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A.2.3 slim Groebner bases
The command slimgb is designed for keeping the polynomials slim (short with small coefficients) during a Groebner basis computation.
It provides, in particular, a fast algorithm for computing Groebner bases
over function fields and with respect to degree orderings.
In the example below (Groebner basis with respect to degree reverse
lexicographic ordering over function field) it is more than 600 times
faster than the std command.
| ring r=(32003,u1, u2, u3, u4),(x1, x2, x3, x4, x5, x6, x7),dp;
timer=1;
ideal i=
-x4*u3+x5*u2,
x1*u3+2*x2*u1-2*x2*u2-2*x3*u3-u1*u4+u2*u4,
-2*x1*x5+4*x4*x6+4*x5*x7+x1*u3-2*x4*u1-2*x4*u4-2*x6*u2-2*x7*u3+u1*u2+u2*u4,
-x1*x5+x1*x7-x4*u1+x4*u2-x4*u4+x5*u3+x6*u1-x6*u2+x6*u4-x7*u3,
-x1*x4+x1*u1-x5*u1+x5*u4,
-2*x1*x3+x1*u3-2*x2*u4+u1*u4+u2*u4,
x1^2*u3+x1*u1*u2-x1*u2^2-x1*u3^2-u1*u3*u4+u3*u4^2;
i=slimgb(i);
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For detailed information and limitations see slimgb.
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