Singular

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