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

Synopsis

• Usage:

  diagonalEntries(beta)

• Inputs:
  • beta, a Grothendieck Witt Class, 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

See also

• diagonalClass -- produces a diagonalized form for any Grothendieck-Witt class, with simplified terms on the diagonal
• congruenceDiagonalize -- diagonalizing a symmetric matrix via congruence