Singular Manual: T_12

| #### 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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