November 9, 2017 — Devendra Kapadia, Kernel Developer, Algorithms R&D

Limits lead image

Here are 10 terms in a sequence:

Table[(2/(2 n + 1)) ((2 n)!!/(2 n - 1)!!)^2, {n, 10}]

And here’s what their numerical values are:

N[%]

But what is the limit of the sequence? What would one get if one continued the sequence forever?

In Mathematica and the Wolfram Language, there’s a function to compute that:

DiscreteLimit[(2/(2 n + 1)) ((2 n)!!/(2 n - 1)!!)^2, n -> \[Infinity]]

Limits are a central concept in many areas, including number theory, geometry and computational complexity. They’re also at the heart of calculus, not least since they’re used to define the very notions of derivatives and integrals.

Mathematica and the Wolfram Language have always had capabilities for computing limits; in Version 11.2, they’ve been dramatically expanded. We’ve leveraged many areas of the Wolfram Language to achieve this, and we’ve invented some completely new algorithms too. And to make sure we’ve covered what people want, we’ve sampled over a million limits from Wolfram|Alpha.

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November 8, 2017 — Christopher Carlson, Senior User Interface Developer, User Interfaces

The One-Liner Competition is a tradition at our annual Wolfram Technology Conference, which took place at our headquarters in Champaign, Illinois, two weeks ago. We challenge attendees to show us the most impressive effects they can achieve with 128 characters or fewer of Wolfram Language code. We are never disappointed, and often surprised by what they show us can be done with the language we work so hard to develop—the language we think is the world’s most powerful and fun.

Melting flags

This year’s winning submissions included melting flags, computer vision and poetry. Read on to see how far you can go with just a few characters of Wolfram Language code…

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