WOLFRAM

Wolfram Language

Computation & Analysis

Wolfram Function Repository Highlights: From Country Borders to Bird Speech Bubbles

In June 2019, Stephen Wolfram announced the Wolfram Function Repository, a curated repository of functions that can be employed immediately in the Wolfram Language. Since then, the Repository has grown to include more than 1,000 functions in over 20 categories.

Functions included in the Repository range from those that are more general and utilitarian in nature to others with very specific applications. As with all Wolfram Language functions, Repository documentation pages contain examples showing how to use the functions. We’re featuring a few of the functions submitted to the Repository so far that showcase the variety of functions our users have built.

Announcements & Events

We’re Building Our Own ERP System: Ten Game-Changing Insights We Discovered along the Way

When people think about Wolfram technology, corporate enterprise resource management (ERP) isn't the first thing that comes to mind. It certainly wasn't our first thought when we started searching for a new solution to manage our own accounting, customer service, licensing and HR needs. But after looking at the current ERP offerings, we found that none of the existing buy-in options did what we wanted.

So we thought, why not build our own?

The resulting project has been a revelation. Not only have we built something to our taste, but something fundamentally different: a new architecture, new interfaces, a new approach. Using Wolfram technology has not only made development easier; it has given us a revolutionary new perspective. By leveraging our uniquely powerful technology stack—and integrating it tightly with the existing infrastructure—we're redefining what an ERP system can be.

Education & Academic

New Wolfram Books: Adventures, Lessons and Computations to Spark Your Curiosity

It's been another big year of exploration with the Wolfram Language. CEO Stephen Wolfram's new book takes us on a tour of his computational adventures throughout the years. We're also excited to introduce a Spanish-language version of the popular An Elementary Introduction to the Wolfram Language, as well as books to enhance the mathematics and engineering curricula. There's something new for everyone, from students to lifelong adventurers, to discover with the Wolfram Language. Just in time for the holidays, find the perfect read for those who love learning new things—including yourself!

Adventures of a Computational Explorer

Join Stephen Wolfram as he brings the reader along on some of his most surprising and engaging intellectual adventures, showcasing his own signature way of thinking about an impressive range of subjects. From science consulting for a Hollywood movie, solving problems of AI ethics, hunting for the source of an unusual polyhedron, communicating with extraterrestrials, to finding the fundamental theory of physics and exploring the digits of pi, this lively book of essays captures the infectious energy and curiosity of one of the great pioneers of the computational world.

Announcements & Events

Advanced Computation for Spreadsheets: Wolfram CloudConnector for Excel

Microsoft Excel is among the most popular tools in the world. For non-technical and advanced users aspiring to extend beyond Excel's built-in feature set, we're proud to announce the easiest and most productive tool for doing so: Wolfram CloudConnector for Excel, now available to anyone running Excel on a Windows system. You can access the advanced computational power of the Wolfram Language for your data directly from your spreadsheets.

Computation & Analysis

Embracing Uncertainty: Better Model Selection with Bayesian Linear Regression

Readers who follow the Mathematica Stack Exchange (which I highly recommend to any Wolfram Language user) may have seen this post recently, in which I showed a function I wrote to make Bayesian linear regression easy to do. After finishing that function, I have been playing around with it to get a better feel of what it can do, and how it compares against regular fitting algorithms such as those used by Fit. In this blog post, I don’t want to focus too much on the underlying technicalities (check out my previous blog post to learn more about Bayesian neural network regression); rather, I will show you some of the practical applications and interpretations of Bayesian regression, and share some of the surprising results you can get from it.

Current Events & History

Spherical Aberration Optics Problem Finally Solved Using the Wolfram Language

Solving a 2,000-Year-Old Mystery

It’s not every day that a 2,000-year-old optics problem is solved. However, Rafael G. González-Acuña, a doctoral student at Tecnológico de Monterrey, set his sights on solving such a problem—spherical aberration in lenses. How can light rays focus on a single point, taking into account differing refraction? It was a problem that, according to Christiaan Huygens back in 1690, even Isaac Newton and Gottfried Leibniz couldn’t sort out, and was formulated two millennia ago in Greek mathematician Diocles’s work, On Burning Mirrors.

But González-Acuña and his colleagues realized that today, they had the use of the Wolfram Language and its computational tools to solve this age-old problem. The result? A breakthrough publication that outlines an analytical solution to why and how lensed images are sharper in the center than at the edges, with 99.999999999% accuracy simulating 500 light beams.

As it happens, González-Acuña was recently at the Wolfram Summer School, and we had the opportunity to ask him a little bit about his work.

Computation & Analysis

Taking the Cerne Abbas Walk: From Conceptual Art to Computational Art

Cerne Abbas Walk is an artwork by Richard Long, in the collection of the Tate Modern in London and on display at the time of this writing. Several of Long’s works involve geographic representations of his walks, some abstract and some concrete. Cerne Abbas Walk is described by the artist as “a six-day walk over all roads, lanes and double tracks inside a six-mile-wide circle centred on the Giant of Cerne Abbas.” The Tate catalog notes that “the map shows his route, retracing and re-crossing many roads to stay within a predetermined circle.”

The Giant in question is a 180-foot-high chalk figure carved into a hill near the village of Cerne Abbas in South West England. Some archaeologists believe it to be of Iron Age pedigree, some think it to date from the Roman or subsequent Saxon periods and yet others find the bulk of evidence to indicate a 17th-century origin as a political satire. (I find the last theory to be both the most amusing and the most convincing.)

I found the geographic premise of Cerne Abbas Walk intriguing, so I decided to replicate it computationally.

Computation & Analysis

The Ultimate Team Generator with the Wolfram Language

Every summer, I play in a recreational Ultimate Frisbee league—just “Ultimate” to those who play. It’s a fun, relaxed, coed league where I tend to win more friends than games.

The league is organized by volunteers, and one year, my friend and teammate Nate was volunteered to coordinate it. A couple weeks before the start of the season, Nate came to me with some desperation in his voice over making the teams. The league allows each player to request to play with up to eight other players—disparagingly referred to as their “baggage.” And Nate discovered that with over 100 players in a league, each one requesting a different combination of teammates, creating teams that would please everyone seemed to become more complicated by the minute.

Luckily for him, the Wolfram Language has a suite of graph and network tools for things like social media. I recognized that this seemingly overwhelming problem was actually a fairly simple graph problem. I asked Nate for the data, spent an evening working in a notebook and sent him the teams that night.

Education & Academic

Building Uniform Polyhedra for Version 12

Since I started working at Wolfram, I’ve been a part of several different projects. For Version 12, my main focus was replicating models of the uniform polyhedra with the Wolfram Language to ensure that the data fulfilled certain criteria to make our models precise, including exact coordinates, consistent face orientation and a closed region in order to create a proper mesh model of each solid.

Working with visual models of polyhedra is one thing, but analyzing them mathematically proved to be much more challenging. Starting with reference models of the polyhedra, I found that the Wolfram Language made mathematical analysis of uniform polyhedra particularly efficient and easy.

But first, what really are polyhedra, and why should we care? With Version 12, we can explore what polyhedra are and how they’ve earned their continued place in our imaginations.