Subring -- The type of all subrings

Functions and methods returning an object of class Subring :

• sagbi -- Subalgebra basis (sagbi basis)
• Subring ^ ZZ -- Construct a product subring.

Methods that use an object of class Subring :

• ambient(Subring) -- Returns the ambient ring (ring containing the generators) of a subring.
• "autoreduce(Subring,Matrix)" -- see autoreduce -- Perform autoreduction of the generators of an ideal of a subring.
• "debugPrintAllMaps(Subring)" -- see debugPrintAllMaps -- Prints the maps associated with a subring.
• "debugPrintGens(Subring)" -- see debugPrintGens -- Print the generators of a subring.
• "extrinsicBuchberger(Subring,Matrix)" -- see extrinsicBuchberger -- Computes a Gröbner basis of an ideal within a subring.
• generators(Subring) -- Returns the generators of a subring as a one-row matrix.
• "genVars(Subring)" -- see genVars -- tensor ring generators
• "Matrix % Subring" -- see internalSubduction -- Performs subduction from a presentation ring
• "intrinsicReduce(Subring,Matrix,Matrix)" -- see intrinsicReduce -- Compute normal forms relative to an ideal within a subring.
• "intrinsicReduce(Subring,Matrix,RingElement)" -- see intrinsicReduce -- Compute normal forms relative to an ideal within a subring.
• "isSubalg(Subring,Subring)" -- see isSubalg -- Calculates whether one subring is contained in another subring.
• "makePresRing(Subring)" -- see makePresRing -- Contstructs an instance of the PresRing type
• "mingensSubring(Subring,Matrix)" -- see mingensSubring -- Auto reduces matrix elements
• "moduleToSubringIdeal(Subring,Matrix)" -- see moduleToSubringIdeal -- Convert a module as a matrix to a subring ideal.
• numgens(Subring) -- Returns the number of generators of a subring.
• ring(Subring) -- Returns tensor ring
• RingElement % Subring -- Remainder modulo a subring
• "Matrix // Subring" -- see RingElement // Subring -- Write a ring element in terms of the generators.
• RingElement // Subring -- Write a ring element in terms of the generators.
• "sagbi(Subring)" -- see sagbi -- Subalgebra basis (sagbi basis)
• "sagbiBasis(Subring)" -- see sagbiBasis -- Constructs a computation object from a subring.
• "subalgebraBasis(Subring)" -- see subalgebraBasis -- Subalgebra basis (sagbi basis) generators
• "subalgEquals(Subring,Subring)" -- see subalgEquals -- Check if two subrings are equal.
• "Subring == Subring" -- see subalgEquals -- Check if two subrings are equal.
• "toricSyz(Subring,Matrix)" -- see toricSyz -- Calculate toric syzygies of monomials in the initial algebra.
• "verifySagbi(Subring)" -- see verifySagbi -- Test if the generators form sagbi basis

For the programmer

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