segreClass -- Compute a motivic Segre class

Synopsis

Usage:

segreClass i

segreClass I

segreClass(i,A)

segreClass(I,A)

segreClass' i

sClass i

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

Description

This function computes a motivic Segre 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 : segreClass "101"

            4                4    2            4    2               2
         -2q                q  + q            q  + q             -2q
o2 = ------------*x x  + ------------*x  + ------------*x  + ------------
      4     2      2 3    4     2      2    4     2      3    4     2
     q  - 2q  + 1        q  - 2q  + 1      q  - 2q  + 1      q  - 2q  + 1

o2 : B

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

i3 : segreClass I

o3 = | q4/(q4-2q2+1)x_2x_3+(-q2)/(q4-2q2+1)x_2+(-q2)/(q4-2q2+1)x_3+1/(q4-2q2+
     ------------------------------------------------------------------------
     1) (-2q4)/(q4-2q2+1)x_2x_3+(q4+q2)/(q4-2q2+1)x_2+(q4+q2)/(q4-2q2+1)x_3
     ------------------------------------------------------------------------
     +(-2q2)/(q4-2q2+1) q4/(q4-2q2+1)x_2x_3+(-q4)/(q4-2q2+1)x_2+(-q4)/(q4-2q2
     ------------------------------------------------------------------------
     +1)x_3+q4/(q4-2q2+1) |

             1      3
o3 : Matrix B  <-- B

sClass differs from segreClass by multiplication by a power of the equivariant parameter $q$. The primed classes are dual classes.

For the programmer

The object segreClass is a method function with options.