Integral Closure of an ideal

Hi there,
does anybody know wether there is a procedure to compute the integral closure of an ideal I in a given ring R? (It consists of all ring elements which are the solution of an equation
t^n + a_1 t^(n-1) + ... + a_n = 0
with a_k in I^k.)Thanks in advance,
Konrad


email: konrad@mathematik.uni-mainz.de
Posted in old Singular Forum on: 2002-09-17 14:02:05+02

Dear Konrad,

the integral closure of an ideal is computed by the
procedure normalI in reesclos.lib.

Example:
LIB"reesclos.lib";
ring R=0,(x,y),dp;
ideal I = x2,xy4,y5;
list J = normalI(I);
J;
//-> [1]:
//-> _[1]=x2
//-> _[2]=y5
//-> _[3]=-xy3

Note that xy^3 satisfies the equation (xy^3)^3-x^2*y^5*xy^4
where the second summand is in I^3.

Christoph

email: lossen@mathematik.uni-kl.de
Posted in old Singular Forum on: 2002-09-30 11:25:53+02