nzmath.imaginary.Complex Class Reference

Inheritance diagram for nzmath.imaginary.Complex:

Collaboration diagram for nzmath.imaginary.Complex:

Public Member Functions
def	__init__ (self, re, im=None)
def	__add__ (self, other)
def	__sub__ (self, other)
def	__rsub__ (self, other)
def	__mul__ (self, other)
def	__div__ (self, other)
def	__rdiv__ (self, other)
def	__pow__ (self, other)
def	__eq__ (self, other)
def	__hash__ (self)
def	__ne__ (self, other)
def	__abs__ (self)
def	__pos__ (self)
def	__neg__ (self)
def	__nonzero__ (self)
def	__repr__ (self)
def	__str__ (self)
def	inverse (self)
def	conjugate (self)
def	copy (self)
def	__lt__ (self, other)
	comparisons are prohibited More...
def	__le__ (self, other)
def	__gt__ (self, other)
def	__ge__ (self, other)
def	arg (self)
def	__complex__ (self)
def	getRing (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
	real
	imag

Static Private Attributes
def	__radd__ = __add__
def	__rmul__ = __mul__
def	__truediv__ = __div__
def	__rtruediv__ = __rdiv__

Detailed Description

Complex is a class for complex numbers.  Each instance has a coupled
numbers; real and imaginary part of the number.

Definition at line 13 of file imaginary.py.

Constructor & Destructor Documentation

__init__()

def nzmath.imaginary.Complex.__init__	(		self,
			re,
			im = None
	)

Definition at line 18 of file imaginary.py.

Member Function Documentation

__abs__()

def nzmath.imaginary.Complex.__abs__

(

self

)

Definition at line 146 of file imaginary.py.

References nzmath.imaginary.Complex.imag, and nzmath.imaginary.Complex.real.

__add__()

def nzmath.imaginary.Complex.__add__	(		self,
			other
	)

Definition at line 29 of file imaginary.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.imaginary.Complex.imag, and nzmath.imaginary.Complex.real.

__complex__()

def nzmath.imaginary.Complex.__complex__

(

self

)

Definition at line 200 of file imaginary.py.

References nzmath.imaginary.Complex.imag, and nzmath.imaginary.Complex.real.

__div__()

def nzmath.imaginary.Complex.__div__	(		self,
			other
	)

Definition at line 81 of file imaginary.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.imaginary.Complex.imag, and nzmath.imaginary.Complex.real.

__eq__()

def nzmath.imaginary.Complex.__eq__	(		self,
			other
	)

Equality test.

Reimplemented from nzmath.ring.RingElement.

Definition at line 125 of file imaginary.py.

References nzmath.imaginary.Complex.imag, and nzmath.imaginary.Complex.real.

Referenced by nzmath.poly.multivar.TermIndices.__ne__(), nzmath.poly.ring.PolynomialRing.__ne__(), nzmath.quad.ReducedQuadraticForm.__ne__(), nzmath.ring.Ring.__ne__(), nzmath.poly.formalsum.FormalSumContainerInterface.__ne__(), nzmath.poly.array.ArrayPoly.__ne__(), nzmath.real.RealField.__ne__(), nzmath.ring.Ideal.__ne__(), and nzmath.prime.FactoredInteger.__ne__().

__ge__()

def nzmath.imaginary.Complex.__ge__	(		self,
			other
	)

Definition at line 192 of file imaginary.py.

__gt__()

def nzmath.imaginary.Complex.__gt__	(		self,
			other
	)

Definition at line 189 of file imaginary.py.

__hash__()

def nzmath.imaginary.Complex.__hash__

(

self

)

Reimplemented from nzmath.ring.RingElement.

Definition at line 134 of file imaginary.py.

References nzmath.imaginary.Complex.imag, and nzmath.imaginary.Complex.real.

__le__()

def nzmath.imaginary.Complex.__le__	(		self,
			other
	)

Definition at line 186 of file imaginary.py.

__lt__()

def nzmath.imaginary.Complex.__lt__	(		self,
			other
	)

comparisons are prohibited

Definition at line 183 of file imaginary.py.

__mul__()

def nzmath.imaginary.Complex.__mul__	(		self,
			other
	)

Definition at line 67 of file imaginary.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.imaginary.Complex.imag, and nzmath.imaginary.Complex.real.

__ne__()

def nzmath.imaginary.Complex.__ne__	(		self,
			other
	)

Inequality test.

Reimplemented from nzmath.ring.RingElement.

Definition at line 137 of file imaginary.py.

References nzmath.imaginary.Complex.imag, and nzmath.imaginary.Complex.real.

__neg__()

def nzmath.imaginary.Complex.__neg__

(

self

)

Definition at line 158 of file imaginary.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.imaginary.Complex.imag, and nzmath.imaginary.Complex.real.

__nonzero__()

def nzmath.imaginary.Complex.__nonzero__

(

self

)

Definition at line 161 of file imaginary.py.

References nzmath.imaginary.Complex.imag, and nzmath.imaginary.Complex.real.

__pos__()

def nzmath.imaginary.Complex.__pos__

(

self

)

Definition at line 153 of file imaginary.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.imaginary.Complex.imag, and nzmath.imaginary.Complex.real.

__pow__()

def nzmath.imaginary.Complex.__pow__	(		self,
			other
	)

Definition at line 111 of file imaginary.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.imaginary.Complex.imag, nzmath.imaginary.Complex.inverse(), nzmath.ecpp.log, and nzmath.imaginary.Complex.real.

__rdiv__()

def nzmath.imaginary.Complex.__rdiv__	(		self,
			other
	)

Definition at line 96 of file imaginary.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.imaginary.Complex.imag, and nzmath.imaginary.Complex.real.

__repr__()

def nzmath.imaginary.Complex.__repr__

(

self

)

Definition at line 164 of file imaginary.py.

References nzmath.imaginary.Complex.imag, and nzmath.imaginary.Complex.real.

__rsub__()

def nzmath.imaginary.Complex.__rsub__	(		self,
			other
	)

Definition at line 55 of file imaginary.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.imaginary.Complex.imag, and nzmath.imaginary.Complex.real.

__str__()

def nzmath.imaginary.Complex.__str__

(

self

)

Definition at line 167 of file imaginary.py.

References nzmath.imaginary.Complex.imag, and nzmath.imaginary.Complex.real.

__sub__()

def nzmath.imaginary.Complex.__sub__	(		self,
			other
	)

Definition at line 43 of file imaginary.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.imaginary.Complex.imag, and nzmath.imaginary.Complex.real.

arg()

def nzmath.imaginary.Complex.arg

(

self

)

Definition at line 195 of file imaginary.py.

References nzmath.imaginary.Complex.imag, and nzmath.imaginary.Complex.real.

conjugate()

def nzmath.imaginary.Complex.conjugate

(

self

)

Definition at line 176 of file imaginary.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.imaginary.Complex.imag, and nzmath.imaginary.Complex.real.

copy()

def nzmath.imaginary.Complex.copy

(

self

)

Definition at line 179 of file imaginary.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.imaginary.Complex.imag, and nzmath.imaginary.Complex.real.

Referenced by nzmath.matrix.RingMatrix.__pos__(), nzmath.prime.FactoredInteger.__pos__(), nzmath.module.Module.__pow__(), nzmath.module.Ideal_with_generator.__pow__(), nzmath.matrix.RingSquareMatrix.__pow__(), nzmath.matrix.FieldMatrix._cohensSimplify(), nzmath.module.Module._module_mul(), nzmath.matrix.RingMatrix._SimplifyHNF(), nzmath.matrix.FieldMatrix.columnEchelonForm(), nzmath.matrix.RingSquareMatrix.determinant(), nzmath.prime.FactoredInteger.exact_division(), nzmath.matrix.RingSquareMatrix.extsmithNormalForm(), nzmath.matrix.RingMatrix.hermiteNormalForm(), nzmath.matrix.FieldSquareMatrix.hessenbergForm(), nzmath.module.Module.intersect(), nzmath.module.Submodule.intersectionOfSubmodules(), nzmath.matrix.Subspace.intersectionOfSubspaces(), nzmath.matrix.FieldSquareMatrix.inverse(), nzmath.matrix.FieldMatrix.inverseImage(), nzmath.matrix.FieldSquareMatrix.LUDecomposition(), nzmath.matrix.RingSquareMatrix.smithNormalForm(), nzmath.matrix.FieldMatrix.solve(), nzmath.matrix.Matrix.subMatrix(), nzmath.module.Submodule.sumOfSubmodules(), nzmath.matrix.Subspace.sumOfSubspaces(), nzmath.matrix.Subspace.supplementBasis(), and nzmath.matrix.FieldSquareMatrix.triangulate().

getRing()

def nzmath.imaginary.Complex.getRing

(

self

)

Return the complex field instance.

Reimplemented from nzmath.ring.RingElement.

Definition at line 203 of file imaginary.py.

Referenced by nzmath.poly.multiutil.RingPolynomial.__add__(), nzmath.ring.QuotientFieldElement.__add__(), nzmath.poly.uniutil.RingPolynomial.__add__(), nzmath.ring.QuotientFieldElement.__eq__(), nzmath.poly.uniutil.FieldPolynomial.__pow__(), nzmath.poly.multiutil.RingPolynomial.__radd__(), nzmath.poly.uniutil.RingPolynomial.__radd__(), nzmath.poly.multiutil.RingPolynomial.__rsub__(), nzmath.ring.QuotientFieldElement.__rsub__(), nzmath.poly.uniutil.RingPolynomial.__rsub__(), nzmath.ring.QuotientFieldElement.__rtruediv__(), nzmath.poly.multiutil.RingPolynomial.__sub__(), nzmath.ring.QuotientFieldElement.__sub__(), nzmath.poly.uniutil.RingPolynomial.__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().

inverse()

def nzmath.imaginary.Complex.inverse

(

self

)

Definition at line 170 of file imaginary.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.imaginary.Complex.imag, and nzmath.imaginary.Complex.real.

Referenced by nzmath.permute.Permute.__pow__(), nzmath.imaginary.Complex.__pow__(), nzmath.intresidue.IntegerResidueClass.__pow__(), nzmath.permute.ExPermute.__pow__(), nzmath.module.Ideal.__pow__(), nzmath.matrix.RingSquareMatrix.__pow__(), nzmath.permute.Permute.__rdiv__(), nzmath.permute.ExPermute.__rdiv__(), and nzmath.ring.QuotientFieldElement.__rtruediv__().

Member Data Documentation

__radd__

def nzmath.imaginary.Complex.__radd__ = __add__

staticprivate

Definition at line 41 of file imaginary.py.

__rmul__

def nzmath.imaginary.Complex.__rmul__ = __mul__

staticprivate

Definition at line 79 of file imaginary.py.

__rtruediv__

def nzmath.imaginary.Complex.__rtruediv__ = __rdiv__

staticprivate

Definition at line 109 of file imaginary.py.

__truediv__

def nzmath.imaginary.Complex.__truediv__ = __div__

staticprivate

Definition at line 94 of file imaginary.py.

imag

nzmath.imaginary.Complex.imag

Definition at line 21 of file imaginary.py.

Referenced by nzmath.imaginary.Complex.__abs__(), nzmath.imaginary.Complex.__add__(), nzmath.imaginary.Complex.__complex__(), nzmath.imaginary.Complex.__div__(), nzmath.imaginary.Complex.__eq__(), nzmath.imaginary.Complex.__hash__(), nzmath.imaginary.Complex.__mul__(), nzmath.imaginary.Complex.__ne__(), nzmath.imaginary.Complex.__neg__(), nzmath.imaginary.Complex.__nonzero__(), nzmath.imaginary.Complex.__pos__(), nzmath.imaginary.Complex.__pow__(), nzmath.imaginary.Complex.__rdiv__(), nzmath.imaginary.Complex.__repr__(), nzmath.imaginary.Complex.__rsub__(), nzmath.imaginary.Complex.__str__(), nzmath.imaginary.Complex.__sub__(), nzmath.imaginary.Complex.arg(), nzmath.imaginary.Complex.conjugate(), nzmath.imaginary.Complex.copy(), and nzmath.imaginary.Complex.inverse().

real

nzmath.imaginary.Complex.real

Definition at line 20 of file imaginary.py.

Referenced by nzmath.imaginary.Complex.__abs__(), nzmath.imaginary.Complex.__add__(), nzmath.imaginary.Complex.__complex__(), nzmath.imaginary.Complex.__div__(), nzmath.imaginary.Complex.__eq__(), nzmath.imaginary.Complex.__hash__(), nzmath.imaginary.Complex.__mul__(), nzmath.imaginary.Complex.__ne__(), nzmath.imaginary.Complex.__neg__(), nzmath.imaginary.Complex.__nonzero__(), nzmath.imaginary.Complex.__pos__(), nzmath.imaginary.Complex.__pow__(), nzmath.imaginary.Complex.__rdiv__(), nzmath.imaginary.Complex.__repr__(), nzmath.imaginary.Complex.__rsub__(), nzmath.imaginary.Complex.__str__(), nzmath.imaginary.Complex.__sub__(), nzmath.imaginary.Complex.arg(), nzmath.imaginary.Complex.conjugate(), nzmath.imaginary.Complex.copy(), and nzmath.imaginary.Complex.inverse().

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

• nzmath/imaginary.py