The Interactive Groebner Framework

4.13.3 The Interactive Groebner Framework

For the following computations:

  * Groebner bases
  * minimal generators
  * syzygies
  * free resolutions
  * elimination of variables

CoCoA provides the following features:

  * step-by-step computation
  * monitoring of the execution (verbose mode)
  * various types of truncation (degree, resolution length, or regularity)
  * customization of algorithms (through the GROEBNER panel and P-Series).

It works like this: instead of using one of the normal Groebner basis-type commands (listed in the previous section), start the computation with one of the commands,

  * GB.Start_GBasis -- start interactive Groebner basis computation
  * GB.Start_MinGens -- start interactive minimal generator calculation
  * GB.Start_Res -- start interactive resolution computation
  * GB.Start_Syz -- start interactive syzygy computation

After starting the computation, the following commands are available:

  * GB.Complete -- Complete an interactive Groebner-type calculation
  * 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
  * GB.Stats -- status of an interactive Groebner-type calculation
  * GB.Step, GB.Steps -- take steps in an interactive Groebner-type calculation
  * ReducedGBasis -- compute a reduced Groebner basis

Almost all of these functions report more information if you set the Verbose flag in the GROEBNER panel by typing

  Set Verbose;

(to unset, enter Unset Verbose). For more possibilities, see Options in the GROEBNER Panel.

Use of the Interactive Groebner Framework is illustrated in the examples below.