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Testing the t-balance: A general Note on Parameter Al
A parameter Al is provided to allow users
to specify the algorithm to be used for balance testing.
The default value is "NoOrbits", which
applies a "brute force" test. One alternative is "Orbits", which
uses the orbits of t-sets under the automorphism group of the
incidence structure under consideration.
This is much faster than "NoOrbits" for some cases,
but slower for others.
The other alternative for checking if an object
is t-balanced is "FastBalanceTest": It is also a "brute
force" test but whose implementation allows for a dramatic
improvement in efficiency, especially for larger t (t ≥4).
This implementation has a drawback however as it may necessitate
more memory space than is available, thus resulting in
an out-of-memory error.
It is for this reason that "FastBalanceTest" is not the
default setting for Al, but as a general rule we strongly
recommend its usage as we surmise that execution should successfully
complete in most cases.
Returns true if and only if the incidence structure D has no repeated blocks.
Returns true if and only if the incidence structure D is a trivial incidence
structure.
Returns true if and only if the incidence structure D is self-dual,
that is, if D is isomorphic to its dual.
Returns true if and only if the incidence structure D is uniform; that is,
each block contains the same number of points. If true, also returns
the blocksize.
Returns true if and only if the incidence structure D is a near--linear space.
Returns true if and only if the incidence structure D is a linear space.
Al: MonStgElt Default: "NoOrbits"
Returns true if and only if 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, see the
introduction to Section Elementary Properties of Incidence Structures and Designs for a full
description of its usage.
Al: MonStgElt Default: "NoOrbits"
Returns true if and only if 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 for balance testing, see the
introduction to Section Elementary Properties of Incidence Structures and Designs for a full
description of its usage.
Return true if and only if D is the complete design.
Return true if and only if the design D is symmetric.
Al: MonStg Default: "NoOrbits"
Return true if and only if the design D is a Steiner t--design.
The optional parameter Al can be used to specify the algorithm
used for balance testing, see the
introduction to Section Elementary Properties of Incidence Structures and Designs for a full
description of its usage.
Return true if and only if the (near--)linear space D is point regular.
If true, the point regularity is also returned.
Return true if and only if the (near--)linear space D is line regular.
If true, the line regularity is also returned.
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