GBRingSolvable Class Reference

GBRing specialisation for solvable polynomial algebras (PBW-style non-commutative rings whose relations have the form x_j * x_i = c_ij * x_i * x_j + lower-order terms). More...

#include <gbring.hpp>

Inheritance diagram for GBRingSolvable:

Public Member Functions
virtual gbvector *	mult_by_term1 (const FreeModule *F, const gbvector *f, ring_elem u, const int *monom, int comp)
virtual	~GBRingSolvable ()
Public Member Functions inherited from GBRing
virtual	~GBRing ()
const Monoid *	get_flattened_monoid () const
const Ring *	get_flattened_coefficients () const
int	n_vars () const
void	memstats ()
bool	is_skew_commutative () const
int	n_skew_commutative_vars () const
int	skew_variable (int i) const
const int *	skew_monomial_var (int i) const
bool	is_weyl_algebra () const
bool	is_schreyer_encoded () const
exponents_t	exponents_make ()
void	exponents_delete (exponents_t e)
size_t	exponent_byte_size () const
const ring_elem	one ()
void	gbvector_remove (gbvector *f)
gbvector *	gbvector_raw_term (ring_elem coeff, const int *monom, int comp)
gbvector *	gbvector_term (const FreeModule *F, ring_elem coeff, int comp)
gbvector *	gbvector_term (const FreeModule *F, ring_elem coeff, const int *monom, int comp)
gbvector *	gbvector_term_exponents (const FreeModule *F, ring_elem coeff, const int *exp, int comp)
gbvector *	gbvector_zero () const
void	gbvector_sort (const FreeModule *F, gbvector *&f)
bool	gbvector_is_zero (const gbvector *f) const
bool	gbvector_is_equal (const gbvector *f, const gbvector *g) const
int	gbvector_n_terms (const gbvector *f) const
void	gbvector_multidegree (const FreeModule *F, const gbvector *f, int *&result_degree)
int	gbvector_compare (const FreeModule *F, const gbvector *f, const gbvector *g) const
gbvector *	gbvector_lead_term (int n, const FreeModule *F, const gbvector *f)
gbvector *	gbvector_parallel_lead_terms (M2_arrayint w, const FreeModule *F, const gbvector *leadv, const gbvector *v)
void	gbvector_get_lead_monomial (const FreeModule *F, const gbvector *f, int *result)
void	gbvector_get_lead_exponents (const FreeModule *F, const gbvector *f, int *result)
int	gbvector_lead_component (const gbvector *f)
void	gbvector_mult_by_coeff_to (gbvector *f, ring_elem u)
gbvector *	gbvector_mult_by_coeff (const gbvector *f, ring_elem u)
void	gbvector_add_to_zzp (const FreeModule *F, gbvector *&f, gbvector *&g)
void	gbvector_add_to (const FreeModule *F, gbvector *&f, gbvector *&g)
void	gbvector_negate_to (gbvector *f) const
gbvector *	gbvector_copy (const gbvector *f)
void	find_reduction_coeffs (const FreeModule *F, const gbvector *f, const gbvector *g, ring_elem &u, ring_elem &v)
bool	find_reduction_coeffs_ZZ (const FreeModule *F, const gbvector *f, const gbvector *g, ring_elem &v)
void	find_reduction_monomial (const FreeModule *F, const gbvector *f, const gbvector *g, int &comp, int *&monom)
void	gbvector_mult_by_term (const FreeModule *F, const FreeModule *Fsyz, ring_elem a, const int *m, const gbvector *f, const gbvector *fsyz, gbvector *&result, gbvector *&esult_syz)
void	gbvector_reduce_lead_term (const FreeModule *F, const FreeModule *Fsyz, gbvector *flead, gbvector *&f, gbvector *&fsyz, const gbvector *g, const gbvector *gsyz, bool use_denom, ring_elem &denom)
void	gbvector_reduce_lead_term (const FreeModule *F, const FreeModule *Fsyz, gbvector *flead, gbvector *&f, gbvector *&fsyz, const gbvector *g, const gbvector *gsyz)
void	gbvector_reduce_with_marked_lead_term (const FreeModule *F, const FreeModule *Fsyz, gbvector *flead, gbvector *&f, gbvector *&fsyz, const gbvector *ginitial, const gbvector *g, const gbvector *gsyz, bool use_denom, ring_elem &denom)
bool	gbvector_reduce_lead_term_ZZ (const FreeModule *F, const FreeModule *Fsyz, gbvector *&f, gbvector *&fsyz, const gbvector *g, const gbvector *gsyz)
void	gbvector_cancel_lead_terms (const FreeModule *F, const FreeModule *Fsyz, const gbvector *f, const gbvector *fsyz, const gbvector *g, const gbvector *gsyz, gbvector *&result, gbvector *&result_syz)
void	gbvector_replace_2by2_ZZ (const FreeModule *F, const FreeModule *Fsyz, gbvector *&f, gbvector *&fsyz, gbvector *&g, gbvector *&gsyz)
void	gbvector_combine_lead_terms_ZZ (const FreeModule *F, const FreeModule *Fsyz, const gbvector *f, const gbvector *fsyz, const gbvector *g, const gbvector *gsyz, gbvector *&result, gbvector *&result_syz)
void	reduce_lead_term_heap (const FreeModule *F, const FreeModule *Fsyz, const gbvector *fcurrent_lead, const_exponents exp, gbvector *flead, gbvectorHeap &f, gbvectorHeap &fsyz, const gbvector *g, const gbvector *gsyz)
void	reduce_marked_lead_term_heap (const FreeModule *F, const FreeModule *Fsyz, const gbvector *fcurrent_lead, const_exponents exp, gbvector *flead, gbvectorHeap &f, gbvectorHeap &fsyz, const gbvector *marked_in_g, const gbvector *g, const gbvector *gsyz)
void	gbvector_remove_content (gbvector *f, gbvector *fsyz, bool use_denom, ring_elem &denom)
void	gbvector_remove_content (gbvector *f, gbvector *fsyz)
void	gbvector_auto_reduce (const FreeModule *F, const FreeModule *Fsyz, gbvector *&f, gbvector *&fsyz, const gbvector *g, const gbvector *gsyz)
void	gbvector_auto_reduce_ZZ (const FreeModule *F, const FreeModule *Fsyz, gbvector *&f, gbvector *&fsyz, const gbvector *g, const gbvector *gsyz)
void	gbvector_text_out (buffer &o, const FreeModule *F, const gbvector *f, int nterms=-1) const
void	gbvector_apply (const FreeModule *F, const FreeModule *Fsyz, gbvector *&f, gbvector *&fsyz, const gbvector *gsyz, const gbvector **elems, const gbvector **elems_syz, const gbvector **quotients)

Protected Member Functions
	GBRingSolvable (const Ring *K0, const Monoid *M0, const SolvableAlgebra *R0)
Protected Member Functions inherited from GBRing
gbvector *	new_raw_term ()
void	gbvector_remove_term (gbvector *f)
gbvector *	gbvector_copy_term (const gbvector *t)
void	divide_exponents (const int *exp1, const int *exp2, int *result) const
void	exponent_syzygy (const int *exp1, const int *exp2, int *exp3, int *exp4)
gbvector *	mult_by_term (const FreeModule *F, const gbvector *f, ring_elem u, const int *monom, int comp)
int	skew_mult_sign (int *exp1, int *exp2) const
void	divide_coeff_exact_to_ZZ (gbvector *f, gmp_ZZ u) const
void	lower_content_ZZ (gbvector *f, mpz_ptr content) const
void	gbvector_remove_content_ZZ (gbvector *f, gbvector *fsyz, bool use_denom, ring_elem &denom) const
const gbvector *	find_coeff (const FreeModule *F, const gbvector *f, const gbvector *g) const
	GBRing (const Ring *K0, const Monoid *M0)

Friends
class	GBRing

Additional Inherited Members
Static Public Member Functions inherited from GBRing
static GBRing *	create_PolynomialRing (const Ring *K, const Monoid *M)
static GBRing *	create_SkewPolynomialRing (const Ring *K0, const Monoid *M0, SkewMultiplication skew0)
static GBRing *	create_WeylAlgebra (const Ring *K0, const Monoid *M0, const WeylAlgebra *W0)
static GBRing *	create_SolvableAlgebra (const Ring *K0, const Monoid *M0, const SolvableAlgebra *R)
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 Attributes inherited from GBRing
bool	_schreyer_encoded
const Monoid *	M
const Ring *	K
bool	_coeffs_ZZ
CoefficientRingZZp *	zzp
size_t	gbvector_size
stash *	mem
int	_nvars
bool	_up_order
bool	_is_skew
SkewMultiplication	_skew
int *const *	_skew_monoms
bool	is_weyl
const WeylAlgebra *	weyl
bool	is_solvable
const SolvableAlgebra *	solvable
ring_elem	_one
size_t	exp_size
size_t	monom_size

Detailed Description

GBRing specialisation for solvable polynomial algebras (PBW-style non-commutative rings whose relations have the form x_j * x_i = c_ij * x_i * x_j + lower-order terms).

Note

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

mult_by_term1 consults the associated SolvableAlgebra to expand the lower-order correction terms whenever a monomial multiplication crosses a non-commuting pair.

Definition at line 670 of file gbring.hpp.

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

• Macaulay2/e/gbring.hpp
• Macaulay2/e/gbring.cpp