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# SubBundles -- get the subbundles of the tautological filtration on a flag bundle

- Usage:
    `F.SubBundles`
- Inputs:
  - F, an abstract flag bundle,
- Outputs:
  - a list whose elements are the subbundles $0 = E_0 \subseteq{} E_1 \subseteq{} ... \subseteq{} E_n = f^* B$ in the tautological filtration of $f^* B$, where $F$ is a flag bundle parametrizing filtrations of an abstract sheaf $B$ on a variety $X$, and $f : F \rightarrow X$ is the structure map of $F$

## Description

    i1 : F = flagBundle {1,1,2}

    o1 = F

    o1 : a flag bundle with subquotient ranks {2:1, 2}

    i2 : F.SubBundles

    o2 = {a sheaf, a sheaf, a sheaf, a sheaf}

    o2 : List

    i3 : rank \ oo

    o3 = {0, 1, 2, 4}

    o3 : List

    i4 : netList \\ chern \ ooo

         +------------------------+
    o4 = |1                       |
         +------------------------+
         |1 + (- H    - H   )     |
         |        2,1    3,1      |
         +------------------------+
         |             2          |
         |1 - H    + (H    - H   )|
         |     3,1     3,1    3,2 |
         +------------------------+
         |1                       |
         +------------------------+

## For the programmer

The object SubBundles is a symbol.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/Schubert2.m2:1857:0.