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The Sage Reference Manual: Graph Theory (available as PDF and HTML) and the Sage Reference Manual: Algebraic Numbers and Number Fields (available as PDF and HTML) give a nice overview of the functionality provided by Sage and, moreover, and provide tons of excellent exemplaric examples.

The Homepage of Oriented Matroids provides all isomorphism classes of oriented matroids for up to $n=8$ elements and, for non-degenerate, up to $n=9$ elements. The (non-degenerate) oriented matroids of rank 3 correspond to (simple) arrangements of great-pseudocircles. All rank 3 oriented matroids of $n=9$ elements are realized or classified as non-realizable.

The Database of Order Types for Small Point Sets provides realization of all combinatorially different realizable sets of up to $n=10$ points in the Euclidean plane; the database for $n=11$ is available on demand. Note that point sets in the plane correspond to great-circle arrangements on a sphere with marked north- and south-pole.

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Last update: November 22 2017 02:17:36. (c) 2017 Stefan Felsner and Manfred Scheucher