### 5.1.39 fglm

`Syntax:`
  `fglm (` ring_name`,` ideal_name `)`
`Type:`
  ideal
`Purpose:`
  computes for the given ideal in the given ring a reduced Groebner basis in the current ring, by applying the so-called FGLM (Faugere, Gianni, Lazard, Mora) algorithm.
  The main application is to compute a lexicographical Groebner basis from a reduced Groebner basis with respect to a degree ordering. This can be much faster than computing a lexicographical Groebner basis directly.
`Assume:`
  The ideal must be zero-dimensional and given as a reduced Groebner basis in the given ring. The monomial ordering must be global.
`Note:`
  The only permissible differences between the given ring and the current ring are the monomial ordering and a permutation of the variables, resp. parameters.
`Example:`

        ring r=0,(x,y,z),dp;
        ideal i=y3+x2, x2y+x2, x3-x2, z4-x2-y;
        option(redSB);   // force the computation of a reduced SB
        i=std(i);
        vdim(i);
      ==> 28
        ring s=0,(z,x,y),lp;
        ideal j=fglm(r,i);
        j;
      ==> j[1]=y4+y3
      ==> j[2]=xy3-y3
      ==> j[3]=x2+y3
      ==> j[4]=z4+y3-y

See fglmquot; option; qring; ring; std; stdfglm; vdim.

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