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

# addGWu -- the direct sum for two unstable Grothendieck-Witt Classes

- Usage:
    `addGWu(beta, gamma)`
- Inputs:
  - beta, an Unstable Grothendieck-Witt Class, the isomorphism class of a non-degenerate symmetric bilinear form represented by a matrix M together with a scalar s
  - gamma, an Unstable Grothendieck-Witt Class, the isomorphism class of a non-degenerate symmetric bilinear form represented by a matrix N together with a scalar t
- Outputs:
  - an Unstable Grothendieck-Witt Class, the isomorphism class of the direct sum of the bilinear forms represented by the matrices M and N, and the scalar is the product st

## Description

This computes the direct sum of the Grothendieck-Witt classes beta and gamma.

    i1 : M = matrix(QQ, {{2,1},{1,2}})

    o1 = | 2 1 |
         | 1 2 |

                  2       2
    o1 : Matrix QQ  <-- QQ

    i2 : N = matrix(QQ, {{1,2},{2,6}})

    o2 = | 1 2 |
         | 2 6 |

                  2       2
    o2 : Matrix QQ  <-- QQ

    i3 : beta = makeGWuClass M

    o3 = (| 2 1 |, 3)
          | 1 2 |

    o3 : UnstableGrothendieckWittClass

    i4 : gamma = makeGWuClass N

    o4 = (| 1 2 |, 2)
          | 2 6 |

    o4 : UnstableGrothendieckWittClass

    i5 : addGWu(beta, gamma)

    o5 = (| 2 1 0 0 |, 6)
          | 1 2 0 0 |
          | 0 0 1 2 |
          | 0 0 2 6 |

    o5 : UnstableGrothendieckWittClass

## Ways to use addGWu:

- `addGWu(UnstableGrothendieckWittClass,UnstableGrothendieckWittClass)`

## For the programmer

The object addGWu 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.m2:278:0.