TwistedChernBasis< xy_poly_t, chern_poly_t > Class Template Reference

Class for half-idempotent symmetric polynomials. More...

#include <Half_Idempotent.hpp>

Inheritance diagram for TwistedChernBasis< xy_poly_t, chern_poly_t >:

Collaboration diagram for TwistedChernBasis< xy_poly_t, chern_poly_t >:

Public Member Functions
	TwistedChernBasis (int n)
	Constructs the generators and the relation set given \(n\) in \(x_1,...,x_n,y_1,...,y_n\). More...
const std::vector< chern_poly_t > &	relations () const
	The relations are \(\gamma_{s,i}\gamma_{t,j}\) for \(0<s<=t<=s+i\) and \(i,j>0\). More...
const xy_poly_t &	generator (int s, int j) const
	The generator \(\gamma_{s,j}\). More...
Public Member Functions inherited from PolynomialBasis< TwistedChernBasis< xy_poly_t, chern_poly_t >, xy_poly_t, chern_poly_t >
chern_poly_t	operator() (xy_poly_t a) const
	Transform a polynomial on the original variables to one on the generating basis. More...
xy_poly_t	operator() (const chern_poly_t &a) const
	Transform a polynomial on the generating basis into a polynomial on the original variables. More...
	PolynomialBasis (int num)
	Constructor given number of variables. More...
const std::vector< xy_poly_t > &	generators () const
	Returns vector containing the generating basis. More...
const std::vector< typename new_poly_t::deg_t > &	dimensions () const
	Returns vector containing the dimensions of the generating basis (can be empty!) More...
const std::vector< std::string > &	names () const
	Returns vector containing the names of the generating basis (can be empty!) More...

Friends
class	PolynomialBasis< TwistedChernBasis< xy_poly_t, chern_poly_t >, xy_poly_t, chern_poly_t >
	Befriending parent for CRTP. More...

Additional Inherited Members
Public Attributes inherited from PolynomialBasis< TwistedChernBasis< xy_poly_t, chern_poly_t >, xy_poly_t, chern_poly_t >
const int	number_of_variables
	The number of (the original) variables of the polynomial ring. More...
Protected Attributes inherited from PolynomialBasis< TwistedChernBasis< xy_poly_t, chern_poly_t >, xy_poly_t, chern_poly_t >
std::vector< xy_poly_t >	_generators
	The generators of the polynomial basis, constructed in the inheriting class. More...
std::vector< typename new_poly_t::deg_t >	generator_dimensions
	The dimensions of the generators, optionally constructed in the inheriting class. More...
std::vector< std::string >	generator_names
	The names of the generators, optionally constructed in the inheriting class. More...

Detailed Description

template<class xy_poly_t, class chern_poly_t>
class symmp::TwistedChernBasis< xy_poly_t, chern_poly_t >

Class for half-idempotent symmetric polynomials.

Facilitates transformation from \(x_i,y_i\) variables to \(\gamma_{s,i}\) variables and vice-versa.

Template Parameters

xy_poly_t	The container type on the HalfIdempotentVariables \(x_i,y_i\)
chern_poly_t	The container type on the TwistedChernVariables \(\gamma_{s,j}\)

Constructor & Destructor Documentation

TwistedChernBasis()

TwistedChernBasis

(

int

n

)

Constructs the generators and the relation set given \(n\) in \(x_1,...,x_n,y_1,...,y_n\).

Parameters

n	Half(!) the number of variables

Attention

The parameter n is half(!) the number of variables (the \(n\) in \(BU(n)\))

Member Function Documentation

relations()

const std::vector<chern_poly_t>& relations

(

)

const

The relations are \(\gamma_{s,i}\gamma_{t,j}\) for \(0<s<=t<=s+i\) and \(i,j>0\).

Returns

const& to vector containing the relation Polynomials \(\gamma_{s,i}\gamma_{t,j}\)

generator()

const xy_poly_t& generator	(	int	s,
		int	j
	)		const

The generator \(\gamma_{s,j}\).

Parameters

s	The index of \(s\) of \(\gamma_{s,j}\).
j	The index of \(j\) of \(\gamma_{s,j}\).

Returns

const& to the polynomial \(\gamma_{s,j}\) on the \(x_i,y_i\) variables

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Friends And Related Function Documentation

PolynomialBasis< TwistedChernBasis< xy_poly_t, chern_poly_t >, xy_poly_t, chern_poly_t >

friend class PolynomialBasis< TwistedChernBasis< xy_poly_t, chern_poly_t >, xy_poly_t, chern_poly_t >

friend

Befriending parent for CRTP.

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

• Half_Idempotent.hpp