Singular

5.1.99 mstd

Syntax:

mstd ( ideal_expression )
mstd ( module_expression )

Type:

list

Purpose:

returns a list whose first entry is a standard basis for the ideal, resp. module, whose second entry is a generating set for the ideal, resp. module. If the coefficient ring is a field and either the ideal/module is homogeneous or the ordering is local, this second entry is a minimal generating set.

Example:

ring r=0,(x,y,z,t),dp; poly f=x3+y4+z6+xyz; ideal j=jacob(f),f; j=homog(j,t);j; ==> j[1]=3x2+yz ==> j[2]=4y3+xzt ==> j[3]=6z5+xyt3 ==> j[4]=0 ==> j[5]=z6+y4t2+x3t3+xyzt3 mstd(j); ==> [1]: ==> _[1]=3x2+yz ==> _[2]=4y3+xzt ==> _[3]=6z5+xyt3 ==> _[4]=xyzt3 ==> _[5]=y2z2t3 ==> _[6]=yz3t4 ==> _[7]=xz3t4 ==> _[8]=yz2t7 ==> _[9]=xz2t7 ==> _[10]=y2zt7 ==> _[11]=xy2t7 ==> [2]: ==> _[1]=3x2+yz ==> _[2]=4y3+xzt ==> _[3]=6z5+xyt3 ==> _[4]=xyzt3