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 x
8, 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 |