Singular Manual: frwalk

  | ### 5.1.44 frwalk `Syntax:` `frwalk (` ring_name`,` ideal_name `)` `frwalk (` ring_name`,` ideal_name `,` int_expression `)` `Type:` ideal `Purpose:` computes for the ideal `ideal_name` in the ring `ring_name` a Groebner basis in the current ring, by applying the fractal walk 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. `Note:` When calling `frwalk`, the only permissible difference between the ring `ring_name` and the active base ring is the monomial ordering. `Example:`
        ring r=0,(x,y,z),dp;
        ideal i=y3+x2, x2y+x2, x3-x2, z4-x2-y;
        i=std(i);
        ring s=0,(x,y,z),lp;
        ideal j=frwalk(r,i);
        j;
      ==> j[1]=z12
      ==> j[2]=yz4-z8
      ==> j[3]=y2+y-z8-z4
      ==> j[4]=xy-xz4-y+z4
      ==> j[5]=x2+y-z4
See fglm; groebner; qring; ring; std.

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