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# ChernClassVariable -- the class of all Chern class variables

## Description

This class supports the creation of variables, analogous to indexed variables, that can be used as generators of intersection rings of abstract varieties that are displayed in the form c_iE, where i is a natural number and E is the name of an abstract sheaf.

    i1 : F = flagBundle({3,2},VariableNames => {{chern_1 S .. chern_3 S},{chern_1 Q,chern_2 Q}})

    o1 = F

    o1 : a flag bundle with subquotient ranks {3, 2}

    i2 : A = intersectionRing F

    o2 = A

    o2 : QuotientRing

    i3 : (S,Q) = bundles F

    o3 = (S, Q)

    o3 : Sequence

    i4 : chern Q

    o4 = 1 + c Q + c Q
              1     2

    o4 : A

    i5 : chern S

                         2                  3
    o5 = 1 - c Q + ((c Q)  - c Q) + (- (c Q)  + 2*c Q*c Q)
              1       1       2          1         1   2

    o5 : A

## See also

- ChernClassVariableTable -- the class of all Chern class variable tables

## Functions and methods returning a Chern class variable:

- chern(ZZ,Symbol) -- make a Chern class symbol

## Methods that use a Chern class variable:

- ChernClassVariable .. ChernClassVariable -- generate a sequence of Chern class variables
- ChernClassVariable <- Thing -- assignment to a Chern class variable
- Ring _ ChernClassVariable -- get a ring generator corresponding to a Chern class variable
- value(ChernClassVariable) -- the value of a Chern class symbol

## For the programmer

The object ChernClassVariable is a type, with ancestor classes BasicList < Thing.

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