LocalRing — localisation of a polynomial ring at a prime ideal P. More...

#include "ring.hpp"
#include "poly.hpp"
#include "polyring.hpp"
#include "comp-gb.hpp"

Classes
struct	local_elem
class	LocalRing
	Engine-side localisation of a polynomial ring at a prime ideal. More...

Detailed Description

LocalRing — localisation of a polynomial ring at a prime ideal P.

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

Declares LocalRing, a Ring subclass whose value type local_elem is a (numer, denom) pair (the same fraction shape as frac.hpp) but with the denominator restricted to R \ P rather than R \ {0}. The class stores the underlying polynomial ring mRing and a GBComputation* mPrime (a GB of P); the private is_in_prime(f) wraps f in a one-column matrix and tests mPrime->contains(M) == -1 to decide ideal membership. is_unit(f) is then !is_in_prime(f.numer), and divide / invert raise exc::engine_error("attempt to divide by a non-unit") exactly when the divisor's numerator lies in P — the check fires per division, not after every arithmetic op.

The constraint is what justifies a distinct class from FractionField: a LocalRing knows how to ask "does this element lie in `P`?", its unit group depends on P, and the simplify pass only cancels GCDs when use_gcd_simplify holds (true by default, flagged with a FIXME remove). Heavy callers are local-cohomology and tangent / normal-cone computations driven from m2/localring.m2; GB work over a LocalRing reaches into the specialised reducedgb-field-local.hpp.

See also: frac.hpp; polyring.hpp; comp-gb.hpp

Definition in file localring.hpp.

Classes

Detailed Description