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D.6.20.18 T_12
Procedure from library sing.lib (see sing_lib).
- Usage:
- T_12(i[,any]); i = ideal
- Return:
- T_12(i): list of 2 modules:
* standard basis of T_1-module =T_1(i), 1st order deformations
* standard basis of T_2-module =T_2(i), obstructions of R=P/i
If a second argument is present (of any type) return a list of
9 modules, matrices, integers:
[1]= standard basis of T_1-module
[2]= standard basis of T_2-module
[3]= vdim of T_1
[4]= vdim of T_2
[5]= matrix, whose cols present infinitesimal deformations
[6]= matrix, whose cols are generators of relations of i(=syz(i))
[7]= matrix, presenting Hom_P(syz/kos,R), lifted to P
[8]= presentation of T_1-module, no std basis
[9]= presentation of T_2-module, no std basis
- Display:
- k-dimension of T_1 and T_2 if printlevel >= 0 (default)
- Note:
- Use proc miniversal from deform.lib to get miniversal deformation of i,
the list contains all objects used by proc miniversal.
Example:
| LIB "sing.lib";
int p = printlevel;
printlevel = 1;
ring r = 199,(x,y,z,u,v),(c,ws(4,3,2,3,4));
ideal i = xz-y2,yz2-xu,xv-yzu,yu-z3,z2u-yv,zv-u2;
//a cyclic quotient singularity
list L = T_12(i,1);
==> // dim T_1 = 5
==> // dim T_2 = 3
print(L[5]); //matrix of infin. deformations
==> 0, 0, 0, 0, 0,
==> yz, y, z2, 0, 0,
==> -z3,-z2,-zu,yz, yu,
==> -z2,-z, -u, 0, 0,
==> zu, u, v, -z2,-zu,
==> 0, 0, 0, u, v
printlevel = p;
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