PointOptions is an option in various functions in this package, which can store options to be passed to the function findANonZeroMinor and other functions in RandomPoints.
i1 : (options regularInCodimension)#PointOptions
o1 = {Strategy => Default, Homogeneous => false, Replacement => Binomial,
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ExtendField => true, PointCheckAttempts => 0, DecompositionStrategy =>
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Decompose, NumThreadsToUse => 1, DimensionFunction => dim, Verbose =>
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false}
o1 : List
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i2 : options findANonZeroMinor
o2 = OptionTable{DecompositionStrategy => null}
DimensionFunction => dim
ExtendField => true
Homogeneous => false
MinorPointAttempts => 5
NumThreadsToUse => 1
PointCheckAttempts => 0
Replacement => Binomial
Strategy => Default
Verbose => false
o2 : OptionTable
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The default setting ExtendField => true means that points whose residue field are finite extensions of the prime field are valid, and are used to study the matrix. Furthermore, we have set Homogeneous=>false by default which means the origin is treated as a valid point. Setting ExtendField=>false will sometimes speed up computation, but can also miss some important submatrices if that determinant (plus what has already been computed) defines a scheme with no or relatively few rational points. In such a case, ExtendField => false will typically substantially slow down computations.
The object PointOptions is a symbol.