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7.5.18.0. ncmodslimgb
Procedure from library ncModslimgb.lib (see ncModslimgb_lib).
- Usage:
- ncmodslimgb(I[, exactness, ncores]); I ideal, optional integers exactness and n(umber of )cores
- Return:
- ideal
- Purpose:
- compute a left Groebner basis of I by modular approach
- Assume:
- basering is a G-algebra; base field is prime field Q of rationals.
- Note:
- - If the given algebra and ideal are graded (it is not checked by this command), then the computed Groebner
basis will be exact. Otherwise, the result will be correct with a very high probability.
- The optional parameter `exactness` justifies, whether the final (expensive)
verification step will be performed or not (exactness=0, default value is 1).
- The optional parameter `ncores` (default value is 1) provides an integer to use
the number of cores (this must not exceed the number of available cores in the computing machine).
Example:
| | LIB "ncModslimgb.lib";
ring r = 0,(x,y),dp;
poly P = y^4+x^3+x*y^3; // a (3,4)-Reiffen curve
def A = Sannfs(P); setring A; // computed D-module data from P
ideal bs = LD, imap(r,P); // preparing the computation of the Bernstein-Sato polynomial
ideal I1 = ncmodslimgb(bs,0,2); // no final verification, use 2 cores
==> // ** going to redefine the algebra structure
==> // ** going to redefine the algebra structure
==> // ** going to redefine the algebra structure
==> // ** going to redefine the algebra structure
==> // ** going to redefine the algebra structure
==> // ** going to redefine the algebra structure
==> // ** going to redefine the algebra structure
==> // ** going to redefine the algebra structure
==> // ** going to redefine the algebra structure
==> // ** going to redefine the algebra structure
==> // ** going to redefine the algebra structure
==> // ** going to redefine the algebra structure
==> // ** going to redefine the algebra structure
==> // ** going to redefine the algebra structure
==> // ** going to redefine the algebra structure
==> // ** going to redefine the algebra structure
==> // ** going to redefine the algebra structure
==> // ** going to redefine the algebra structure
==> // ** going to redefine the algebra structure
==> // ** going to redefine the algebra structure
==> // ** going to redefine the algebra structure
==> // ** going to redefine the algebra structure
==> // ** going to redefine the algebra structure
==> // ** going to redefine the algebra structure
==> // ** going to redefine the algebra structure
==> // ** going to redefine the algebra structure
==> // ** going to redefine the algebra structure
==> // ** going to redefine the algebra structure
==> // ** going to redefine the algebra structure
==> // ** going to redefine the algebra structure
I1[1]; // the Bernstein-Sato polynomial of P, univariate in s
==> s^7+7*s^6+499/24*s^5+815/24*s^4+227563/6912*s^3+43627/2304*s^2+4461779/74\
6496*s+595595/746496
ideal I2 = ncmodslimgb(bs); // do the final verification, use 1 core (default)
I2[1]; // the Bernstein-Sato polynomial of P, univariate in s
==> s^7+7*s^6+499/24*s^5+815/24*s^4+227563/6912*s^3+43627/2304*s^2+4461779/74\
6496*s+595595/746496
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