SolvableAlgebra Class Reference

PolyRing subclass for solvable polynomial algebras (PBW-type non-commutative rings where each pair of non-commuting variables satisfies a relation of the form x_j x_i = c_ij x_i x_j + lower). More...

#include <solvable.hpp>

Inheritance diagram for SolvableAlgebra:

Public Member Functions
virtual bool	is_commutative_ring () const
virtual bool	is_solvable_algebra () const
virtual const SolvableAlgebra *	cast_to_SolvableAlgebra () const
virtual SolvableAlgebra *	cast_to_SolvableAlgebra ()
virtual ring_elem	power (const ring_elem f, mpz_srcptr n) const
	Exponentiation. This is the default function, if a class doesn't define this.
virtual ring_elem	power (const ring_elem f, int n) const
virtual ring_elem	mult_by_term (const ring_elem f, const ring_elem c, const int *m) const
Public Member Functions inherited from PolyRing
virtual void	clear ()
virtual const PolyRing *	cast_to_PolyRing () const
virtual PolyRing *	cast_to_PolyRing ()
virtual void	text_out (buffer &o) const
ring_elem	fromCoefficient (ring_elem &coeff) const
virtual ring_elem	from_long (long n) const
virtual ring_elem	from_int (mpz_srcptr n) const
virtual bool	from_rational (mpq_srcptr q, ring_elem &result) const
virtual bool	from_BigComplex (gmp_CC z, ring_elem &result) const
virtual bool	from_BigReal (gmp_RR z, ring_elem &result) const
virtual bool	from_Interval (gmp_RRi z, ring_elem &result) const
virtual bool	from_ComplexInterval (gmp_CCi z, ring_elem &result) const
virtual bool	from_double (double a, ring_elem &result) const
virtual bool	from_complex_double (double re, double im, ring_elem &result) const
virtual ring_elem	var (int v) const
virtual int	index_of_var (const ring_elem a) const
virtual M2_arrayint	support (const ring_elem a) const
virtual bool	promote (const Ring *R, const ring_elem f, ring_elem &result) const
virtual bool	lift (const Ring *R, const ring_elem f, ring_elem &result) const
virtual ring_elem	preferred_associate (ring_elem f) const
ring_elem	preferred_associate_divisor (ring_elem ff) const
virtual bool	is_unit (const ring_elem f) const
virtual bool	is_zero (const ring_elem f) const
virtual bool	is_equal (const ring_elem f, const ring_elem g) const
virtual int	compare_elems (const ring_elem f, const ring_elem g) const
virtual bool	is_homogeneous (const ring_elem f) const
virtual bool	multi_degree (const ring_elem f, monomial d) const
virtual void	degree_weights (const ring_elem f, const std::vector< int > &wts, int &lo, int &hi) const
virtual ring_elem	homogenize (const ring_elem f, int v, int deg, const std::vector< int > &wts) const
virtual ring_elem	homogenize (const ring_elem f, int v, const std::vector< int > &wts) const
virtual ring_elem	copy (const ring_elem f) const
virtual void	remove (ring_elem &f) const
void	internal_negate_to (ring_elem &f) const
void	internal_add_to (ring_elem &f, ring_elem &g) const
void	internal_subtract_to (ring_elem &f, ring_elem &g) const
virtual ring_elem	negate (const ring_elem f) const
virtual ring_elem	add (const ring_elem f, const ring_elem g) const
virtual ring_elem	subtract (const ring_elem f, const ring_elem g) const
virtual ring_elem	mult (const ring_elem f, const ring_elem g) const
virtual ring_elem	invert (const ring_elem f) const
virtual ring_elem	divide (const ring_elem f, const ring_elem g) const
	Warning! This function works even if g does not divide f.
ring_elem	gcd (const ring_elem f, const ring_elem g) const
ring_elem	gcd_extended (const ring_elem f, const ring_elem g, ring_elem &u, ring_elem &v) const
virtual ring_elem	remainder (const ring_elem f, const ring_elem g) const
virtual ring_elem	quotient (const ring_elem f, const ring_elem g) const
virtual ring_elem	remainderAndQuotient (const ring_elem f, const ring_elem g, ring_elem &quot) const
virtual void	syzygy (const ring_elem a, const ring_elem b, ring_elem &x, ring_elem &y) const
virtual ring_elem	random () const
virtual void	elem_text_out (buffer &o, const ring_elem f, bool p_one=true, bool p_plus=false, bool p_parens=false) const
virtual ring_elem	eval (const RingMap *map, const ring_elem f, int first_var) const
virtual int	n_flat_terms (const ring_elem f) const
virtual int	n_logical_terms (int nvars0, const ring_elem f) const
virtual ring_elem	get_coeff (const Ring *coeffR, const ring_elem f, const_varpower vp) const
virtual ring_elem	get_terms (int nvars0, const ring_elem f, int lo, int hi) const
virtual ring_elem	make_flat_term (const ring_elem a, const_monomial m) const
virtual ring_elem	make_logical_term (const Ring *coeffR, const ring_elem a, const_exponents exp) const
virtual ring_elem	lead_flat_coeff (const ring_elem f) const
virtual ring_elem	lead_logical_coeff (const Ring *coeffR, const ring_elem f) const
virtual const_monomial	lead_flat_monomial (const ring_elem f) const
virtual void	lead_logical_exponents (int nvars0, const ring_elem f, exponents_t result_exp) const
ring_elem	lead_term (const ring_elem f) const
virtual engine_RawArrayPairOrNull	list_form (const Ring *coeffR, const ring_elem f) const
virtual ring_elem *	get_parts (const std::vector< int > &wts, const ring_elem f, long &result_len) const
virtual ring_elem	get_part (const std::vector< int > &wts, const ring_elem f, bool lobound_given, bool hibound_given, long lobound, long hibound) const
virtual void	mult_coeff_to (ring_elem a, ring_elem &f) const
virtual void	divide_coeff_to (ring_elem &f, ring_elem a) const
virtual ring_elem	lead_term (int nparts, const ring_elem f) const
ring_elem	fromSmallIntegerCoefficients (const std::vector< long > &coeffs, int var) const
virtual ring_elem	zeroize_tiny (gmp_RR epsilon, const ring_elem f) const
virtual void	increase_maxnorm (gmp_RRmutable norm, const ring_elem f) const
virtual vec	vec_lead_term (int nparts, const FreeModule *F, vec v) const
virtual vec	vec_top_coefficient (const vec v, int &var, int &exp) const
const vecterm *	vec_locate_lead_term (const FreeModule *F, vec v) const
virtual void	monomial_divisor (const ring_elem a, exponents_t exp) const
virtual ring_elem	diff (ring_elem a, ring_elem b, int use_coeff) const
virtual bool	in_subring (int nslots, const ring_elem a) const
virtual void	degree_of_var (int n, const ring_elem a, int &lo, int &hi) const
virtual ring_elem	divide_by_var (int n, int d, const ring_elem a) const
virtual ring_elem	divide_by_expvector (const_exponents exp, const ring_elem a) const
virtual void	lower_content (ring_elem &cont, ring_elem new_coeff) const
virtual ring_elem	content (ring_elem f) const
virtual ring_elem	content (ring_elem f, ring_elem g) const
virtual ring_elem	divide_by_given_content (ring_elem f, ring_elem c) const
void	sort (Nterm *&f) const
void	determine_common_denominator_QQ (ring_elem f, mpz_ptr denom_so_far) const
ring_elem	get_denominator_QQ (ring_elem f) const
ring_elem	vec_get_denominator_QQ (vec f) const
gbvector *	translate_gbvector_from_vec_QQ (const FreeModule *F, const vec v, ring_elem &result_denominator) const
vec	translate_gbvector_to_vec_QQ (const FreeModule *F, const gbvector *v, const ring_elem denom) const
gbvector *	translate_gbvector_from_ringelem_QQ (ring_elem coeff) const
gbvector *	translate_gbvector_from_ringelem (ring_elem coeff) const
gbvector *	translate_gbvector_from_vec (const FreeModule *F, const vec v, ring_elem &result_denominator) const
vec	translate_gbvector_to_vec (const FreeModule *F, const gbvector *v) const
vec	translate_gbvector_to_vec_denom (const FreeModule *F, const gbvector *v, const ring_elem denom) const
Public Member Functions inherited from PolyRingFlat
virtual Nterm *	numerator (ring_elem f) const
virtual const PolyRingFlat *	cast_to_PolyRingFlat () const
virtual PolyRingFlat *	cast_to_PolyRingFlat ()
Public Member Functions inherited from PolynomialRing
Matrix *	getPresentation () const
unsigned long	get_precision () const
bool	is_basic_ring () const
bool	is_poly_ring () const
bool	is_graded () const
CoefficientType	coefficient_type () const
int	n_vars () const
QRingInfo *	get_quotient_info () const
const Ring *	getCoefficientRing () const
MonomialTable *	get_quotient_MonomialTable () const
const MonomialIdeal *	get_quotient_monomials () const
const MonomialTableZZ *	get_quotient_MonomialTableZZ () const
int	n_quotients () const
Nterm *	quotient_element (int i) const
const gbvector *	quotient_gbvector (int i) const
const MonomialIdeal *	make_basis_MonomialIdeal () const
bool	is_quotient_ring () const
bool	is_skew_commutative () const
int	n_skew_commutative_vars () const
int	skew_variable (int i) const
bool	is_skew_var (int v) const
const SkewMultiplication &	getSkewInfo () const
virtual bool	is_weyl_algebra () const
virtual bool	is_skew_commutative_ring () const
virtual const PolyRing *	getNumeratorRing () const
virtual const PolynomialRing *	getAmbientRing () const
virtual const Ring *	getDenominatorRing () const
virtual GBRing *	get_gb_ring () const
virtual const Ring *	getCoefficients () const
virtual const Monoid *	getMonoid () const
virtual bool	is_fraction_poly_ring () const
virtual int	n_fraction_vars () const
virtual const PolynomialRing *	cast_to_PolynomialRing () const
virtual PolynomialRing *	cast_to_PolynomialRing ()
SumCollector *	make_SumCollector () const
virtual unsigned int	computeHashValue (const ring_elem a) const
int	n_terms (const ring_elem f) const
virtual ring_elem	make_logical_term (const Ring *coeffR, const ring_elem a, const_exponents exp) const =0
virtual ring_elem	get_coeff (const Ring *coeffR, const ring_elem f, const_varpower vp) const =0
virtual void	lead_logical_exponents (int nvars0, const ring_elem f, exponents_t result_exp) const =0
virtual void	monomial_divisor (const ring_elem a, exponents_t exp) const =0
virtual ring_elem	divide_by_expvector (const_exponents exp, const ring_elem a) const =0
Public Member Functions inherited from Ring
virtual	~Ring ()
const CoefficientRingR *	getCoefficientRingR () const
long	characteristic () const
const Monoid *	degree_monoid () const
const PolynomialRing *	get_degree_ring () const
const std::vector< int > &	get_heft_vector () const
virtual M2::RingID	ringID () const
virtual bool	isFinitePrimeField () const
virtual bool	isGaloisField () const
virtual bool	is_ZZ () const
virtual bool	is_QQ () const
virtual bool	is_RRR () const
virtual bool	is_RRi () const
virtual bool	is_CCC () const
virtual bool	is_fraction_field () const
bool	is_field () const
bool	declare_field ()
ring_elem	get_non_unit () const
void	set_non_unit (ring_elem zero_div) const
virtual bool	has_associate_divisors () const
virtual const RingZZ *	cast_to_RingZZ () const
virtual RingZZ *	cast_to_RingZZ ()
virtual const Z_mod *	cast_to_Z_mod () const
virtual Z_mod *	cast_to_Z_mod ()
virtual const GF *	cast_to_GF () const
virtual GF *	cast_to_GF ()
virtual const Tower *	cast_to_Tower () const
virtual Tower *	cast_to_Tower ()
virtual const PolyQQ *	cast_to_PolyQQ () const
virtual PolyQQ *	cast_to_PolyQQ ()
virtual const FractionField *	cast_to_FractionField () const
virtual FractionField *	cast_to_FractionField ()
virtual const LocalRing *	cast_to_LocalRing () const
virtual LocalRing *	cast_to_LocalRing ()
virtual const M2FreeAlgebra *	cast_to_M2FreeAlgebra () const
virtual M2FreeAlgebra *	cast_to_M2FreeAlgebra ()
virtual const M2FreeAlgebraQuotient *	cast_to_M2FreeAlgebraQuotient () const
virtual M2FreeAlgebraQuotient *	cast_to_M2FreeAlgebraQuotient ()
virtual const M2FreeAlgebraOrQuotient *	cast_to_M2FreeAlgebraOrQuotient () const
virtual M2FreeAlgebraOrQuotient *	cast_to_M2FreeAlgebraOrQuotient ()
virtual const SchurRing *	cast_to_SchurRing () const
virtual SchurRing *	cast_to_SchurRing ()
virtual const SchurRing2 *	cast_to_SchurRing2 () const
virtual SchurRing2 *	cast_to_SchurRing2 ()
virtual const SchurSnRing *	cast_to_SchurSnRing () const
virtual SchurSnRing *	cast_to_SchurSnRing ()
virtual const SkewPolynomialRing *	cast_to_SkewPolynomialRing () const
virtual SkewPolynomialRing *	cast_to_SkewPolynomialRing ()
virtual const WeylAlgebra *	cast_to_WeylAlgebra () const
virtual RRR *	cast_to_RRR ()
virtual const RRR *	cast_to_RRR () const
virtual RRi *	cast_to_RRi ()
virtual const RRi *	cast_to_RRi () const
virtual CCC *	cast_to_CCC ()
virtual const CCC *	cast_to_CCC () const
virtual const RingElement *	getMinimalPolynomial () const
virtual const RingElement *	getGenerator () const
virtual long	discreteLog (const ring_elem &a) const
virtual const RingElement *	getRepresentation (const ring_elem &a) const
virtual MutableMatrix *	makeMutableMatrix (size_t nrows, size_t ncols, bool dense) const
virtual FreeModule *	make_FreeModule () const
virtual FreeModule *	make_Schreyer_FreeModule () const
virtual FreeModule *	make_FreeModule (int n) const
virtual std::pair< bool, long >	coerceToLongInteger (ring_elem a) const
ring_elem	one () const
ring_elem	minus_one () const
ring_elem	zero () const
virtual bool	lower_associate_divisor (ring_elem &f, ring_elem g) const
void	negate_to (ring_elem &f) const
void	add_to (ring_elem &f, const ring_elem &g) const
void	subtract_to (ring_elem &f, const ring_elem &g) const
void	mult_to (ring_elem &f, const ring_elem g) const
const_monomial	degree (const ring_elem f) const
virtual ring_elem	antipode (ring_elem f) const
vec	vec_zeroize_tiny (gmp_RR epsilon, const vec f) const
void	vec_increase_maxnorm (gmp_RRmutable norm, const vec f) const
void	vec_sort (vecterm *&f) const
int	compare_vecs (vec v, vec w) const
vec	e_sub_i (int r) const
vec	make_vec (int r, ring_elem a) const
vec	make_vec_from_array (int len, Nterm **array) const
vec	copy_vec (const vecterm *v) const
void	remove_vec (vec v) const
bool	is_equal (const vecterm *a, const vecterm *b) const
bool	get_entry (const vecterm *v, int r, ring_elem &result) const
ring_elem	get_entry (vec v, int r) const
vec	sub_vector (const vecterm *v, M2_arrayint r) const
int	n_nonzero_terms (const vecterm *v) const
void	vec_text_out (buffer &o, const vecterm *v, bool p_one=true, bool p_plus=false, bool p_parens=false) const
vec	vec_eval (const RingMap *map, const FreeModule *F, const vec v) const
vec	negate_vec (vec v) const
vec	add_vec (vec v, vec w) const
vec	subtract_vec (vec v, vec w) const
vec	mult_vec (int n, vec v) const
vec	mult_vec (const ring_elem f, const vec w) const
vec	rightmult_vec (const vec w, const ring_elem f) const
void	set_entry (vec &v, int i, ring_elem r) const
void	mult_vec_to (vec &v, const ring_elem r, bool opposite_mult) const
void	mult_row (vec &v, const ring_elem r, int i, bool opposite_mult) const
void	negate_vec_to (vec &v) const
void	add_vec_to (vec &v, vec &w) const
void	subtract_vec_to (vec &v, vec &w) const
vec	mult_vec_matrix (const Matrix *m, vec v, bool opposite_mult) const
vec	component_shift (int n, vec v) const
vec	tensor_shift (int n, int m, vec v) const
vec	tensor (const FreeModule *F, vec v, const FreeModule *G, vec w) const
void	divide_vec_to (vec &v, const ring_elem a) const
void	divide_row (vec &v, int r, const ring_elem a) const
ring_elem	dot_product (const vecterm *v, const vecterm *w) const
vec	vec_diff (vec v, int rankFw, vec w, int use_coeff) const
int	vec_in_subring (int n, const vec v) const
void	vec_degree_of_var (int n, const vec v, int &lo, int &hi) const
vec	vec_divide_by_var (int n, int d, const vec v) const
vec	vec_divide_by_expvector (const_exponents exp, const vec v) const
bool	vec_is_scalar_multiple (vec f, vec g) const
vec	vec_remove_monomial_factors (vec f, bool make_squarefree_only) const
bool	vec_multi_degree (const FreeModule *F, const vec f, monomial degf) const
void	vec_degree_weights (const FreeModule *F, const vec f, const std::vector< int > &wts, int &lo, int &hi) const
bool	vec_is_homogeneous (const FreeModule *F, const vec f) const
vec	vec_homogenize (const FreeModule *F, const vec f, int v, int deg, const std::vector< int > &wts) const
vec	vec_homogenize (const FreeModule *F, const vec f, int v, const std::vector< int > &wts) const
ring_elem	divide_by_content (ring_elem f) const
ring_elem	split_off_content (ring_elem f, ring_elem &result) const
ring_elem	vec_content (vec f) const
vec	vec_divide_by_given_content (vec f, ring_elem c) const
vec	vec_divide_by_content (vec f) const
ring_elem	vec_split_off_content (vec f, vec &result) const
Public Member Functions inherited from MutableEngineObject
	MutableEngineObject ()
virtual	~MutableEngineObject ()
unsigned int	hash () const
Public Member Functions inherited from our_gc_cleanup
	our_gc_cleanup ()
virtual	~our_gc_cleanup ()

Static Public Member Functions
static SolvableAlgebra *	create (const PolynomialRing *R, const Matrix *Q)
Static Public Member Functions inherited from PolyRing
static const PolyRing *	create (const Ring *K, const Monoid *M)
static const PolyRing *	get_trivial_poly_ring ()
Static Public Member Functions inherited from PolynomialRing
static PolynomialRing *	create_quotient (const PolynomialRing *R, const Matrix *M)
static PolynomialRing *	create_quotient (const PolynomialRing *R, const PolynomialRing *B)
static PolynomialRing *	create_quotient_ring (const Matrix *M)
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)

Protected Member Functions
bool	initialize_solvable (const Matrix *Q)
	SolvableAlgebra ()
virtual	~SolvableAlgebra ()
Protected Member Functions inherited from PolyRing
void	initialize_poly_ring (const Ring *K, const Monoid *M)
virtual	~PolyRing ()
	PolyRing ()
void	minimal_monomial (ring_elem f, monomial &monom) const
Nterm *	division_algorithm (Nterm *f, Nterm *g, Nterm *&quot) const
Nterm *	division_algorithm (Nterm *f, Nterm *g) const
Nterm *	powerseries_division_algorithm (Nterm *f, Nterm *g, Nterm *&quot) const
std::vector< int >	setNegativeExponentMonomial (Nterm *f) const
	Create an exponent vector whose i-th value is the minimum of the exponents of that variable, if that variable is a Laurent variable (i.e. allows negative exponents).
Nterm *	division_algorithm_with_laurent_variables (Nterm *f, Nterm *g, Nterm *&quot) const
vec	vec_coefficient_of_var (vec v, int var, int exp) const
ring_elem	diff_term (const_monomial m, const_monomial n, monomial resultmon, int use_coeff) const
ring_elem	power_direct (const ring_elem f, int n) const
ring_elem	get_logical_coeff (const Ring *coeffR, const Nterm *&f) const
Nterm *	new_term () const
Nterm *	copy_term (const Nterm *t) const
bool	imp_attempt_to_cancel_lead_term (ring_elem &f, ring_elem g, ring_elem &coeff, monomial monom) const
ring_elem	imp_skew_mult_by_term (const ring_elem f, const ring_elem c, const_monomial m) const
void	imp_subtract_multiple_to (ring_elem &f, ring_elem a, const_monomial m, const ring_elem g) const
Protected Member Functions inherited from PolynomialRing
void	setIsGraded (bool new_val)
void	setQuotientInfo (QRingInfo *qinfo0)
void	initialize_PolynomialRing (const Ring *K, const Monoid *M, const PolyRing *numeratorR, const PolynomialRing *ambientR, const Ring *denomR)
virtual	~PolynomialRing ()
	PolynomialRing ()
void	sort (Nterm *&f) const
Protected Member Functions inherited from Ring
const ARing *	getARing () const
void	initialize_ring (long charac, const PolynomialRing *DR=nullptr, const std::vector< int > &heft_vec={})
	Ring ()
vec	new_vec () const
	vector operations ////////////////////
void	remove_vec_node (vec n) const

Static Private Member Functions
static SolvableAlgebra *	create (const Ring *K, const Monoid *M, const Matrix *Q)

Private Attributes
const Matrix *	Q_

Additional Inherited Members
Public Types inherited from Ring
enum	CoefficientType { COEFF_ZZ , COEFF_QQ , COEFF_BASIC }
Static Protected Member Functions inherited from PolyRing
static void	make_trivial_ZZ_poly_ring ()
Static Protected Member Functions inherited from PolynomialRing
static PolynomialRing *	create_quotient (const PolynomialRing *R, VECTOR(Nterm *) &elems)
Protected Attributes inherited from PolynomialRing
bool	is_skew_
SkewMultiplication	skew_
bool	is_weyl_
bool	is_solvable_
Ring::CoefficientType	coeff_type_
bool	overZZ_
QRingInfo *	qinfo_
bool	is_ZZ_quotient_
ring_elem	ZZ_quotient_value_
size_t	poly_size_
int	nvars_
int	exp_size
const Ring *	K_
const Monoid *	M_
const PolyRing *	numerR_
const Ring *	denomR_
const PolynomialRing *	ambientR_
GBRing *	gb_ring_
Protected Attributes inherited from Ring
long	mCharacteristic
const PolynomialRing *	degree_ring
std::vector< int >	mHeftVector
const ARing *	AR
const CoefficientRingR *	cR
ring_elem	_non_unit
int	_isfield
ring_elem	zeroV
ring_elem	oneV
ring_elem	minus_oneV
Static Protected Attributes inherited from PolyRing
static PolyRing *	trivial_poly_ring = nullptr

Detailed Description

PolyRing subclass for solvable polynomial algebras (PBW-type non-commutative rings where each pair of non-commuting variables satisfies a relation of the form x_j x_i = c_ij x_i x_j + lower).

Note

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

Q_ is the matrix of lower correction terms indexed by variable pairs — when mult_by_term1 would normally commute x_j past x_i, the engine looks up Q_ to add in the lower-order polynomial that the relation demands. Constructed via create(R, Q) so the relations can be validated against the ambient PolynomialRing before the new ring is exposed.

Definition at line 56 of file solvable.hpp.

---

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

• Macaulay2/e/solvable.hpp
• Macaulay2/e/solvable.cpp