2.14.1 Commands and Functions for MODULE |
BettiDiagram | the diagram of the graded Betti numbers |
BettiMatrix | the matrix of the 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 |
IntersectList | 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 |
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 |