FreeMonoid.hpp File Reference

FreeMonoid — monoid of length-prefixed non-commutative words with weight-vector prefix. More...

#include "Polynomial.hpp"
#include "newdelete.hpp"
#include "polyring.hpp"
#include "style.hpp"
#include "NCAlgebras/Word.hpp"
#include "MemoryBlock.hpp"
#include <iosfwd>
#include <vector>

Go to the source code of this file.

Classes
class	FreeMonoidLogger
	Static counter for non-commutative monomial comparisons. More...
class	FreeMonoid
	The free non-commutative monoid on a set of named variables, with monomial ordering and degree / weight machinery. More...
class	MonomEq
	Strict comparator on Monoms under a FreeMonoid order: returns true exactly when the first monomial is greater than the second. More...
class	MonomHash
	Hash functor on Monom (or Word) suitable for std::unordered_map / std::unordered_set. More...
class	MonomHashEqual
	Equality functor on Monom (or Word), the KeyEqual companion of MonomHash for std::unordered_map<Monom, ...>. More...
struct	MonomSort< T >

Functions
std::ostream &	operator<< (std::ostream &o, FreeMonoidLogger a)

Detailed Description

FreeMonoid — monoid of length-prefixed non-commutative words with weight-vector prefix.

Note

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

Declares the word-side counterpart of the commutative Monoid: a non-commutative monomial is a sequence of variable indices [v_1, v_2, ..., v_s], and FreeMonoid stores it in the packed form [total length] wt_0 ... wt_{r-1} w_0 ... w_s — a leading length so the word can be memcpyed, r weight values used to short-circuit comparison, and the indices themselves. Multiplication is plain concatenation: no reordering, no normalisation, since the algebra is free. The intended comparison is weight-first then lexicographic, matching the "leading word" convention of the non-commutative Gröbner literature; the in-file TODOs track wiring the weight values through the front end so compare can use them consistently.

The companion FreeMonoidLogger at the top of the header is a debug helper that counts monomial compares for profiling. NCGroebner.cpp resets the counter and prints it after each reduction, but the logCompare() call inside FreeMonoid.cpp is currently commented out, so the counter only ticks if a developer re-enables it.

See also

Word.hpp

FreeAlgebra.hpp

NCGroebner.hpp

Polynomial.hpp

Definition in file FreeMonoid.hpp.