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D.15.12.1 modNormal
Procedure from library modnormal.lib (see modnormal_lib).
- Usage:
- modNormal(I, n [,options]); I = prime ideal, n = positive integer, options = list of options.
Optional parameters in list options (can be entered in any order):
noVerificication: do not verify the result.
printTimings: print timings.
int ncores: number of cores to be used (default = 1).
- Assume:
- I is a prime ideal (the algorithm will also work for radical ideals as long as the
normal command does not detect that the ideal under consideration is not prime).
- Return:
- a list of an ideal U and a universal denominator d such that U/d is the normalization.
- Remarks:
- We use the algorithm given in [1] to compute the normalization of A = R/I where R is the
basering. We apply the algorithm for n primes at a time until the result lifted to the
rationals is correct modulo one additional prime. Depending on whether the option
noVerificication is used or not, the result is returned as a probabilistic result
or verified over the rationals.
The normalization of A is represented as an R-module by returning a list of U and d,
where U is an ideal of A and d is an element of A such that U/d is the normalization of A.
In fact, U and d are returned as an ideal and a polynomial of the base ring R.
Example:
See also:
locnormal_lib;
normal_lib.
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