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D.4.4.5 isCI
Procedure from library cisimplicial.lib (see cisimplicial_lib).
- Usage:
- isCI(A); A is an integral matrix
- Return:
- 1 if the simplicial toric ideal I(A) is a complete intersection
and 0 otherwise. If printlevel > 0 and I(A) is a complete
intersection it also shows a minimal set of generators of I(A)
- Assume:
- A is an m x n integral matrix with nonnegative entries and for
every 1 <= i <= m, there exist a column in A whose i-th coordinate
is not null and the rest are 0.
Example:
| | LIB "cisimplicial.lib";
intmat A[2][5] = 60,0,140,150,21,0,60,140,150,21;
print(A);
==> 60 0 140 150 21
==> 0 60 140 150 21
printlevel = 0;
isCI(A);
==> // It is a complete intersection
==> 1
printlevel = 1;
isCI(A);
==> // Generators of the toric ideal
==> toric[1]=-x(1)^7*x(2)^7+x(3)^3
==> toric[2]=x(5)^10-x(1)*x(2)*x(4)
==> toric[3]=-x(1)^5*x(2)^5+x(4)^2
==> // It is a complete intersection
==> 1
intmat B[3][5] = 12,0,0,1,2,0,10,0,3,2,0,0,8,3,3;
print(B);
==> 12 0 0 1 2
==> 0 10 0 3 2
==> 0 0 8 3 3
isCI(B);
==> // It is NOT a Complete Intersection.
==> 0
printlevel=0;
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