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6.48.8  Characteristic polynomial using Hessenberg algorithm: pcar_hessenberg

The pcar_hessenberg command finds the characteristic polynomial of a matrix. It computes the polynomial using the Hessenberg algorithm (see e.g. Henri Cohen, A Course in Computational Algebraic Number Theory) which is more efficient (O(n3) deterministic) if the coefficients of the matrix are in a finite field or use a finite representation like approximate numeric coefficients. Note however that this algorithm behaves badly if the coefficients are, for example, in ℚ.


Examples.


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