next | previous | forward | backward | up | index | toc

# diagonalEntries -- extracts a list of diagonal entries for a GrothendieckWittClass

## Synopsis

• Usage:
diagonalEntries(beta)
• Inputs:
• beta, , over a field $k$, where $k$ is the rationals, reals, complex numbers, or a finite field of characteristic not 2
• Outputs:
• L, a list, of elements $a_i\in k$, where $i = 1,\dots,n$, such that $\beta \cong \langle a_1,\ldots,a_n\rangle$

## Description

Given a diagonal form, diagonalEntries will extract the elements along the diagonal.

 i1 : beta = gwClass(matrix(QQ,{{3,0,0},{0,2,0},{0,0,7}})) o1 = GrothendieckWittClass{cache => CacheTable{}} matrix => | 3 0 0 | | 0 2 0 | | 0 0 7 | o1 : GrothendieckWittClass i2 : diagonalEntries beta o2 = {3, 2, 7} o2 : List

If the form is not given with a diagonal representative, this method will first diagonalize it.

 i3 : gamma = gwClass(matrix(RR,{{0,0,1},{0,1,0},{1,0,0}})) o3 = GrothendieckWittClass{cache => CacheTable{}} matrix => | 0 0 1 | | 0 1 0 | | 1 0 0 | o3 : GrothendieckWittClass i4 : diagonalEntries gamma o4 = {2, 1, -.5} o4 : List