Singular

D.6.15.17 T_2

Usage:

T_2(id[,<any>]); id = ideal

Return:

T_2(id): T_2-module of id . This is a std basis of a presentation of the module of obstructions of R=P/id, if P is the basering. If a second argument is present (of any type) return a list of 4 modules and 1 ideal:
[1]= T_2(id)
[2]= standard basis of id (ideal)
[3]= module of relations of id (=1st syzygy module of id)
[4]= presentation of syz/kos
[5]= relations of Hom_P([3]/kos,R), lifted to P
The list contains all non-easy objects which must be computed to get T_2(id).

Display:

k-dimension of T_2(id) if printlevel >= 0 (default)

Note:

The most important information is probably vdim(T_2(id)). Use proc miniversal to get equations of the miniversal deformation.

LIB "sing.lib";
int p      = printlevel;
printlevel = 1;
ring  r    = 32003,(x,y),(c,dp);
ideal j    = x6-y4,x6y6,x2y4-x5y2;
module T   = T_2(j);
==> // dim T_2 = 6
vdim(T);
==> 6
hilb(T);"";
==> //         1 t^0
==> //        -1 t^2
==> //        -1 t^3
==> //         1 t^5
==> 
==> //         1 t^0
==> //         2 t^1
==> //         2 t^2
==> //         1 t^3
==> // dimension (affine) = 0
==> // degree (affine)  = 6
==> 
ring r1    = 0,(x,y,z),dp;
ideal id   = xy,xz,yz;
list L     = T_2(id,"");
==> // dim T_2 = 0
vdim(L[1]);                           // vdim of T_2
==> 0
print(L[3]);                          // syzygy module of id
==> -z,-z,
==> y, 0, 
==> 0, x  
printlevel = p;