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D.5.8.16 T_2
Procedure from library sing.lib (see section 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;
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