https://dhoekstra.xyz/Recent content on Douwe HoekstraHugoen-gbWed, 13 May 2026 00:00:00 +0200https://dhoekstra.xyz/posts/the-boring-internet/Wed, 13 May 2026 00:00:00 +0200https://dhoekstra.xyz/posts/the-boring-internet/<p>A few days ago I read the essay <a href="https://www.terrygodier.com/the-boring-internet">The Boring Internet</a> by Terry Godier. This essay really resonated with me and reminded me of appeal that old school internet technologies always have had on me. I will share some of my thoughts on the essay here.</p>https://dhoekstra.xyz/posts/basis-of-pure-monomials/Thu, 30 Apr 2026 00:00:00 +0200https://dhoekstra.xyz/posts/basis-of-pure-monomials/<p>For of my research projects, I needed to decompose a multivariate polynomial into a linear combination of so-called <em>pure</em> monomials. These are monomials of the form \(\lambda^r\) where \(\lambda\) is some linear form. I had never read the proof that such a basis exists, but it turned out that the proof is quite neat, so I decided to write a short exposition of this proof here (mainly for my own reference). This is based on parts of the first two chapters of (<a href="#citeproc_bib_item_2">Reznick 1992</a>).</p>https://dhoekstra.xyz/posts/hello/Fri, 03 Apr 2026 00:00:00 +0000https://dhoekstra.xyz/posts/hello/<p>Hello world! Welcome to my blog. In this first post I will tell a bit about the changes to my website (spoiler! It has a blog now), and what I may (or may not) write about here.</p> <p>Over the past few days I have been using my evening hours to work on my website (a little hobby project, so you will). If you have visited my site before some of the changes are probably clear: The colour theme changed, the styling is updated and it comes with a blog now.</p>