up previous next
 2.14.1 Commands and Functions for MODULE
 BettiDiagram the diagram of the graded Betti numbers BettiMatrix the matrix of the graded Betti numbers BettiNumbers (Multi-)graded Betti numbers colon ideal or module quotient elim eliminate variables GBasis calculate a Groebner basis GBasisTimeout compute a Groebner basis with a timeout GenRepr representation in terms of generators gens list of generators of an ideal GensAsCols, GensAsRows matrix of generators of a module HilbertSeries the Hilbert-Poincare series HilbertSeriesShifts the Hilbert-Poincare series homog homogenize wrt an indeterminate HVector the h-vector of a module or quotient object IntersectionList intersect lists, ideals, or modules IsContained checks if A is Contained in B IsElem checks if A is an element of B IsHomog test whether given polynomials are homogeneous IsIn check if one object is contained in another IsZero test whether an object is zero LT the leading term of an object MinGens list of minimal generators minimalize [OBSOLESCENT] [OBSOLESCENT] MinSubsetOfGens list of minimal generators ModuleElem create a module element ModuleOf the module environment of the object multiplicity the multiplicity (degree) of a ring NF normal form NumCompts the number of components PrintBettiDiagram print the diagram of the graded Betti numbers PrintBettiMatrix print the matrix of the graded Betti numbers PrintBettiNumbers print the (multi-)graded Betti numbers ReducedGBasis reduced Groebner basis res free resolution RingOf the ring of the object RingsOf list of the rings of an object rk rank of a matrix or module submodule submodule generated by list SubmoduleCols, SubmoduleRows convert a matrix into a module SubmoduleOfMinGens submodule generated by minimal generators syz syzygy modules SyzOfGens syzygy module for a given set of generators