CoCoA:Res

Res

free resolution

Description

This function returns the minimal free resolution of M. If M is a

quotient of a ring by an ideal I or a quotient of a free

module by a submodule N, then the resolution of M is defined to be that of I or N, respectively.

Res only works in the homogeneous context, and the coefficient ring

must be a field.

Example

  Use R ::= Q[x,y,z];
  I := Ideal(x,y,z^2);
  Res(R/I);
0 --> R(-4) --> R(-2)(+)R^2(-3) --> R^2(-1)(+)R(-2) --> R
-------------------------------
  Describe It;

Mat([
  [y, x, z^2]
])
Mat([
  [x, z^2, 0],
  [-y, 0, z^2],
  [0, -y, -x]
])
Mat([
  [z^2],
  [-x],
  [y]
])
-------------------------------

For fine control and monitoring of Groebner basis calculations, including various types of truncations, see [[The Interactive Groebner Framework]] and Introduction to Panels.

Syntax

Res(M):TAGGED(<quotes>$gb.Res</quotes>)

where M is of type IDEAL or MODULE or TAGGED(<quotes>Quotient</quotes>).

Introduction to Groebner Bases in CoCoA

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