CoCoA:GB.GetRes

GB.GetRes

returns the resolution computed so far

Description

This function returns the part of the resolution of M computed so

far. It does not compute the resolution of M as does <ttref>Res</ttref>, rather,

GB.GetRes is intended primarily to be used within the Interactive Groebner Framework. Thus, for example, GB.GetRes may be used to examine the resolution as it is computed, one step at a time.

Example

  Use R ::= Q[t,x,y,z];
  I := Ideal(x^2-yt,xy-zt,xy);
  $gb.Start_Res(I); -- start Interactive Groebner Framework
  $gb.Step(I); -- take one step in calculation of resolution
  $gb.GetRes(I);  -- the resolution so far
0 --> R(-2)
-------------------------------
  $gb.Step(I);  -- one more step
  $gb.GetResLen(I);  -- the computed resolution still has length 1
1
-------------------------------
  $gb.GetBettiMatrix(I);  -- the Betti Matrix so far
----

----
   0
   2
----

-------------------------------
  $gb.GetRes(I);
0 --> R^2(-2)
-------------------------------
  $gb.Steps(I,5); -- five more steps
  $gb.GetRes(I);
0 --> R(-4) --> R^3(-2)
-------------------------------
  $gb.Complete(I); -- complete the calculation
  $gb.GetResLen(I);
3
-------------------------------
  $gb.GetBettiMatrix(I);
--------------

--------------
   0    0    0
   0    0    3
   0    0    0
   0    4    0
   2    0    0
--------------

-------------------------------
  $gb.GetRes(I);
0 --> R^2(-5) --> R^4(-4) --> R^3(-2)
-------------------------------

Syntax

$gb.GetRes(M:IDEAL or MODULE):TAGGED(<quotes><tt>$gb.Res</tt></quotes>)

GB.GetBettiMatrix

GB.GetResLen

Res

The Interactive Groebner Framework

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