nzmath.rational.Rational Class Reference

Inheritance diagram for nzmath.rational.Rational:

Collaboration diagram for nzmath.rational.Rational:

Public Member Functions
def	__init__ (self, numerator, denominator=1)
def	__add__ (self, other)
def	__sub__ (self, other)
def	__mul__ (self, other)
def	__truediv__ (self, other)
def	__radd__ (self, other)
def	__rsub__ (self, other)
def	__rmul__ (self, other)
def	__rtruediv__ (self, other)
def	__pow__ (self, index)
def	__lt__ (self, other)
def	__le__ (self, other)
def	__eq__ (self, other)
def	__ne__ (self, other)
def	__gt__ (self, other)
def	__ge__ (self, other)
def	__pos__ (self)
def	__neg__ (self)
def	__abs__ (self)
def	__long__ (self)
def	__str__ (self)
def	__repr__ (self)
def	__nonzero__ (self)
def	__hash__ (self)
def	expand (self, base, limit)
def	trim (self, max_denominator)
def	compare (self, other)
def	getRing (self)
def	__float__ (self)
def	toFloat (self)
def	decimalString (self, N)
Public Member Functions inherited from nzmath.ring.QuotientFieldElement
def	inverse (self)
Public Member Functions inherited from nzmath.ring.FieldElement
def	__init__ (self)
def	exact_division (self, other)
Public Member Functions inherited from nzmath.ring.CommutativeRingElement
def	mul_module_action (self, other)
Public Member Functions inherited from nzmath.ring.RingElement
def	__init__ (self, *args, **kwd)

Public Attributes
	denominator
	numerator
Public Attributes inherited from nzmath.ring.QuotientFieldElement
	numerator
	denominator

Private Member Functions
def	_reduce (self)
def	_init_by_Rational_Rational (self, numerator, denominator)
def	_init_by_float_Rational (self, numerator, denominator)
def	_init_by_int_Rational (self, numerator, denominator)
def	_init_by_Rational_float (self, numerator, denominator)
def	_init_by_float_float (self, numerator, denominator)
def	_init_by_int_float (self, numerator, denominator)
def	_init_by_Rational_int (self, numerator, denominator)
def	_init_by_float_int (self, numerator, denominator)
def	_init_by_int_int (self, numerator, denominator)

Static Private Attributes
def	__div__ = __truediv__
def	__floordiv__ = __truediv__
def	__rdiv__ = __rtruediv__
def	__rfloordiv__ = __rtruediv__
def	__int__ = __long__

Detailed Description

Rational is the class of rational numbers.

Definition at line 10 of file rational.py.

Constructor & Destructor Documentation

__init__()

def nzmath.rational.Rational.__init__	(		self,
			numerator,
			denominator = 1
	)

Create a rational from:
  * integers,
  * float, or
  * Rational.
Other objects can be converted if they have toRational
methods.  Otherwise raise TypeError.

Reimplemented from nzmath.ring.QuotientFieldElement.

Definition at line 15 of file rational.py.

References nzmath.rational.continued_fraction_expansion().

Member Function Documentation

__abs__()

def nzmath.rational.Rational.__abs__

(

self

)

Definition at line 302 of file rational.py.

References nzmath.rational.Rational.denominator, nzmath.module.Module.denominator, and nzmath.rational.Rational.numerator.

__add__()

def nzmath.rational.Rational.__add__	(		self,
			other
	)

self + other

If other is a rational or an integer, the result will be a
rational.  If other is a kind of float the result is an
instance of other's type.  Otherwise, other would do the
computation.

Reimplemented from nzmath.ring.QuotientFieldElement.

Definition at line 68 of file rational.py.

References nzmath.rational.Rational.denominator, nzmath.module.Module.denominator, nzmath.rational.isIntegerObject(), nzmath.rational.Rational.numerator, and nzmath.rational.Rational.toFloat().

__eq__()

def nzmath.rational.Rational.__eq__	(		self,
			other
	)

Equality test.

Reimplemented from nzmath.ring.QuotientFieldElement.

Definition at line 270 of file rational.py.

References nzmath.rational.Rational.denominator, nzmath.module.Module.denominator, and nzmath.rational.isIntegerObject().

Referenced by nzmath.ring.Ring.__ne__(), nzmath.real.RealField.__ne__(), and nzmath.ring.Ideal.__ne__().

__float__()

def nzmath.rational.Rational.__float__

(

self

)

Definition at line 417 of file rational.py.

References nzmath.rational.Rational.decimalString().

__ge__()

def nzmath.rational.Rational.__ge__	(		self,
			other
	)

Definition at line 289 of file rational.py.

References nzmath.rational.Rational.compare().

__gt__()

def nzmath.rational.Rational.__gt__	(		self,
			other
	)

Definition at line 286 of file rational.py.

References nzmath.rational.Rational.compare().

__hash__()

def nzmath.rational.Rational.__hash__

(

self

)

a==b => hash(a)==hash(b)

Reimplemented from nzmath.ring.QuotientFieldElement.

Definition at line 322 of file rational.py.

References nzmath.matrix.Matrix.__class__, nzmath.matrix.RingMatrix.__class__, nzmath.matrix.RingSquareMatrix.__class__, nzmath.matrix.FieldMatrix.__class__, nzmath.matrix.MatrixRing.__class__, nzmath.matrix.Subspace.__class__, nzmath.rational.Rational.denominator, nzmath.module.Module.denominator, and nzmath.rational.Rational.numerator.

__le__()

def nzmath.rational.Rational.__le__	(		self,
			other
	)

Definition at line 267 of file rational.py.

References nzmath.rational.Rational.compare().

__long__()

def nzmath.rational.Rational.__long__

(

self

)

Definition at line 305 of file rational.py.

References nzmath.rational.Rational.denominator, nzmath.module.Module.denominator, and nzmath.rational.Rational.numerator.

__lt__()

def nzmath.rational.Rational.__lt__	(		self,
			other
	)

Definition at line 264 of file rational.py.

References nzmath.rational.Rational.compare().

__mul__()

def nzmath.rational.Rational.__mul__	(		self,
			other
	)

self * other

If other is a rational or an integer, the result will be a
rational.  If other is a kind of float the result is an
instance of other's type.  Otherwise, other would do the
computation.

Reimplemented from nzmath.ring.QuotientFieldElement.

Definition at line 116 of file rational.py.

References nzmath.rational.Rational.denominator, nzmath.module.Module.denominator, nzmath.rational.isIntegerObject(), nzmath.rational.Rational.numerator, and nzmath.rational.Rational.toFloat().

__ne__()

def nzmath.rational.Rational.__ne__	(		self,
			other
	)

Inequality test.

Reimplemented from nzmath.ring.RingElement.

Definition at line 283 of file rational.py.

References nzmath.rational.Rational.compare().

__neg__()

def nzmath.rational.Rational.__neg__

(

self

)

Reimplemented from nzmath.ring.QuotientFieldElement.

Definition at line 299 of file rational.py.

References nzmath.rational.Rational.denominator, nzmath.module.Module.denominator, and nzmath.rational.Rational.numerator.

__nonzero__()

def nzmath.rational.Rational.__nonzero__

(

self

)

Definition at line 316 of file rational.py.

References nzmath.rational.Rational.numerator.

__pos__()

def nzmath.rational.Rational.__pos__

(

self

)

Definition at line 292 of file rational.py.

References nzmath.rational.Rational.denominator, nzmath.module.Module.denominator, and nzmath.rational.Rational.numerator.

__pow__()

def nzmath.rational.Rational.__pow__	(		self,
			index
	)

Reimplemented from nzmath.ring.QuotientFieldElement.

Definition at line 253 of file rational.py.

References nzmath.rational.Rational.denominator, nzmath.module.Module.denominator, nzmath.rational.isIntegerObject(), and nzmath.rational.Rational.numerator.

__radd__()

def nzmath.rational.Rational.__radd__	(		self,
			other
	)

other + self

If other is an integer, the result will be a rational.  If
other is a kind of float the result is an instance of other's
type.  Otherwise, other would do the computation.

Definition at line 171 of file rational.py.

References nzmath.rational.Rational.denominator, nzmath.module.Module.denominator, nzmath.rational.isIntegerObject(), nzmath.rational.Rational.numerator, and nzmath.rational.Rational.toFloat().

__repr__()

def nzmath.rational.Rational.__repr__

(

self

)

Definition at line 313 of file rational.py.

References nzmath.matrix.Matrix.__class__, nzmath.matrix.RingMatrix.__class__, nzmath.matrix.RingSquareMatrix.__class__, nzmath.matrix.FieldMatrix.__class__, nzmath.matrix.MatrixRing.__class__, nzmath.matrix.Subspace.__class__, nzmath.rational.Rational.denominator, nzmath.module.Module.denominator, and nzmath.rational.Rational.numerator.

__rmul__()

def nzmath.rational.Rational.__rmul__	(		self,
			other
	)

other * self

If other is an integer, the result will be a rational.  If
other is a kind of float the result is an instance of other's
type.  Otherwise, other would do the computation.

Definition at line 209 of file rational.py.

References nzmath.rational.Rational.denominator, nzmath.module.Module.denominator, nzmath.rational.isIntegerObject(), nzmath.rational.Rational.numerator, and nzmath.rational.Rational.toFloat().

__rsub__()

def nzmath.rational.Rational.__rsub__	(		self,
			other
	)

other - self

If other is an integer, the result will be a rational.  If
other is a kind of float the result is an instance of other's
type.  Otherwise, other would do the computation.

Reimplemented from nzmath.ring.QuotientFieldElement.

Definition at line 190 of file rational.py.

References nzmath.rational.Rational.denominator, nzmath.module.Module.denominator, nzmath.rational.isIntegerObject(), nzmath.rational.Rational.numerator, and nzmath.rational.Rational.toFloat().

__rtruediv__()

def nzmath.rational.Rational.__rtruediv__	(		self,
			other
	)

other / self
other // self

If other is an integer, the result will be a rational.  If
other is a kind of float the result is an instance of other's
type.  Otherwise, other would do the computation.

Reimplemented from nzmath.ring.QuotientFieldElement.

Definition at line 228 of file rational.py.

References nzmath.rational.Rational.denominator, nzmath.module.Module.denominator, nzmath.rational.isIntegerObject(), nzmath.rational.Rational.numerator, and nzmath.rational.Rational.toFloat().

__str__()

def nzmath.rational.Rational.__str__

(

self

)

Definition at line 310 of file rational.py.

References nzmath.rational.Rational.denominator, nzmath.module.Module.denominator, and nzmath.rational.Rational.numerator.

__sub__()

def nzmath.rational.Rational.__sub__	(		self,
			other
	)

self - other

If other is a rational or an integer, the result will be a
rational.  If other is a kind of float the result is an
instance of other's type.  Otherwise, other would do the
computation.

Reimplemented from nzmath.ring.QuotientFieldElement.

Definition at line 92 of file rational.py.

References nzmath.rational.Rational.denominator, nzmath.module.Module.denominator, nzmath.rational.isIntegerObject(), nzmath.rational.Rational.numerator, and nzmath.rational.Rational.toFloat().

__truediv__()

def nzmath.rational.Rational.__truediv__	(		self,
			other
	)

self / other
self // other

If other is a rational or an integer, the result will be a
rational.  If other is a kind of float the result is an
instance of other's type.  Otherwise, other would do the
computation.

Reimplemented from nzmath.ring.QuotientFieldElement.

Definition at line 140 of file rational.py.

References nzmath.rational.Rational.denominator, nzmath.module.Module.denominator, nzmath.rational.isIntegerObject(), nzmath.rational.Rational.numerator, and nzmath.rational.Rational.toFloat().

_init_by_float_float()

def nzmath.rational.Rational._init_by_float_float (   self,   numerator,   denominator  )

private

Initialize by a float numbers.

Definition at line 474 of file rational.py.

References nzmath.rational.Rational.denominator, nzmath.module.Module.denominator, and nzmath.rational.Rational.numerator.

_init_by_float_int()

def nzmath.rational.Rational._init_by_float_int (   self,   numerator,   denominator  )

private

Initialize by a float number and an integer.

Definition at line 500 of file rational.py.

References nzmath.rational.Rational.denominator, nzmath.module.Module.denominator, and nzmath.rational.Rational.numerator.

_init_by_float_Rational()

def nzmath.rational.Rational._init_by_float_Rational (   self,   numerator,   denominator  )

private

Initialize by a float number and a rational number.

Definition at line 449 of file rational.py.

References nzmath.rational.Rational.denominator, nzmath.module.Module.denominator, and nzmath.rational.Rational.numerator.

_init_by_int_float()

def nzmath.rational.Rational._init_by_int_float (   self,   numerator,   denominator  )

private

Initailize by an integer and a float

Definition at line 484 of file rational.py.

References nzmath.rational.Rational.denominator, nzmath.module.Module.denominator, and nzmath.rational.Rational.numerator.

_init_by_int_int()

def nzmath.rational.Rational._init_by_int_int (   self,   numerator,   denominator  )

private

Initailize by an integers.

Definition at line 509 of file rational.py.

References nzmath.rational.Rational.denominator, nzmath.module.Module.denominator, and nzmath.rational.Rational.numerator.

_init_by_int_Rational()

def nzmath.rational.Rational._init_by_int_Rational (   self,   numerator,   denominator  )

private

Initailize by an integer and a rational number.

Definition at line 458 of file rational.py.

References nzmath.rational.Rational.denominator, nzmath.module.Module.denominator, and nzmath.rational.Rational.numerator.

_init_by_Rational_float()

def nzmath.rational.Rational._init_by_Rational_float (   self,   numerator,   denominator  )

private

Initialize by a rational number and a float.

Definition at line 465 of file rational.py.

References nzmath.rational.Rational.denominator, nzmath.module.Module.denominator, and nzmath.rational.Rational.numerator.

_init_by_Rational_int()

def nzmath.rational.Rational._init_by_Rational_int (   self,   numerator,   denominator  )

private

Initialize by a rational number and integer.

Definition at line 493 of file rational.py.

References nzmath.rational.Rational.denominator, nzmath.module.Module.denominator, and nzmath.rational.Rational.numerator.

_init_by_Rational_Rational()

def nzmath.rational.Rational._init_by_Rational_Rational (   self,   numerator,   denominator  )

private

Initialize by a rational numbers.

Definition at line 442 of file rational.py.

References nzmath.rational.Rational.denominator, nzmath.module.Module.denominator, and nzmath.rational.Rational.numerator.

_reduce()

def nzmath.rational.Rational._reduce (   self )

private

Definition at line 409 of file rational.py.

References nzmath.rational.Rational.denominator, nzmath.module.Module.denominator, and nzmath.rational.Rational.numerator.

compare()

def nzmath.rational.Rational.compare	(		self,
			other
	)

Definition at line 397 of file rational.py.

References nzmath.compatibility.cmp, nzmath.rational.Rational.compare(), nzmath.rational.Rational.denominator, nzmath.module.Module.denominator, nzmath.rational.isIntegerObject(), nzmath.rational.Rational.numerator, and nzmath.rational.Rational.toFloat().

Referenced by nzmath.rational.Rational.__ge__(), nzmath.rational.Rational.__gt__(), nzmath.rational.Rational.__le__(), nzmath.rational.Rational.__lt__(), nzmath.rational.Rational.__ne__(), and nzmath.rational.Rational.compare().

decimalString()

def nzmath.rational.Rational.decimalString	(		self,
			N
	)

Return a string of the number to N decimal places.

Definition at line 423 of file rational.py.

References nzmath.rational.Rational.denominator, nzmath.module.Module.denominator, and nzmath.rational.Rational.numerator.

Referenced by nzmath.rational.Rational.__float__().

expand()

def nzmath.rational.Rational.expand	(		self,
			base,
			limit
	)

r.expand(k, limit) returns the nearest rational number whose
denominator is a power of k and at most limit, if k > 0.  if
k==0, it returns the nearest rational number whose denominator
is at most limit, i.e. r.expand(0, limit) == r.trim(limit).

Definition at line 334 of file rational.py.

References nzmath.rational.Rational.denominator, nzmath.module.Module.denominator, nzmath.rational.isIntegerObject(), nzmath.rational.Rational.numerator, and nzmath.rational.Rational.trim().

getRing()

def nzmath.rational.Rational.getRing

(

self

)

getRing returns an object of a subclass of Ring,
to which the element belongs.

Reimplemented from nzmath.ring.RingElement.

Definition at line 406 of file rational.py.

Referenced by nzmath.ring.QuotientFieldElement.__add__(), nzmath.ring.QuotientFieldElement.__eq__(), nzmath.ring.QuotientFieldElement.__rsub__(), nzmath.ring.QuotientFieldElement.__rtruediv__(), nzmath.ring.QuotientFieldElement.__sub__(), nzmath.ring.QuotientFieldElement.__truediv__(), nzmath.poly.uniutil.PrimeCharacteristicFunctionsProvider._small_index_mod_pow(), nzmath.ring.CommutativeRingElement.exact_division(), nzmath.poly.uniutil.DivisionProvider.extgcd(), nzmath.poly.uniutil.PrimeCharacteristicFunctionsProvider.factor(), nzmath.poly.uniutil.DivisionProvider.mod_pow(), nzmath.poly.uniutil.PrimeCharacteristicFunctionsProvider.mod_pow(), nzmath.poly.uniutil.PseudoDivisionProvider.monic_pow(), nzmath.ring.CommutativeRingElement.mul_module_action(), and nzmath.poly.uniutil.SubresultantGcdProvider.subresultant_gcd().

toFloat()

def nzmath.rational.Rational.toFloat

(

self

)

Definition at line 420 of file rational.py.

References nzmath.rational.Rational.denominator, nzmath.module.Module.denominator, and nzmath.rational.Rational.numerator.

Referenced by nzmath.rational.Rational.__add__(), nzmath.rational.Rational.__mul__(), nzmath.rational.Rational.__radd__(), nzmath.rational.Rational.__rmul__(), nzmath.rational.Rational.__rsub__(), nzmath.rational.Rational.__rtruediv__(), nzmath.rational.Rational.__sub__(), nzmath.rational.Rational.__truediv__(), and nzmath.rational.Rational.compare().

trim()

def nzmath.rational.Rational.trim	(		self,
			max_denominator
	)

Definition at line 370 of file rational.py.

References nzmath.rational.Rational.denominator, nzmath.module.Module.denominator, and nzmath.rational.Rational.numerator.

Referenced by nzmath.rational.Rational.expand().

Member Data Documentation

__div__

def nzmath.rational.Rational.__div__ = __truediv__

staticprivate

Definition at line 168 of file rational.py.

__floordiv__

def nzmath.rational.Rational.__floordiv__ = __truediv__

staticprivate

Definition at line 169 of file rational.py.

__int__

def nzmath.rational.Rational.__int__ = __long__

staticprivate

Definition at line 308 of file rational.py.

__rdiv__

def nzmath.rational.Rational.__rdiv__ = __rtruediv__

staticprivate

Definition at line 250 of file rational.py.

__rfloordiv__

def nzmath.rational.Rational.__rfloordiv__ = __rtruediv__

staticprivate

Definition at line 251 of file rational.py.

denominator

nzmath.rational.Rational.denominator

Definition at line 60 of file rational.py.

Referenced by nzmath.rational.Rational.__abs__(), nzmath.rational.Rational.__add__(), nzmath.ring.QuotientFieldElement.__add__(), nzmath.round2.ModuleWithDenominator.__add__(), nzmath.poly.ratfunc.RationalFunction.__call__(), nzmath.rational.Rational.__eq__(), nzmath.ring.QuotientFieldElement.__eq__(), nzmath.rational.Rational.__hash__(), nzmath.ring.QuotientFieldElement.__hash__(), nzmath.poly.ratfunc.RationalFunction.__init__(), nzmath.rational.Rational.__long__(), nzmath.rational.Rational.__mul__(), nzmath.ring.QuotientFieldElement.__mul__(), nzmath.round2.ModuleWithDenominator.__mul__(), nzmath.rational.Rational.__neg__(), nzmath.ring.QuotientFieldElement.__neg__(), nzmath.rational.Rational.__pos__(), nzmath.rational.Rational.__pow__(), nzmath.ring.QuotientFieldElement.__pow__(), nzmath.rational.Rational.__radd__(), nzmath.poly.ratfunc.RationalFunction.__repr__(), nzmath.rational.Rational.__repr__(), nzmath.rational.Rational.__rmul__(), nzmath.rational.Rational.__rsub__(), nzmath.ring.QuotientFieldElement.__rsub__(), nzmath.rational.Rational.__rtruediv__(), nzmath.ring.QuotientFieldElement.__rtruediv__(), nzmath.poly.ratfunc.RationalFunction.__str__(), nzmath.rational.Rational.__str__(), nzmath.rational.Rational.__sub__(), nzmath.ring.QuotientFieldElement.__sub__(), nzmath.rational.Rational.__truediv__(), nzmath.ring.QuotientFieldElement.__truediv__(), nzmath.round2.ModuleWithDenominator.__truediv__(), nzmath.rational.Rational._init_by_float_float(), nzmath.rational.Rational._init_by_float_int(), nzmath.rational.Rational._init_by_float_Rational(), nzmath.rational.Rational._init_by_int_float(), nzmath.rational.Rational._init_by_int_int(), nzmath.rational.Rational._init_by_int_Rational(), nzmath.rational.Rational._init_by_Rational_float(), nzmath.rational.Rational._init_by_Rational_int(), nzmath.rational.Rational._init_by_Rational_Rational(), nzmath.rational.Rational._reduce(), nzmath.rational.Rational.compare(), nzmath.rational.Rational.decimalString(), nzmath.round2.ModuleWithDenominator.determinant(), nzmath.rational.Rational.expand(), nzmath.round2.ModuleWithDenominator.get_polynomials(), nzmath.round2.ModuleWithDenominator.get_rationals(), nzmath.ring.QuotientFieldElement.inverse(), nzmath.rational.Rational.toFloat(), and nzmath.rational.Rational.trim().

numerator

nzmath.rational.Rational.numerator

Definition at line 273 of file rational.py.

Referenced by nzmath.rational.Rational.__abs__(), nzmath.rational.Rational.__add__(), nzmath.ring.QuotientFieldElement.__add__(), nzmath.poly.ratfunc.RationalFunction.__call__(), nzmath.ring.QuotientFieldElement.__eq__(), nzmath.rational.Rational.__hash__(), nzmath.ring.QuotientFieldElement.__hash__(), nzmath.poly.ratfunc.RationalFunction.__init__(), nzmath.rational.Rational.__long__(), nzmath.rational.Rational.__mul__(), nzmath.ring.QuotientFieldElement.__mul__(), nzmath.rational.Rational.__neg__(), nzmath.ring.QuotientFieldElement.__neg__(), nzmath.rational.Rational.__nonzero__(), nzmath.rational.Rational.__pos__(), nzmath.rational.Rational.__pow__(), nzmath.ring.QuotientFieldElement.__pow__(), nzmath.rational.Rational.__radd__(), nzmath.poly.ratfunc.RationalFunction.__repr__(), nzmath.rational.Rational.__repr__(), nzmath.rational.Rational.__rmul__(), nzmath.rational.Rational.__rsub__(), nzmath.ring.QuotientFieldElement.__rsub__(), nzmath.rational.Rational.__rtruediv__(), nzmath.ring.QuotientFieldElement.__rtruediv__(), nzmath.poly.ratfunc.RationalFunction.__str__(), nzmath.rational.Rational.__str__(), nzmath.rational.Rational.__sub__(), nzmath.ring.QuotientFieldElement.__sub__(), nzmath.rational.Rational.__truediv__(), nzmath.ring.QuotientFieldElement.__truediv__(), nzmath.rational.Rational._init_by_float_float(), nzmath.rational.Rational._init_by_float_int(), nzmath.rational.Rational._init_by_float_Rational(), nzmath.rational.Rational._init_by_int_float(), nzmath.rational.Rational._init_by_int_int(), nzmath.rational.Rational._init_by_int_Rational(), nzmath.rational.Rational._init_by_Rational_float(), nzmath.rational.Rational._init_by_Rational_int(), nzmath.rational.Rational._init_by_Rational_Rational(), nzmath.rational.Rational._reduce(), nzmath.rational.Rational.compare(), nzmath.rational.Rational.decimalString(), nzmath.rational.Rational.expand(), nzmath.poly.ratfunc.RationalFunction.getRing(), nzmath.ring.QuotientFieldElement.inverse(), nzmath.rational.Rational.toFloat(), and nzmath.rational.Rational.trim().

---

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

• nzmath/rational.py