makeGWClass -- the Grothendieck-Witt class of a symmetric matrix

• Usage:

  makeGWClass M

• Inputs:
  • M, a matrix, a non-singular symmetric matrix defined over a field or finite étale algebra of characteristic not 2
• Outputs:
  • a Grothendieck-Witt Class, the isomorphism class of the non-degenerate symmetric bilinear form represented by M

i1 : R = QQ[x]/(x^2 + 1);

i2 : M = matrix(R, {{1,2},{2,x}});

             2      2
o2 : Matrix R  <-- R

i3 : beta = makeGWClass M

o3 = | 1 2 |
     | 2 x |

o3 : GrothendieckWittClass