Singular Manual: ncmodslimgb

| ##### 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
    ==> // ** 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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