Regina Calculation Engine
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regina::Laurent< T > Class Template Reference

Represents a single-variable Laurent polynomial with coefficients of type T. More...

#include <maths/laurent.h>

Public Types

typedef T Coefficient
 The type of each coefficient of the polynomial. More...
 

Public Member Functions

 Laurent ()
 Creates the zero polynomial. More...
 
 Laurent (long exponent)
 Creates the polynomial x^d for the given exponent d. More...
 
 Laurent (const Laurent< T > &value)
 Creates a new copy of the given polynomial. More...
 
template<typename U >
 Laurent (const Laurent< U > &value)
 Creates a new copy of the given polynomial. More...
 
 Laurent (Laurent< T > &&value) noexcept
 Moves the contents of the given polynomial to this new polynomial. More...
 
template<typename iterator >
 Laurent (long minExp, iterator begin, iterator end)
 Creates a new polynomial from the given sequence of coefficients. More...
 
 ~Laurent ()
 Destroys this polynomial. More...
 
void init ()
 Sets this to become the zero polynomial. More...
 
void init (long exponent)
 Sets this to become the polynomial x^d for the given exponent d. More...
 
template<typename iterator >
void init (long minExp, iterator begin, iterator end)
 Sets this to become the polynomial described by the given sequence of coefficients. More...
 
long minExp () const
 Returns the smallest exponent that appears in this polynomial with a non-zero coefficient. More...
 
long maxExp () const
 Returns the largest exponent that appears in this polynomial with a non-zero coefficient. More...
 
bool isZero () const
 Returns whether this is the zero polynomial. More...
 
const T & operator[] (long exp) const
 Returns the given coefficient of this polynomial. More...
 
void set (long exp, const T &value)
 Changes the given coefficient of this polynomial. More...
 
bool operator== (const Laurent< T > &rhs) const
 Tests whether this and the given polynomial are equal. More...
 
bool operator!= (const Laurent< T > &rhs) const
 Tests whether this and the given polynomial are not equal. More...
 
Laurentoperator= (const Laurent< T > &value)
 Sets this to be a copy of the given polynomial. More...
 
template<typename U >
Laurentoperator= (const Laurent< U > &value)
 Sets this to be a copy of the given polynomial. More...
 
Laurentoperator= (Laurent< T > &&value) noexcept
 Moves the contents of the given polynomial to this polynomial. More...
 
void swap (Laurent< T > &other)
 Swaps the contents of this and the given polynomial. More...
 
void shift (long s)
 Multiplies this polynomial by x^s for some integer s. More...
 
void scaleUp (long k)
 Multiplies all exponents in this polynomial by k for some integer k. More...
 
void scaleDown (long k)
 Divides all exponents in this polynomial by k for some integer k. More...
 
void negate ()
 Negates this polynomial. More...
 
Laurentoperator*= (const T &scalar)
 Multiplies this polynomial by the given constant. More...
 
Laurentoperator/= (const T &scalar)
 Divides this polynomial by the given constant. More...
 
Laurentoperator+= (const Laurent< T > &other)
 Adds the given polynomial to this. More...
 
Laurentoperator-= (const Laurent< T > &other)
 Subtracts the given polynomial from this. More...
 
Laurentoperator*= (const Laurent< T > &other)
 Multiplies this by the given polynomial. More...
 
void writeTextShort (std::ostream &out, bool utf8=false, const char *variable=nullptr) const
 Writes this polynomial to the given output stream, using the given variable name instead of x. More...
 
std::string str (const char *variable) const
 Returns this polynomial as a human-readable string, using the given variable name instead of x. More...
 
std::string utf8 (const char *variable) const
 Returns this polynomial as a human-readable string using unicode characters, using the given variable name instead of x. More...
 
template<typename U >
Laurent< T > & operator= (const Laurent< U > &other)
 

Friends

template<typename U >
Laurent< U > operator+ (const Laurent< U > &, const Laurent< U > &)
 
template<typename U >
Laurent< U > operator+ (Laurent< U > &&, Laurent< U > &&)
 
template<typename U >
Laurent< U > operator* (const Laurent< U > &, const Laurent< U > &)
 

Detailed Description

template<typename T>
class regina::Laurent< T >

Represents a single-variable Laurent polynomial with coefficients of type T.

A Laurent polynomial differs from an ordinary polynomial in that it allows negative exponents (so, unlike the Polynomial class, you can represent both 2+3x and 1+1/x).

The type T must represent a ring with no zero divisors. In particular, it must:

This means that Regina's numerical types such as Integer and Rational are supported, but native data types such as int and long are not (since they have no zero-initialising default constructor).

This class is designed to avoid deep copies wherever possible. In particular, it supports C++11 move constructors and move assignment. Functions that take or return objects by value are designed to be just as efficient as working with references or pointers (any variations to this are noted in the method documentation), and long chains of operators such as a = b * c + d do not make unwanted deep copies.

The underlying storage method for this class is dense (i.e., all coefficients are explicitly stored, including zero coefficients).

See also the class Laurent2, which describes Laurent polynomials in two variables.

Python:\n In Python, the class Laurent refers to the specific
template class Laurent<Integer>.

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

Copyright © 1999-2018, The Regina development team
This software is released under the GNU General Public License, with some additional permissions; see the source code for details.
For further information, or to submit a bug or other problem, please contact Ben Burton (bab@maths.uq.edu.au).