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Algebraic and geometric theory of quadratic forms and symmetric bilinear forms, e.g., values attained by quadratic forms, isotropic subspaces, the Witt ring, invariants of quadratic forms, the discriminant and Clifford algebra of a quadratic form, Pfister forms, automorphisms of quadratic forms.

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orbits of automorphism group for indefinite lattices

There's a simple criterion for equivalence of two vectors in a lattice if the lattice contains two copies of the hyperbolic plane: you look at the length of the vector and its image in the discriminan …
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