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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 with respect to an indeterminate
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 ideal, submodule with minimal generators
minimalized ideal, submodule with minimal generators
MinSubsetOfGens list of minimal generators
ModuleElem create a module element
ModuleOf the module environment of the object
NF normal form
NumCompts the number of components
operators, shortcuts Special characters equivalent to commands
PrintBettiDiagram the diagram of the graded Betti numbers
PrintBettiMatrix print the matrix of the graded Betti numbers
PrintBettiNumbers print the (multi-)graded Betti numbers
ReducedGBasis compute 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
syz syzygy modules
SyzOfGens syzygy module for a given set of generators