![]() ![]() The design decisions of the Ma's are not made openly by the community. One of my favorite quotes from history is Newton: `If I had seen further, it has been by standing on the shoulders of giants.'" Open source is all about the fact that it is open people can actually look at what you are doing, and they can improve it, and they can build on top of it. Traditional software development models, where you keep things inside a company and hide what you are doing, are basically Witchcraft. If you don't spread your ideas in the open, if you don't allow other people to look at how your ideas work and verify that they work, you are not doing Science, you are doing Witchcraft. Linus Torvalds: "I see open source as Science. Everything included in Sage is free and open source, and it will foreover remain that way. Moreover, by browsing the Mercurial repository, you can see exactly who wrote or modified any particular line of code in the Sage library, when they did it, and why. ![]() Returns a solution to a Chinese Remainder Theorem. Sage: crt? # ? = documentation and examples Sage: crt(2, 1, 3, 5) # Chinese Remainder Theorem Indeed, Sage's growth depends on you analyzing how Sage works, improving it, and contributing your improvements back. We want you to know about the internals, and when they are quite complicated, we want you to help make them more understandable. The philosophy espoused in Sage, and indeed by the vast open source software community, is exactly the opposite. For the internals of Mathematica are quite complicated." ![]() But most often the analyses will not be worthwhile. Particularly in more advanced applications of Mathematica, it may sometimes seem worthwhile to try to analyze internal algorithms in order to predict which way of doing a given computation will be the most efficient. Indeed, in almost all practical uses of Mathematica, issues about how Mathematica works inside turn out to be largely irrelevant. The Mathematica Documentation: "You should realize at the outset that while knowing about the internals of Mathematica may be of intellectual interest, it is usually much less important in practice than you might at first suppose. ![]() The Ma's are closed, which means that the implementation of some algorithms are secret, in which case you are not allowed to modify or extend them. The Ma's are not owned by the community like Sage is, or Wikipedia is, for that matter. The culture, architecture, and general look and feel of such a system would be very different than that of the Ma's.Įach of the Ma's cost substantial money, and is hence expensive for me, my collaborators, and students. Development would instead focus on implementing functions that users demand, rather than systematically trying to implement every single function of the Ma's. Thus it need not be like Octave or R, which (nearly) clone the languages of MATLAB and S, respectively. A single alternative to all of the Ma's is not necessarily a drop-in replacement for any of the Ma's in particular, it need not run programs written in the custom languages of those systems. It will have 2d and 3d graphics, an interactive notebook-based graphical user interface, and documentation, including books, papers, school and college curriculum materials, etc. Together there are over 3,000 employees working at the companies that produce the four Ma's listed above, which take in over a hundred million dollars of revenue annually.īy a viable free alternative to the Ma's, we mean a system that will have the important mathematical features of each Ma, with comparable speed. I will refer to the four systems together as ``Ma'' in the rest of this article.) Magma is (by far) the most advanced non-free system for structured abstract algebraic computation, Mathematica and Maple are popular and highly developed systems that shine at symbolic manipulation, and MATLAB is the most popular system for applied numerical mathematics. MATLAB is a registered trademark of MathWorks. Mathematica is a registered trademark of Wolfram Research Incorporated. (Maple is a trademark of Waterloo Maple Inc. The goal of the Sage project is to create a viable fre open source alternative to Magma, Maple(TM), Mathematica(R), and MATLAB(R), which are the most popular non-free closed source mathematical software systems. ![]()
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