CoCoA:BettiDiagram

BettiDiagram

the diagram of the graded Betti numbers

Description

This function returns the (Macaulay style) Betti

diagram for M.

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)
-------------------------------
  BettiDiagram(I);
        0    1    2
--------------------
 2:     3    -    -
 3:     -    4    2
--------------------
Tot:    3    4    2
-------------------------------
  Untagged(BettiDiagram(I));
Record[Diagram = Mat([
  [3, 0, 0],
  [0, 4, 2]
]), FirstShift = 2]

Syntax

BettiDiagram(M:IDEAL or MODULE):TAGGED(<quotes>$gb.BettiDiagram</quotes>)

Res

GB.GetBettiMatrix

BettiMatrix

   <type>groebner</type>
   <type>ideal</type>
   <type>module</type>