ring

LinBox rings, ring wrappers, ring construction tools. More...

Collaboration diagram for ring:

Modules
	Integers
	LinBox integer representation and operations.
	Polynomials
	NO DOC YET.

Files
file	ring/archetype.h
	Specification and archetypic instance for the ring interface.
file	modular.h
	A Givaro::Modular ring is a representations of Z/mZ.
file	ntl-lzz_pex.h
	NO DOC.
file	ntl-lzz_px.h
	NO DOC.
file	ntl-zz_p.h
	NO DOC.

Data Structures
class	RingAbstract
	Abstract ring base class. More...
class	RingArchetype
	specification and archetypic instance for the ring interfaceThe RingArchetype and its encapsulated element class contain pointers to the RingAbstract and its encapsulated ring element, respectively. More...
class	RingEnvelope< Ring >
	implement the ring archetype to minimize code bloat. More...
class	NTL_ZZ
	the integer ring. More...
struct	NTL_PID_zz_p
	extend Wrapper of zz_p from NTL. More...
class	PolynomialRing< BaseRing, StorageTag >
	Polynomials. More...

Detailed Description

LinBox rings, ring wrappers, ring construction tools.

LinBox ring classes implement the BasicRing concept, which has the same members as the field concept. The difference is that some functions have different semantics. Specifically, inv and div are partial functions.

Some ring classes extend BasicRing:

The PIR concept (principal ideal ring) has, beyond BasicRing, gcd(g, a, b), g = (a,b), greatest common divisor of a, b. gcd(g, s, a, b), g = (a,b) = sa modulo b. s < b/g. gcd(g, s, t, a, b), g = (a,b) = sa + tb, s < b/g, t < a/g. gcd(g, s, t, u, v, a, b), (a,b) = g = sa + tb, u = a/g, v = b/g. gcdin(g, a), g = (g,a) lcm(), isUnit(), isZeroDivisor().

The PID concept (principal ideal domain) has the same members as the PIR concept, but it is promised that there are no zero divisors.

The LocalPIR concept has the members of PIR, but there is a unique prime ideal. Some algorithms exploit this.

Local2_32 exploits a few additional functions and the type Exponent. This concept could be used for other small rings extending tiny fields as well.

Example of BasicRing: Givaro::Modular<int32_t> when the modulus may be non-prime. Example of PIR: PIRModular Example of PID: PIDInteger. Example of LocalPIR: Local2_32.