Top
Back: elimlinearpart
Forward: elimpartanyr
FastBack: Symbolic-numerical solving
FastForward: solve_lib
Up: presolve_lib
Top: Singular Manual
Contents: Table of Contents
Index: Index
About: About this document

D.7.1.3 elimpart

Procedure from library presolve.lib (see presolve_lib).

Usage:
elimpart(i [,n,e] ); i=ideal, n,e=integers
n : only the first n vars are considered for substitution,
e =0: substitute from linear part of i (same as elimlinearpart)
e!=0: eliminate also by direct substitution
(default: n = nvars(basering), e = 1)

Return:
list of 5 objects:
 
  [1]: ideal obtained by substituting from the first n variables those
       from i, which appear in the linear part of i (or, if e!=0, which
       can be expressed directly in the remaining vars)
  [2]: ideal, variables which have been substituted
  [3]: ideal, i-th element defines substitution of i-th var in [2]
  [4]: ideal of variables of basering, substituted ones are set to 0
  [5]: ideal, describing the map from the basering, say k[x(1..m)], to
       itself onto k[..variables fom [4]..] and [1] is the image of i
The ideal i is generated by [1] and [3] in k[x(1..m)], the map [5] maps [3] to 0, hence induces an isomorphism
 
            k[x(1..m)]/i -> k[..variables fom [4]..]/[1]

Note:
If the basering has ordering (c,dp), this is faster for big ideals, since it avoids internal ring change and mapping.

Example:
 
LIB "presolve.lib";
ring s=0,(x,y,z),dp;
ideal i =x2+y2,x2+y+1;
elimpart(i,3,0);
==> [1]:
==>    _[1]=y2-y-1
==>    _[2]=x2+y+1
==> [2]:
==>    _[1]=0
==> [3]:
==>    _[1]=0
==> [4]:
==>    _[1]=x
==>    _[2]=y
==>    _[3]=z
==> [5]:
==>    _[1]=x
==>    _[2]=y
==>    _[3]=z
elimpart(i,3,1);
==> [1]:
==>    _[1]=x4+3x2+1
==> [2]:
==>    _[1]=y
==> [3]:
==>    _[1]=x2+y+1
==> [4]:
==>    _[1]=x
==>    _[2]=0
==>    _[3]=z
==> [5]:
==>    _[1]=x
==>    _[2]=-x2-1
==>    _[3]=z


Top Back: elimlinearpart Forward: elimpartanyr FastBack: Symbolic-numerical solving FastForward: solve_lib Up: presolve_lib Top: Singular Manual Contents: Table of Contents Index: Index About: About this document
            User manual for Singular version 3-0-1, October 2005, generated by texi2html.