Detailed Description

template<typename T = Rational>
class Util::Polynomial< T >

a list of coefficents).

Definition at line 30 of file Polynomial.h.

#include <Polynomial.h>

Inheritance diagram for Util::Polynomial< T >:

Public Member Functions
Constructors, Destructors, and Assignment
	Polynomial (int capacity=10)
	Construct a zero polynomial. More...

	Polynomial (T c)
	Construct a constant polynomial. More...

	Polynomial (Array< T > const &coeffs)
	Construct a polynomial from array of coefficients. More...

	Polynomial (Polynomial< T > const &other)
	Copy constructor. More...

template<typename U >
Polynomial< T > &	operator= (Polynomial< U > const &other)
	Assignment from another polynomial. More...

void	setToZero ()
	Assign this polynomial a value of zero. More...

Simple Accessors
int	degree () const
	Return degree of polynomial. More...

Arithmetic Assignment Operators
Polynomial< T > &	operator+= (const Polynomial< T > &a)
	Add another polynomial to this one. More...

Polynomial< T > &	operator+= (T a)
	Add a constant to this polynomial. More...

Polynomial< T > &	operator-= (const Polynomial< T > &a)
	Subtract another polynomial from this one. More...

Polynomial< T > &	operator-= (T a)
	Subtract a constant from this polynomial. More...

Polynomial< T > &	operator*= (T a)
	Multiply this polynomial by a scalar. More...

Polynomial< T > &	operator/= (T a)
	Divide this polynomial by a scalar. More...

Polynomial< T > &	operator*= (const Polynomial< T > &a)
	Multiply this polynomial by another. More...

Mathematical Functions (return polynomials)
Polynomial< T >	integrate () const
	Compute and return indefinite integral of this polynomial. More...

Polynomial< T >	differentiate () const
	Compute and return derivative of this polynomial. More...

Polynomial< T >	reflect () const
	Compute and return reflected polynomial f(-x). More...

Polynomial< T >	shift (T a) const
	Compute and return shifted polynomial f(x+a). More...

Polynomial Evaluation Functions
T	operator() (T x) const
	Evaluate polynomial at specific argument of type T. More...

double	evaluate (double x) const
	Evaluate polynomial at specific floating point argument. More...

Static Public Member Functions
static Polynomial< T >	monomial (int n)
	Return a monomial f(x) = x^{n}. More...

Constructor & Destructor Documentation

template<typename T >

Util::Polynomial< T >::Polynomial ( int capacity = 10 )

inline

Construct a zero polynomial.

Creates a zero polynomial f(x) = 0, with no stored coefficients. The capacity parameter specifies how much physical space to allocate for subsqequent growth in the array of coefficients.

Parameters

capacity initial capacity of coefficient array.

Definition at line 264 of file Polynomial.h.

References Util::GArray< Data >::reserve().

template<typename T>

Util::Polynomial< T >::Polynomial ( T c )

inlineexplicit

Construct a constant polynomial.

Creates a polynomial f(x) = c, with degree() = 0.

Parameters

c	constant coefficient value

Definition at line 272 of file Polynomial.h.

References Util::GArray< Data >::append(), and Util::GArray< Data >::reserve().

template<typename T>

Util::Polynomial< T >::Polynomial ( Array< T > const & coeffs )

inline

Construct a polynomial from array of coefficients.

Constructs a polynomial in which the coefficient of x^{i} is given by coeffs[i]. The logical and physical size of the coefficient array are both set to the capacity of coeffs.

Parameters

coeffs array of coefficients.

Definition at line 283 of file Polynomial.h.

References Util::GArray< Data >::append(), Util::Array< Data >::capacity(), and Util::GArray< Data >::reserve().

template<typename T>

Util::Polynomial< T >::Polynomial ( Polynomial< T > const & other )

inline

Copy constructor.

Parameters

other Polynomial to be copied

Definition at line 298 of file Polynomial.h.

References Util::GArray< Data >::append(), Util::GArray< T >::capacity(), Util::Polynomial< T >::operator=(), Util::GArray< Data >::reserve(), Util::Polynomial< T >::setToZero(), and Util::GArray< T >::size().

Member Function Documentation

template<typename T = Rational>

template<typename U >

Polynomial<T>& Util::Polynomial< T >::operator= ( Polynomial< U > const & other )

Assignment from another polynomial.

Parameters

other Polynomial to assign.

Referenced by Util::Polynomial< T >::Polynomial().

template<typename T >

void Util::Polynomial< T >::setToZero ( )

inline

Assign this polynomial a value of zero.

Equivalent to GArray::clear(): Clears all coefficients, setting size = 0 and degree = -1.

Definition at line 335 of file Polynomial.h.

References Util::GArray< Data >::clear().

Referenced by Util::Polynomial< T >::differentiate(), Util::Polynomial< T >::integrate(), Util::Polynomial< T >::operator*=(), and Util::Polynomial< T >::Polynomial().

template<typename T >

int Util::Polynomial< T >::degree ( ) const

inline

Return degree of polynomial.

Returns size() - 1, number of coefficients - 1. By convention, a zero polynomial has degree = -1.

Definition at line 343 of file Polynomial.h.

References Util::GArray< Data >::size().

Referenced by Util::Polynomial< T >::evaluate(), Util::Polynomial< T >::operator()(), and Util::Polynomial< T >::shift().

template<typename T>

Polynomial< T > & Util::Polynomial< T >::operator+= ( const Polynomial< T > & a )

Add another polynomial to this one.

Upon return, *this = this + a.

Parameters

a	increment (input)

Definition at line 350 of file Polynomial.h.

References Util::GArray< Data >::append(), Util::GArray< T >::size(), and UTIL_CHECK.

template<typename T>

Polynomial< T > & Util::Polynomial< T >::operator+= ( T a )

Add a constant to this polynomial.

Upon return, *this = this + a.

Parameters

a	increment (input)

Definition at line 373 of file Polynomial.h.

References Util::GArray< T >::size().

template<typename T>

Polynomial< T > & Util::Polynomial< T >::operator-= ( const Polynomial< T > & a )

Subtract another polynomial from this one.

Upon return, *this = this + a.

Parameters

a	decrement (input)

Definition at line 387 of file Polynomial.h.

References Util::GArray< Data >::append(), Util::GArray< T >::size(), and UTIL_CHECK.

template<typename T>

Polynomial< T > & Util::Polynomial< T >::operator-= ( T a )

Subtract a constant from this polynomial.

Upon return, *this = this + a.

Parameters

a	increment (input)

Definition at line 410 of file Polynomial.h.

References Util::GArray< T >::size().

template<typename T>

Polynomial< T > & Util::Polynomial< T >::operator*= ( T a )

inline

Multiply this polynomial by a scalar.

Upon return, *this = this*a.

Parameters

a	scalar factor

Definition at line 425 of file Polynomial.h.

References Util::GArray< T >::size().

template<typename T>

Polynomial< T > & Util::Polynomial< T >::operator/= ( T a )

inline

Divide this polynomial by a scalar.

Upon return, *this = this*a.

Parameters

a	scalar factor (input)

Definition at line 440 of file Polynomial.h.

References Util::GArray< T >::size().

template<typename T>

Polynomial< T > & Util::Polynomial< T >::operator*= ( const Polynomial< T > & a )

Multiply this polynomial by another.

Upon return, *this = this*a.

Parameters

a	increment (input)

Definition at line 454 of file Polynomial.h.

References Util::GArray< Data >::append(), Util::GArray< T >::capacity(), Util::GArray< Data >::reserve(), Util::Polynomial< T >::setToZero(), Util::GArray< T >::size(), Util::GArray< Data >::size(), and UTIL_ASSERT.

template<typename T >

Polynomial< T > Util::Polynomial< T >::integrate ( ) const

Compute and return indefinite integral of this polynomial.

Returns an indefinite integral with zero constant term.

Returns: indefinite integral polynomial.

Definition at line 502 of file Polynomial.h.

References Util::DArray< Data >::allocate(), Util::Polynomial< T >::setToZero(), and Util::GArray< T >::size().

template<typename T >

Polynomial< T > Util::Polynomial< T >::differentiate ( ) const

Compute and return derivative of this polynomial.

Returns a polynomial of one smaller degree.

Returns: derivative polynomial

Definition at line 528 of file Polynomial.h.

References Util::DArray< Data >::allocate(), Util::Polynomial< T >::setToZero(), and Util::GArray< T >::size().

template<typename T >

Polynomial< T > Util::Polynomial< T >::reflect ( ) const

Compute and return reflected polynomial f(-x).

If this polynomial is f(x), this returns a polynomial g(x) = f(-x) created by the reflection operation x-> -x. This yields a polynomial in which the sign is reversed for all coefficients of odd powers of x.

Returns: polynomial created by reflection x -> -x.

Definition at line 557 of file Polynomial.h.

References Util::GArray< T >::size().

template<typename T>

Polynomial< T > Util::Polynomial< T >::shift ( T a ) const

Compute and return shifted polynomial f(x+a).

If this polynomial is f(x), this returns a polynomial g(x) = f(x+a) created by the shift operation x-> x + a.

Returns: polynomial created by shift operation x -> x + a.

Definition at line 576 of file Polynomial.h.

References Util::Binomial::coeff(), Util::Polynomial< T >::degree(), Util::Binomial::setup(), and Util::GArray< T >::size().

template<typename T>

T Util::Polynomial< T >::operator() ( T x ) const

inline

Evaluate polynomial at specific argument of type T.

Parameters

x	value of argument

Returns: Value f(x) of this polynomial at specified x

Definition at line 602 of file Polynomial.h.

References Util::Polynomial< T >::degree(), and Util::GArray< T >::size().

template<typename T >

double Util::Polynomial< T >::evaluate ( double x ) const

inline

Evaluate polynomial at specific floating point argument.

Parameters

x	value of argument x

Returns: Value f(x) of polynomial at specified x

Definition at line 623 of file Polynomial.h.

References Util::Polynomial< T >::degree(), and Util::GArray< T >::size().

template<typename T >

Polynomial< T > Util::Polynomial< T >::monomial ( int n )

static

Return a monomial f(x) = x^{n}.

Return a monomial.

Parameters

n	power of x in monomial.

Definition at line 646 of file Polynomial.h.

References UTIL_CHECK.

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

Polynomial.h

Detailed Description

template<typename T = Rational> class Util::Polynomial< T >

Public Member Functions

Static Public Member Functions

Constructor & Destructor Documentation

Member Function Documentation

template<typename T = Rational>
class Util::Polynomial< T >