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

• 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 $M$

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 = subquotient ({-1} | -x_1   0      x_2x_4 |, {-1} | -x_2x_3x_4 x_1^2      0      |)
                  {-1} | 0      x_1    x_3x_5 |  {-1} | -x_3^2x_5  0          x_1    |
                  {-2} | x_3x_5 x_2x_4 0      |  {-2} | 0          -x_1x_3x_5 x_2x_4 |

                               3
o4 : S-module, subquotient of S