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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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