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Derivatives of symplectic spectral functions
A symplectic spectral function of a $2n \times 2n$ real positive definite matrix $A$ is a function of its symplectic eigenvalues $0< d_1(A) \leq \cdots \leq d_n(A)$, which is given by a composition $f \circ d$ of some symmetric function $f$ on the set of $n$-vectors with positive entries and the sym
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