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PointOptions -- options to pass to functions in the package RandomPoints

Description

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,
     ------------------------------------------------------------------------
     ExtendField => true, PointCheckAttempts => 0, DecompositionStrategy =>
     ------------------------------------------------------------------------
     Decompose, NumThreadsToUse => 1, DimensionFunction => dim, Verbose =>
     ------------------------------------------------------------------------
     false}

o1 : List
 
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

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.

See also

Functions with optional argument named PointOptions :

For the programmer

The object PointOptions is a symbol.