monideal.hpp File Reference

MonomialIdeal — exponent-vector-only representation of an ideal generated by monomials. More...

#include "ExponentVector.hpp"
#include "ExponentList.hpp"
#include "int-bag.hpp"
#include "ring.hpp"
#include "polyring.hpp"
#include "mem.hpp"

Go to the source code of this file.

Classes
class	Nmi_node
	Internal tree node of the MonomialIdeal decision tree. More...
class	MonomialIdeal
	Engine-side monomial ideal: a decision tree of Nmi_nodes storing the (typically minimal) generators by variable / exponent path. More...
class	MonomialIdeal::Iterator
	Bidirectional forward iterator over the Bags stored in a MonomialIdeal. More...
struct	monideal_pair

Detailed Description

MonomialIdeal — exponent-vector-only representation of an ideal generated by monomials.

Note

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

Declares MonomialIdeal, the specialised type the engine uses for ideals whose generators are pure monomials. Generators are not held as a flat list but as a tree of Nmi_nodes indexed by (var, exp): each internal node branches on a variable and exponent, each leaf carries a Bag* whose monom() returns the generator as a gc_vector<int> in varpower form. The trie shape supports fast divisibility / containment lookups by walking the tree variable-by-variable rather than scanning a list of monomials. The combinatorial structure lets every operation skip coefficient arithmetic and monomial-ordering work entirely: intersection, sum, quotient, saturation, radical, Borel closure, and monomial primary decomposition all reduce to tree walks.

The class is EngineObject-backed and intentionally immutable once interned (its hash is computed lazily). The #if 0 block at the top of the header sketches a SparseMonomial view interface that has not been implemented — ignore it when reading the active code. The same monomial shape is what hilb.hpp's Hilbert-series recursion consumes, and the initial-ideal output of a Groebner basis lives here.

See also

ExponentList.hpp

assprime.hpp

hilb.hpp

Definition in file monideal.hpp.