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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.