Regina Calculation Engine
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regina::NRational Class Reference

Represents an arbitrary precision rational number. More...

#include <maths/nrational.h>

List of all members.

Public Member Functions

 NRational ()
 Initialises to 0/1.
 NRational (const NRational &value)
 Initialises to the given rational value.
 NRational (const NLargeInteger &value)
 Initialises to the given integer value.
 NRational (long value)
 Initialises to the given integer value.
 NRational (const NLargeInteger &newNum, const NLargeInteger &newDen)
 Initialises to newNum/newDen.
 NRational (long newNum, unsigned long newDen)
 Initialises to newNum/newDen.
virtual ~NRational ()
 Destroys this rational.
NRationaloperator= (const NRational &value)
 Sets this rational to the given rational value.
NRationaloperator= (const NLargeInteger &value)
 Sets this rational to the given integer value.
NRationaloperator= (long value)
 Sets this rational to the given integer value.
void swap (NRational &other)
 Swaps the values of this and the given rational.
NLargeInteger getNumerator () const
 Returns the numerator of this rational.
NLargeInteger getDenominator () const
 Returns the denominator of this rational.
NRational operator* (const NRational &r) const
 Calculates the product of two rationals.
NRational operator/ (const NRational &r) const
 Calculates the ratio of two rationals.
NRational operator+ (const NRational &r) const
 Calculates the sum of two rationals.
NRational operator- (const NRational &r) const
 Calculates the difference of two rationals.
NRational operator- () const
 Determines the negative of this rational.
NRational inverse () const
 Calculates the inverse of this rational.
NRational abs () const
 Determines the absolute value of this rational.
NRationaloperator+= (const NRational &other)
 Adds the given rational to this.
NRationaloperator-= (const NRational &other)
 Subtracts the given rational from this.
NRationaloperator*= (const NRational &other)
 Multiplies the given rational by this.
NRationaloperator/= (const NRational &other)
 Divides this by the given rational.
void negate ()
 Negates this rational.
void invert ()
 Inverts this rational.
bool operator== (const NRational &compare) const
 Determines if this is equal to the given rational.
bool operator!= (const NRational &compare) const
 Determines if this is not equal to the given rational.
bool operator< (const NRational &compare) const
 Determines if this is less than the given rational.
bool operator> (const NRational &compare) const
 Determines if this is greater than the given rational.
bool operator<= (const NRational &compare) const
 Determines if this is less than or equal to the given rational.
bool operator>= (const NRational &compare) const
 Determines if this is greater than or equal to the given rational.
double doubleApprox (bool *inRange=0) const
 Attempts to convert this rational to a real number.
std::string getTeX () const
 Returns this rational as written using TeX formatting.
std::ostream & writeTeX (std::ostream &out) const
 Writes this rational in TeX format to the given output stream.

Static Public Attributes

static const NRational zero
 Globally available zero.
static const NRational one
 Globally available one.
static const NRational infinity
 Globally available infinity.
static const NRational undefined
 Globally available undefined.

Friends

std::ostream & operator<< (std::ostream &out, const NRational &rat)
 Writes the given rational to the given output stream.

Detailed Description

Represents an arbitrary precision rational number.

Calculations with NRational objects will be exact.

Infinity (1/0) and undefined (0/0) are catered for. (-1/0) is considered the same as (1/0), and is represented as (1/0). Any operation involving (0/0) will return (0/0).

Since infinity is the same as negative infinity, both infinity plus infinity and infinity minus infinity will return infinity. Infinity divided by infinity returns undefined, as does infinity times zero.

For the purposes of ordering, undefined is the smallest rational and infinity is the largest. Undefined is always equal to itself, and infinity is always equal to itself.

Rationals will always be stored in lowest terms with non-negative denominator.

Test:
Included in the test suite.

Constructor & Destructor Documentation

regina::NRational::NRational ( ) [inline]

Initialises to 0/1.

regina::NRational::NRational ( const NRational value) [inline]

Initialises to the given rational value.

Parameters:
valuethe new rational value of this rational.
regina::NRational::NRational ( const NLargeInteger value) [inline]

Initialises to the given integer value.

Parameters:
valuethe new integer value of this rational.
regina::NRational::NRational ( long  value) [inline]

Initialises to the given integer value.

Parameters:
valuethe new integer value of this rational.
regina::NRational::NRational ( const NLargeInteger newNum,
const NLargeInteger newDen 
)

Initialises to newNum/newDen.

Precondition:
gcd(newNum, newDen) = 1 or newDen = 0.
newDen is non-negative.
Warning:
Failing to meet the preconditions above can result in misleading or even undefined behaviour. As an example, NRational(4,4) (which breaks the gcd requirement) is considered different from NRational(1,1) (a valid rational), which is different again from NRational(-1,-1) (which breaks the non-negativity requirement).
Parameters:
newNumthe new numerator.
newDenthe new denominator.
regina::NRational::NRational ( long  newNum,
unsigned long  newDen 
)

Initialises to newNum/newDen.

Precondition:
gcd(newNum, newDen) = 1 or newDen = 0.
newDen is non-negative.
Warning:
Failing to meet the preconditions above can result in misleading or even undefined behaviour. As an example, NRational(4,4) (which breaks the gcd requirement) is considered different from NRational(1,1) (a valid rational), which is different again from NRational(-1,-1) (which breaks the non-negativity requirement).
Parameters:
newNumthe new numerator.
newDenthe new denominator.
regina::NRational::~NRational ( ) [inline, virtual]

Destroys this rational.


Member Function Documentation

NRational regina::NRational::abs ( ) const

Determines the absolute value of this rational.

This rational is not changed.

Returns:
the absolute value of this rational.
double regina::NRational::doubleApprox ( bool *  inRange = 0) const

Attempts to convert this rational to a real number.

If this rational can be approximated by a double (specifically, if it lies within double's allowable range) then a such an approximation is returned. Otherwise zero is returned instead.

The optional inRange argument allows the result of range checking to be returned explicitly as a boolean (*inRange will be set to true if a double approximation is possible and false otherwise).

It is safe to pass inRange as null, in which case this boolean is not returned. Range checking is still performed internally however, i.e., zero is still returned if the rational is out of range.

Note that "lies with double's allowable range" is machine-dependent, and may vary between different installations. Infinity and undefined are always considered out of range. Otherwise a rational is out of range if its absolute value is finite but too large (e.g., 10^10000) or non-zero but too small (e.g., 10^-10000).

Parameters:
inRangereturns the result of range checking as described above; this pointer may be passed as null if the caller does not care about this result.
Returns:
the double approximation to this rational, or zero if this rational lies outside double's allowable range.
Python:
The inRange argument is not present. Instead there are two versions of this routine. The first is doubleApprox(), which returns a single real number. The second is doubleApproxCheck(), which returns a (real, bool) pair containing the converted real number followed by the result of range checking.
Author:
Ryan Budney, B.B.
NLargeInteger regina::NRational::getDenominator ( ) const

Returns the denominator of this rational.

Note that rationals are always stored in lowest terms with non-negative denominator.

Returns:
the denominator.
NLargeInteger regina::NRational::getNumerator ( ) const

Returns the numerator of this rational.

Note that rationals are always stored in lowest terms with non-negative denominator. Infinity will be stored as 1/0.

Returns:
the numerator.
std::string regina::NRational::getTeX ( ) const

Returns this rational as written using TeX formatting.

No leading or trailing dollar signs will be included.

Returns:
this rational as written using TeX formatting.
Author:
Ryan Budney
NRational regina::NRational::inverse ( ) const

Calculates the inverse of this rational.

This rational is not changed.

Returns:
the inverse 1 / this.
void regina::NRational::invert ( )

Inverts this rational.

This rational is changed to reflect the result.

void regina::NRational::negate ( ) [inline]

Negates this rational.

This rational is changed to reflect the result.

bool regina::NRational::operator!= ( const NRational compare) const [inline]

Determines if this is not equal to the given rational.

Parameters:
comparethe rational with which this will be compared.
Returns:
true if and only if this rational is not equal to compare.
NRational regina::NRational::operator* ( const NRational r) const

Calculates the product of two rationals.

This rational is not changed.

Parameters:
rthe rational with which to multiply this.
Returns:
the product this * r.
NRational& regina::NRational::operator*= ( const NRational other)

Multiplies the given rational by this.

This rational is changed to reflect the result.

Parameters:
otherthe rational to multiply by this.
Returns:
a reference to this rational with its new value.
NRational regina::NRational::operator+ ( const NRational r) const

Calculates the sum of two rationals.

This rational is not changed.

Parameters:
rthe rational to add to this.
Returns:
the sum this + r.
NRational& regina::NRational::operator+= ( const NRational other)

Adds the given rational to this.

This rational is changed to reflect the result.

Parameters:
otherthe rational to add to this.
Returns:
a reference to this rational with its new value.
NRational regina::NRational::operator- ( const NRational r) const

Calculates the difference of two rationals.

This rational is not changed.

Parameters:
rthe rational to subtract from this.
Returns:
the difference this - r.
NRational regina::NRational::operator- ( ) const

Determines the negative of this rational.

This rational is not changed.

Returns:
the negative of this rational.
NRational& regina::NRational::operator-= ( const NRational other)

Subtracts the given rational from this.

This rational is changed to reflect the result.

Parameters:
otherthe rational to subtract from this.
Returns:
a reference to this rational with its new value.
NRational regina::NRational::operator/ ( const NRational r) const

Calculates the ratio of two rationals.

This rational is not changed.

Parameters:
rthe rational to divide this by.
Returns:
the ratio this / r.
NRational& regina::NRational::operator/= ( const NRational other)

Divides this by the given rational.

This rational is changed to reflect the result.

Parameters:
otherthe rational to divide this by.
Returns:
a reference to this rational with its new value.
bool regina::NRational::operator< ( const NRational compare) const

Determines if this is less than the given rational.

Parameters:
comparethe rational with which this will be compared.
Returns:
true if and only if this rational is less than compare.
bool regina::NRational::operator<= ( const NRational compare) const [inline]

Determines if this is less than or equal to the given rational.

Parameters:
comparethe rational with which this will be compared.
Returns:
true if and only if this rational is less than or equal to compare.
NRational & regina::NRational::operator= ( const NLargeInteger value) [inline]

Sets this rational to the given integer value.

Parameters:
valuethe new value of this rational.
Returns:
a reference to this rational with its new value.
NRational & regina::NRational::operator= ( const NRational value) [inline]

Sets this rational to the given rational value.

Parameters:
valuethe new value of this rational.
Returns:
a reference to this rational with its new value.
NRational & regina::NRational::operator= ( long  value) [inline]

Sets this rational to the given integer value.

Parameters:
valuethe new value of this rational.
Returns:
a reference to this rational with its new value.
bool regina::NRational::operator== ( const NRational compare) const

Determines if this is equal to the given rational.

Parameters:
comparethe rational with which this will be compared.
Returns:
true if and only if this rational is equal to compare.
bool regina::NRational::operator> ( const NRational compare) const

Determines if this is greater than the given rational.

Parameters:
comparethe rational with which this will be compared.
Returns:
true if and only if this rational is greater than compare.
bool regina::NRational::operator>= ( const NRational compare) const [inline]

Determines if this is greater than or equal to the given rational.

Parameters:
comparethe rational with which this will be compared.
Returns:
true if and only if this rational is greater than or equal to compare.
void regina::NRational::swap ( NRational other) [inline]

Swaps the values of this and the given rational.

Parameters:
otherthe rational whose value will be swapped with this.
std::ostream& regina::NRational::writeTeX ( std::ostream &  out) const

Writes this rational in TeX format to the given output stream.

No leading or trailing dollar signs will be included.

Python:
The parameter out does not exist; instead standard output will be used.
Parameters:
outthe output stream to which to write.
Returns:
a reference to the given output stream.
Author:
Ryan Budney

Friends And Related Function Documentation

std::ostream& operator<< ( std::ostream &  out,
const NRational rat 
) [friend]

Writes the given rational to the given output stream.

Infinity will be written as Inf. Undefined will be written as Undef. A rational with denominator one will be written as a single integer. All other rationals will be written in the form r/s.

Parameters:
outthe output stream to which to write.
ratthe rational to write.
Returns:
a reference to out.

Member Data Documentation

Globally available infinity.

Note that both 1/0 and -1/0 evaluate to this same rational. When queried, the representation 1/0 will be returned.

Globally available one.

Globally available undefined.

This is represented as 0/0.

Globally available zero.


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

Copyright © 1999-2011, The Regina development team
This software is released under the GNU General Public License.
For further information, or to submit a bug or other problem, please contact Ben Burton (bab@debian.org).