### 5.1.100 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.

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