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D.4.15.6 primeClosure

Procedure from library normal.lib (see normal_lib).

Usage:
primeClosure(L [,c]); L a list of a ring containing a prime ideal ker, c an optional integer

Return:
a list L (of size n+1) consisting of rings L[1],...,L[n] such that - L[1] is a copy of (not a reference to!) the input ring L[1] - all rings L[i] contain ideals ker, L[2],...,L[n] contain ideals phi such that
L[1]/ker --> ... --> L[n]/ker
are injections given by the corresponding ideals phi, and L[n]/ker is the integral closure of L[1]/ker in its quotient field. - all rings L[i] contain a polynomial nzd such that elements of L[i]/ker are quotients of elements of L[i-1]/ker with denominator nzd via the injection phi.
L[n+1] is the delta invariant

Note:
- L is constructed by recursive calls of primeClosure itself. - c determines the choice of nzd:
- c not given or equal to 0: first generator of the ideal SL, the singular locus of Spec(L[i]/ker)
- c<>0: the generator of SL with least number of monomials.

Example:
 


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