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D.4.2.12 nonZeroEntry

Procedure from library algebra.lib (see algebra_lib).

Usage:
nonZeroEntry(id); id=object for which the test 'id[i]!=0', i=1,..,N, N=size(id) (resp. ncols(id) for id of type ideal or module) is defined (e.g. ideal, vector, list of polynomials, intvec,...)

Return:
 
         a list, say l, with l[1] an integer, l[2], l[3] integer vectors:
         - l[1] number of non-zero entries of id
         - l[2] intvec of size l[1] with l[2][i]=i if id[i] != 0
           in case l[1]!=0 (and l[2]=0 if l[1]=0)
         - l[3] intvec with l[3][i]=1 if id[i]!=0 and l[3][i]=0 else

Note:

Example:
 
LIB "algebra.lib";
ring r = 0,(a,b,c),dp;
poly f = a3c+b3+c2+a;
intvec v = leadexp(f);
nonZeroEntry(v);
==> [1]:
==>    2
==> [2]:
==>    1,3
==> [3]:
==>    1,0,1
intvec w;
list L = 37,0,f,v,w;
nonZeroEntry(L);
==> [1]:
==>    3
==> [2]:
==>    1,3,4
==> [3]:
==>    1,0,1,1,0

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