chernClass -- Compute a motivic Chern class

Synopsis

Usage:

chernClass i

chernClass I

chernClass(i,A)

chernClass(I,A)

chernClass' i

stableClass i

stableClass' i
Inputs:
- i, a string,
- I, a list,
- A, a ring,

Description

This function computes a motivic Chern class with label i (a string made of characters from "0" to "d" where d is the number of steps of the flag variety) or list of labels I in a K-theory ring A previously built using setupCotangent. If A is not specified, then the ring that was defined last is used.

i1 : (A,B,FF,I)=setupCotangent(1,3,Presentation=>Borel,Ktheory=>true,Equivariant=>false);

i2 : chernClass "101"

         2             2           2
     - 2q  + 3        q  - 2      q  - 2       1
o2 = ---------*x x  + ------*x  + ------*x  + --
          2     2 3      2    2      2    3    2
         q              q           q         q

o2 : B

If a list of labels I is used, then a matrix of classes is returned.

i3 : chernClass I

o3 = | (q4-6q2+6)/q4x_2x_3+(2q2-3)/q4x_2+(2q2-3)/q4x_3+1/q4
     ------------------------------------------------------------------------
     (-2q2+3)/q2x_2x_3+(q2-2)/q2x_2+(q2-2)/q2x_3+1/q2 x_2x_3-x_2-x_3+1 |

             1      3
o3 : Matrix B  <-- B

stableClass differs from chernClass by division by the canonical class of the flag variety. The primed classes are dual classes.

For the programmer

The object chernClass is a method function with options.