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Free (rational) Derivation
Konrad Schrempf
By representing elements in free fields (over a commutative field and a finite alphabet) using Cohn and Reutenauer's linear representations, we provide an algorithmic construction…
Horner Systems: How to efficiently evaluate non-commutative polynomials (by matrices)
Konrad Schrempf
By viewing non-commutative polynomials, that is, elements in free associative algebras, in terms of linear representations, we generalize Horner's rule to the non-commutative (mult…
Free Fractions: An Invitation to (applied) Free Fields
Konrad Schrempf
Long before we learn to construct the field of rational numbers (out of the ring of integers) at university, we learn how to calculate with fractions at school. When it comes to "n…
A Standard Form in (some) Free Fields: How to construct Minimal Linear Representations
Konrad Schrempf
We describe a standard form for the elements in the universal field of fractions of free associative algebras (over a commutative field). It is a special version of the normal form…