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GroebnerWalk :: groebnerWalk

groebnerWalk -- convert a Groebner basis



The Groebner walk takes a Groebner basis of an ideal with respect to one monomial order and changes it into a Groebner basis of the same ideal over a different monomial order. The initial order is given by the ring of G and the target order is the order in R. When given an ideal I as input a Groebner basis of I in the ring of I is initially computed directly, and then this Groebner basis is converted into a Groebner basis in the ring R.

i1 : KK = ZZ/32003;
i2 : R1 = KK[x,y,z,u,v, MonomialOrder=>Eliminate 3];
i3 : I1 = ideal(3 - 2*u + 2*u^2 - 2*u^3 - v + u*v + 2*u^2*v^3 - x,
                6*u + 5*u^2 - u^3 + v + u*v + v^2 - y,
                -2 + 3*u - u*v + 2*u*v^2 - z);

o3 : Ideal of R1
i4 : R2 = KK[x,y,z,u,v, MonomialOrder=>Weights=>{0,0,0,1,1}];
i5 : groebnerWalk(I1, R2)

o5 = GroebnerBasis[status: done; S-pairs encountered up to degree 0]

o5 : GroebnerBasis


The target ring R must be the same ring as the ring of G or I, except with different monomial order. R must be a polynomial ring over a field.

See also

Ways to use groebnerWalk :

For the programmer

The object groebnerWalk is a method function with options.