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D.4.23.3 modNormal
Procedure from library normal.lib (see normal_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):
noVerification: 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
noVerification 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:
| LIB "normal.lib";
ring R = 0,(x,y,z),dp;
int k = 4;
poly f = (x^(k+1)+y^(k+1)+z^(k+1))^2-4*(x^(k+1)*y^(k+1)+y^(k+1)*z^(k+1)+z^(k+1)*x^(k+1));
f = subst(f,z,3x-2y+1);
ring S = 0,(x,y),dp;
poly f = imap(R,f);
ideal i = f;
list L = modNormal(i,1,"noVerification");
| See also:
integralbasis_lib.
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