theoretica::polynomial< Type > Class Template Reference

A polynomial of arbitrary order with coefficients of a specified type. More...

#include <polynomial.h>

Public Member Functions
	polynomial ()=default
	Default constructor.
	polynomial (Type a)
	Initialize as a constant.
template<typename Vector , enable_vector< Vector > = true>
	polynomial (const Vector &c)
	Initialize from a vector of coefficients where the n-th order coefficient is given by the n-th element of the vector.
	polynomial (std::initializer_list< Type > l)
	Initialize from an std::initializer_list.
template<typename ... Args>
	polynomial (Args... args)
	Construct a polynomial from its coefficients, where the n-th order coefficient is given by the n-th element of the vector.
const Type &	at (unsigned int i) const
	Get i-th coefficient by constant reference, with bound checking.
Type &	at (unsigned int i)
	Access i-th coefficient by reference, with bound checking.
const Type &	operator[] (unsigned int i) const
	Get the n-th order coefficient by constant reference.
Type &	operator[] (unsigned int i)
	Get the n-th order coefficient by reference.
template<typename InputType = Type>
Type	eval (InputType x) const
	Evaluate the polynomial for a given value.
template<typename InputType = Type>
Type	operator() (InputType x) const
	Evaluate the polynomial for a given value.
unsigned int	degree (real tolerance=MACH_EPSILON) const
	Find the true order of the polynomial (ignoring trailing null coefficients)
void	trim (real tolerance=MACH_EPSILON)
	Remove trailing zero coefficients.
const vec< Type > &	coeffs () const
	Get the coefficients of the polynomial as const reference.
vec< Type > &	coeffs ()
	Get the coefficients of the polynomial as reference.
size_t	size () const
	Get the number of coefficients.
void	resize (size_t sz)
	Change the number of coefficients of the polynomial.
polynomial	operator+ (const polynomial &p) const
	Sum two polynomials.
polynomial	operator- (const polynomial &p) const
	Subtract a polynomial from another.
polynomial	operator* (const polynomial &p) const
	Multiply two polynomials.
polynomial	operator/ (const polynomial &d) const
	Polynomial division.
template<typename ScalarType , disable_vector< ScalarType > = true>
polynomial	operator* (ScalarType a) const
	Multiply a polynomial by a scalar.
template<typename ScalarType , disable_vector< ScalarType > = true>
polynomial	operator/ (ScalarType a) const
	Divide a polynomial by a scalar, provided it has coefficients supporting division.
polynomial &	operator+= (const polynomial &p)
	Sum a polynomial to this one.
polynomial &	operator-= (const polynomial &p)
	Subtract a polynomial from this one.
polynomial &	operator*= (const polynomial &p)
	Multiply two polynomials.
template<typename ScalarType , disable_vector< ScalarType > = true>
polynomial &	operator*= (ScalarType a)
	Multiply a polynomial by a scalar value.
polynomial &	operator/= (const polynomial &a)
	Divide a polynomial by a polynomial.
template<typename ScalarType , disable_vector< ScalarType > = true>
polynomial &	operator/= (ScalarType a)
	Divide a polynomial by a scalar value, provided it has coefficients supporting division.
bool	operator== (const polynomial &other) const
	Check whether two polynomials are equal.
auto	begin ()
	Get an iterator for the first coefficient of the polynomial.
auto	end ()
	Get an iterator for the one plus last coefficient of the polynomial.
auto	cbegin () const
	Get a const iterator for the first coefficient of the polynomial.
auto	cend () const
	Get a const iterator for the one plus last coefficient of the polynomial.
vec< complex<>, 2 >	quadratic_roots () const
	Compute the roots of a quadratic polynomial.
std::string	to_string (const std::string &unknown="x", const std::string &exponentiation="^") const
	Convert the polynomial to string representation.
	operator std::string ()
	Convert the polynomial to string representation.

Static Public Member Functions
template<typename Vector , enable_vector< Vector > = true>
static polynomial< Type >	from_roots (const Vector &roots)
	Construct a polynomial from its roots Uses numerically stable pairwise multiplication with sorted roots.
static polynomial< Type >	monomial (Type c, unsigned int order)
	Returns a monomial of the given degree and coefficient.

Friends
std::ostream &	operator<< (std::ostream &out, const polynomial &obj)
	Stream the polynomial in string representation to an output stream (std::ostream)

Detailed Description

template<typename Type = real>
class theoretica::polynomial< Type >

A polynomial of arbitrary order with coefficients of a specified type.

The n-th order coefficient is accessed with p[n] and corresponds to the term \(x^n\).

Constructor & Destructor Documentation

polynomial()

template<typename Type = real>

template<typename Vector , enable_vector< Vector > = true>

theoretica::polynomial< Type >::polynomial ( const Vector &  c )

inlineexplicit

Initialize from a vector of coefficients where the n-th order coefficient is given by the n-th element of the vector.

The constructor may be used explicitly, as polynomial(v).

Member Function Documentation

eval()

template<typename Type = real>

template<typename InputType = Type>

Type theoretica::polynomial< Type >::eval ( InputType  x ) const

inline

Evaluate the polynomial for a given value.

Horner's method is used for efficient evaluation.

operator()()

template<typename Type = real>

template<typename InputType = Type>

Type theoretica::polynomial< Type >::operator() ( InputType  x ) const

inline

Evaluate the polynomial for a given value.

Horner's method is used for efficient evaluation.

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

• polynomial/polynomial.h