SubalgebraBases : Index

• ambient(Subring) -- Returns the ambient ring (ring containing the generators) of a subring.
• autoreduce -- Perform autoreduction of the generators of an ideal of a subring.
• autoreduce(Subring,Matrix) -- Perform autoreduction of the generators of an ideal of a subring.
• Autosubduce -- Flag for autosubduction before the Sagbi algorithm
• autosubduce -- Performs autosubduction on the generators of a subring.
• autosubduce(Matrix) -- Performs autosubduction on the generators of a subring.
• debugPrintAllMaps -- Prints the maps associated with a subring.
• debugPrintAllMaps(Subring) -- Prints the maps associated with a subring.
• debugPrintGens -- Print the generators of a subring.
• debugPrintGens(...,StrWidth=>...) -- Print the generators of a subring.
• debugPrintGens(Subring) -- Print the generators of a subring.
• debugPrintMap -- Prints a RingMap in human-readable format.
• debugPrintMap(RingMap) -- Prints a RingMap in human-readable format.
• debugPrintMat -- Prints a one-row matrix
• debugPrintMat(...,StrWidth=>...) -- Prints a one-row matrix
• debugPrintMat(Matrix) -- Prints a one-row matrix
• Example: Translation and rotation sub-actions of the adjoint action of SE(3)
• Experimental feature: modules over subrings
• Experimental feature: SAGBI bases of subrings of quotient rings
• extractEntries -- Inverse of moduleToSubringIdeal
• extractEntries(Matrix,Matrix) -- Inverse of moduleToSubringIdeal
• extrinsicBuchberger -- Computes a Gröbner basis of an ideal within a subring.
• extrinsicBuchberger(Subring,Matrix) -- Computes a Gröbner basis of an ideal within a subring.
• generators(SAGBIBasis) -- Returns a partial sagbi generating set
• generators(Subring) -- Returns the generators of a subring as a one-row matrix.
• genVars -- tensor ring generators
• genVars(Subring) -- tensor ring generators
• internalSubduction -- Performs subduction from a presentation ring
• internalSubduction(PresRing,Matrix) -- Performs subduction from a presentation ring
• internalSubduction(PresRing,RingElement) -- Performs subduction from a presentation ring
• intrinsicReduce -- Compute normal forms relative to an ideal within a subring.
• intrinsicReduce(Subring,Matrix,Matrix) -- Compute normal forms relative to an ideal within a subring.
• intrinsicReduce(Subring,Matrix,RingElement) -- Compute normal forms relative to an ideal within a subring.
• isSubalg -- Calculates whether one subring is contained in another subring.
• isSubalg(Subring,Subring) -- Calculates whether one subring is contained in another subring.
• makePresRing -- Contstructs an instance of the PresRing type
• makePresRing(...,VarBaseName=>...) -- Contstructs an instance of the PresRing type
• makePresRing(Ring,List) -- Contstructs an instance of the PresRing type
• makePresRing(Ring,Matrix) -- Contstructs an instance of the PresRing type
• makePresRing(Subring) -- Contstructs an instance of the PresRing type
• Matrix % Subring -- Performs subduction from a presentation ring
• Matrix // Subring -- Write a ring element in terms of the generators.
• mingensSubring -- Auto reduces matrix elements
• mingensSubring(Subring,Matrix) -- Auto reduces matrix elements
• moduleToSubringIdeal -- Convert a module as a matrix to a subring ideal.
• moduleToSubringIdeal(Subring,Matrix) -- Convert a module as a matrix to a subring ideal.
• numgens(Subring) -- Returns the number of generators of a subring.
• PresRing -- Stores data on the lifted presentation ring of a subring.
• PrintLevel -- A verbose mode for the Sagbi algorithm.
• ring(Subring) -- Returns tensor ring
• RingElement % Subring -- Remainder modulo a subring
• RingElement // Subring -- Write a ring element in terms of the generators.
• sagbi -- Subalgebra basis (sagbi basis)
• sagbi(...,Autosubduce=>...) -- Subalgebra basis (sagbi basis)
• sagbi(...,Limit=>...) -- Subalgebra basis (sagbi basis)
• sagbi(...,PrintLevel=>...) -- Subalgebra basis (sagbi basis)
• sagbi(...,storePending=>...) -- Subalgebra basis (sagbi basis)
• sagbi(List) -- Subalgebra basis (sagbi basis)
• sagbi(Matrix) -- Subalgebra basis (sagbi basis)
• sagbi(SAGBIBasis) -- Subalgebra basis (sagbi basis)
• sagbi(Subring) -- Subalgebra basis (sagbi basis)
• SAGBIBasis -- The type of all sagbi bases
• sagbiBasis -- Constructs a computation object from a subring.
• sagbiBasis(...,storePending=>...) -- Constructs a computation object from a subring.
• sagbiBasis(...,VarBaseName=>...) -- Constructs a computation object from a subring.
• sagbiBasis(MutableHashTable) -- Constructs a computation object from a subring.
• sagbiBasis(Subring) -- Constructs a computation object from a subring.
• sagbiDone -- Test if sagbi basis computation is complete
• sagbiDone(SAGBIBasis) -- Test if sagbi basis computation is complete
• StrWidth -- Print the generators of a subring.
• SubalgebraBases -- A package for finding canonical subalgebra bases (Sagbi bases)
• subalgebraBasis -- Subalgebra basis (sagbi basis) generators
• subalgebraBasis(...,Autosubduce=>...) -- Subalgebra basis (sagbi basis) generators
• subalgebraBasis(...,Limit=>...) -- Subalgebra basis (sagbi basis) generators
• subalgebraBasis(...,PrintLevel=>...) -- Subalgebra basis (sagbi basis) generators
• subalgebraBasis(List) -- Subalgebra basis (sagbi basis) generators
• subalgebraBasis(Matrix) -- Subalgebra basis (sagbi basis) generators
• subalgebraBasis(Subring) -- Subalgebra basis (sagbi basis) generators
• subalgEquals -- Check if two subrings are equal.
• subalgEquals(Subring,Subring) -- Check if two subrings are equal.
• subduction -- Performs subduction by the generators of a subring.
• subduction(Matrix,Matrix) -- Performs subduction by the generators of a subring.
• subduction(Matrix,RingElement) -- Performs subduction by the generators of a subring.
• Subring -- The type of all subrings
• subring -- Constructs a subring of a polynomial ring.
• Subring == Subring -- Check if two subrings are equal.
• Subring ^ ZZ -- Construct a product subring.
• subring(...,VarBaseName=>...) -- Constructs a subring of a polynomial ring.
• subring(List) -- Constructs a subring of a polynomial ring.
• subring(Matrix) -- Constructs a subring of a polynomial ring.
• subring(SAGBIBasis) -- Constructs a subring of a polynomial ring.
• toricSyz -- Calculate toric syzygies of monomials in the initial algebra.
• toricSyz(Subring,Matrix) -- Calculate toric syzygies of monomials in the initial algebra.
• verifySagbi -- Test if the generators form sagbi basis
• verifySagbi(List) -- Test if the generators form sagbi basis
• verifySagbi(Matrix) -- Test if the generators form sagbi basis
• verifySagbi(Subring) -- Test if the generators form sagbi basis