Kronecker-Algorithm

The algorithm is based on the package galois.m von William Paulsen, cf. Computing Galois Groups with Mathematica.
This package was enlarged by Michael Taktikos and Timm Lampert in order to implement the complete Kronecker algorithm.
It splits polynomials and calculates the dimension of an irreducible polynomial, cf. also: Teo Mora, Solving Polynomial Equation Systems I. The Kronecker-Duval Philosophy, 2003.
By the implementation, one can decide questions of Euclidian geometry, like the possibility to construct polygons, cf. Lecture on Algebra 1 (look at the end).

Enter only rational polynomials (not more than degree 17). The Kronecker-algorithm is only applied in case of irreducible monic polynomials with variable X.

X^4+X^3+X^2+X+1

The result is {input,factorization,dimension}:

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© Timm Lampert / 2014-11-08