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:

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 .