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

Description

By default outputs the rank two hyperbolic form over the input field $k$.

i1 : makeHyperbolicForm GF(7)

o1 = | 1 0  |
     | 0 -1 |

o1 : GrothendieckWittClass

Specifying a rank yields a copy of sums of the rank two hyperbolic form. Only even rank inputs are accepted.

i2 : makeHyperbolicForm(RR, 4)

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

o2 : GrothendieckWittClass

See also

Ways to use makeHyperbolicForm:

  • makeHyperbolicForm(InexactFieldFamily)
  • makeHyperbolicForm(InexactFieldFamily,ZZ)
  • makeHyperbolicForm(Ring)
  • makeHyperbolicForm(Ring,ZZ)

For the programmer

The object makeHyperbolicForm is a method function.


The source of this document is in /build/reproducible-path/macaulay2-1.25.06+ds/M2/Macaulay2/packages/A1BrouwerDegrees/Documentation/BuildingFormsDoc.m2:74:0.