# filtration -- the filtration matrices of the vector bundle

## Synopsis

• Usage:
f = filtration E
• Inputs:
• Outputs:
• f,

## Description

For each ray of the fan there is a filtration matrix. If the bundle has rank $k$ then this is a one row matrix over ZZ with $k$ entries. This defines the filtration on the corresponding base matrix (see base) such that the $j$-th filtration is generated by all columns of the base matrix for which the entry in the same column of the filtration matrix is less or equal to $j$.

 i1 : E = tangentBundle hirzebruchFan 2 o1 = {dimension of the variety => 2 } number of affine charts => 4 number of rays => 4 rank of the vector bundle => 2 o1 : ToricVectorBundleKlyachko i2 : filtration E o2 = HashTable{| -1 | => | -1 0 |} | 2 | | 0 | => | -1 0 | | -1 | | 0 | => | -1 0 | | 1 | | 1 | => | -1 0 | | 0 | o2 : HashTable

So in this example for each ray the first column of the basis appears at -1 and the second at 0.