rational_field.hpp - Rationals

rational_field.hpp - Rationals#

struct RationalField#

Models some features of a number field with an embedding into the real. In practice you won’t be using instances of this but just use it as a type parameter to specify that a module should be considered over the rationals. 

#include <exact-real/rational_field.hpp>
#include <exact-real/module.hpp>
#include <exact-real/real_number.hpp>
#include <gmpxx.h>

auto M = exactreal::Module<exactreal::RationalField>::make({exactreal::RealNumber::rational(mpq_class{1, 2})}, exactreal::RationalField{});

Public Types

typedef mpq_class ElementClass#

The internal representation of element of this ring, i.e., GMP rationals.

Public Functions

RationalField()#

Create the rational field.

RationalField(const mpq_class&)#

Create “a” rational field that contains the argument.

This is identical to RationalField::RationalField() but other rings, say number fields, have different rings and need to be able to construct the smallest ring that contains a certain element.

ElementClass coerce(const ElementClass &x) const#

Convert the rational argument into this rational field, i.e., just return the rational unchanged.

Number fields need the equivalent of this method to convert elements between different number fields.

bool operator==(const RationalField&) const#

Return whether this field is equal to another rational field, i.e., true. 

exactreal::RationalField{} == exactreal::RationalField{1337}
// -> true

Public Static Functions

static RationalField compositum(const RationalField &lhs, const RationalField &rhs)#

Return the rational field that contains both arguments.

This is just the RationalField::RationalField() but other rings need such functionality to compute a composite ring.

static bool unit(const ElementClass &x)#

Return whether x is a unit, i.e., whether it is non-zero.

static Arb arb(const ElementClass &x, long prec)#

Return an Arb approximation of the rational x. 

#include <exact-real/arb.hpp>
exactreal::RationalField::arb(mpq_class{1, 3}, 64)
// -> [0.333333 +/- 3.34e-7]

static mpz_class floor(const ElementClass &x)#

Return the integer floor of the rational x.

static std::optional<mpq_class> rational(const ElementClass &x)#

Return the rational x as a rational number, i.e, x unchanged.

template<typename T>
static ElementClass &imul(ElementClass&, const T&)#

Multiply the rational x with t.

The argument may be a primitive integer, a GMP integer, or a GMP rational.

template<typename T>
static ElementClass &idiv(ElementClass&, const T&)#

Divide the rational x by t.

The argument may be a primitive integer, a GMP integer, or a GMP rational.

Public Static Attributes

static bool contains_rationals = true#

Whether this ring contains the rational numbers, i.e., true.

static bool isField = true#

Whether this ring is a field, i.e., true.

Contents