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

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