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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;