Namespace for the Sturm library. More...

Classes
class	Poly
	Polynomial class. More...
class	Sequence
	Sturm sequence class. More...

Typedefs
using	Integer = STURM_DEFAULT_INTEGER_TYPE
	The Integer type as used for the API.

Functions
template<typename Real>
Poly< Real >	operator+ (const Poly< Real > &p_1, const Poly< Real > &p_2)
	Define the sum between two polynomials.
template<typename Real>
Poly< Real >	operator+ (const Poly< Real > &p, Real s)
	Define the sum between a polynomial and a scalar.
template<typename Real>
Poly< Real >	operator+ (Real s, const Poly< Real > &p)
	Define the sum between a polynomial and a scalar.
template<typename Real>
Poly< Real >	operator- (const Poly< Real > &p_1, const Poly< Real > &p_2)
	Define the difference between two polynomials.
template<typename Real>
Poly< Real >	operator- (const Poly< Real > &p, Real s)
	Define the difference between a scalar and a polynomial.
template<typename Real>
Poly< Real >	operator- (Real s, const Poly< Real > &p)
	Define the difference between a scalar and a polynomial.
template<typename Real>
Poly< Real >	operator* (const Poly< Real > &p_1, const Poly< Real > &p_2)
	Define the multiplication between two polynomials.
template<typename Real>
Poly< Real >	operator* (Real p, const Poly< Real > &s)
	Define the multiplication between a scalar and a polynomial.
template<typename Real>
Poly< Real >	operator* (const Poly< Real > &s, Real p)
	Define the multiplication between a scalar and a polynomial.
template<typename Real>
void	divide (const Poly< Real > &p_1, const Poly< Real > &p_2, Poly< Real > &q, Poly< Real > &r)
	Divide the polynomial.
template<typename Real>
void	GCD (const Poly< Real > &p_1, const Poly< Real > &p_2, Poly< Real > &gcd, Real eps=Poly< Real >::EPSILON)
	Compute the greatest common divisor of two polynomials.
template<typename Real>
std::ostream &	operator<< (std::ostream &os, const Poly< Real > &p)
	Print the polynomial on an output stream.
template<typename Real>
std::ostream &	operator<< (std::ostream &os, const Sequence< Real > &s)
	Print the Sturm sequence on an output stream.

Detailed Description

This namespace contains all the classes and functions of the Sturm library for the computation of the Sturm sequences and the greatest common divisor polynomials. Other basic functions to manipulate polynomials and sequences are also included.

Typedef Documentation

◆ Integer

using Sturm::Integer = STURM_DEFAULT_INTEGER_TYPE

The Integer type, #define the preprocessor symbol STURM_DEFAULT_INTEGER_TYPE. The default value is int.

Function Documentation

◆ divide()

template<typename Real>

void Sturm::divide	(	const Poly< Real > &	p_1,
		const Poly< Real > &	p_2,
		Poly< Real > &	q,
		Poly< Real > &	r )

inline

Divide the polynomial \( p_1(x) \) by \( p_2(x) \) with remainder \(r(x) \) and quotient \( q(x) \).

Parameters

[in]	p_1	Polynomial to divide.
[in]	p_2	Polynomial to divide by.
[out]	q	Quotient polynomial.
[out]	r	Remainder polynomial.

Template Parameters

Real	Scalar number type.

◆ GCD()

template<typename Real>

void Sturm::GCD	(	const Poly< Real > &	p_1,
		const Poly< Real > &	p_2,
		Poly< Real > &	gcd,
		Real	eps = Poly<Real>::EPSILON )

inline

Parameters

[in]	p_1	First polynomial.
[in]	p_2	Second polynomial.
[out]	gcd	Greatest common divisor polynomial.
[in]	eps	Epsilon value for purging coefficients.

Template Parameters

Real	Scalar number type.

◆ operator*() [1/3]

template<typename Real>

Poly< Real > Sturm::operator*	(	const Poly< Real > &	p_1,
		const Poly< Real > &	p_2 )

inline

Parameters

[in]	p_1	First polynomial to multiply.
[in]	p_2	Second polynomial to multiply.

Returns: The operation result.

Template Parameters

Real	Scalar number type.

◆ operator*() [2/3]

template<typename Real>

Poly< Real > Sturm::operator*	(	const Poly< Real > &	s,
		Real	p )

inline

Parameters

[in]	s	Scalar to multiply.
[in]	p	Polynomial to multiply.

Returns: The operation result.

Template Parameters

Real	Scalar number type.

◆ operator*() [3/3]

template<typename Real>

Poly< Real > Sturm::operator*	(	Real	p,
		const Poly< Real > &	s )

inline

Parameters

[in]	p	Polynomial to multiply.
[in]	s	Scalar to multiply.

Returns: The operation result.

Template Parameters

Real	Scalar number type.

◆ operator+() [1/3]

template<typename Real>

Poly< Real > Sturm::operator+	(	const Poly< Real > &	p,
		Real	s )

inline

Parameters

[in]	p	Polynomial to sum.
[in]	s	Scalar to sum.

Returns: The operation result.

Template Parameters

Real	Scalar number type.

◆ operator+() [2/3]

template<typename Real>

Poly< Real > Sturm::operator+	(	const Poly< Real > &	p_1,
		const Poly< Real > &	p_2 )

inline

Parameters

[in]	p_1	First polynomial to sum.
[in]	p_2	Second polynomial to sum.

Returns: The operation result.

Template Parameters

Real	Scalar number type.

◆ operator+() [3/3]

template<typename Real>

Poly< Real > Sturm::operator+	(	Real	s,
		const Poly< Real > &	p )

inline

Parameters

[in]	s	Scalar to sum.
[in]	p	Polynomial to sum.

Returns: The operation result.

Template Parameters

Real	Scalar number type.

◆ operator-() [1/3]

template<typename Real>

Poly< Real > Sturm::operator-	(	const Poly< Real > &	p,
		Real	s )

inline

Parameters

[in]	p	Polynomial to subtract.
[in]	s	Scalar to subtract.

Returns: The operation result.

Template Parameters

Real	Scalar number type.

◆ operator-() [2/3]

template<typename Real>

Poly< Real > Sturm::operator-	(	const Poly< Real > &	p_1,
		const Poly< Real > &	p_2 )

inline

Parameters

[in]	p_1	First polynomial to subtract.
[in]	p_2	Second polynomial to subtract.

Returns: The operation result.

Template Parameters

Real	Scalar number type.

◆ operator-() [3/3]

template<typename Real>

Poly< Real > Sturm::operator-	(	Real	s,
		const Poly< Real > &	p )

inline

Parameters

[in]	s	Scalar to subtract.
[in]	p	Polynomial to subtract.

Returns: The operation result.

Template Parameters

Real	Scalar number type.

◆ operator<<() [1/2]

template<typename Real>

std::ostream & Sturm::operator<<	(	std::ostream &	os,
		const Poly< Real > &	p )

inline

Parameters

[in]	os	Output stream.
[in]	p	Polynomial.

Returns: The output stream.

Template Parameters

Real	Scalar number type.

◆ operator<<() [2/2]

template<typename Real>

std::ostream & Sturm::operator<<	(	std::ostream &	os,
		const Sequence< Real > &	s )

inline

Parameters

[in]	os	Output stream.
[in]	s	Sturm sequence.

Returns: The output stream.

Template Parameters

Real	Scalar number type.

Classes

Typedefs

Functions

Detailed Description

Typedef Documentation

◆ Integer

Function Documentation

◆ divide()

◆ GCD()

◆ 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<<() [1/2]

◆ operator<<() [2/2]