Section II.5.1

Quadratic functions

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Problem II.5.1.1

Assuming $2 s \geqslant r>0$ , find the number of classes of equivalent non-central quadratic functions on an $n$ -dimensional real affine space.

Problem II.5.1.2

Find $C(Q)$ for the quadratic function $Q$ over $\mathbb {R}$ of the form

x_{1}^{2}+2 \sum _{1 \leqslant i<j \leqslant n} x_{i} x_{j}+2 \sum _{i=1}^{n} x_{i}+1