getBlock -- Extract a block of the matrix representation of an adjoint operator for ExteriorExtensions

Description

The blocks get extracted based on their grade

i1 : ea = exteriorExtension(3, 6, e, QQ);

i2 : A = ea.ad(first ea.bases#1);

              55       55
o2 : Matrix QQ   <-- QQ

i3 : printWidth = 300;

i4 : ea.getBlock(1, 1, A)

o4 = 0

              20       20
o4 : Matrix QQ   <-- QQ

i5 : ea.getBlock(1, 0, A)

o5 = | 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 |
     | 0 0 0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0  0  0  0 0 0 0 -1 0  0  0 0 0 |
     | 0 0 0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0  0  0  0 0 0 0 0  -1 0  0 0 0 |
     | 0 0 0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0  0  0  0 0 0 0 0  0  -1 0 0 0 |
     | 0 0 0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0  0  0  0 1 0 0 0  0  0  0 0 0 |
     | 0 0 0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0  0  0  0 0 1 0 0  0  0  0 0 0 |
     | 0 0 0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0  0  0  0 0 0 1 0  0  0  0 0 0 |
     | 0 0 0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 |
     | 0 0 0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 |
     | 0 0 0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 |
     | 0 0 0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 0  0  0 0 0 0 0  0  0  0 0 0 |
     | 0 0 0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0  -1 0  0 0 0 0 0  0  0  0 0 0 |
     | 0 0 0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0  0  -1 0 0 0 0 0  0  0  0 0 0 |
     | 0 0 0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 |
     | 0 0 0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 |
     | 0 0 0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 |
     | 0 0 0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 |
     | 0 0 0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 |
     | 0 0 0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 |
     | 0 0 0  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0  0  0  0 0 0 0 0  0  0  0 0 0 |

              20       35
o5 : Matrix QQ   <-- QQ

This extracts blocks of the operator. The sizes are determined by the graded pieces of the algebra.

For the programmer

The object getBlock is a symbol.

The source of this document is in ExteriorExtensions.m2:708:0.