Symbolic math lib

Question

I have a planned project that will need to manipulate symbolic expressions like:

a * b = c^2 + sin(d)

I'm wondering what libs are out there for this kind of thing.

Two that I found a while ago are openaxiom and FriCAS. neither of these seem like a good fit. An ideal lib would be a light as possible. At a minimum it must be able to define expressions as some type of data structure and, once values are assigned to the variables, evaluate expressions. I would prefer that it have as many of the following as possible:

• tools to transform expressions and ensure that the transformations are algebraically valid.
• tools to perform differentiation
• tools to parse expressions from text
• have some form of re-wright rule engine
• be able to "compile" expressions for fast execution
• emit C code that equates to execution
• emit ASM for the same

C linkage is a major boon but C++ would do, other options (C#,lisp) might work but are way less desirable

Answer 1

Checkout the AXIOM library, I don't know that it is exactly what you want... but it looks reasonable.

Answer 2

I know you're looking for C, but...

Sympy is a truly amazing Python library. One of the great things about it is how effortless it is: operator overloading automatically changes normal operators and functions into symbolic computations. It's got a very active user community, a lot of features, and Python is really easy to interface with from C.

Answer 3

In the spirit of earlier posters you could look at Wikipedia's Comparison of computer algebra systems, though there is no information on the page just now about programatic interfaces and/or bindings.

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I take it back. Some of the notes are useful this way. It seem that GiNaC is a C++ library. A bunch of them are in the form of Java or Python libraries.

Answer 4

Maybe this is helpful:

The Spirit framework enables a target grammar to be written exclusively in C++. Inline EBNF grammar specifications can mix freely with other C++ code and, thanks to the generative power of C++ templates, are immediately executable.

As introduction example they build a basic calculator. Seems quite the thing you are looking for.