Polynomial.hpp File Reference

#include <cassert>
#include <iostream>

Go to the source code of this file.

Classes
class	Polynomial< MaxDeg >

Functions
int64_t	RingInverse (const int64_t x, const int64_t mod)
	Integer multiplicative inverse in a modular ring. More...
template<const uint64_t MaxDeg>
bool	operator== (const Polynomial< MaxDeg > &P1, const Polynomial< MaxDeg > &P2)
	Equality operator. More...
template<const uint64_t MaxDeg>
bool	operator!= (const Polynomial< MaxDeg > &P1, const Polynomial< MaxDeg > &P2)
	Inequality operator. More...
template<const uint64_t MaxDeg>
std::ostream &	operator<< (std::ostream &os, const Polynomial< MaxDeg > &P)
	Print operator. More...
template<const uint64_t MaxDeg>
Polynomial< MaxDeg >	operator* (const int64_t x, const Polynomial< MaxDeg > &P)
	Multiplication-by-scalar operator. More...
template<const uint64_t MaxDeg>
Polynomial< MaxDeg >	operator+ (const Polynomial< MaxDeg > &P1, const Polynomial< MaxDeg > &P2)
	Addition operator. More...
template<const uint64_t MaxDeg>
Polynomial< MaxDeg >	operator- (const Polynomial< MaxDeg > &P1, const Polynomial< MaxDeg > &P2)
	Subtraction operator. More...
template<const uint64_t MaxDeg>
Polynomial< MaxDeg >	operator* (const Polynomial< MaxDeg > &P1, const Polynomial< MaxDeg > &P2)
	Convolution multiplication in a polynomial quotient ring operator. More...
template<const uint64_t MaxDeg>
Polynomial< MaxDeg >	operator% (const Polynomial< MaxDeg > &P, const int64_t x)
	Coefficient reduction modulo a scalar. More...
template<const uint64_t MaxDeg>
void	CenteredLift (Polynomial< MaxDeg > *P, const int64_t mod)
	Center-lift polynomial in a modular quotient ring. More...
template<const uint64_t MaxDeg>
Polynomial< MaxDeg >	RingInverse (const Polynomial< MaxDeg > &P, const int64_t &mod)
	Inverse polynomial in a modular quotient ring. More...

Function Documentation

CenteredLift()

template<const uint64_t MaxDeg>

void CenteredLift	(	Polynomial< MaxDeg > *	P,
		const int64_t	mod
	)

Center-lift polynomial in a modular quotient ring.

Parameters

[in]	P	existing class instance (pointer)
[in]	mod	positive integer

operator!=()

template<const uint64_t MaxDeg>

bool operator!=	(	const Polynomial< MaxDeg > &	P1,
		const Polynomial< MaxDeg > &	P2
	)

Inequality operator.

Parameters

[in]	P1	LHS operand
[in]	P2	RHS operand

Returns

boolean value after the comparison

operator%()

template<const uint64_t MaxDeg>

Polynomial< MaxDeg > operator%	(	const Polynomial< MaxDeg > &	P,
		const int64_t	x
	)

Coefficient reduction modulo a scalar.

Parameters

[in]	P	LHS operand (polynomial)
[in]	x	RHS operand (scalar)

Returns

new class instance

operator*() [1/2]

template<const uint64_t MaxDeg>

Polynomial< MaxDeg > operator*	(	const int64_t	x,
		const Polynomial< MaxDeg > &	P
	)

Multiplication-by-scalar operator.

Parameters

[in]	x	LHS operand (scalar)
[in]	P	RHS operand (polynomial)

Returns

new class instance

operator*() [2/2]

template<const uint64_t MaxDeg>

Polynomial< MaxDeg > operator*	(	const Polynomial< MaxDeg > &	P1,
		const Polynomial< MaxDeg > &	P2
	)

Convolution multiplication in a polynomial quotient ring operator.

Parameters

[in]	P1	LHS operand
[in]	P2	RHS operand

Returns

new class instance

operator+()

template<const uint64_t MaxDeg>

Polynomial< MaxDeg > operator+	(	const Polynomial< MaxDeg > &	P1,
		const Polynomial< MaxDeg > &	P2
	)

Addition operator.

Parameters

[in]	P1	LHS operand
[in]	P2	RHS operand

Returns

new class instance

operator-()

template<const uint64_t MaxDeg>

Polynomial< MaxDeg > operator-	(	const Polynomial< MaxDeg > &	P1,
		const Polynomial< MaxDeg > &	P2
	)

Subtraction operator.

Parameters

[in]	P1	LHS operand
[in]	P2	RHS operand

Returns

new class instance

operator<<()

template<const uint64_t MaxDeg>

std::ostream & operator<<	(	std::ostream &	os,
		const Polynomial< MaxDeg > &	P
	)

Print operator.

Parameters

[in,out]	os	output stream
[in]	P	existing class instance

Returns

output stream

operator==()

template<const uint64_t MaxDeg>

bool operator==	(	const Polynomial< MaxDeg > &	P1,
		const Polynomial< MaxDeg > &	P2
	)

Equality operator.

Parameters

[in]	P1	LHS operand
[in]	P2	RHS operand

Returns

boolean value after the comparison

RingInverse() [1/2]

int64_t RingInverse	(	const int64_t	x,
		const int64_t	mod
	)

Integer multiplicative inverse in a modular ring.

Parameters

[in]	x	positive integer
[in]	mod	positive integer

Returns

positive integer

RingInverse() [2/2]

template<const uint64_t MaxDeg>

Polynomial< MaxDeg > RingInverse	(	const Polynomial< MaxDeg > &	P,
		const int64_t &	mod
	)

Inverse polynomial in a modular quotient ring.

Parameters

[in]	P	existing class instance
[in]	mod	positive integer

Returns

new class instance