Geodesic
A computation of the characteristic polynomial of an endomorphism of a~free module
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part IV, Tome 258 (1999), pp. 101-114

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Two methods are given for computation of the characteristic polynomial of an endomorphism of a free module over a commutative domain, that require $O(n^3)$ and $O(n^{\log7})$ ring operations. 
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     author = {G. I. Malashonok},
     title = {A computation of the characteristic polynomial of an endomorphism of a~free module},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {101--114},
     publisher = {mathdoc},
     volume = {258},
     year = {1999},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1999_258_a4/}
}
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G. I. Malashonok. A computation of the characteristic polynomial of an endomorphism of a~free module. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part IV, Tome 258 (1999), pp. 101-114. http://geodesic.mathdoc.fr/item/ZNSL_1999_258_a4/