SchurSnRing Class Reference

SchurRing2 subclass implementing the symmetric-group character ring (the "Schur ring of `S_n`"), with multiplication given by inner-product convolution rather than Littlewood-Richardson. More...

#include <schurSn.hpp>

Inheritance diagram for SchurSnRing:

Public Member Functions
	SchurSnRing (const Ring *A, int n=-1)
virtual const SchurSnRing *	cast_to_SchurSnRing () const
virtual SchurSnRing *	cast_to_SchurSnRing ()
virtual ring_elem	mult (const ring_elem f, const ring_elem g) const
ring_elem	tensor_mult (const ring_elem f, const ring_elem g) const
Public Member Functions inherited from SchurRing2
int	n_vars () const
const Ring *	getCoefficientRing () const
virtual const SchurRing2 *	cast_to_SchurRing2 () const
virtual SchurRing2 *	cast_to_SchurRing2 ()
bool	is_valid_partition (M2_arrayint part, bool set_error=true) const
ring_elem	from_coeff (ring_elem a) const
ring_elem	from_partition (M2_arrayint part) const
schur_poly *	mult_by_coefficient (ring_elem a, const schur_poly *f) const
bool	get_scalar (const schur_poly *f, ring_elem &result) const
size_t	size (ring_elem f) const
void	dimension (const int *exp, mpz_t result) const
ring_elem	dimension (const ring_elem f) const
engine_RawArrayPairOrNull	list_form (const Ring *coeffR, const ring_elem f) const
virtual unsigned int	computeHashValue (const ring_elem a) const
virtual void	text_out (buffer &o) 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	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	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 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 ring_elem	copy (const ring_elem f) const
virtual void	remove (ring_elem &f) 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	eval (const RingMap *map, const ring_elem f, int first_var) const
virtual ring_elem	invert (const ring_elem f) const
virtual ring_elem	divide (const ring_elem f, const ring_elem g) const
virtual void	syzygy (const ring_elem a, const ring_elem b, ring_elem &x, ring_elem &y) const
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	is_basic_ring () 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
virtual bool	is_fraction_poly_ring () const
virtual bool	is_poly_ring () const
virtual bool	is_commutative_ring () const
virtual bool	is_quotient_ring () const
virtual bool	is_weyl_algebra () const
virtual bool	is_skew_commutative_ring () const
virtual bool	is_solvable_algebra () const
virtual bool	is_graded () const
bool	is_field () const
bool	declare_field ()
ring_elem	get_non_unit () const
void	set_non_unit (ring_elem zero_div) const
virtual CoefficientType	coefficient_type () 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 PolynomialRing *	cast_to_PolynomialRing () const
virtual PolynomialRing *	cast_to_PolynomialRing ()
virtual const PolyRing *	cast_to_PolyRing () const
virtual PolyRing *	cast_to_PolyRing ()
virtual const PolyQQ *	cast_to_PolyQQ () const
virtual PolyQQ *	cast_to_PolyQQ ()
virtual const PolyRingFlat *	cast_to_PolyRingFlat () const
virtual PolyRingFlat *	cast_to_PolyRingFlat ()
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 SkewPolynomialRing *	cast_to_SkewPolynomialRing () const
virtual SkewPolynomialRing *	cast_to_SkewPolynomialRing ()
virtual const SolvableAlgebra *	cast_to_SolvableAlgebra () const
virtual SolvableAlgebra *	cast_to_SolvableAlgebra ()
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 SumCollector *	make_SumCollector () 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	from_BigReal (gmp_RR a, ring_elem &result) const
virtual bool	from_Interval (gmp_RRi a, ring_elem &result) const
virtual bool	from_BigComplex (gmp_CC 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 ring_elem	preferred_associate (ring_elem f) 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
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	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 ring_elem	random () const
virtual int	index_of_var (const ring_elem a) const
virtual M2_arrayint	support (const ring_elem a) 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 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 bool	is_homogeneous (const ring_elem f) const
const_monomial	degree (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	antipode (ring_elem f) const
virtual unsigned long	get_precision () 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
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
virtual vec	vec_lead_term (int nparts, const FreeModule *F, 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
virtual void	lower_content (ring_elem &c, ring_elem g) 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
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 SchurSnRing *	create (const Ring *A, int n=-1)
Static Public Member Functions inherited from SchurRing2
static SchurRing2 *	create (const Ring *A, int n=-1)
static SchurRing2 *	createInfinite (const Ring *A)
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)

Additional Inherited Members
Public Types inherited from Ring
enum	CoefficientType { COEFF_ZZ , COEFF_QQ , COEFF_BASIC }
Protected Member Functions inherited from SchurRing2
bool	initialize_schur ()
bool	initialize_SchurRing2 ()
	SchurRing2 ()
	SchurRing2 (const Ring *A, int n=-1)
virtual	~SchurRing2 ()
int	compare_partitions (const_schur_partition a, const_schur_partition b) const
ring_elem	truncate (const ring_elem f) const
bool	promote_coeffs (const SchurRing2 *Sf, const ring_elem f, ring_elem &resultRE) const
bool	lift_coeffs (const SchurRing2 *Sg, const ring_elem f, ring_elem &resultRE) 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
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

Detailed Description

SchurRing2 subclass implementing the symmetric-group character ring (the "Schur ring of `S_n`"), with multiplication given by inner-product convolution rather than Littlewood-Richardson.

Note

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

Overrides mult to compute the symmetric-group analogue: the coefficient of s_lambda in s_mu * s_nu is the number of ways to decompose representations rather than the LR count. cast_to_SchurSnRing() lets engine code distinguish this ring from the plain SchurRing2 it inherits from.

Definition at line 50 of file schurSn.hpp.

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

• Macaulay2/e/schurSn.hpp
• Macaulay2/e/schurSn.cpp