makeDiagonalUnstableForm -- the unstable Grothendieck-Witt class of a diagonal matrix

• Usage:

  makeDiagonalUnstableForm(k, a)

  makeDiagonalUnstableForm(k, L)

• Inputs:
  • k, a ring, a field or finite étale algebra over a field
  • a, a ring element, any element in the field or finite étale algebra over a field
  • L, a sequence, of elements in the field or finite étale algebra $a_{i}$ where $i = 1,\dots, n$
• Outputs:
  • an Unstable Grothendieck-Witt Class, the unstable Grothendieck-Witt class represented by the diagonal form $\langle a_{1},\ldots,a_{n}\rangle$ in the unstable Grothendieck-Witt group of the field or finite étale algebra

i1 : makeDiagonalUnstableForm(QQ, (3,5,7))

o1 = (| 3 0 0 |, 105)
      | 0 5 0 |
      | 0 0 7 |

o1 : UnstableGrothendieckWittClass

i2 : makeDiagonalUnstableForm(GF(29), 5/13)

o2 = (| -13 |, -13)

o2 : UnstableGrothendieckWittClass

i3 : makeDiagonalUnstableForm(RR, 2)

o3 = (| 2 |, 2)

o3 : UnstableGrothendieckWittClass