True iff the incidence structure D has no repeated blocks.

True iff the incidence structure D is a trivial incidence structure.

True iff the incidence structure D is self-dual; i.e. if D is isomorphic to its dual.

True iff the incidence structure D is uniform; that is, each block contains the same number of points. If true, also returns the blocksize.

True iff the incidence structure D is a near-linear space.

True iff the incidence structure D is a linear space.

    Al: MonStgElt                       Default: "NoOrbits"

True iff the incidence structure D is a t-design. If true, then the number of blocks of D containing a general t-set is also returned. The optional parameter Al can be used to specify the algorithm used for balance testing. The default value is "NoOrbits", which applies a "brute force" test. The alternative is "Orbits", which uses the orbits of t-sets under the automorphism group of D. This is much faster for some cases, but slower for others.

    Al: MonStgElt                       Default: "NoOrbits"

True iff the incidence structure D is balanced (with respect to t). If true, then the number of blocks of D containing a general t-set is also returned. The optional parameter Al can be used to specify the algorithm used. The default value is "NoOrbits", which applies a "brute force" test. The alternative is "Orbits", which uses the orbits of t-sets under the automorphism group of D. This is much faster for some cases, but slower for others.

True iff there exists a resolution of the incidence structure D; i.e. a partition of the blocks of D into parallel classes. If true, also returns a resolution.

True iff D is the complete design.

True iff the design D is symmetric.

True iff the design D is a Steiner t-design.

True iff the (near-)linear space D is point regular. If true, the point regularity is also returned.

True iff the (near-)linear space D is line regular. If true, the line regularity is also returned.