sym_arrow

C++ library for symbolic differentiation. Sym_arrow provides only basic algebraic capabilities but instead is concentraced on calculating symbolic derivatives of expressions as fast as possible.

Code example

A complete C++ program that computes (not normalized) Laguerre Polynomials and the associated Laguerre Polynomials.

#include "sym_arrow/sym_arrow.h"

using namespace sym_arrow;

// Laguerre Polynomial L_n(x) == exp(x) * (d/dx)^n [x^n * exp(-x)]
expr laguerre_poly(int n, const symbol & x)
{
    expr ker    = exp(-x);
    expr poly   = power_int(x, n) * ker;
    return diff(poly, x, n) / ker;
}

// associated Laguerre Polynomial L_{n,m}(x) == (d/dx)^m [L_n(x)]
expr assoc_laguerre_poly(int n, int m, const symbol & x)
{
    expr poly   = laguerre_poly(n, x);
    poly        = simplify(poly);
    return diff(poly, x, m);
}
void example()
{    
    tic();

    expr poly   = assoc_laguerre_poly(100, 100, symbol("x"));

    tocdisp();
};

Output:
Elapsed time is 0.003435 seconds.

For comparison Matlab needs 19.047018 sec to compute this polynomial, over 5500 times longer.

Licence

Copyright (C) 2017 Paweł Kowal

This library is published under GPL licence.