nestedObstruction -- calculate secondary obstruction space for nested deformations

Description

The module image F0Y should be contained in image F0X. The output N is a matrix over the same ring as F0X whose columns form a basis for (a graded piece of) the quotient of the module Hom(image F0Y,coker F0X) by the images of the modules Hom(image F0Y,coker F0Y) and Hom(image F0X,coker F0X). Selection of graded pieces is done in the same manner as with basis. If the selected pieces are infinite dimensional, an error occurs.

For example, consider embedded deformations of the fat points in the plane defined by the square and cube of the homogeneous maximal ideal:

i1 : R=QQ[x,y];

i2 : F0Y=basis(3,R);

             1      4
o2 : Matrix R  <-- R

i3 : F0X=basis(2,R);

             1      3
o3 : Matrix R  <-- R

i4 : nestedObstruction(F0X,F0Y)

o4 = {-3} | y x 0 0 0 0 0 0 |
     {-3} | 0 0 y x 0 0 0 0 |
     {-3} | 0 0 0 0 y x 0 0 |
     {-3} | 0 0 0 0 0 0 y x |

             4      8
o4 : Matrix R  <-- R

The space of nested obstructions is eight-dimensional.