# 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.