4.12.4 Commands and Functions for Modules |
BettiDiagram | the diagram of the graded Betti numbers |
BettiMatrix | the matrix of the graded Betti numbers |
Colon | ideal or module quotient |
Depth | Depth of a module |
E_ | canonical vector |
Elim | eliminate variables |
Ext | presentation Ext modules as quotients of free modules |
GB.GetBettiMatrix | returns the Betti matrix computed so far |
GB.GetNthSyz | returns the part of the Nth syzygy module computed so far |
GB.GetNthSyzShifts | shifts of the Nth syzygy module computed so far |
GB.GetRes | returns the resolution computed so far |
GB.GetResLen | returns the length of the resolution computed so far |
GB.ResReport | status of an interactive resolution calculation |
GBasis | calculate a Groebner basis |
GBasis5, and more | calculations using the CoCoAServer |
GBasisTimeout | compute a Groebner basis with a timeout |
GenRepr | representation in terms of generators |
Gens | list of generators of an ideal |
HColon | ideal or module quotient |
Interreduce, Interreduced | interreduce a list of polynomials or vectors |
Intersection | intersect lists, ideals, or modules |
IntersectionList | intersect lists, ideals, or modules |
IsIn | check if one object is contained in another |
IsZero | test whether an object is zero |
Len | the length of an object |
LT | the leading term of an object |
Max, Min | a maximum or minimum element of a sequence or list |
MinGens | list minimal generators |
Minimalize | remove redundant generators |
Minimalized | remove redundant generators |
MinimalPresentation | minimal presentation for a quotient |
MinSyzMinGens | minimal generators of syzygies of minimal generators |
Module | convert an expression into a module |
NF | normal form |
NFsAreZero | test if normal forms are zero |
Rank | rank of a module |
ReducedGBasis | compute reduced Groebner basis |
Res | free resolution |
Size | the amount of memory used by an object |
Syz | syzygy modules |
SyzMinGens | syzygy module for a set of minimal generators |
SyzOfGens | syzygy module for a given set of generators |