The algorithm of Lang and Frenzel Author: Markus Lang Polynomial Root Finder is a reliable and fast C program (+Matlab gateway) for finding all roots of a complex polynomial. The algorithms of Fox, Lindsey, Burrus, Sitton, and Treitel These algorithms are used to find the roots and unwrapped phase of real coefficient polynomials.

Sage is a free mathematics software system licensed under the GPL. It combines the power of many existing open-source packages into a common Python-based interface. Mission: Creating a viable free open source alternative to Magma, Maple, Mathematica and Matlab.

Abstract: This paper shows how linear algebra can be done better without determinants. The standard proof that a square matrix of complex numbers has an eigenvalue uses determinants. The simpler and clearer proof presented here provides more insight and avoids determinants. Without using determinants, this allows us to define the multiplicity of an eigenvalue and to prove that the number of eigenvalues, counting multiplicities, equals the dimension of the underlying space. Without using determinants, we can define the characteristic and minimal polynomials and then prove that they behave as expected. This leads to an easy proof that every matrix is similar to a nice upper-triangular one. Turning to inner product spaces, and still without mentioning determinants, this paper gives a simple proof of the finite-dimensional spectral theorem.

This paper was published in the American Mathematical Monthly 102 (1995), 139-154.
In 1996 this paper received the Lester R. Ford Award for expository writing from the Mathematical Association of America.

On-line manual for the Maxima Computer Algebra System