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Normaliz :: The generators of the integral closure of the Rees algebra of a monomial ideal.

The generators of the integral closure of the Rees algebra of a monomial ideal.

We use intclMonIdeal to compute the integral closure of a monomial ideal and of its Rees algebra.

R=ZZ/37[x_1..x_7];
I=ideal(x_1..x_6, x_1*x_2*x_3*x_7, x_1*x_2*x_4*x_7, x_1*x_3*x_5*x_7, x_1*x_4*x_6*x_7, x_1*x_5*x_6*x_7, x_2*x_3*x_6*x_7, x_2*x_4*x_5*x_7, x_2*x_5*x_6*x_7,x_3*x_4*x_5*x_7,x_3*x_4*x_6*x_7);
(intcl,rees)=intclMonIdeal I;
intcl
rees

The first entry is an ideal, the integral closure of the original ideal, the second one a monomial subalgebra. Each variable in the example appears in a generator of the ideal. Therefore an auxiliary variable a is added to the ring. If there were a free variable in the ring, say x8, then one can give this variable as a second argument to the function, which then is used as auxiliary variable.

R=ZZ/37[x_1..x_8];
I=ideal(x_1..x_6, x_1*x_2*x_3*x_7, x_1*x_2*x_4*x_7, x_1*x_3*x_5*x_7, x_1*x_4*x_6*x_7, x_1*x_5*x_6*x_7, x_2*x_3*x_6*x_7, x_2*x_4*x_5*x_7, x_2*x_5*x_6*x_7,x_3*x_4*x_5*x_7,x_3*x_4*x_6*x_7);
(intcl,rees)=intclMonIdeal(I,x_8);
intcl
rees