An object that contains an NTL::ZZX polynomial along with a coefficient modulus p2r and a polynomial modulus G. More...

#include <PolyMod.h>

Public Member Functions
	PolyMod ()
	Default constructor. More...

	PolyMod (const std::shared_ptr< PolyModRing > &ringDescriptor)
	No-data constructor. More...

	PolyMod (long input, const std::shared_ptr< PolyModRing > &ringDescriptor)
	Constant constructor. More...

	PolyMod (const std::vector< long > &input, const std::shared_ptr< PolyModRing > &ringDescriptor)
	Coefficient vector constructor. More...

	PolyMod (const NTL::ZZX &input, const std::shared_ptr< PolyModRing > &ringDescriptor)
	Polynomial constructor. More...

	PolyMod (const PolyMod &input)=default
	Default copy constructor. More...

	PolyMod (PolyMod &&input) noexcept=default
	Default move constructor. More...

	~PolyMod ()=default
	Default destructor. More...

PolyMod &	operator= (const PolyMod &input)=default
	Assignment operator. More...

PolyMod &	operator= (PolyMod &&input)=default
	default move assignment operator More...

PolyMod &	operator= (long input)
	`long` assignment operator, creates a constant polynomial mod G and p2r. More...

PolyMod &	operator= (const std::vector< long > &input)
	`std::vector<long>` assignment operator, creates a polynomial mod G and p2r. More...

PolyMod &	operator= (const std::initializer_list< long > &input)
	`std::initializer_list<long>` assignment operator, creates a polynomial mod G and p2r. More...

PolyMod &	operator= (const NTL::ZZX &input)
	`NTL::ZZX` assignment operator, creates a polynomial mod G and p2r. More...

	operator long () const
	Explicit conversion to a `long`. More...

	operator std::vector< long > () const
	Explicit conversion to `std::vector<long>` (coefficient vector). More...

	operator NTL::ZZX () const
	Explicit conversion to an `NTL::ZZX`. More...

bool	isValid () const
	Gets the validity of `this`. This will be `false` iff `this` was default constructed. More...

long	getp2r () const
	Get current p^r value. More...

NTL::ZZX	getG () const
	Get current G value. More...

const NTL::ZZX &	getData () const
	Getter function that returns the data of `PolyMod` as an `NTL::ZZX` const reference. More...

bool	operator== (const PolyMod &rhs) const
	Equals operator between two `PolyMod` objects. More...

bool	operator== (long rhs) const
	Equals operator between a `PolyMod` and a `long`. More...

bool	operator== (const std::vector< long > &rhs) const
	Equals operator between two `PolyMod` objects. More...

bool	operator== (const NTL::ZZX &rhs) const
	Equals operator between two `PolyMod` objects. More...

template<typename T >
bool	operator!= (T &&rhs) const
	Not equals operator. More...

PolyMod &	negate ()
	Negate function. More...

PolyMod	operator- () const
	Unary minus operator. More...

PolyMod	operator* (const PolyMod &rhs) const
	Infix multiplication operator. More...

PolyMod	operator* (long rhs) const
	Infix multiplication operator with `long`. More...

PolyMod	operator* (const NTL::ZZX &rhs) const
	Infix multiplication operator with `NTL::ZZX`. More...

PolyMod	operator+ (const PolyMod &rhs) const
	Infix plus operator. More...

PolyMod	operator+ (long rhs) const
	Infix plus operator with `long`. More...

PolyMod	operator+ (const NTL::ZZX &rhs) const
	Infix plus operator with `NTL::ZZX`. More...

PolyMod	operator- (const PolyMod &rhs) const
	Infix minus operator. More...

PolyMod	operator- (long rhs) const
	Infix minus operator with `long`. More...

PolyMod	operator- (const NTL::ZZX &rhs) const
	Infix minus operator with `NTL::ZZX`. More...

PolyMod &	operator*= (const PolyMod &otherPoly)
	Times equals operator with `PolyMod` rhs. More...

PolyMod &	operator*= (long scalar)
	Times equals operator with `long` rhs. More...

PolyMod &	operator*= (const NTL::ZZX &otherPoly)
	Times equals operator with `NTL::ZZX` rhs. More...

PolyMod &	operator+= (const PolyMod &otherPoly)
	Plus equals operator with `PolyMod` rhs. More...

PolyMod &	operator+= (long scalar)
	Plus equals operator with `long` rhs. More...

PolyMod &	operator+= (const NTL::ZZX &otherPoly)
	Plus equals operator with `NTL::ZZX` rhs. More...

PolyMod &	operator-= (const PolyMod &otherPoly)
	Minus equals operator with `PolyMod` rhs. More...

PolyMod &	operator-= (long scalar)
	Minus equals operator with `long` rhs. More...

PolyMod &	operator-= (const NTL::ZZX &otherPoly)
	Minus equals operator with `NTL::ZZX` rhs. More...

void	writeToJSON (std::ostream &os) const
	Serialize `this` `PolyMod` to the output stream `os`. More...

JsonWrapper	writeToJSON () const
	Serialize `this` `PolyMod` to the `JsonWrapper` object. More...

void	readJSON (std::istream &is)
	In-place deserialize a `PolyMod` object from the input stream `is`. More...

void	readJSON (const JsonWrapper &jw)
	In-place deserialize a `PolyMod` object from the from the `JsonWrapper` `jw`. More...

Static Public Member Functions
static PolyMod	readFromJSON (std::istream &is, const std::shared_ptr< PolyModRing > &ringDescriptor)
	Deserialize a `PolyMod` object from the input stream `is`. More...

static PolyMod	readFromJSON (const JsonWrapper &jw, const std::shared_ptr< PolyModRing > &ringDescriptor)
	Deserialize a `PolyMod` object from the `JsonWrapper` `jw`. More...

Friends
std::istream &	operator>> (std::istream &is, PolyMod &poly)
	Input shift operator. More...

std::ostream &	operator<< (std::ostream &os, const PolyMod &poly)
	Output shift operator. More...

Detailed Description

An object that contains an NTL::ZZX polynomial along with a coefficient modulus p2r and a polynomial modulus G.

A PolyMod object can be considered to be an element of $\mathbb{Z}_{p^r}[x]/G$ where $p^r$ and $ G$ are the passed-in parameters p2r and G.

This allows for inter-PolyMod operations with the modulo operations performed automatically.

General usage:

helib::PolyMod poly(input_data, p2r, G);

helib::PolyMod

An object that contains an NTL::ZZX polynomial along with a coefficient modulus p2r and a polynomial ...

Definition: PolyMod.h:49

Calling an operation on a default constructed PolyMod will throw an helib::LogicError.

Constructor & Destructor Documentation

◆ PolyMod() [1/7]

helib::PolyMod::PolyMod ( )

Default constructor.

Note: PolyMod objects constructed using this are marked as invalid. If used for any operation whether directly on a PolyMod or via another object such as Ptxt this will produce an error.

◆ PolyMod() [2/7]

helib::PolyMod::PolyMod ( const std::shared_ptr< PolyModRing > & ringDescriptor )

explicit

No-data constructor.

Parameters

ringDescriptor Descriptor object for the plaintext ring. Contains p^r and G which are to be used for modular reduction.

Note: This constructor does not take in input data but can be assigned data later via operator=.

◆ PolyMod() [3/7]

helib::PolyMod::PolyMod	(	long	input,
		const std::shared_ptr< PolyModRing > &	ringDescriptor
	)

Constant constructor.

Parameters

input	Input data as a `long`.
ringDescriptor	Descriptor object for the plaintext ring. Contains p^r and G which are to be used for modular reduction.

Note: This constructor accepts input data as a long and converts it into an NTL::ZZX polynomial.

◆ PolyMod() [4/7]

helib::PolyMod::PolyMod	(	const std::vector< long > &	input,
		const std::shared_ptr< PolyModRing > &	ringDescriptor
	)

Coefficient vector constructor.

Parameters

input	Input data as a vector of `long` (the i'th element of the vector corresponds to the coefficient of x^i).
ringDescriptor	Descriptor object for the plaintext ring. Contains p^r and G which are to be used for modular reduction.

Note: This constructor accepts input data as a std::vector<long> and converts it into an NTL::ZZX polynomial.

◆ PolyMod() [5/7]

helib::PolyMod::PolyMod	(	const NTL::ZZX &	input,
		const std::shared_ptr< PolyModRing > &	ringDescriptor
	)

Polynomial constructor.

Parameters

input	Input data as an `NTL::ZZX`.
ringDescriptor	Descriptor object for the plaintext ring. Contains p^r and G which are to be used for modular reduction.

Note: This constructor accepts input data as an NTL::ZZX.

◆ PolyMod() [6/7]

helib::PolyMod::PolyMod ( const PolyMod & input )

default

Default copy constructor.

Parameters

input PolyMod object that is copied.

◆ PolyMod() [7/7]

helib::PolyMod::PolyMod ( PolyMod && input )

defaultnoexcept

Default move constructor.

◆ ~PolyMod()

helib::PolyMod::~PolyMod ( )

default

Default destructor.

Member Function Documentation

◆ getData()

const NTL::ZZX & helib::PolyMod::getData ( ) const

Getter function that returns the data of PolyMod as an NTL::ZZX const reference.

◆ getG()

NTL::ZZX helib::PolyMod::getG ( ) const

Get current G value.

Returns: The current G value in use.

◆ getp2r()

long helib::PolyMod::getp2r ( ) const

Get current p^r value.

Returns: The current p^r value in use.

◆ isValid()

bool helib::PolyMod::isValid ( ) const

Gets the validity of this. This will be false iff this was default constructed.

Returns: true if this is valid, false otherwise.

◆ negate()

PolyMod & helib::PolyMod::negate ( )

Negate function.

Returns: Reference to *this post negation.

◆ operator long()

helib::PolyMod::operator long ( ) const

explicit

Explicit conversion to a long.

Note: This function returns only the constant term even if the polynomial contains higher order terms.

◆ operator NTL::ZZX()

helib::PolyMod::operator NTL::ZZX ( ) const

explicit

Explicit conversion to an NTL::ZZX.

◆ operator std::vector< long >()

helib::PolyMod::operator std::vector< long > ( ) const

explicit

Explicit conversion to std::vector<long> (coefficient vector).

◆ operator!=()

template<typename T >

bool helib::PolyMod::operator!= ( T && rhs ) const

inline

Not equals operator.

Parameters

rhs	Right-hand side of comparison.

Returns: true if not equal, false otherwise

Note: Simply forwards to the correct operator== method.

◆ operator*() [1/3]

PolyMod helib::PolyMod::operator* ( const NTL::ZZX & rhs ) const

Infix multiplication operator with NTL::ZZX.

Parameters

rhs	Right hand side of multiplication.

Returns: Product of the two objects.

◆ operator*() [2/3]

PolyMod helib::PolyMod::operator* ( const PolyMod & rhs ) const

Infix multiplication operator.

Parameters

rhs	Right hand side of multiplication.

Returns: Product of the two PolyMod objects.

◆ operator*() [3/3]

PolyMod helib::PolyMod::operator* ( long rhs ) const

Infix multiplication operator with long.

Parameters

rhs	Right hand side of multiplication.

Returns: Product of the two values.

◆ operator*=() [1/3]

PolyMod & helib::PolyMod::operator*= ( const NTL::ZZX & otherPoly )

Times equals operator with NTL::ZZX rhs.

Parameters

otherPoly Right hand side of multiplication.

Returns: Reference to *this post multiplication.

◆ operator*=() [2/3]

PolyMod & helib::PolyMod::operator*= ( const PolyMod & otherPoly )

Times equals operator with PolyMod rhs.

Parameters

otherPoly Right hand side of multiplication.

Returns: Reference to *this post multiplication.

◆ operator*=() [3/3]

PolyMod & helib::PolyMod::operator*= ( long scalar )

Times equals operator with long rhs.

Parameters

scalar Right hand side of multiplication.

Returns: Reference to *this post multiplication.

◆ operator+() [1/3]

PolyMod helib::PolyMod::operator+ ( const NTL::ZZX & rhs ) const

Infix plus operator with NTL::ZZX.

Parameters

rhs	Right hand side of addition.

Returns: Sum of the two objects.

◆ operator+() [2/3]

PolyMod helib::PolyMod::operator+ ( const PolyMod & rhs ) const

Infix plus operator.

Parameters

rhs	Right hand side of addition.

Returns: Sum of the two PolyMod objects.

◆ operator+() [3/3]

PolyMod helib::PolyMod::operator+ ( long rhs ) const

Infix plus operator with long.

Parameters

rhs	Right hand side of addition.

Returns: Sum of the two values.

◆ operator+=() [1/3]

PolyMod & helib::PolyMod::operator+= ( const NTL::ZZX & otherPoly )

Plus equals operator with NTL::ZZX rhs.

Parameters

otherPoly Right hand side of addition.

Returns: Reference to *this post addition.

◆ operator+=() [2/3]

PolyMod & helib::PolyMod::operator+= ( const PolyMod & otherPoly )

Plus equals operator with PolyMod rhs.

Parameters

otherPoly Right hand side of addition.

Returns: Reference to *this post addition.

◆ operator+=() [3/3]

PolyMod & helib::PolyMod::operator+= ( long scalar )

Plus equals operator with long rhs.

Parameters

scalar Right hand side of addition.

Returns: Reference to *this post addition.

◆ operator-() [1/4]

PolyMod helib::PolyMod::operator- ( ) const

Unary minus operator.

Returns: Negation of the PolyMod.

◆ operator-() [2/4]

PolyMod helib::PolyMod::operator- ( const NTL::ZZX & rhs ) const

Infix minus operator with NTL::ZZX.

Parameters

rhs	Right hand side of subtraction.

Returns: Difference of the two objects.

◆ operator-() [3/4]

PolyMod helib::PolyMod::operator- ( const PolyMod & rhs ) const

Infix minus operator.

Parameters

rhs	Right hand side of subtraction.

Returns: Difference of the two PolyMod objects.

◆ operator-() [4/4]

PolyMod helib::PolyMod::operator- ( long rhs ) const

Infix minus operator with long.

Parameters

rhs	Right hand side of subtraction.

Returns: Difference of the two values.

◆ operator-=() [1/3]

PolyMod & helib::PolyMod::operator-= ( const NTL::ZZX & otherPoly )

Minus equals operator with NTL::ZZX rhs.

Parameters

otherPoly Right hand side of subtraction.

Returns: Reference to *this post subtraction.

◆ operator-=() [2/3]

PolyMod & helib::PolyMod::operator-= ( const PolyMod & otherPoly )

Minus equals operator with PolyMod rhs.

Parameters

otherPoly Right hand side of subtraction.

Returns: Reference to *this post subtraction.

◆ operator-=() [3/3]

PolyMod & helib::PolyMod::operator-= ( long scalar )

Minus equals operator with long rhs.

Parameters

scalar Right hand side of subtraction.

Returns: Reference to *this post subtraction.

◆ operator=() [1/6]

PolyMod & helib::PolyMod::operator= ( const NTL::ZZX & input )

NTL::ZZX assignment operator, creates a polynomial mod G and p2r.

Parameters

input Polynomial.

◆ operator=() [2/6]

PolyMod& helib::PolyMod::operator= ( const PolyMod & input )

default

Assignment operator.

Parameters

input Another PolyMod to copy.

◆ operator=() [3/6]

PolyMod & helib::PolyMod::operator= ( const std::initializer_list< long > & input )

std::initializer_list<long> assignment operator, creates a polynomial mod G and p2r.

Parameters

input coefficient vector as an initializer list of long (the i'th element of the vector corresponds to the coefficient of x^i).

◆ operator=() [4/6]

PolyMod & helib::PolyMod::operator= ( const std::vector< long > & input )

std::vector<long> assignment operator, creates a polynomial mod G and p2r.

Parameters

input Coefficient vector of long (the i'th element of the vector corresponds to the coefficient of x^i).

◆ operator=() [5/6]

PolyMod & helib::PolyMod::operator= ( long input )

long assignment operator, creates a constant polynomial mod G and p2r.

Parameters

input long datum.

◆ operator=() [6/6]

PolyMod& helib::PolyMod::operator= ( PolyMod && input )

default

default move assignment operator

◆ operator==() [1/4]

bool helib::PolyMod::operator== ( const NTL::ZZX & rhs ) const

Equals operator between two PolyMod objects.

Parameters

rhs	Other `PolyMod` to compare to.

Returns: true if identical, false otherwise.

Note: Always returns false when called on invalid PolyMod objects.

◆ operator==() [2/4]

bool helib::PolyMod::operator== ( const PolyMod & rhs ) const

Equals operator between two PolyMod objects.

Parameters

rhs	Other `PolyMod` to compare to.

Returns: true if PolyMod objects are identical, false otherwise.

◆ operator==() [3/4]

bool helib::PolyMod::operator== ( const std::vector< long > & rhs ) const

Equals operator between two PolyMod objects.

Parameters

rhs	Other `PolyMod` to compare to.

Returns: true if identical, false otherwise.

Note: Always returns false when called on invalid PolyMod objects.

◆ operator==() [4/4]

bool helib::PolyMod::operator== ( long rhs ) const

Equals operator between a PolyMod and a long.

Parameters

rhs	`long` to compare the data against.

Returns: true if identical, false otherwise.

Note: Always returns false when called on invalid PolyMod objects.

◆ readFromJSON() [1/2]

PolyMod helib::PolyMod::readFromJSON	(	const JsonWrapper &	jw,
		const std::shared_ptr< PolyModRing > &	ringDescriptor
	)

static

Deserialize a PolyMod object from the JsonWrapper jw.

Parameters

jw	Input `JsonWrapper`.
ringDescriptor	Descriptor object for the plaintext ring.

Returns: The deserialized PolyMod object.
PolyMod my_poly = PolyMod::readFromJSON(..., context);

helib::PolyMod::readFromJSON
static PolyMod readFromJSON(std::istream &is, const std::shared_ptr< PolyModRing > &ringDescriptor)
Deserialize a PolyMod object from the input stream is.
Definition: PolyMod.cpp:303

helib::PolyMod::PolyMod
PolyMod()
Default constructor.
Definition: PolyMod.cpp:24

The input stream has to be a JSON list.
Each element of the list will be deserialized as a coefficient of the polynomial.
For example '['coef0', 'coef1', 'coef2']' will be deserialized as a PolyMod object poly where poly[0]=coef0, poly[1]=coef1, poly[2]=coef2 and poly[i]=0 for i>2.

◆ readFromJSON() [2/2]

PolyMod helib::PolyMod::readFromJSON	(	std::istream &	is,
		const std::shared_ptr< PolyModRing > &	ringDescriptor
	)

static

Deserialize a PolyMod object from the input stream is.

Parameters

is	Input `std::istream`.
ringDescriptor	Descriptor object for the plaintext ring.

Returns: The deserialized PolyMod object.

Exceptions

IOError

if the stream is not a valid JSON.

PolyMod my_poly = PolyMod::readFromJSON(std::cin, context);

The input stream has to be formatted as a JSON list.
Each element of the list will be deserialized as a coefficient of the polynomial.
For example '['coef0', 'coef1', 'coef2']' will be deserialized as a PolyMod object poly where poly[0]=coef0, poly[1]=coef1, poly[2]=coef2 and poly[i]=0 for i>2.

◆ readJSON() [1/2]

void helib::PolyMod::readJSON ( const JsonWrapper & jw )

In-place deserialize a PolyMod object from the from the JsonWrapper jw.

Parameters

jw	Input `JsonWrapper`.

Note: poly must be constructed with an appropriate p2r and G BEFORE calling this function. For example,
PolyMod my_poly(p2r, G);

my_poly.readJSON(...);

The input stream has to a JSON list.
Each element of the list will be deserialized as a coefficient of the polynomial.
For example '['coef0', 'coef1', 'coef2']' will be deserialized as a PolyMod object poly where poly[0]=coef0, poly[1]=coef1, poly[2]=coef2 and poly[i]=0 for i>2.

◆ readJSON() [2/2]

void helib::PolyMod::readJSON ( std::istream & is )

In-place deserialize a PolyMod object from the input stream is.

Parameters

is	Input `std::istream`.

Exceptions

IOError if the stream is not a valid JSON.

Note: poly must be constructed with an appropriate p2r and G BEFORE calling this function. For example,
PolyMod my_poly(p2r, G);

my_poly.readJSON(std::cin);

The input stream has to be formatted as a JSON list.
Each element of the list will be deserialized as a coefficient of the polynomial.
For example '['coef0', 'coef1', 'coef2']' will be deserialized as a PolyMod object poly where poly[0]=coef0, poly[1]=coef1, poly[2]=coef2 and poly[i]=0 for i>2.

◆ writeToJSON() [1/2]

JsonWrapper helib::PolyMod::writeToJSON ( ) const

Serialize this PolyMod to the JsonWrapper object.

Returns: The JsonWrapper containing the serialized PolyMod.

Note: p2r and G are not serialized, see note of deserialize.

The output will be a JSON list.
Each coefficient of poly will be serialized in an element of such list.
For example if we have a PolyMod object poly such that poly[0]=coef0, poly[1]=coef1, poly[2]=coef2, and poly[i]=0 for i>2, it will be serialized as '['coef0', 'coef1', 'coef2']'.

◆ writeToJSON() [2/2]

void helib::PolyMod::writeToJSON ( std::ostream & os ) const

Serialize this PolyMod to the output stream os.

Parameters

os	Output `std::ostream`.

Note: p2r and G are not serialized, see note of deserialize.

The output stream will be formatted as a JSON list.
Each coefficient of poly will be serialized in an element of such list.
For example if we have a PolyMod object poly such that poly[0]=coef0, poly[1]=coef1, poly[2]=coef2, and poly[i]=0 for i>2, it will be serialized as '['coef0', 'coef1', 'coef2']'.

Friends And Related Function Documentation

◆ operator<<

std::ostream& operator<<	(	std::ostream &	os,
		const PolyMod &	poly
	)

friend

Output shift operator.

Parameters

os	Output `std::ostream`.
poly	`PolyMod` object to be written.

Returns: Input std::ostream post writing.

Note: p2r and G are not serialized, see note of operator>>.

The output stream will be formatted as a comma-separated list surrounded by '[' and ']'.
Each coefficient of poly will be serialized in an element of such list by the >> operator.
For example if we have a PolyMod object poly such that poly[0]=coef0, poly[1]=coef1, poly[2]=coef2, and poly[i]=0 for i>2, it will be serialized as '['coef0', 'coef1', 'coef2']'.

◆ operator>>

std::istream& operator>>	(	std::istream &	is,
		PolyMod &	poly
	)

friend

Input shift operator.

Parameters

is	Input `std::istream`.
poly	Destination `PolyMod` object.

Returns: Input std::istream post reading.

Note: poly must be constructed with an appropriate p2r and G BEFORE calling this function. For example,
PolyMod my_poly(p2r, G);

std::cin >> my_poly;

The input stream has to be formatted as a comma-separated list surrounded by '[' and ']'.
Each element of the list will be deserialized as a coefficient of the polynomial.
If the number of tokens in the list is less than the number of coefficients, the higher-degree coefficients will be padded by 0.
For example '['coef0', 'coef1', 'coef2']' will be deserialized as a PolyMod object poly where poly[0]=coef0, poly[1]=coef1, poly[2]=coef2 and poly[i]=0 for i>2.

Public Member Functions

Static Public Member Functions

Friends

Detailed Description

Constructor & Destructor Documentation

◆ PolyMod() [1/7]

◆ PolyMod() [2/7]

◆ PolyMod() [3/7]

◆ PolyMod() [4/7]

◆ PolyMod() [5/7]

◆ PolyMod() [6/7]

◆ PolyMod() [7/7]

◆ ~PolyMod()

Member Function Documentation

◆ getData()

◆ getG()

◆ getp2r()

◆ isValid()

◆ negate()

◆ operator long()

◆ operator NTL::ZZX()

◆ operator std::vector< long >()

◆ operator!=()

◆ operator*() [1/3]

◆ operator*() [2/3]

◆ operator*() [3/3]

◆ operator*=() [1/3]

◆ operator*=() [2/3]

◆ operator*=() [3/3]

◆ operator+() [1/3]

◆ operator+() [2/3]

◆ operator+() [3/3]

◆ operator+=() [1/3]

◆ operator+=() [2/3]

◆ operator+=() [3/3]

◆ operator-() [1/4]

◆ operator-() [2/4]

◆ operator-() [3/4]

◆ operator-() [4/4]

◆ operator-=() [1/3]

◆ operator-=() [2/3]

◆ operator-=() [3/3]

◆ operator=() [1/6]

◆ operator=() [2/6]

◆ operator=() [3/6]

◆ operator=() [4/6]

◆ operator=() [5/6]

◆ operator=() [6/6]

◆ operator==() [1/4]

◆ operator==() [2/4]

◆ operator==() [3/4]

◆ operator==() [4/4]

◆ readFromJSON() [1/2]

◆ readFromJSON() [2/2]

◆ readJSON() [1/2]

◆ readJSON() [2/2]

◆ writeToJSON() [1/2]

◆ writeToJSON() [2/2]

Friends And Related Function Documentation

◆ operator<<

◆ operator>>