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Packages » NAGtypes :: WitnessSet

Description

This type stores a witness set of an equidimensional solution component. The following methods can be used to access a WitnessSet:

• 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)

Also one may determine

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

Only dimension and degree are displayed (by net); to see the data stored in a witness set use peek.

For developers:

Required keys in a WitnessSet are

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

Optional keys:

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

See also

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