CoCoA:GB.GetBettiMatrix

GB.GetBettiMatrix

returns the Betti matrix computed so far

Description

This function, if used after executing Res(M), prints the Betti

matrix for M. Within the Interactive Groebner Framework, in which

resolutions may be computed one step at a time, the function returns the Betti matrix for the part of the resolution computed so far. See <ttref>GB.GetRes</ttref> for an example.

Example

  Use R ::= Q[t,x,y,z];
  I := Ideal(x^2-yt,xy-zt,xy);
  Res(I);
0 --> R^2(-5) --> R^4(-4) --> R^3(-2)
-------------------------------
  $gb.GetBettiMatrix(I);
--------------

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

-------------------------------

Syntax

$gb.GetBettiMatrix(M:IDEAL or MODULE):TAGGED(<quotes>$io.Matrix</quotes>)

GB.GetRes

GB.GetResLen

Res

The Interactive Groebner Framework

BettiDiagram

BettiMatrix

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