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D.5.8.12 DeltaList

Procedure from library resolve.lib (see resolve_lib).

Usage:
DeltaList (BO);
BO = basic object, a list: ideal W,
ideal J,
intvec b,
list Ex,
ideal ab,
intvec v,
intvec w,
matrix M

Assume:
R = basering, a polynomial ring, W an ideal of R,
J = ideal containing W

Compute:
Delta-operator iteratively applied to J in the notation of [Bravo,Encinas,Villamayor]

Return:
list l of length ((max w-ord) * b),
l[i+1]=Delta^i(J)

Example:
 
LIB "resolve.lib";
ring R=0,(x,y,z),dp;
ideal W=z^2-x;
ideal J=x*y^2+x^3;
intvec b=1;
list E;
ideal abb=maxideal(1);
intvec v;
intvec w=-1;
matrix M;
list BO=W,J,b,E,abb,v,w,M;
DeltaList(BO);
==> [1]:
==>    _[1]=x3+xy2
==> [2]:
==>    _[1]=z2-x
==>    _[2]=xy
==>    _[3]=3x2z+y2z
==>    _[4]=x3
==> [3]:
==>    _[1]=x
==>    _[2]=z2
==>    _[3]=yz
==>    _[4]=y2
==> [4]:
==>    _[1]=z
==>    _[2]=y
==>    _[3]=x