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D.6.15.11 nf_icis

Procedure from library sing.lib (see sing_lib).

Usage:
nf_icis(i); i ideal

Return:
ideal = generic linear combination of generators of i if i is an ICIS (isolated complete intersection singularity), return i if not

Note:
this proc is useful in connection with proc milnor
printlevel >=0: display comments (default)

Example:
 
LIB "sing.lib";
int p      = printlevel;
printlevel = 1;
ring r     = 32003,(x,y,z),ds;
ideal i    = x3+y4,z4+yx;
nf_icis(i);
==> // complete intersection of dim 1
==> // dim-sequence:
==> // dim of singular locus = 0
==> // isolated singularity if last number is 0 in dim-sequence:
==> // dim of singular locus = 0
==> // isolated singularity if last number is 0 in dim-sequence:
==> // ICIS in generic form after 1 genericity loop(s)
==> _[1]=2xy+x3+y4+2z4
==> _[2]=xy+z4
ideal j    = x3+y4,xy,yz;
nf_icis(j);
==> // no complete intersection
==> // dim-sequence:
==> // no complete intersection
==> _[1]=x3+y4
==> _[2]=xy
==> _[3]=yz
printlevel = p;