symmp Namespace Reference

The namespace which contains every method and class in the library. More...

Classes
class	FactoryGenerator
	Prototype for coroutine-like iterators that generate elements such as combinations. More...
class	PermutationGenerator
	Generates all permutations on a number of letters. More...
class	CombinationGenerator
	Generates all combinations on a number of letters making a number of choices. More...
struct	ArrayVectorWrapper
	Wrapping array and vector in the same interface. More...
struct	HalfIdempotentVariables
	Variables \(x_1,...,x_n,y_1,...,y_n\) with \(y_i^2=y_i\) and \(|x_i|=1\), \(|y_i|=0\). More...
struct	TwistedChernVariables
	The twisted Chern generators as variables \(\gamma_{s,j}\). More...
class	TwistedChernBasis
	Class for half-idempotent symmetric polynomials. More...
class	BaseContainer
	The base of all monomial containers. More...
class	DefaultContainer
	The default ordered/unordered monomial container. More...
class	Polynomial
	Class for polynomials in multiple variables with relations. More...
struct	StandardVariables
	The standard variables \(x_i\) in a polynomial, with \(|x_i|=1\) and no relations. More...
struct	ElementarySymmetricVariables
	Variables \(e_1,...,e_n\) of degrees \(|e_i|=i\). More...
class	PolynomialBasis
	Factory class that provides the general interface of a generating basis for a subring of a polynomial ring. More...
class	SymmetricBasis
	Class for symmetric polynomials with no relations, allowing transformation from \(x_i\) variables to \(e_i\) variables and vice-versa. More...

Typedefs
template<class _scl , class _exp , bool _ord = 1>
using	Poly = Polynomial< std::conditional_t< _ord, DefaultContainer< _scl, _exp, std::map, 1 >, DefaultContainer< _scl, _exp, std::unordered_map, 0 > >>
	Polynomial using the default containers std::map or std::unordered_map. More...

Functions
template<typename T , typename hasher = boost_hash>
size_t	generic_hasher (const T &v)
	A generic hashing function that calls other hashing functions. More...
template<typename R , typename T , typename S >
R	general_compute_degree (const T &exp, const S &dim)
	Degree computation given exponent and dimensions (grading). More...
template<class T >
std::vector< std::vector< T > >	all_permutations (T n)
	Returns vector of all permutations on n letters. More...
template<class T >
std::vector< std::vector< T > >	all_combinations (T n, T m)
	Returns vector of all combinations on n letters choosing m many. More...
template<class xy_poly_t , class chern_poly_t >
void	print_half_idempotent_relations (int n, bool print=1, bool verify=1, bool verify_verbose=1)
	Prints the relations of \(\Big(\mathbf Z[x_1,...,x_n,y_1,...,y_n]/(y_i^2=y_i)\Big)^{\Sigma_n}\). More...
template<class container_t >
std::ostream &	operator<< (std::ostream &os, const Polynomial< container_t > &a)
	Prints polynomial to output stream. More...

Detailed Description

The namespace which contains every method and class in the library.

Typedef Documentation

Poly

using Poly = Polynomial<std::conditional_t<_ord, DefaultContainer<_scl, _exp, std::map, 1>, DefaultContainer<_scl, _exp, std::unordered_map, 0> >>

Polynomial using the default containers std::map or std::unordered_map.

Template Parameters

_scl	The scalar/coefficient type of the polynomial
_exp	The variable/exponent type of the Polynomial eg StandardVariables or HalfIdempotentVariables
_ord	If _ord==1 then std::map is used as the container for the polynomial; otherwise std::unordered_map is used

Function Documentation

generic_hasher()

size_t symmp::generic_hasher

(

const T &

v

)

A generic hashing function that calls other hashing functions.

Template Parameters

T	The type of element to be hashed (must have a for range loop)
hasher	The hashing algorithm. boost_hash by default. If SSE4.1 is supported you can also use crc

Parameters

v	The element to be hashed

Returns

The hash of the element

general_compute_degree()

R symmp::general_compute_degree	(	const T &	exp,
		const S &	dim
	)

Degree computation given exponent and dimensions (grading).

Template Parameters

T	The exponent type (eg std::vector<int>)
S	The dimensions type (eg std::vector<int>)
R	The degree type (eg uint64_t)

Parameters

exp	The monomial whose degree will be computed, provided via its exponent vector
dim	The dimensions of the variables in the monomial

Returns

The degree \(\sum_{i=1}^na_id_i\) where exponent= \([a_1,...,a_n]\) and dimensions= \([d_1,...,d_n]\)

all_permutations()

std::vector<std::vector<T> > symmp::all_permutations

(

T

n

)

Returns vector of all permutations on n letters.

Template Parameters

T	The value type of the permutations

Parameters

n	The number of letters

Returns

Vector of vectors each of which is \([a_0,...,a_{n-1}]\) with \(0\le a_i\le n-1\) all distinct

all_combinations()

std::vector<std::vector<T> > symmp::all_combinations	(	T	n,
		T	m
	)

Returns vector of all combinations on n letters choosing m many.

Template Parameters

T	The value type of the combinations

Parameters

n	The number of letters
m	The number of choices

Returns

Vector of vectors each of which is \([a_0,...,a_{n-1}]\) with \(0\le a_i\le n-1\) all distinct

print_half_idempotent_relations()

void symmp::print_half_idempotent_relations	(	int	n,
		bool	print = 1,
		bool	verify = 1,
		bool	verify_verbose = 1
	)

Prints the relations of \(\Big(\mathbf Z[x_1,...,x_n,y_1,...,y_n]/(y_i^2=y_i)\Big)^{\Sigma_n}\).

The generators \(\alpha_i, c_i, \gamma_{s,j}\) are printed as a_i, c_i, c_{s,j} in the console.

Template Parameters

xy_poly_t	The type of polynomial on the \(x_i,y_i\) variables
chern_poly_t	The type of polynomial on the \(\gamma_{s,j}\) variables

Parameters

n	Half the number of variables (the \(n\))
print	Whether we want to print the relations to the console
verify	Whether to verify the relations
verify_verbose	Whether to verify and print the verification to the console

operator<<()

std::ostream& symmp::operator<<	(	std::ostream &	os,
		const Polynomial< container_t > &	a
	)

Prints polynomial to output stream.

Template Parameters

container_t

The data store type (container) of the polynomial eg DefaultContainer

Parameters

os	The output stream
a	The polynomial to be printed

Returns

The output stream where the polynomial has been printed