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Fractional Calculus in Wolfram Language 13.1

What is the half-derivative of x?

Fractional calculus studies the extension of derivatives and integrals to such fractional orders, along with methods of solving differential equations involving these fractional-order derivatives and integrals. This branch is becoming more and more popular in fluid dynamics, control theory, signal processing and other areas. Realizing the importance and potential of this topic, we have added support for fractional derivatives and integrals in the recent release of Version 13.1 of the Wolfram Language.
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Launching Version 13.1 of Wolfram Language & Mathematica 🙀🤠🥳

The Epic Continues…

Last week it was 34 years since the original launch of Mathematica and what’s now the Wolfram Language. And through all those years we’ve energetically continued building further and further, adding ever more capabilities, and steadily extending the domain of the computational paradigm.

In recent years we’ve established something of a rhythm, delivering the fruits of our development efforts roughly twice a year. We released Version 13.0 on December 13, 2021. And now, roughly six months later, we’re releasing Version 13.1. As usual, even though it’s a “.1” release, it’s got a lot of new (and updated) functionality, some of which we’ve worked on for many years but finally now brought to fruition.

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New in 13: Geometric Computation

Two years ago we released Version 12.0 of the Wolfram Language. Here are the updates in geometric computation since then, including the latest features in 13.0. The contents of this post are compiled from Stephen Wolfram's Release Announcements for 12.1, 12.2, 12.3 and 13.0.

 

Euclidean Geometry Goes Interactive (December 2020)

One of the major advances in Version 12.0 was the introduction of a symbolic representation for Euclidean geometry: you specify a symbolic GeometricScene, giving a variety of objects and constraints, and the Wolfram Language can “solve” it, and draw a diagram of a random instance that satisfies the constraints. In Version 12.2 we’ve made this interactive, so you can move the points in the diagram around, and everything will (if possible) interactively be rearranged so as to maintain the constraints.

Here's a random instance of a simple geometric scene:

Announcements & Events

New in 13: Cloud & Webpage Construction

Two years ago we released Version 12.0 of the Wolfram Language. Here are the updates in cloud and webpage construction since then, including the latest features in 13.0. The contents of this post are compiled from Stephen Wolfram's Release Announcements for 12.1, 12.2, 12.3 and 13.0.

 

WSTPServer: A New Deployment of Wolfram Engine (December 2020)

Our long-term goal is to make the Wolfram Language and the computational intelligence it provides as ubiquitous as possible. And part of doing this is to set up the Wolfram Engine which implements the language so that it can be deployed in as broad a range of computational infrastructure settings as possible.

Wolfram Desktop—as well as classic Mathematica—primarily provides a notebook interface to the Wolfram Engine, running on a local desktop system. It's also possible to run Wolfram Engine directly—as a command-line program (e.g. through WolframScript)—on a local computer system. And, of course, one can run the Wolfram Engine in the cloud, either through the full Wolfram Cloud (public or private), or through more lightweight cloud and server offerings (both existing and forthcoming).
Announcements & Events

New in 13: Data & Function Repositories

Two years ago we released Version 12.0 of the Wolfram Language. Here are the updates to the Data and Function Repositories since then, including the latest features in 13.0. The contents of this post are compiled from Stephen Wolfram's Release Announcements for 12.1, 12.2, 12.3 and 13.0.

 

Making the Data Repository Easy (March 2020)

We launched the Wolfram Function Repository in June 2019, and there are already 1146 functions published in it. One of the innovations in the Function Repository is a very streamlined process for submitting new functions, applicable both for the public Function Repository, and for individual deployment on a single machine, or in the cloud.
Announcements & Events

New in 13: Molecules & Biomolecular Sequences

Two years ago we released Version 12.0 of the Wolfram Language. Here are the updates in molecules and biomolecular sequences since then, including the latest features in 13.0. The contents of this post are compiled from Stephen Wolfram's Release Announcements for 12.1, 12.2, 12.3 and 13.0.

 

What Is That Molecule? Advances in Chemical Computation (March 2020)

You have an image of a molecular structure diagram, say from a paper. But how can you get the molecule it represents in a computable form? Well, with Version 12.1 all you need do is use MoleculeRecognize:
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New in 13: Trees

Two years ago we released Version 12.0 of the Wolfram Language. Here are the updates in trees since then, including the latest features in 13.0. The contents of this post are compiled from Stephen Wolfram's Release Announcements for 12.1, 12.2, 12.3 and 13.0.

 

Trees! (May 2021)

Based on the number of new built-in functions the clear winner for the largest new framework in Version 12.3 is the one for trees. We’ve been able to handle trees as a special case of graphs for more than a decade (and of course all symbolic expressions in the Wolfram Language are ultimately represented as trees). But in Version 12.3 we’re introducing trees as first-class objects in the system.
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New in 13: Symbolic & Numeric Computation

Math is big, and math is important. And for the Wolfram Language (which also means for Mathematica) we’re always pushing the frontiers of what’s computable in math.

One long-term story has to do with special functions. Back in Version 1.0 we already had 70 special functions.

Announcements & Events

New in 13: Notebook Interfaces

An important feature of Wolfram Notebooks is that they’re set up to operate both on the desktop and in the cloud. And even between versions of Wolfram Language there’s lots of continued enhancement in the way notebooks work in the cloud. But in Version 12.2 there’s been some particular streamlining of the interface for notebooks between desktop and cloud.