RandomPoints : Table of Contents

• RandomPoints -- Obtain random points in a variety
• DecompositionStrategy -- control how ideals of points are factored into minimal primes
• DimensionFunction -- an option for specifying custom dimension functions
• dimViaBezout -- computes the dimension of the given ideal $I$ probabilistically
• ExtendField -- an option used to specify if extending the finite field is permissible here
• extendIdealByNonZeroMinor -- extends the ideal to aid finding singular locus
• findANonZeroMinor -- finds a non-vanishing minor at some randomly chosen point
• genericProjection -- finds a random (somewhat) generic projection of the ring or ideal
• genericProjection(...,Verbose=>...) -- turns out Verbose (debugging) output
• getRandomLinearForms -- retrieve a list of random degree 1 and 0 forms of specified types
• MaxCoordinatesToReplace -- The maximum number of coordinates to turn into non-monomial functions when calling {\tt randomCoordinateChange}
• NumThreadsToUse -- number of threads that the function will use in a brute force search for a point
• PointCheckAttempts -- Number of times that the function will search for a point
• projectionToHypersurface -- Generic projection to a hypersurface
• randomCoordinateChange -- produce linear automorphism of the ring
• randomPoints -- a function to find random points in a variety.
• randomPoints(...,Strategy=>...) -- values for the option Strategy when calling randomPoints
• Replacement -- When changing coordinates, whether to replace variables by general degree 1 forms, binomials, etc.