Regina Calculation Engine
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Represents an arbitrary precision rational number. More...
#include <maths/nrational.h>
Public Member Functions | |
NRational () | |
Initialises to 0/1. More... | |
NRational (const NRational &value) | |
Initialises to the given rational value. More... | |
template<bool supportInfinity> | |
NRational (const NIntegerBase< supportInfinity > &value) | |
Initialises to the given integer value. More... | |
NRational (long value) | |
Initialises to the given integer value. More... | |
template<bool supportInfinity> | |
NRational (const NIntegerBase< supportInfinity > &newNum, const NIntegerBase< supportInfinity > &newDen) | |
Initialises to newNum/newDen. More... | |
NRational (long newNum, unsigned long newDen) | |
Initialises to newNum/newDen. More... | |
virtual | ~NRational () |
Destroys this rational. More... | |
NRational & | operator= (const NRational &value) |
Sets this rational to the given rational value. More... | |
template<bool supportInfinity> | |
NRational & | operator= (const NIntegerBase< supportInfinity > &value) |
Sets this rational to the given integer value. More... | |
NRational & | operator= (long value) |
Sets this rational to the given integer value. More... | |
void | swap (NRational &other) |
Swaps the values of this and the given rational. More... | |
NInteger | getNumerator () const |
Returns the numerator of this rational. More... | |
NInteger | getDenominator () const |
Returns the denominator of this rational. More... | |
NRational | operator* (const NRational &r) const |
Calculates the product of two rationals. More... | |
NRational | operator/ (const NRational &r) const |
Calculates the ratio of two rationals. More... | |
NRational | operator+ (const NRational &r) const |
Calculates the sum of two rationals. More... | |
NRational | operator- (const NRational &r) const |
Calculates the difference of two rationals. More... | |
NRational | operator- () const |
Determines the negative of this rational. More... | |
NRational | inverse () const |
Calculates the inverse of this rational. More... | |
NRational | abs () const |
Determines the absolute value of this rational. More... | |
NRational & | operator+= (const NRational &other) |
Adds the given rational to this. More... | |
NRational & | operator-= (const NRational &other) |
Subtracts the given rational from this. More... | |
NRational & | operator*= (const NRational &other) |
Multiplies the given rational by this. More... | |
NRational & | operator/= (const NRational &other) |
Divides this by the given rational. More... | |
void | negate () |
Negates this rational. More... | |
void | invert () |
Inverts this rational. More... | |
bool | operator== (const NRational &compare) const |
Determines if this is equal to the given rational. More... | |
bool | operator!= (const NRational &compare) const |
Determines if this is not equal to the given rational. More... | |
bool | operator< (const NRational &compare) const |
Determines if this is less than the given rational. More... | |
bool | operator> (const NRational &compare) const |
Determines if this is greater than the given rational. More... | |
bool | operator<= (const NRational &compare) const |
Determines if this is less than or equal to the given rational. More... | |
bool | operator>= (const NRational &compare) const |
Determines if this is greater than or equal to the given rational. More... | |
double | doubleApprox (bool *inRange=0) const |
Attempts to convert this rational to a real number. More... | |
std::string | getTeX () const |
Returns this rational as written using TeX formatting. More... | |
std::ostream & | writeTeX (std::ostream &out) const |
Writes this rational in TeX format to the given output stream. More... | |
Static Public Attributes | |
static const NRational | zero |
Globally available zero. More... | |
static const NRational | one |
Globally available one. More... | |
static const NRational | infinity |
Globally available infinity. More... | |
static const NRational | undefined |
Globally available undefined. More... | |
Friends | |
std::ostream & | operator<< (std::ostream &out, const NRational &rat) |
Writes the given rational to the given output stream. More... | |
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 (i.e., with relatively prime numerator and denominator), and with a non-negative denominator.
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Initialises to 0/1.
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Initialises to the given rational value.
value | the new rational value of this rational. |
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Initialises to the given integer value.
The given integer may be infinite.
value | the new integer value of this rational. |
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Initialises to the given integer value.
value | the new integer value of this rational. |
regina::NRational::NRational | ( | const NIntegerBase< supportInfinity > & | newNum, |
const NIntegerBase< supportInfinity > & | newDen | ||
) |
Initialises to newNum/newDen.
newNum | the new numerator. |
newDen | the new denominator. |
regina::NRational::NRational | ( | long | newNum, |
unsigned long | newDen | ||
) |
Initialises to newNum/newDen.
newNum | the new numerator. |
newDen | the new denominator. |
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Destroys this rational.
NRational regina::NRational::abs | ( | ) | const |
Determines the absolute value of this rational.
This rational is not changed.
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).
inRange | returns the result of range checking as described above; this pointer may be passed as null if the caller does not care about this result. |
NInteger regina::NRational::getDenominator | ( | ) | const |
Returns the denominator of this rational.
Note that rationals are always stored in lowest terms with non-negative denominator. Infinity will be stored as 1/0.
NInteger 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.
std::string regina::NRational::getTeX | ( | ) | const |
Returns this rational as written using TeX formatting.
No leading or trailing dollar signs will be included.
NRational regina::NRational::inverse | ( | ) | const |
Calculates the inverse of this rational.
This rational is not changed.
void regina::NRational::invert | ( | ) |
Inverts this rational.
This rational is changed to reflect the result.
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Negates this rational.
This rational is changed to reflect the result.
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Determines if this is not equal to the given rational.
compare | the rational with which this will be compared. |
true
if and only if this rational is not equal to compare. Calculates the product of two rationals.
This rational is not changed.
r | the rational with which to multiply this. |
Multiplies the given rational by this.
This rational is changed to reflect the result.
other | the rational to multiply by this. |
Calculates the sum of two rationals.
This rational is not changed.
r | the rational to add to this. |
Adds the given rational to this.
This rational is changed to reflect the result.
other | the rational to add to this. |
Calculates the difference of two rationals.
This rational is not changed.
r | the rational to subtract from this. |
NRational regina::NRational::operator- | ( | ) | const |
Determines the negative of this rational.
This rational is not changed.
Subtracts the given rational from this.
This rational is changed to reflect the result.
other | the rational to subtract from this. |
Calculates the ratio of two rationals.
This rational is not changed.
r | the rational to divide this by. |
Divides this by the given rational.
This rational is changed to reflect the result.
other | the rational to divide this by. |
bool regina::NRational::operator< | ( | const NRational & | compare | ) | const |
Determines if this is less than the given rational.
compare | the rational with which this will be compared. |
true
if and only if this rational is less than compare.
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Determines if this is less than or equal to the given rational.
compare | the rational with which this will be compared. |
true
if and only if this rational is less than or equal to compare. Sets this rational to the given rational value.
value | the new value of this rational. |
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Sets this rational to the given integer value.
The given integer may be infinite.
value | the new value of this rational. |
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Sets this rational to the given integer value.
value | the new value of this rational. |
bool regina::NRational::operator== | ( | const NRational & | compare | ) | const |
Determines if this is equal to the given rational.
compare | the rational with which this will be compared. |
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.
compare | the rational with which this will be compared. |
true
if and only if this rational is greater than compare.
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Determines if this is greater than or equal to the given rational.
compare | the rational with which this will be compared. |
true
if and only if this rational is greater than or equal to compare.
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Swaps the values of this and the given rational.
other | the 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.
out | the output stream to which to write. |
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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
.
out | the output stream to which to write. |
rat | the rational to write. |
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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.
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Globally available one.
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Globally available undefined.
This is represented as 0/0.
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Globally available zero.