- ideal -- get the defining ideal of the algebraic superset
- equations -- get the list of defining polynomials of the algebraic superset
- slice -- get linear functions defining the slicing plane
- points -- get the list of witness points (which are zeroes of all above)

- dim -- the dimension
- codim -- the codimension
- deg -- the degree (the number of witness points)
- ring -- the ring of the defining polynomials

- Equations -- an ideal
- Slice -- a list or a matrix
- Points-- a list of points
- cache.IsIrreducible -- takes values null(not determined), true, or false

- ProjectionDimension -- an integer, the witness set describes a lifted variety (its projection on the first ProjectionDimension coordinates is the variety the witness set represents)

- witnessSet -- construct a WitnessSet
- ProjectiveWitnessSet -- a projective witness set
- NumericalVariety -- a numerical variety
- declareIrreducible -- declares a component represented by the witness set irreducible

- ProjectiveWitnessSet -- a projective witness set

- witnessSet -- construct a WitnessSet

- declareIrreducible(WitnessSet) -- see declareIrreducible -- declares a component represented by the witness set irreducible
- generalEquations(WitnessSet) -- see generalEquations -- random linear combinations of equations/generators
- codim(WitnessSet)
- degree(WitnessSet)
- dim(WitnessSet)
- equations(WitnessSet)
- ideal(WitnessSet)
- net(WitnessSet)
- points(WitnessSet)
- ring(WitnessSet)
- slice(WitnessSet)

The object WitnessSet is a type, with ancestor classes WSet < HashTable < Thing.