Using SymbolicC++ to solve systems of equations symbolically
<p>I am looking for a way to programmatically solve systems of (not necessarily linear) equations, symbolically. My main focus has been on SymbolicC++, but I was unable to find much documentation, and I am unable to get it working.</p>

<p>The code below yields <code>a == 1/2*(-4*b^(2)+4*c^(2))^(1/2)</code>, which is clearly not simplified properly (I even explicitly call <code>simplify</code>.) :</p>

<pre><code>#include &lt;symbolicc++.h&gt;
#include &lt;iostream&gt;

int main()
{
    Symbolic a("a");
    Symbolic b("b");
    Symbolic c("c");

    auto eq1 = (a^2) + (b^2) == (c^2);
    auto solutions = solve(eq1, a);

    for (auto i = solutions.begin(); i != solutions.end(); i++)
        std::cout &lt;&lt; (*i).simplify() &lt;&lt; std::endl;
}
</code></pre>

<p>The code below is supposed to yield among many solutions <code>a==2, b==2, c==2, d==2</code> and <code>a == 5-2*sqrt(6), b == 5+2*sqrt(6), c == 5-2*sqrt(6), d == 5+2*sqrt(6)</code> but instead encounters the following exception after executing for about 10 seconds:</p>

<blockquote>
  <p>Unhandled exception at 0x73203D5C (vcruntime140.dll) in test.exe: 0xC0000005: Access violation reading location 0x00000018.</p>
</blockquote>

<pre><code>#include &lt;symbolicc++.h&gt;
#include &lt;iostream&gt;

int main()
{
    Symbolic a("a");
    Symbolic b("b");
    Symbolic c("c");
    Symbolic d("d");

    auto eq1 = a + b*c*d == 10;
    auto eq2 = b + a*c*d == 10;
    auto eq3 = c + a*b*d == 10;
    auto eq4 = d + a*b*c == 10;
    auto eq = (eq1, eq2, eq3, eq4);
    auto solutions = solve(eq, (a, b, c, d));

    for (auto i = solutions.begin(); i != solutions.end(); i++)
        std::cout &lt;&lt; *i &lt;&lt; std::endl;
}
</code></pre>

<p>(I used Visual Studio to compile the library.)</p>

<p>My test equations seem to be solvable, since WolframAlpha solves them with ease. (I just used <code>solve a^2+b^2 = c^2 for a</code> and <code>solve a+bcd=10, b+acd=10, c+abd=10, d+abc=10</code>.)</p>

<p>Am I doing something wrong? What do I need to get these examples to work correctly?</p>

<p><em>Notes about other libraries:</em><br>
If possible, I would like to compile the library to ARM systems (Windows Phone). As far as I can tell, only C++ and .NET libraries come into play. Since currently I use MSVC to compile SymbolicC++ anyway, I think cross-compiling it to WP won't be a problem.</p>

<p><em>Notes about sympy:</em><br>
The code below throws <code>ZeroDivisionError</code> with the message <code>polynomial division</code>. Since it does not really fit my portability needs anyway, I just gave up on it.</p>

<pre><code>import sympy.solvers
from sympy import Equality
from sympy.abc import a, b, c, d
equations = [ Equality(a + b*c*d, 10), Equality(b + a*c*d, 10), Equality(c + a*b*d, 10), Equality(d + a*b*c, 10) ]
print sympy.solvers.solve(equations, [a, b, c, d])
</code></pre>