CoCoA:ReducedGBasis

ReducedGBasis

compute reduced Groebner basis

Description

If M is an ideal or module, this function returns a list whose

components form a reduced Groebner basis for M with respect to the

term-ordering of the polynomial ring of M. If M is a quotient of a ring by an ideal I or of a free module by a submodule N, then the Groebner basis for M is defined to be that of I or N, respectively.

Example

  Use R ::= Q[t,x,y,z];
  I := Ideal(t^3-x,t^4-y,t^5-z);
  $gb.Start_GBasis(I);  -- start the Interactive Groebner Framework
  $gb.Step(I);  -- take one step towards computing the Groebner basis
  I.GBasis;  -- the Groebner basis so far
[t^3 - x]
-------------------------------
  $gb.Complete(I);  -- finish the computation
  I.GBasis;
[t^3 - x, -tx + y, -ty + z, -y^2 + xz, -x^2 + tz, t^2z - xy]
-------------------------------
  ReducedGBasis(I);
[t^3 - x, tx - y, ty - z, y^2 - xz, x^2 - tz, t^2z - xy]
-------------------------------

Syntax

ReducedGBasis(M:IDEAL, MODULE, or TAGGED(<quotes>Quotient</quotes>)):LIST

Introduction to Groebner Bases in CoCoA

The Interactive Groebner Framework

GBasis5, and more

   <type>groebner</type>
   <type>groebner-interactive</type>
   <type>ideal</type>
   <type>module</type>
   <type>quotient</type>