Mathematica++¶

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symbol x("x");
value  res;
std::string method = "Newton";

shell << Values(FindRoot(ArcTan(1000 * Cos(x)), List(x, 1, 2),  Rule("Method") = method));
shell >> res;
std::vector<double> results = cast<std::vector<double>>(res);
std::cout << results[0] << std::endl; // Prints 10.9956

A C++ Library that talks Mathematica¶

Dot product and Determinant calculation in Mathematica Language

mata = Table[Mod[i + j, 2], {i, 1, 2}, {j, 1, 2}];
matb = Table[Mod[i + j, 3], {i, 1, 2}, {j, 1, 2}];
matc = Dot[mata, matb];
matd = Det[matc];

Equivalent C++ code with Mathematica++

mathematica::m mata = Table(Mod(i + j, 2), List(i, 1, 2), List(j, 1, 2));
mathematica::m matb = Table(Mod(i + j, 3), List(i, 1, 2), List(j, 1, 2)];
mathematica::m matc = Dot(mata, matb);
mathematica::m matd = Det(matc);

// Execute mathematica constructs and fetch the response
shell << matd;
shell >> determinant;

// determinant can be converted to C++ machine sized types
std::cout << determinant << std::endl; // Prints -2

The Mathematica functions declared with MATHEMATICA_DECLARE outside any function (may be inside a header) e.g. MATHEMATICA_DECLARE(Table), MATHEMATICA_DECLARE(Det)
A symbols created using mathematica::symbol e.g. mathematica::symbol i("i"), mathematica::symbol j("j")
mathematica::m creates a mathematica construct
mathematica::value holds the value returnd from mathematica

// Declare Mathematica functions 
MATHEMATICA_DECLARE(Table)
MATHEMATICA_DECLARE(Mod)
MATHEMATICA_DECLARE(Dot)
MATHEMATICA_DECLARE(Det)

// connect to mathematica (optionally pass argc, argv) See http://reference.wolfram.com/language/ref/c/WSOpenArgcArgv.html
connector shell;

// Declare symbols
mathematica::symbol i("i");
mathematica::symbol j("j");

// declare variable to contain mathematica output
mathematica::value determinant;

// create mathematica constructs
mathematica::m mata = Table(Mod(i + j, 2), List(i, 1, 2), List(j, 1, 2));
mathematica::m matb = Table(Mod(i + j, 3), List(i, 1, 2), List(j, 1, 2)];
mathematica::m matc = Dot(mata, matb);
mathematica::m matd = Det(matc);

// Execute mathematica constructs and fetch the response
shell << matd;
shell >> determinant;

// determinant can be converted to C++ machine sized types
std::cout << determinant << std::endl; // Prints -2

Simple Example of adding all numbers in a list¶

using namespace mathematica;
symbol i("i"); // declare mathematica symbol i
value result_sum; // declare the variable to hold the result

shell << Total(Table(i, List(i, 1, 10))); // In Mathematica Total[Table[i, {i, 1, 10}]]
shell >> result_sum;

result_sum is the result object that can be converted to int, double, std::string and streamed to std::ostream.

std::cout << result_sum << std::endl; // Prints 55
std::cout << result_sum->stringify() << std::endl; // Prints 55
int sum1 = *result_sum; // auto coercion through type operator overloading for scaler types
int sum2 = cast<int>(result_sum);
double sum3 = *result_sum;
double sum4 = cast<double>(result_sum); 
std::cout << sum1 << " " << sum2 << " " << sum3 << " " << sum4 << std::endl; // Prints 55 55 55 55

Fetching composite results (in STL containers)¶

mathematica::value can hold composite values returned from mathematica like this example of List

symbol i("i"); // declare mathematica symbol i
value result_list; // declare the variable to hold the result

shell << Table(i, List(i, 1, 10)); // In Mathematica Table[i, {i, 1, 10}]
shell >> result_list;
std::cout << result_list << std::endl; // Prints List[1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
std::cout << result_list->stringify() << std::endl; // Prints List[1, 2, 3, 4, 5, 6, 7, 8, 9, 10]

mathematica::value object can be converted to an equivalent STL container like std::vector using mathematica::cast

std::vector<int> list;
list = cast<std::vector<int>>(result_list);

Executing intermediate returned output¶

An mathematica::value object can be using to build a mathematica::m construct. Here res_mata and res_matb are values returned by mathematica that we are passing inside Det.

value res_mata;
value res_matb;
value res_matc;
value res_det;

shell << Table(Mod(i+j, 2), List(i, 1, 2), List(j, 1, 2));
shell >> res_mata;
shell << Table(Mod(i+j, 3), List(i, 1, 2), List(j, 1, 2));
shell >> res_matb;
shell << Dot(res_mata, res_matb);
shell >> res_matc;
shell << Det(res_matc);
shell >> res_det;

Serialize `struct` to Mathematica `Association`¶

struct point{
    std::pair<int, int> location;
    std::string name;
    double elevation;

    point(): location(std::make_pair(0, 0)), name(""), elevation (0.0f){}
    point (std::pair<int, int> loc, const std::string& name_, double elevation_): location(loc), name(name_), elevation(elevation_){}
};
value result;
point pti(std::make_pair(1, 1), "Hallo", 100.0f);
shell << Evaluate(pti);
shell >> result;
point pto = cast<point>(result);

The object pti of type struct point is the above example will be serialized as Association[Rule["location", List[1, 1]], Rule["name", "Hallo"], Rule["elevation", 100]]. The associations need to be declared as following.

MATHEMATICA_ASSOCIATE(point, std::pair<int, int>, std::string, double){
    MATHEMATICA_PROPERTY(0, location)
    MATHEMATICA_PROPERTY(1, name)
    MATHEMATICA_PROPERTY(2, elevation)
};