deficiencyModule -- computes the $i$th module of deficiency of a module $M$ or an ideal $I$.

Synopsis

• Usage:

  deficiencyModule(M,i)

  deficiencyModule(I,i)

• Inputs:
  • M, a module, module over the polynomial ring $S=K[x_1,\ldots,x_n]$, with $K$ a field or an ideal $I\subset S$
  • i, an integer, an integer
• Outputs:
  • D, a module, the ith module of deficiency of $M$

Description

i1 : S=QQ[x_1..x_5];

i2 : I=(x_1^2*x_3,x_2*x_3^2*x_4,x_1*x_3^3*x_5);

i3 : M=S^1/I;

i4 : deficiencyModule(M,3)

o4 = cokernel {0} | x_1 0   x_2x_4 |
              {1} | 0   x_3 x_1    |

                            2
o4 : S-module, quotient of S

See also

• canonicalModule -- computes the canonical module of a module $M$ or an ideal $I$.
• isSCM -- checks whether a module or an ideal is sequentially Cohen-Macaulay