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

- Usage:
    `getDiagonalEntries beta`
- Inputs:
  - beta, a Grothendieck-Witt Class, over a field or finite étale algebra over a field
- Outputs:
  - L, a list, of elements $a_i$ of the field or finite étale algebra over a field, where $i = 1,\dots,n $, such that $\beta \cong \langle a_1,\ldots,a_n\rangle$

## Description

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

    i1 : beta = makeGWClass matrix(QQ, {{3,0,0},{0,2,0},{0,0,7}});

    i2 : getDiagonalEntries 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 = makeGWClass matrix(RR, {{0,0,1},{0,1,0},{1,0,0}});

    i4 : getDiagonalEntries gamma

    o4 = {2, 1, -.5}

    o4 : List

## See also

- getDiagonalClass -- produces a diagonalized form for any (unstable) Grothendieck-Witt class, with simplified terms on the diagonal
- diagonalizeViaCongruence -- diagonalizes a symmetric matrix via congruence

## Ways to use getDiagonalEntries:

- `getDiagonalEntries(GrothendieckWittClass)`

## For the programmer

The object getDiagonalEntries is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/A1BrouwerDegrees/Documentation/SimplifiedRepresentativesDoc.m2:66:0.