D.7.1.2 elimlinearpart

Procedure from library presolve.lib (see presolve_lib).

Usage:

elimlinearpart(i[,n]); i=ideal, n=integer,
default: n=nvars(basering)

Return:

list L with 5 entries:

L[1]: (interreduced) ideal obtained from i by substituing from the first n variables those, which appear in a linear part of i, by putting this part into triangular form L[2]: ideal of variables which have been substituted L[3]: ideal, j-th element defines substitution of j-th var in [2] L[4]: ideal of variables of basering, eliminated ones are set to 0 L[5]: ideal, describing the map from the basering to itself such that L[1] is the image of i

Note:

the procedure does always interreduce the ideal i internally w.r.t. ordering dp.

Example:

LIB "presolve.lib";
ring s=0,(x,y,z),dp;
ideal i = x3+y2+z,x2y2+z3,y+z+1;
elimlinearpart(i);
→ [1]:
→    _[1]=x3+z2+3z+1
→    _[2]=x2z2+2x2z+z3+x2
→ [2]:
→    _[1]=y
→ [3]:
→    _[1]=y+z+1
→ [4]:
→    _[1]=x
→    _[2]=0
→    _[3]=z
→ [5]:
→    _[1]=x
→    _[2]=-z-1
→    _[3]=z