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D.15.19.6 syModStd
Procedure from library symodstd.lib (see symodstd_lib).
- Usage:
- syModStd(I,sigma); I ideal, sigma intvec
- Assume:
- size(sigma) = nvars(basering) and sigma(I) = I. If size(#) > 0, then
# contains either 1, 2 or 4 integers such that
- #[1] is the number of available processors for the computation,
- #[2] is an optional parameter for the exactness of the computation,
if #[2] = 1, the procedure computes a standard basis for sure,
- #[3] is the number of primes until the first lifting,
- #[4] is the constant number of primes between two liftings until
the computation stops.
- Return:
- ideal, a standard basis of I if no warning appears;
- Note:
- The procedure computes a standard basis of the ideal I (over the
rational numbers) by using modular methods and the fact that I is
invariant under the variable permutation sigma.
By default the procedure computes a standard basis of I for sure, but
if the optional parameter #[2] = 0, it computes a standard basis of I
with high probability.
The procedure distinguishes between different variants for the standard
basis computation in positive characteristic depending on the ordering
of the basering, the parameter #[2] and if the ideal I is homogeneous.
- variant = 1, if I is homogeneous,
- variant = 2, if I is not homogeneous, 1-block-ordering,
- variant = 3, if I is not homogeneous, complicated ordering (lp or
> 1 block),
- variant = 4, if I is not homogeneous, ordering lp, dim(I) = 0.
Example:
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