Home Online Manual
Top
Back: impart
Forward: insert
FastBack: Functions and system variables
FastForward: Control structures
Up: Functions
Top: Singular Manual
Contents: Table of Contents
Index: Index
About: About this document

5.1.59 indepSet

Syntax:
indepSet ( ideal_expression )
Type:
intvec
Purpose:
computes a maximal set U of independent variables (in the sense defined in the note below) of the ideal given by a standard basis. If v is the result then v[i] is 1 if and only if the i-th variable of the ring, x(i), is an independent variable. Hence, the set U consisting of all variables x(i) with v[i]=1 is a maximal independent set.

Note:
U is a set of independent variables for I if and only if $I \cap K[U]=(0)$,i.e., eliminating the remaining variables gives (0). U is maximal if dim(I)=#U.
Syntax:
indepSet ( ideal_expression, int_expression )
Type:
list
Purpose:
computes a list of all maximal independent sets of the leading ideal (if the flag is 0), resp. of all those sets of independent variables of the leading ideal which cannot be enlarged.
Example:
 
  ring r=32003,(x,y,u,v,w),dp;
  ideal I=xyw,yvw,uyw,xv;
  attrib(I,"isSB",1);
  indepSet(I);
==> 1,1,1,0,0
  eliminate(I,vw);
==> _[1]=0
  indepSet(I,0);
==> [1]:
==>    1,1,1,0,0
==> [2]:
==>    0,1,1,1,0
==> [3]:
==>    1,0,1,0,1
==> [4]:
==>    0,0,1,1,1
  indepSet(I,1);
==> [1]:
==>    1,1,1,0,0
==> [2]:
==>    0,1,1,1,0
==> [3]:
==>    1,0,1,0,1
==> [4]:
==>    0,0,1,1,1
==> [5]:
==>    0,1,0,0,1
  eliminate(I,xuv);
==> _[1]=0
See ideal; std.