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data [2014/01/12 14:26] – Table with database information silke | polydb [2020/09/01 14:09] – [polyDB] paffenholz |
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====== The polymake database ====== | ====== polyDB ====== |
There is an online database with polymake objects that can be accessed from within polymake. | |
You need the extension [[http://solros.de/polymake/poly_db|poly_db]] for this. | ''polyDB'' is a database for objects in discrete geometry and related areas. The database can be accessed from within polymake or via a REST API. There is also a web interface at [[https://db.polymake.org|db.polymake.org]]. Internally, the database is build upon ''MongoDB'', and you can use the full ''MongoDB'' query language to send requests to the database. |
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| * [[user_guide:howto:polydb_tutorial|tutorial for querying the database]] |
| * [[polydb:rest:intro|(Experimental) polyDB REST API]] |
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Here is a list of the current content of the database. | |
There are two levels of hierarchy: Databases and collections. | |
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^Database ^ Collection ^ | | |
|LatticePolytopes | SmoothReflexive | All smooth reflexive lattice polytopes in dimensions up to 8. In dimensions up to 7 the database contains the properties H_STAR_VECTOR, REFLEXIVE, CONE_DIM, date, _id, LATTICE_CODEGREE, N_INTERIOR_LATTICE_POINTS, SMOOTH, N_LATTICE_POINTS, FACET_WIDTHS, VERTICES, FACETS, CENTROID, N_VERTICES, contributor, LATTICE_DEGREE, LATTICE_VOLUME, EHRHART_POLYNOMIAL_COEFF, N_BOUNDARY_LATTICE_POINTS, ESSENTIALLY_GENERIC, VERY_AMPLE, F_VECTOR, GORENSTEIN, FEASIBLE, LINEALITY_SPACE, AFFINE_HULL. In dimension 8 it only contains the minimal set LINEALITY_SPACE, CONE_DIM, date, _id, VERTICES, FEASIBLE, N_VERTICES, contributor. | | |
|LatticePolytopesR | SmoothReflexive | All smooth reflexive lattice polytopes in dimension 8. (Properties are still incomplete!) Note that you need a password to access this database. | | |
|Tropical |TOM | All known non-realisable tropical oriented matroids with parameters n=6, d=3 or n=d=4. You need the extension [[http://solros.de/polymake/tropmat|tropmat]] for this. | | |
====== Other data in polymake format ====== | ====== Other data in polymake format ====== |
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This is a collection of objects from geometric combinatorics available in polymake format. | This is a collection of objects from geometric combinatorics available in polymake format. |
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* [[http://math.berkeley.edu/~bernd/|Bernd Sturmfels]] and [[http://www-math.mit.edu/~jyu/|Josephine Yu]]: tight spans of [[http://bio.math.berkeley.edu/SixPointMetrics/|triangulations and coarsest subdivisions of hypersimplex Delta(2,6)]]. | * [[http://math.berkeley.edu/~bernd/|Bernd Sturmfels]] and [[http://people.math.gatech.edu/~jyu67/|Josephine Yu]]: tight spans of [[http://bio.math.berkeley.edu/SixPointMetrics/|triangulations and coarsest subdivisions of hypersimplex Delta(2,6)]] (**note: link currently broken**). |
* [[http://www3.mathematik.tu-darmstadt.de/index.php?id=508|Katja Kulas]]: list of all [[http://wwwopt.mathematik.tu-darmstadt.de/~kulas/polytrope.html|3-dimensional polytropes]]. | |
* Sven Herrmann, Anders Jensen, Michael Joswig, and Bernd Sturmfels: list of [[http://www.uni-math.gwdg.de/jensen/Research/G3_7/grassmann3_6.html|Generic planes in tropical projective space TP5]] and [[http://www.uni-math.gwdg.de/jensen/Research/G3_7/grassmann3_7.html|TP6]]. | * Sven Herrmann, Anders Jensen, Michael Joswig, and Bernd Sturmfels: list of [[http://www.uni-math.gwdg.de/jensen/Research/G3_7/grassmann3_6.html|Generic planes in tropical projective space TP5]] and [[http://www.uni-math.gwdg.de/jensen/Research/G3_7/grassmann3_7.html|TP6]]. |
* Debbie Grier, Peter Huggins, Bernd Sturmfels, and Josephine Yu: list of [[http://bio.math.berkeley.edu/4cube/|triangulations of the 4-cube]]. | * Debbie Grier, Peter Huggins, Bernd Sturmfels, and Josephine Yu: list of [[http://bio.math.berkeley.edu/4cube/|triangulations of the 4-cube]] (**note: link currently broken**). |
* Mikkel <html>Ø</html>bro; Benjamin Lorenz, Andreas Paffenholz: [[http://polymake.org/polytopes/paffenholz/www/fano.html|Smooth reflexive lattice polytopes in dimensions up to 9]] | * Mikkel <html>Ø</html>bro; Benjamin Lorenz, Andreas Paffenholz: [[http://polymake.org/polytopes/paffenholz/www/fano.html|Smooth reflexive lattice polytopes in dimensions up to 9]] |
* Barbara Baumeister, Christian Haase, Benjamin Nill, and Andreas Paffenholz: [[http://polymake.org/polytopes/paffenholz/www/permutations.html|low-dimensional permutation polytopes]] | * Barbara Baumeister, Christian Haase, Benjamin Nill, and Andreas Paffenholz: [[http://polymake.org/polytopes/paffenholz/www/permutations.html|low-dimensional permutation polytopes]] |
* Andreas Paffenholz: [[http://www.mathematik.tu-darmstadt.de/~paffenholz/data.html|Various lists of polytopes]] | * Andreas Paffenholz: [[http://www.mathematik.tu-darmstadt.de/~paffenholz/data.html|Various lists of polytopes]] |
* [[http://www.math.tu-berlin.de/~springb|Boris Springborn]]: [[http://www.math.tu-berlin.de/~springb/typegallery|gallery of polyhedral types]] | * [[http://www.math.tu-berlin.de/~springb|Boris Springborn]]: [[http://www.math.tu-berlin.de/~springb/typegallery|gallery of polyhedral types]] |
* [[http://www3.mathematik.tu-darmstadt.de/hp/optimierung/herr-katrin/startseite.html|Katrin Herr]] and [[http://www.math.uni-rostock.de/~rehn/|Thomas Rehn]]: [[http://www.polymake.org/polytopes/core-point-polytopes/2-homog-groups/|2-homogeneous groups]] up to degree 12 and orbit polytopes of representatives of all their [[http://www.polymake.org/polytopes/core-point-polytopes/|core points]]. | * Katrin Herr and [[http://www.math.uni-rostock.de/~rehn/|Thomas Rehn]]: [[http://www.polymake.org/polytopes/core-point-polytopes/2-homog-groups/|2-homogeneous groups]] up to degree 12 and orbit polytopes of representatives of all their [[http://www.polymake.org/polytopes/core-point-polytopes/|core points]]. |
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| /** |
| old data: |
| * [[http://www3.mathematik.tu-darmstadt.de/index.php?id=508|Katja Kulas]]: list of all [[http://wwwopt.mathematik.tu-darmstadt.de/~kulas/polytrope.html|3-dimensional polytropes]]. |
| **/ |
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You can also check [[http://www.computeralgebra.de/index.php?option=com_content&view=article&id=89&Itemid=53|here]] for other classes of polytopes. | You can also check [[http://www.computeralgebra.de/index.php?option=com_content&view=article&id=89&Itemid=53|here]] for other classes of polytopes. |
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Contributions are welcome! | Contributions are welcome! |