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SymPy
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SymPy is an open source python library for symbolic computing. In the SymPy community we all believe in the merits and greatness of the open source approach but for the moment let us focus on the 'symbolic computing' part.
Symbolic computing systems, also called computer algebra systems (CASs) are used in research and engineering for solving a variety of mathematical problems symbolically. In modern labs you will rarely see a researcher solving mundane equations by hand. They usually give them to a computer algebra system to solve so they can spend their time on more interesting and intricate work.
What does it mean to solve problems symbolically? It means that instead of giving a numerical solution, as many systems do, a CAS will derive the solution using symbolic algebra, the same way that you would do it if you were to do it by hand on paper. So if you tell SymPy to solve the equation x2 = 2 for x, it will give you √2 and -√2, exactly.
You can see for examples Quick examples to start to get an idea of the rich set of abstract operations that a CAS supports. Some of the math may be unknown to you but do not be afraid: there is much that you can do for the project that does not involve hard math. You can look also at Wolfram Alpha to see another example of a CAS. This one is more feature complete than SymPy, but proprietary, so the source code is not available to the public. Actually Wolfram Alpha is just one service based on the Mathematica CAS, a popular proprietary CAS.
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