Relativistic energy by Ciro Santilli 35 Updated +Created
vader.vim by Ciro Santilli 35 Updated +Created
Eclipse (IDE) by Ciro Santilli 35 Updated +Created
Once upon a time (early 2010's), Eclipse dominated the IDE landscape and all was good. NetBeans was around too. And Java was still unmarred by Google LLC v. Oracle America, Inc..
But then something happened.
For some reason, Eclipse started to decay.
And the project that had once been a vibrant community of awesomeness, started to become... a zombie of its former self.
Buggyness started increasing. And not even hard to fix bugs. One liners that affect every user immediately after startup.
Sometimes, to Eclipse's defense they weren't "bugs". Just features that it became evident with time every programmer expected from a modern IDE.
But somehow the Eclipse community had a deep problem. A cancer. It had completely lost touch with user experience.
Perhaps is was due to the increasing interest of the several corporations that had adopted Eclipse as the base IDE for the proprietary solutions?
Perhaps.
Many users stuck to the IDE.
Some heroic efforts were made as plugins that drastically improved certain defects. The Darkest Dark plugin comes to mind.
But all those efforts required configuration. A setup time that most users simply don't have. The core devteam had become dumb and dead, unable to incorporate such changes.
This greatly opened up the space for other competing IDEs to come along. The "semi feature complete but at least easy to use and not so buggy" Visual Studio Code and the proprietary JetBrains IDEs being some of the most notable ones.
Using Eclipse as of the early 2020's is such a mixed experience. If you spend enough time to configure out the key buggyness, there are moments where you can feel "OMG, this feature is amazing".
But the effort is just too great, and soon another bug or obvious missing feature hits you and brings you back to reality.
Every young person uses VS Code now. Eclipse is dead, and there is no way back, usage will just continue dropping.
RIP, Eclipse. It wasn't meant to be.
Figure 1.
Eclipse. usage from 2012 to 2016 according to a JRebel survey
. Source.
JetBrains by Ciro Santilli 35 Updated +Created
Tests of general relativity by Ciro Santilli 35 Updated +Created
Holomorphic function by Ciro Santilli 35 Updated +Created
Being a complex holomorphic function is an extremely strong condition.
The existence of the first derivative implies the existence of all derivatives.
Another extremely strong consequence is the identity theorem.
"Holos" means "entire" in Greek, so maybe this is a reference to the fact that due to the identity theorem, knowing the function on a small open ball implies knowing the function everywhere.
Denominator by Ciro Santilli 35 Updated +Created
Matrix representation of a bilinear form by Ciro Santilli 35 Updated +Created
As usual, it is useful to think about how a bilinear form looks like in terms of vectors and matrices.
Unlike a linear form, which was a vector, because it has two inputs, the bilinear form is represented by a matrix which encodes the value for each possible pair of basis vectors.
In terms of that matrix, the form is then given by:

Pinned article: ourbigbook/introduction-to-the-ourbigbook-project

Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
We have two killer features:
  1. topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculus
    Articles of different users are sorted by upvote within each article page. This feature is a bit like:
    • a Wikipedia where each user can have their own version of each article
    • a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
    This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.
    Figure 1.
    Screenshot of the "Derivative" topic page
    . View it live at: ourbigbook.com/go/topic/derivative
  2. local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:
    This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
    Figure 5. . You can also edit articles on the Web editor without installing anything locally.
    Video 3.
    Edit locally and publish demo
    . Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension.
  3. https://raw.githubusercontent.com/ourbigbook/ourbigbook-media/master/feature/x/hilbert-space-arrow.png
  4. Infinitely deep tables of contents:
    Figure 6.
    Dynamic article tree with infinitely deep table of contents
    .
    Descendant pages can also show up as toplevel e.g.: ourbigbook.com/cirosantilli/chordate-subclade
All our software is open source and hosted at: github.com/ourbigbook/ourbigbook
Further documentation can be found at: docs.ourbigbook.com
Feel free to reach our to us for any help or suggestions: docs.ourbigbook.com/#contact