that you need to follow in your development are explained below (to be written).

Initializing Access

You need a database connection before you can work with polyDB (and a working internet connection if you want to access a database that is not stored in your local computer). For the main instance of polyDB you can just call 

  $polydb = polyDB();

If you have a personal account in the database (e.g. if you maintain a collection or work on a provate project), you should pass your username and password: 

  $polydb = polyDB(username=><username>, passwd=><password>);

You can also store this in the custom variables 

$PolyDB::default::db_user

and 

$PolyDB::default::db_pwd

… Then you don't have to specify them in the connection method, they will be picked up automatically and are preserved over sessions.

Learning which Data is Available

The data in polyDB is stored in collections, which can be organized in nested sections. Access to a certain collection requires the full path to it, i.e. both the (nested) section containing the collection and the collection name. E.g. the collection of smooth reflexive Fano polytopes up to dimension nine is in the collection SmoothReflexive contained in the Lattice subsection of the section Polytopes. The section separator is a dot (.), so you find the data in

The info method gives you a list of collections you can read, ordered by sections. If you have a private account in the database then this command will also list the additional collections you have been granted access to. 

$polydb->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.
[...]

You can restrict the search by

Reading Data

Before you can access a collection you need to establish a connection handle with the method get_collection. For example, if you want to acess the list of 0/1-polytopes up to combinatorial equivalence you would call 

$collection=$polydb->get_collection("Polytopes.Combinatorial.01Polytopes");

Now you can query this ist the various methods provided:

The main argument of the first three functions is a MongoDD query hash. You can use the full MongoDB query syntax as decribed here. Note that polymake uses the perl interface interface of MongoDB, so the query should be given as a perl hash instead of a json document (it mostly suffices to use ⇒ instead of :). For some perl examples see here. Basic queries for one or more parameter look like 

{"N_VERTICES"=>10}
{"DIM"=>5, "N_FACETS"=>7}

Bounds or ranges can be defined with the operators &gt, &gte, &lt and &lte. For example 

{"N_VERTICES"=> { "&gte" => 5, "&lte" => 10 } }

returns documents where the number of vertices is between five and ten (including the boundaries). More operators can be found here. You can also query for elements in arrays either somewhere in the array or at a specific position.

The last function allows to pass an aggregation pipeline as described here (note again that the pipeline needs to be passed as a perl hash instead of a json document).

All queries need the name of the section and collection. You can either pass this via the options section and collection or, in particular if you query the same collection several times in a row, via the variables $PolyDB:“default::db_section_name and $PolyDB:“default::db_collection_name. If you set them via set_custom. this is even persistent over polymake sessions. So a query could look like 

$cur=$collection->find({"DIM"=>4}, section=>"Polytopes.Lattice", collection=>"SmoothReflexive");

or 

$PolyDB::default::db_section="Polytopes.Lattice";
$PolyDB:"default::db_collection="SmoothReflexive";
$cur=$collection->find({"DIM"=>4});

find returns a cursor over the list of results, count just counts the number of objects matching your query. You can iterate over the result of find via 

$cur=$collection->find({"DIM"=>4}, section=>"Polytopes.Lattice", collection=>"SmoothReflexive");
while ( $cur->has_next() ) { 
  $p=$cur->next();
  print $p->N_VERTICES;
}

There are further options to control the return:

You can reset the cursor with 

$cur->reset

if you want to iterate over the results again.

Inserting new Data

Note that you need write access to write data into polyDB. Also, initiating a new collection needs administrator permissions on the database. Please contact us (directly or via the forum) to obtain write acces to a (new) collection and have us do the basic initialization of a new collection.

Inserting data requires several steps:

Meta information, schema and documentation are stored with the methods 

$collection->set_info($meta); 
$collection->set_schema($schema); 
$collection->set_collection_doc($doc, replace=>true/false, update=>true/false);

where the first argument is the data as a perl hash.

Insertion of data is done with the method insert. This function either takes a file, a single polymake big object or an array of such as first argument and writes this data into the collection specified by the options section and collection (these can also be specified with the same custom variables as for queries). This has some more options, see 

help "insert";

in the polymake shell.

Administrative Tasks (only for polyDB admins)

Starting a new collection

A new collection is started with the command 

$polydb->initiate_collection(section=><section>, collection=><collection>);

If the collection should not be public, then also pas the option public⇒false. For a public collection the read access role of the new collection is added to the default role polymakeUser which is granted to every user of polyDB. One can add this later if one wants to build up and test the collection befor making it publicly available.

If this creates new intermediate subsections you should set the section documentation with 

$polydb->set_section_doc($doc, section=>...);

so that the new collection appears in the list printed by db_info for all users with sufficient permissions.

Note that the first command essentially only creates two new roles in MongoDB, one for read access to the collection (and all sections up to the root) and one for write access to the collection (and only to the collection, not to the sections). The actual collections are only created once the first document is written into the collection. This implies that collections will not be listed with db_info if any of the intermediate sections has no documentation, as then the collection where this is stored is not created.

You can add users for read acces with the method add_user_to_collection. Note that this is only useful if the collection is not public. Any user that has the write access rule (which you can assign with $polydb→add_user_to_collection(user⇒…, collection⇒…, admin⇒true) can insert, delete and modify documents in the collection, the meta information, the schema and to documentation of the collection. Note that in this method the collection must be given fully qualified, e.g. as Polytopes.Combinatorial.01Polytopes.