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D.7.1.16 idealSplit

Procedure from library presolve.lib (see presolve_lib).

Usage:

idealSplit(id,timeF,timeS); id ideal and optional
timeF ,timeS integers to bound the time which can be used for factorization resp. standard basis computation

Return:

a list of ideals such that their intersection
has the same radical as id

Example:

 
LIB "presolve.lib";
ring r=32003,(b,s,t,u,v,w,x,y,z),dp;
ideal i=
bv+su,
bw+tu,
sw+tv,
by+sx,
bz+tx,
sz+ty,
uy+vx,
uz+wx,
vz+wy,
bvz;
idealSplit(i);
→ [1]:
→    _[1]=x
→    _[2]=u
→    _[3]=t
→    _[4]=s
→    _[5]=b
→    _[6]=wy+vz
→ [2]:
→    _[1]=z
→    _[2]=w
→    _[3]=t
→    _[4]=s
→    _[5]=b
→    _[6]=vx+uy
→ [3]:
→    _[1]=z
→    _[2]=x
→    _[3]=w
→    _[4]=u
→    _[5]=t
→    _[6]=b
→ [4]:
→    _[1]=z
→    _[2]=y
→    _[3]=x
→    _[4]=t
→    _[5]=s
→    _[6]=b
→ [5]:
→    _[1]=z
→    _[2]=y
→    _[3]=x
→    _[4]=u
→    _[5]=b
→    _[6]=tv+sw
→ [6]:
→    _[1]=z
→    _[2]=y
→    _[3]=x
→    _[4]=w
→    _[5]=t
→    _[6]=su+bv
→ [7]:
→    _[1]=w
→    _[2]=v
→    _[3]=u
→    _[4]=t
→    _[5]=s
→    _[6]=b
→ [8]:
→    _[1]=x
→    _[2]=w
→    _[3]=v
→    _[4]=u
→    _[5]=b
→    _[6]=ty+sz
→ [9]:
→    _[1]=z
→    _[2]=w
→    _[3]=v
→    _[4]=u
→    _[5]=t
→    _[6]=sx+by
→ [10]:
→    _[1]=z
→    _[2]=y
→    _[3]=x
→    _[4]=w
→    _[5]=v
→    _[6]=u
→ [11]:
→    _[1]=y
→    _[2]=v
→    _[3]=t
→    _[4]=s
→    _[5]=b
→    _[6]=wx+uz
→ [12]:
→    _[1]=y
→    _[2]=x
→    _[3]=v
→    _[4]=u
→    _[5]=s
→    _[6]=b
→ [13]:
→    _[1]=z
→    _[2]=y
→    _[3]=x
→    _[4]=v
→    _[5]=s
→    _[6]=tu+bw
→ [14]:
→    _[1]=z
→    _[2]=y
→    _[3]=w
→    _[4]=v
→    _[5]=t
→    _[6]=s
→ [15]:
→    _[1]=y
→    _[2]=w
→    _[3]=v
→    _[4]=u
→    _[5]=s
→    _[6]=tx+bz

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