-- -*- M2-comint -*- hash: 3359491612988627334

i1 : alpha = makeGWClass matrix(CC, {{2,3,1},{3,-1,0},{1,0,0}})

o1 = | 2 3  1 |
     | 3 -1 0 |
     | 1 0  0 |

o1 : GrothendieckWittClass

i2 : beta = makeGWClass matrix(CC, {{2,4,-1},{4,5,7},{-1,7,9}})

o2 = | 2  4 -1 |
     | 4  5 7  |
     | -1 7 9  |

o2 : GrothendieckWittClass

i3 : isIsomorphicForm(alpha,beta)

o3 = true

i4 : gamma = makeGWClass matrix(RR, {{1,0,0},{0,-1,0},{0,0,1}});

i5 : getSignature gamma

o5 = 1

i6 : delta = makeGWClass matrix(RR, {{0,0,1},{0,1,0},{1,0,0}});

i7 : isIsomorphicForm(gamma, delta)

o7 = true

i8 : getHilbertSymbol(2,1,7)

o8 = 1

i9 : alphaQ = makeGWClass matrix(QQ, {{1,4,7},{4,3,2},{7,2,-1}})

o9 = | 1 4 7  |
     | 4 3 2  |
     | 7 2 -1 |

o9 : GrothendieckWittClass

i10 : betaQ = makeGWClass matrix(QQ, {{0,0,1},{0,2,7},{1,7,3}})

o10 = | 0 0 1 |
      | 0 2 7 |
      | 1 7 3 |

o10 : GrothendieckWittClass

i11 : isIsomorphicForm(alphaQ,betaQ)

o11 = false

i12 : alphaF = makeGWClass matrix(GF(7), {{1,2,2},{2,0,1},{2,1,5}})

o12 = | 1 2 2  |
      | 2 0 1  |
      | 2 1 -2 |

o12 : GrothendieckWittClass

i13 : betaF = makeGWClass matrix(GF(7), {{2,5,1},{5,6,1},{1,1,3}})

o13 = | 2  -2 1 |
      | -2 -1 1 |
      | 1  1  3 |

o13 : GrothendieckWittClass

i14 : gammaF = makeGWClass matrix(GF(7), {{0,2,4},{2,3,3},{4,3,1}})

o14 = | 0  2 -3 |
      | 2  3 3  |
      | -3 3 1  |

o14 : GrothendieckWittClass

i15 : det getMatrix alphaF

o15 = 1

o15 : GF 7

i16 : det getMatrix betaF

o16 = -2

o16 : GF 7

i17 : det getMatrix gammaF

o17 = 3

o17 : GF 7

i18 : alpha = makeGWuClass(matrix(QQ, {{2,3,1},{3,-1,0},{1,0,0}}), 1)

o18 = (| 2 3  1 |, 1)
       | 3 -1 0 |
       | 1 0  0 |

o18 : UnstableGrothendieckWittClass

i19 : beta = makeGWuClass(matrix(QQ, {{2,3,1},{3,-1,0},{1,0,0}}), 4)

o19 = (| 2 3  1 |, 4)
       | 3 -1 0 |
       | 1 0  0 |

o19 : UnstableGrothendieckWittClass

i20 : isIsomorphicForm(alpha,beta)

o20 = false

i21 : alpha = makeGWuClass(matrix(CC, {{2,3,1},{3,-1,0},{1,0,0}}), 1)

o21 = (| 2 3  1 |, 1)
       | 3 -1 0 |
       | 1 0  0 |

o21 : UnstableGrothendieckWittClass

i22 : beta = makeGWuClass(matrix(CC, {{2,4,-1},{4,5,7},{-1,7,9}}), 1)

o22 = (| 2  4 -1 |, 1)
       | 4  5 7  |
       | -1 7 9  |

o22 : UnstableGrothendieckWittClass

i23 : isIsomorphicForm(alpha,beta)

o23 = true

i24 : 
