In real and complex analysis, the Taylor series expansion is a very important tool. For polynomials over arbitrary unitary rings, it is possible to define a derivative which behaves similar to the usual derivative; unfortunately, the Identity Theorem and Taylor's formula do not transfer to this new situation. Fortunately, there exists a different definition of derivatives for these cases, namely the Hasse derivative. Not only does it gives a Identity Theorem and Taylor's formula back, but also allows to write other identities in a simpler way.

## About Me.

My name is Felix Fontein and I'm currently a software developer at
Dybuster AG. Until February 2014, I used to
be a postdoctoral fellow at the University of
Zurich. I'm working in the area of Computational Number Theory, in particular
on arithmetic in global fields, the infrastructure of such fields, computation of
regulators and fundamental units, and related areas. I studied at
University of Oldenburg and at the
University of Zurich, and was a postdoctoral
fellow at the University of Calgary before
going back to Zurich.

## About This Blog.

This blog focusses on my research as well as other mathematical topics which I
am interested in.

## Overview Pages.

## Categories.

- Algebra (21)
- Analysis (7)
- Complex Analysis (1)

- Beautiful Proofs (3)
- Category Theory (1)
- Cryptography (1)
- General (1)
- Linear Algebra (9)
- Number Theory (11)
- Uncategorized (1)

## Recent Posts.

- Partial Fractions.
- The Probability That Two Numbers Are Coprime.
- The Power of the Distributive Law.
- A Cute Identity.
- Solving Certain Linear Systems over the Integers.
- On a Certain Determinant.
- A Strange Inequality.
- Multiplicity of the Determinant.
- Rigorous Arithmetic in the Arakelov Divisor Class Group of a Number Field.
- Inequalities.

## Archives.

2009 (16)
| |||||||||||||||||||||||||||

2010 (8)
| |||||||||||||||||||||||||||

2011 (3)
| |||||||||||||||||||||||||||

2012 (3)
| |||||||||||||||||||||||||||

## Tags.

baby steps Cayley-Hamliton Chinese Remainder Theorem determinant DLP finite abelian group f-representation function field genus giant steps group functors Hasse derivative Hensel's lemma inequality of arithmetic and geometric mean infrastructure Jordan decomposition Leibniz rule linear system of equations Muirhead's inequality n-dimensional number field one-dimensional Parseval's identity probability of being coprime Rao-Blackwell Theorem reduction Taylor's formula tensor product topological argument universal property