A Groebner basis in Macaulay 2 consists of a Groebner basis computation, and several associated matrices. Normally you don't need to refer to these objects directly, as many operations on matrices and modules create them, and refer to them. Nonetheless it is sometimes useful to have control over the creation of Groebner bases.
Groebner bases are attached to a matrix using one of the following operations. Recomputation is avoided, in that if a Groebner basis has already been partially computed, then it will be used whenever possible. Each of these routines takes a matrix as input, together with optional Degree and Hilb, parameters, and returns a matrix. Eventually, these commands will handle the situtation when the ring of m is a quotient ring, or is not graded, or is a local ring
Operations which produce Greobner bases:
Operations on Groebner bases:
Operations on matrices which use Groebner bases to produce matrices:
Each of these operations may be interrupted or stopped (by typing CNTRL-C). The computation is continued by re-issuing the same command.
To obtain information from a Groebner basis, use one of the following routines. These return matrices which represent the current state of the computation. Further computation of the Groebner basis will not change matrices previously obtained from these routines.
Status of the computation can be determined by the following routines
Keys used:
See also gbTrace.