D.5.8.16 T_2

Procedure from library sing.lib (see sing_lib).

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 miniversal deformation.

Example:

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      = 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;