FractionField — field of fractions of an integral domain, with on-the-fly normalisation. More...

#include "monoid.hpp"
#include "ring.hpp"
#include "polyring.hpp"

Classes
struct	frac_elem
class	FractionField
	Engine-side fraction field of a polynomial domain R_. More...

Detailed Description

FractionField — field of fractions of an integral domain, with on-the-fly normalisation.

Note: AI-generated documentation. Verify against the source before relying on it.

Declares FractionField (a Ring subclass) along with its value type frac_elem, a (numer, denom) pair of ring_elems. Construction wraps a base ring R_ that the caller asserts is an integral domain; the engine does not verify this, so a non-domain input produces silent garbage and the M2-side wrapper is responsible for the check. Every arithmetic op (a/b + c/d = (ad + bc)/bd, similarly for multiplication) is followed by a simplify pass that normalises the denominator's sign / leading coefficient so that 2/3 and 4/6 compare equal.

When the base is ZZ[x_1, ..., x_n] or (Z/p)[x_1, ..., x_n] the use_gcd_simplify flag turns on an explicit GCD reduction that puts fractions into canonical form; other domains fall back to a weaker normalisation that still preserves equality but may leave common factors in place. The base must currently be a PolyRingFlat; iterated frac(frac(R)) works only because the engine flattens first, an artefact the header comment flags as removable once fractions themselves become flat.

See also: localring.hpp; qring.hpp; polyring.hpp

Definition in file frac.hpp.

Classes

Detailed Description