FreeAlgebra Class Reference

Free associative algebra over a coefficient ring: the non-commutative analogue of PolynomialRing. More...

#include <FreeAlgebra.hpp>

Inheritance diagram for FreeAlgebra:

Public Member Functions
const Ring *	coefficientRing () const
const FreeMonoid &	monoid () const
const Monoid &	degreeMonoid () const
int	numVars () const
unsigned int	computeHashValue (const Poly &a) const
void	init (Poly &f) const
void	clear (Poly &f) const
void	setZero (Poly &f) const
void	copy (Poly &result, Poly::const_iterator fBegin, Poly::const_iterator fEnd) const
void	from_coefficient (Poly &result, const ring_elem a) const
void	from_long (Poly &result, long n) const
void	from_int (Poly &result, mpz_srcptr n) const
bool	from_rational (Poly &result, const mpq_srcptr q) const
void	copy (Poly &result, const Poly &f) const
void	swap (Poly &f, Poly &g) const
void	var (Poly &result, int v) const
M2_arrayint	support (const Poly &f) const
void	from_word (Poly &result, const Word &word) const
void	from_word (Poly &result, const std::vector< int > &word) const
void	from_word (Poly &result, ring_elem coeff, const Word &word) const
void	from_word (Poly &result, ring_elem coeff, const std::vector< int > &word) const
long	n_terms (const Poly &f) const
bool	is_unit (const Poly &f) const
bool	is_zero (const Poly &f) const
bool	is_equal (const Poly &f, const Poly &g) const
int	compare_elems (const Poly &f, const Poly &g) const
void	add (Poly &result, Poly::const_iterator fBegin, Poly::const_iterator fEnd, Poly::const_iterator gBegin, Poly::const_iterator gEnd) const
void	addScalarMultipleOf (Poly &result, Poly::const_iterator fBegin, Poly::const_iterator fEnd, Poly::const_iterator gBegin, Poly::const_iterator gEnd, ring_elem coeff) const
void	negate (Poly &result, const Poly &f) const
void	add (Poly &result, const Poly &f, const Poly &g) const
void	subtract (Poly &result, const Poly &f, const Poly &g) const
void	subtractScalarMultipleOf (Poly &result, const Poly &f, const Poly &g, ring_elem coeff) const
void	mult (Poly &result, const Poly &f, const Poly &g) const
void	power (Poly &result, const Poly &f, int n) const
void	power (Poly &result, const Poly &f, mpz_srcptr n) const
ring_elem	eval (const RingMap *map, const Poly &f, int first_var) const
void	makeMonic (Poly &result, Poly &f) const
void	makeMonicInPlace (Poly &f) const
void	elem_text_out (buffer &o, const Poly &f, bool p_one, bool p_plus, bool p_parens) const
bool	is_homogeneous (const Poly &f) const
const_monomial	degree (const Poly &f) const
bool	multi_degree (const Poly &f, monomial already_allocated_degree_vector) const
std::pair< int, bool >	heft_degree (const Poly &f) const
void	mult_by_term_right (Poly &result, const Poly &f, const ring_elem c, const Monom m) const
void	mult_by_term_left (Poly &result, const Poly &f, const ring_elem c, const Monom m) const
void	mult_by_term_left_and_right (Poly &result, const Poly &f, const ring_elem c, const Monom leftM, const Monom rightM) const
void	mult_by_term_left_and_right (Poly &result, const Poly &f, const Monom leftM, const Monom rightM) const
void	mult_by_term_left (Poly &result, const Poly &f, const ring_elem c, const Word &w) const
void	mult_by_term_right (Poly &result, const Poly &f, const ring_elem c, const Word &w) const
void	mult_by_term_left_and_right (Poly &result, const Poly &f, const ring_elem c, const Word &leftW, const Word &rightW) const
void	mult_by_term_left_and_right (Poly &result, const Poly &f, const Word &leftW, const Word &rightW) const
void	add_to_end (Poly &f, const Poly &g) const
void	add_to_end (Poly &f, ring_elem coeff, const Monom &monom) const
void	lead_term_as_poly (Poly &result, const Poly &f) const
void	mult_by_coeff (Poly &result, const Poly &f, const ring_elem c) const
SumCollector *	make_SumCollector () const
Word	lead_word (const Poly &f) const
Word	lead_word_prefix (const Poly &f, int endIndex) const
Word	lead_word_suffix (const Poly &f, int beginIndex) const

Static Public Member Functions
static FreeAlgebra *	create (const Ring *K, const std::vector< std::string > &names, const PolynomialRing *degreeRing, const std::vector< int > &degrees, const std::vector< int > &wtvecs, const std::vector< int > &heftVector)
Static Public Member Functions inherited from our_new_delete
static void *	operator new (size_t size)
static void *	operator new[] (size_t size)
static void	operator delete (void *obj)
static void	operator delete[] (void *obj)
static void *	operator new (size_t size, void *existing_memory)
static void *	operator new[] (size_t size, void *existing_memory)
static void	operator delete (void *obj, void *existing_memory)
static void	operator delete[] (void *obj, void *existing_memory)

Private Member Functions
	FreeAlgebra (const Ring *K, std::shared_ptr< FreeMonoid > M)

Private Attributes
const Ring &	mCoefficientRing
std::shared_ptr< FreeMonoid >	mMonoid

Detailed Description

Free associative algebra over a coefficient ring: the non-commutative analogue of PolynomialRing.

Note

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

Bundles the coefficient ring with a FreeMonoid of words on the generators and exposes the operation surface the non-commutative arithmetic / Groebner stack (NCGroebner, NCF4) reduces against: from_word, add, subtract, mult, mult_by_term_left_and_right, power, and the lead-term accessors. Created through the static create() factory from a coefficient ring plus the variable names, degrees, weight vectors, and heft vector; the constructor itself is private.

Definition at line 68 of file FreeAlgebra.hpp.

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The documentation for this class was generated from the following files:

• Macaulay2/e/NCAlgebras/FreeAlgebra.hpp
• Macaulay2/e/NCAlgebras/FreeAlgebra.cpp