Tour of the C++ Interface

There are two main objects in e-antic: number fields, which are represented by a eantic::renf_class, and their elements, represented by a eantic::renf_elem_class. These objects are provided by the headers e-antic/renf_class.hpp and e-antic/renf_elem_class.hpp, respectively.

To work with e-antic, you first need to create a number field, typically by providing a minimal polynomial and an approximation of one of its roots.

Once a eantic::renf_class has been initialized, its elements can be created with the various constructors. The lifetime of all these objects is managed by smart pointers, so you usually do not need to worry about allocating and freeing resources manually.

Example

We construct a totally real field with the minimal polynomial \(x^3 - 3x + 1\) and fix its real root, which is approximately 0.34:

#include <e-antic/renf_class.hpp>

auto K = eantic::renf_class::make("x^3 - 3*x + 1", "x", "0.34 +/- .01");

Let a be the selected root of this number field:

#include <e-antic/renf_elem_class.hpp>

auto a = K->gen();

We compute \(b = a^2 - 2\) and print its value:

auto b = a.pow(2) - 2;

std::cout << b;
// -> (x^2 - 2 ~ -1.8793852)

Note

The same example is also explained in detail in the documentation of the C interface.