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D.4.9.1 modStd

Procedure from library modstd.lib (see modstd_lib).

Usage:
modStd(I);

Return:
a standard basis of I if no warning appears;

Note:
the procedure computes a standard basis of I (over the
rational numbers) by using modular methods. If a
warning appears then the result is a standard basis
containing I and with high probability a standard basis of I. For further experiments see procedure modS.

Example:
 
LIB "modstd.lib";
ring r=0,(x,y,z,t),dp;
ideal I=3x3+x2+1,11y5+y3+2,5z4+z2+4;
ideal J=modStd(I);
==> ==================================================================
==>     The input is not homogeneous and the ordering is not
==> local.   
==> WARNING: ideal generated by output may be greater then
==> input ideal
==> ==================================================================
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=modStd(I);
J;
==> J[1]=x3+1/3x2t+1/3t3
==> J[2]=z4+1/5z2t2+4/5t4
==> J[3]=y5+1/11y3t2+2/11t5
ring s=0,(x,y,z),ds;
ideal I=jacob(x5+y6+z7+xyz);
ideal J=modStd(I);
J;
==> J[1]=xy+7z6
==> J[2]=xz+6y5
==> J[3]=yz+5x4
==> J[4]=x5-7/5z7
==> J[5]=y6-7/6z7
==> J[6]=z8


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