symbolic computation in C++

Question

I need to do analytical integration in C++. For example, I should integrate expressions like this: exp[I(x-y)], I is an imaginary number.

How can I do this in C++?

I tried GiNaC but it can just integrate polynomials. I also tried SymbolicC++. It can integrate functions like sine, cosine or exp(x) and ln(x), but it is not very powerful. For example, it can not integrate x*ln(x) which can be easily obtained by use of Mathematica or by integration by parts.

Are there any other tools or libraries which are able to do symbolic computation like analytical integration in C++?

Answer 1

If you need to do symbolic integration, then you're probably not going to get anything faster than running it in mathematica or maxima - they're already written in (something like) C++. So unless your equations have a very specific formulae that you can exploit in a way that Mathematica or Maxima can not then you're probably out of luck -- and at very least you're not going to get that kind of custom manipulation from an off-the-shelf library.

You may be justified in writing your own code to get a speed boost if you needed to do numerical solutions. ( I know that I did for generating numerical solutions to PDEs).

Answer 2

The other C++ libraries I am aware of that do symbolic computation are

• SymEngine (https://github.com/symengine/symengine)
• Piranha (https://github.com/bluescarni/piranha)

If I am not mistaken, SymEngine does not yet support integration; however, Piranha does. The documentation for Piranha is somewhat limited at the moment and is under development, but you can see the integration function here. Note that the second link uses the syntax for the Python wrapper Piranha. However, Piranha "is a computer-algebra library for the symbolic manipulation of sparse multivariate polynomials and other closely-related symbolic objects (such as Poisson series)", so I do not think it can integrate the particular functions in which you may be interested.

Though it is not C++, you may also be interested in SymPy for Python, which can perform some of the more complicated symbolic integration you may be interested in. The documentation for SymPy's integrate is here.

Answer 3

A couple of days ago, I was searching for a symbolic math library like SymPy for C++, because I bedazzled by its speed comparing to Python or most of the other programming languages.

I found Vienna Math Library, an awesome library with very modern syntax, and SymPy's features to the best of my knowledge. This library also has an integral function that can be used for your problem.

It was good enough for solving IK (Inverse Kinematics) of 3 degrees of freedom articulated manipulator.