Cadabra handles tensor polynomial simplifications very effectively by utilizing Bianchi and Schouten identities and can also be used for fermions and anti-commuting variables, Clifford algebras, Fierz transformations, and many other problems. Get Cadabra. Wolfram Mathematica is a modern-day computer algebra system that encompasses most areas of technical computing, including geometry, data science , visualizations, neural networks, image processing, and such.
It is used very widely by both researchers and professionals for a broad spectrum of tasks. Although very powerful, Wolfram Mathematica is not free and requires a paid license before using it for your research. It supports thousands of mathematical functions, real-time data, natural language input, and many more exciting features. Features of Wolfram Mathematica. Get Wolfram Mathematica. Magma is a robust computer algebra system that combines advanced numerical computing features seamlessly with an easy-to-use yet effective user interface.
It has widespread usage in the fields of pure mathematics and is featured extensively in research. Magma can handle several types of problems associated with the areas of algebra, number theory, algebraic geometry, and algebraic combinatorics. It is distributed by the University of Sydney and comes with a non-commercial proprietary license. Get Magma. Reduce is a robust computer algebra system aimed at physics researchers.
It offers an extensive list of features that make it a suitable choice for anyone handling complex physics problems. It comes under the BSD license, enabling developers to extend the software any way they like and distribute it. Reduce has been under development since the 60s and is used in physics labs around the world. However, the growth seems to slow down, and the last stable release saw the light eight years back.
Get Reduce. Number theory plays a significant role in modern computing, and there are numerous applications of this growing field. It comes with a broad set of advanced function implementations alongside the more traditional ones and can be used extensively by both number theory researchers and computer scientists alike. GAP is a powerful open-source system for solving computational discrete algebra problems.
It is an exciting platform that combines features from the best computer algebra systems with a high-level, intuitive, and convenient programming language. GAP can tackle different types of discrete mathematical problems but emphasizes heavily computational Group theory.
The default library is quite extensive and features more than thousands of function implementations right out of the box. Get GAP. SMath Studio is a free, cross-platform computer algebra system for Linux.
It is written using the C programming language and supports almost every major operating system. It also has added support for the Android and iOS smartphone platform alongside some handheld devices. Get SMath Studio. Axiom is a general-purpose computer algebra system that has widespread usage in different types of computational tasks. It can be used for either academic research purposes or for developing complex, modern-day mathematical algorithms. Axiom emphasizes a strongly typed, mathematically correct type hierarchy that ensures maximum optimization boost for your algorithms.
Axiom features a modified BSD license that enables researchers to extend the software to meet customized demands. Get Axiom. It is a lightweight interactive system that offers a number of powerful features for making commutative algebra computations easier than ever. Get CoCoA. Yacas, short for Yet Another Computer Algebra System , is a general-purpose computer algebra system that can effectively perform a wide range of numeric and symbolic mathematical calculations.
It comes pre-equipped with its own programming language, which provides a high-level abstraction of the underlying complex mathematical expressions. It can compute arbitrary-precision numerical computations with exact results and offers powerful plotting capabilities for efficient data visualization and analysis.
Get Yacas. FriCAS is an advanced computer algebra system built on top of Axiom. It offers a self-contained toolbox used in a number of different mathematical computations ranging from traditional calculus to geometric algebra.
The browser-based interactive shell called Notebook has the ability to remember previous inputs and outputs for review and reuse. SageMath is a relatively new tool with most of the development being done using Python; the initial release came out in Figure 5 shows the logo of SageMath.
R is a mathematical tool mainly used for statistical computing. It is used by mathematicians in general and by statisticians in particular for data mining and developing statistical software. R is a cross-platform tool that can be used in various operating systems like Linux, Microsoft Windows, etc.
But R being freely available is not the main reason for its widespread adoption by the statistical community; rather, its popularity is based on its power. R can be used as a command line utility as well as with a graphical user interface GUI. R is also capable of performing various graphical techniques.
While choosing ten useful mathematical tools for this article, we made sure that what we selected is used in diverse fields of mathematics, rather than choosing ten popular software from a single field, like numerical computations, for instance.
So, this tool may not be as popular as many other mathematical this tools left out from this list. Let us clarify further—the general public is familiar with numerical computing tools like MATLAB, Scilab, etc, but may not be aware of SageMath or Maxima because the latter two are mostly used in the more abstract areas of mathematics like combinatorics, graph theory, number theory, etc.
Mathematics itself is often considered an abstract subject — sometimes even by famous mathematicians. Not many people are interested in automatic-theorem proving, but for the select few who work in this area, a tool to aid their quest will be like a gift from heaven.
So, with that rationale, we introduce Isabelle, an interactive theorem-proving software. It is free, open source and available for use under the BSD licence. Isabelle has been developed by using two programming languages, ML and Scala. It can be used to encode first-order logic, higher-order logic, etc, for further processing. Figure 7 shows the logo of Isabelle.
SciPy is an open source Python library used for scientific computing. It contains modules for optimisation, linear algebra, calculus, interpolation, Fast Fourier Transforms, signal processing, image processing, etc. Matplotlib is a plotting library and SymPy is a library for symbolic computing in Python. Figure 8 shows how SciPy is used to find the factorial of Even in a modest computer system, we were able to find the factorial of , But we will not dare to show the output in this article because the resulting number is digits long.
The page we randomly chose in that issue had 54 lines of text and the line we randomly chose had characters, so, a simple calculation will tell you that it will take at least 68 pages of the next issue of OSFY to print this number. This tells us about the power of SciPy. And with a powerful computer, you could do wonders with SciPy. Scientific research involves representing data in a neat and concise manner.
Graphs are often used to do this. It is frequently used in vector graphics. In fact, the inclusion of gnuplot in this list can be contested because, in a very strict sense, it is not free and open source software because it is licensed under the gnuplot licence, which gives users the right to modify the source code but the right to distribute modified versions is withheld.
But the extreme popularity of gnuplot made us select it rather than a free and open source graph plotting utility like xgraph. Some would actually argue that LibreOffice is the more fully-featured of the two, thanks to its dedicated developer community which is adding new tools and tricks all the time.
For example, in the latest update, LibreOffice added a QR code generator tool so you can quickly create mobile-friendly links. An alternative well-known open source office tool is Open Office, which offers many similar features to LibreOffice. The reason that LibreOffice has taken the top spot today is that it is much better at preserving Microsoft file formats.
The only downside to this awesome free office software is that editing documents collaboratively online is a bit tricky. Recently, an online editing option has been added but it still requires some technical know-how to implement. Read our full LibreOffice review.
You can use VLC media player to open audio and video files in just about any format without having to hunt down extra codecs. VLC also works for streaming media such as podcasts and online radio stations. But perhaps the greatest VLC media player feature is playback control. You can change almost everything about how your media is displayed from hardware optimization to adding subtitle files from third-party sources.
Like some of the other amazing open source offerings mentioned here, VLC is constantly being upgraded with new goodies and features to explore. The latest updates to the free video player have included the ability to stream to other devices like Chromecasts and degree video support for VR headsets. Beloved by Linux users since its original release in , GIMP is one of the most famous and best-maintained open source software tools out there.
GIMP has built-in support for layers, filters, and automatic photo enhancement. It also makes it easy to create new graphic design elements and you can really take things to the next level by downloading plug-ins created by the broader GIMP open source community. Just like Photoshop, GIMP has a fairly steep learning curve but anyone who puts in a bit of time is sure to appreciate its customizable interface and GPU hardware acceleration. NET instead. Read our full GIMP review.
Shotcut is open source free video editing software. In earlier versions, the Shotcut interface was a little bare, but later releases have added extra dockable panels, an intuitive timeline, and other touches that put Shotcut in the same league as premium video editors like Adobe Premiere Pro.
This video tool supports non-destructive audio and video editing, meaning you can compile effects without any quality loss. You can also use this platform to do color keying and grading operations, as well as more basic clip splicing and trimming.
Perhaps the coolest thing about Shotcut is its ability to work with more or less any format of video, audio, or photo media. Read our full Shotcut review. For even more secure browsing, it has a built-in Tor function.
Another interesting thing about the Brave browser is something called Brave Rewards.
0コメント