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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


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            User manual for Singular version 2-0-4, May 2003, generated by texi2html.