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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
See ideal; minbase; module; std.