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D.6.13.16 T_1
Procedure from library sing.lib (see sing_lib).
- Usage:
- T_1(id[,<any>]); id = ideal or poly
- Return:
- T_1(id): of type module/ideal if id is of type ideal/poly.
We call T_1(id) the T_1-module of id. It is a std basis of the
presentation of 1st order deformations of P/id, if P is the basering.
If a second argument is present (of any type) return a list of
3 modules:
[1]= T_1(id)
[2]= generators of normal bundle of id, lifted to P
[3]= module of relations of [2], lifted to P
(note: transpose[3]*[2]=0 mod id)
The list contains all non-easy objects which must be computed
to get T_1(id).
- Display:
- k-dimension of T_1(id) if printlevel >= 0 (default)
- Note:
- T_1(id) itself is usually of minor importance. Nevertheless, from it
all relevant information can be obtained. The most important are
probably vdim(T_1(id)); (which computes the Tjurina number),
hilb(T_1(id)); and kbase(T_1(id)).
If T_1 is called with two arguments, then matrix([2])*(kbase([1]))
represents a basis of 1st order semiuniversal deformation of id
(use proc 'deform', to get this in a direct way).
For a complete intersection the proc Tjurina is faster.
Example:
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