D.5.8.17 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     = 200,(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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&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; User manual for <a href="http://www.singular.uni-kl.de/"><i>Singular</i></a> version 2-0-4, October 2002,
generated by <a href="http://www.gnu.org/software/texinfo/"><i>texi2html</i></a>.
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