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D.4.18.2 modGB

Procedure from library modstd.lib (see modstd_lib).

Usage:
modGB(method, I[, exactness]); I ideal/module, exactness int method can be: std, slimgb, sba

Return:
a standard basis of I

Note:
The procedure computes a standard basis of I (over the rational numbers) by using modular methods.
An optional parameter 'exactness' can be provided. If exactness = 1(default), the procedure computes a standard basis of I for sure; if exactness = 0, it computes a standard basis of I with high probability.

Example:
 
LIB "modstd.lib";
ring R1 = 0, (x,y,z,t), dp;
ideal I = 3x3+x2+1, 11y5+y3+2, 5z4+z2+4;
ideal J = modGB("slimgb",I);
J;
==> J[1]=x3+1/3x2+1/3
==> J[2]=z4+1/5z2+4/5
==> J[3]=y5+1/11y3+2/11
I = homog(I, t);
J = modGB("slimgb",I);
J;
==> J[1]=x3+1/3x2t+1/3t3
==> J[2]=z4+1/5z2t2+4/5t4
==> J[3]=y5+1/11y3t2+2/11t5
ring R3 = 0, x(1..4), lp;
ideal I = cyclic(4);
ideal J1 = modGB("slimgb",I, 1);   // default
ideal J2 = modGB("slimgb",I, 0);
size(reduce(J1, J2));
==> 0
size(reduce(J2, J1));
==> 0
See also: modular.


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