Macaulay2 » Documentation
Packages » A1BrouwerDegrees :: getGWClass
next | previous | forward | backward | up | index | toc

# getGWClass -- returns the Grothendieck-Witt class of the stable part of an unstable Grothendieck-Witt class

- Usage:
    `getGWClass(beta)`
- Inputs:
  - beta, an Unstable Grothendieck-Witt Class, an unstable Grothendieck-Witt class
- Outputs:
  - a Grothendieck-Witt Class, the Grothendieck-Witt class of the stable part of the unstable Grothendieck-Witt class

## Description

Given an UnstableGrothendieckWittClass object beta, this method returns the Grothendieck-Witt class of the stable part of the unstable Grothendieck-Witt class.

    i1 : M = matrix(QQ, {{0,1},{1,0}})

    o1 = | 0 1 |
         | 1 0 |

                  2       2
    o1 : Matrix QQ  <-- QQ

    i2 : alpha = makeGWuClass(M, -9)

    o2 = (| 0 1 |, -9)
          | 1 0 |

    o2 : UnstableGrothendieckWittClass

    i3 : getGWClass alpha

    o3 = | 0 1 |
         | 1 0 |

    o3 : GrothendieckWittClass

## See also

- UnstableGrothendieckWittClass -- a new type intended to capture an element of the unstable Grothendieck-Witt group of a field or finite étale algebras over a field
- makeGWuClass -- constructor for unstable Grothendieck-Witt classes
- getMatrix -- returns the Gram matrix of a stable or unstable Grothendieck-Witt class

## Ways to use getGWClass:

- `getGWClass(UnstableGrothendieckWittClass)`

## For the programmer

The object getGWClass is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/A1BrouwerDegrees/Documentation/UnstableGrothendieckWittClassesDoc.m2:340:0.