isCCM -- checks whether a module or an ideal is canonically Cohen-Macaulay

• Usage:

  isCCM M

  isCCM I

• Inputs:
  • M, a module, a finitely generated graded $S$-module, $S=K[x_1,\ldots,x_n]$, with $K$ a field or an ideal $I\subset S$
• Outputs:
  • b, a Boolean value, whether the module $M$ or the graded algebra $S/I$ is canonically Cohen-Macaulay

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

i2 : M=coker matrix{{x_1*x_2,x_3*x_4,0,0},{0,x_1*x_5,x_2*x_4,0}};

i3 : isCCM M

o3 = true

i4 : S = QQ[x_1..x_10,y_1..y_10];

i5 : E = {{1,2},{1,3},{1,4},{1,5},{1,6},{1,7},{1,8},{1,9},{1,10},{6,7},{8,9},{8,10},{9,10}};

i6 : J=ideal(for e in E list x_(e#0)*y_(e#1)-x_(e#1)*y_(e#0));

o6 : Ideal of S

i7 : isCCM J

o7 = true