# 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:

## 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 .