mty::SumIrrep Class Reference

Contains a sum of Irrep (irreducible representation) of a given SemiSimpleAlgebra. More...

#include <representation.h>

Inheritance diagram for mty::SumIrrep:

Public Member Functions
	SumIrrep ()
	Default constructor. Initializes an empty SumIrrep.
	SumIrrep (const std::vector< Irrep > &t_irrep)
	Constructor with one parameter. More...
	SumIrrep (const Irrep &other)
	Constructor with one parameter. More...
	~SumIrrep ()
	Destructor.
int	getDim () const
	Calculates and returns the total dimension of the SumIrrep, i.e. the sum of the dimensions of all representations in the sum. More...
const SemiSimpleAlgebra *	getAlgebra () const
void	insertSort (const Irrep &other)
	Inserts a new Irrep in the sum, sorting by dimension (lower dimensions first). More...
SumIrrep	operator+ (const Irrep &other) const
	Implements the sum of the SumIrrep with an Irrep (other), stores it in a SumIrrep and returns it. More...
SumIrrep	operator+ (const SumIrrep &other) const
	Implements the sum of the SumIrrep with a SumIrrep (other), stores it in a SumIrrep and returns it. More...
SumIrrep	operator* (const Irrep &other) const
	Calculates and returns the product of ***this** and other in the form of a sum of irreducible representations. More...
SumIrrep	operator* (const SumIrrep &other) const
	Calculates and returns the product of ***this** and other in the form of a sum of irreducible representations. More...

Protected Attributes
const SemiSimpleAlgebra *	algebra
	Pointer to the algebra from which the Irreps in the sum are irreducible representations.

Friends
std::ostream &	operator<< (std::ostream &fout, const SumIrrep &s)
	Overload of the operator<< for SumIrrep. Displays the total dimension and all dimensions of Irrep in the Sum. More...

Detailed Description

Contains a sum of Irrep (irreducible representation) of a given SemiSimpleAlgebra.

This class is a containor of a set of irreducible representations, Irrep objects, result of the decomposition of a tensor product of different Irrep. An example in \( SU(2)\):

\[2 \times 2 = 1 \oplus 3\]

, \(1 \oplus 3\) is a SumIrrep of size 2, containing the trivial representation of dimension 1, and the triplet. This class keeps its different Irrep sorted by increasing dimension at all time in order to respect usual conventions to display them.

Constructor & Destructor Documentation

SumIrrep() [1/2]

mty::SumIrrep::SumIrrep ( const std::vector< Irrep > &  t_irrep )

explicit

Constructor with one parameter.

Parameters

t_irrep

std::vector of Irrep in the sum.

SumIrrep() [2/2]

mty::SumIrrep::SumIrrep ( const Irrep &  other )

explicit

Constructor with one parameter.

Parameters

other

First (and unique for now) representation in the sum.

Member Function Documentation

getAlgebra()

const SemiSimpleAlgebra * mty::SumIrrep::getAlgebra

(

)

const

Returns

A pointer to the (const) SemiSimpleAlgebra of which the Irreps are representations.

getDim()

int mty::SumIrrep::getDim

(

)

const

Calculates and returns the total dimension of the SumIrrep, i.e. the sum of the dimensions of all representations in the sum.

For example, the dimension of \( 1\oplus 8\oplus8 \oplus 10 \) is 27.

Returns

The dimension of the SumIrrep.

insertSort()

void mty::SumIrrep::insertSort

(

const Irrep &

other

)

Inserts a new Irrep in the sum, sorting by dimension (lower dimensions first).

Parameters

other

Irrep to insert.

operator*() [1/2]

SumIrrep mty::SumIrrep::operator*

(

const Irrep &

other

)

const

Calculates and returns the product of ***this** and other in the form of a sum of irreducible representations.

The product is exanded the same way as Irrep::operator*(SumIrrep const& other) to yield a direct sum of Irrep, stored in a new SumIrrep that is returned.

Parameters

other

Right operand in the product of representation.

Returns

The product decomposed in sum of Irrep.

operator*() [2/2]

SumIrrep mty::SumIrrep::operator*

(

const SumIrrep &

other

)

const

Calculates and returns the product of ***this** and other in the form of a sum of irreducible representations.

The product is exanded the same way as Irrep::operator*(SumIrrep const& other) to yield a direct sum of Irrep, stored in a new SumIrrep that is returned. For example,

\[ (2\oplus 2) \times (1\oplus 3) = (2\times 1)\oplus (2\times 3)\oplus (2\times 1) \oplus (2\times 3) = 1\oplus 1\oplus 2\oplus 2\oplus 4\oplus 4.\]

Parameters

other

Right operand in the product of representation.

Returns

The product decomposed in sum of Irrep.

operator+() [1/2]

SumIrrep mty::SumIrrep::operator+

(

const Irrep &

other

)

const

Implements the sum of the SumIrrep with an Irrep (other), stores it in a SumIrrep and returns it.

A SumIrrep similar to *this is created, and other is inserted in it, calling SumIrrep::insertSort().

Parameters

other

Second operand in the sum.

Returns

The SumIrrep of ***this** and other.

operator+() [2/2]

SumIrrep mty::SumIrrep::operator+

(

const SumIrrep &

other

)

const

Implements the sum of the SumIrrep with a SumIrrep (other), stores it in a SumIrrep and returns it.

The two lists of Irrep objects are simply merged in a new SumIrrep and sorted. The total dimension of the result is the sum of the two operands' dimensions.

Parameters

other

Second operand in the sum.

Returns

The SumIrrep of ***this** and other.

Friends And Related Function Documentation

operator<<

std::ostream& operator<< ( std::ostream &  fout, const SumIrrep &  s  )

friend

Overload of the operator<< for SumIrrep. Displays the total dimension and all dimensions of Irrep in the Sum.

Parameters

fout	Output flux.
irrep	SumIrrep to display.

Returns

The modified flux.

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

• include/representation.h
• src/representation.cpp