makeHyperbolicForm -- the Grothendieck-Witt class of a hyperbolic form

• Usage:

  makeHyperbolicForm(k)

  makeHyperbolicForm(k, n)

• Inputs:
  • k, a ring, a field or finite étale algebra over a field
  • n, an integer, an even number, giving an optional rank $n$ for a totally hyperbolic form
• Outputs:
  • a Grothendieck-Witt Class, the hyperbolic form $\mathbb{H} = \langle 1, -1\rangle$ in the Grothendieck-Witt ring or the totally hyperbolic form $\left(\frac{n}{2}\right)\mathbb{H}$ if an optional rank $n$ is specified

i1 : makeHyperbolicForm(GF(7))

o1 = | 1 0  |
     | 0 -1 |

o1 : GrothendieckWittClass

i2 : makeHyperbolicForm(RR, 4)

o2 = | 1 0  0 0  |
     | 0 -1 0 0  |
     | 0 0  1 0  |
     | 0 0  0 -1 |

o2 : GrothendieckWittClass