Overview 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 eantic::renf_elem_class constructors. Lifetime of all these objects is taken care of 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 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 that the same example is also explained in detail in the documentation of the C interface.