arctans.numbers

Numbers.

Attributes

j
zero
one

Classes

AbstractNumber	Base class for number.
RealNumber	A real number.
Integer	An integer.
Rational	A rational number.
GaussianInteger	A Gaussian integer.
GaussianRational	A Gaussian rational.

Functions

_simplify_type(→ AbstractNumber)	Convert i to a simpler type if possible.
_as_common_type(→ tuple[AbstractNumber, AbstractNumber])	Convert a and b to the same type.

Module Contents

class arctans.numbers.AbstractNumber

Bases: arctans.core.Representable

Base class for number.

property real: RealNumber

Abstractmethod:

Real part.

property imag: RealNumber

Abstractmethod:

Imaginary part.

property numerator: AbstractNumber

Abstractmethod:

Numerator.

property denominator: Integer

Abstractmethod:

Denominator.

abstractmethod conjugate() → AbstractNumber

Compute the complex conjugate.

abstractmethod __int__() → int

abstractmethod __float__() → float

abstractmethod __complex__() → complex

abstractmethod _to_same_type(other: Any) → Self

Convert other to the same type as self.

abstractmethod _add(other: Self) → AbstractNumber

Add something of the same type to this.

abstractmethod _sub(other: Self) → AbstractNumber

Subtract something of the same type from this.

abstractmethod _mul(other: Self) → AbstractNumber

Multiply something of the same type by this.

abstractmethod _truediv(other: Self) → AbstractNumber

Divide this by something of the same type.

_mod(other: Self) → AbstractNumber

Find the remainder when dividing this by something of the same type.

_floordiv(other: Self) → AbstractNumber

Find the remainder when dividing this by something of the same type.

abstractmethod _eq(other: Self) → bool

Check if something of the same type is equal to this.

_pow(other: int) → AbstractNumber

Raise to an integer power.

__add__(other: Any)

__radd__(other: Any)

__sub__(other: Any)

__rsub__(other: Any)

__mul__(other: Any)

__rmul__(other: Any)

__neg__()

__truediv__(other: Any)

__rtruediv__(other: Any)

__mod__(other: Any)

__rmod__(other: Any)

__floordiv__(other: Any)

__rfloordiv__(other: Any)

__eq__(other) → bool

__pow__(other)

__rpow__(other)

__iadd__(other)

__isub__(other)

__imul__(other)

__abs__()

__hash__()

class arctans.numbers.RealNumber

Bases: AbstractNumber

A real number.

property real: RealNumber

Real part.

property imag: RealNumber

Imaginary part.

conjugate() → AbstractNumber

Compute the complex conjugate.

__lt__(other) → bool

__le__(other) → bool

__gt__(other) → bool

__ge__(other) → bool

class arctans.numbers.Integer(i: int)

Bases: RealNumber

An integer.

_i

__str__()

__repr__()

as_latex() → str

Represent in LaTeX.

property numerator: AbstractNumber

Numerator.

property denominator: Integer

Denominator.

__int__() → int

__float__() → float

__complex__() → complex

_to_same_type(other: Any) → Integer

Convert other to the same type as self.

_add(other: Self) → AbstractNumber

Add something of the same type to this.

_sub(other: Self) → AbstractNumber

Subtract something of the same type from this.

_mul(other: Self) → AbstractNumber

Multiply something of the same type by this.

_truediv(other: Self) → AbstractNumber

Divide this by something of the same type.

_pow(other: int) → AbstractNumber

Raise to an integer power.

_mod(other: Self) → AbstractNumber

Find the remainder when dividing this by something of the same type.

_floordiv(other: Self) → AbstractNumber

Find the remainder when dividing this by something of the same type.

_eq(other: Self) → bool

Check if something of the same type is equal to this.

__abs__()

__hash__()

class arctans.numbers.Rational(numerator: int, denominator: int)

Bases: RealNumber

A rational number.

_num

_den

as_latex() → str

Represent in LaTeX.

__str__()

__repr__()

property numerator: AbstractNumber

Numerator.

property denominator: Integer

Denominator.

__int__() → int

__float__() → float

__complex__() → complex

_to_same_type(other: Any) → Rational

Convert other to the same type as self.

_add(other: Self) → AbstractNumber

Add something of the same type to this.

_sub(other: Self) → AbstractNumber

Subtract something of the same type from this.

_mul(other: Self) → AbstractNumber

Multiply something of the same type by this.

_truediv(other: Self) → AbstractNumber

Divide this by something of the same type.

_pow(other: int) → AbstractNumber

Raise to an integer power.

_eq(other: Self) → bool

Check if something of the same type is equal to this.

__abs__()

class arctans.numbers.GaussianInteger(re: int, im: int)

Bases: AbstractNumber

A Gaussian integer.

_re

_im

__str__()

__repr__()

property real: RealNumber

Real part.

property imag: RealNumber

Imaginary part.

conjugate() → AbstractNumber

Compute the complex conjugate.

as_latex() → str

Represent in LaTeX.

property numerator: AbstractNumber

Numerator.

property denominator: Integer

Denominator.

__int__() → int

__float__() → float

__complex__() → complex

_to_same_type(other: Any) → GaussianInteger

Convert other to the same type as self.

_add(other: Self) → AbstractNumber

Add something of the same type to this.

_sub(other: Self) → AbstractNumber

Subtract something of the same type from this.

_mul(other: Self) → AbstractNumber

Multiply something of the same type by this.

_truediv(other: Self) → AbstractNumber

Divide this by something of the same type.

_mod(other: Self) → AbstractNumber

Find the remainder when dividing this by something of the same type.

_floordiv(other: Self) → AbstractNumber

Find the remainder when dividing this by something of the same type.

_eq(other: Self) → bool

Check if something of the same type is equal to this.

class arctans.numbers.GaussianRational(re_numerator: int, re_denominator, im_numerator: int, im_denominator: int)

Bases: AbstractNumber

A Gaussian rational.

_re_num

_re_den

_im_num

_im_den

__str__()

__repr__()

property real: RealNumber

Real part.

property imag: RealNumber

Imaginary part.

as_latex() → str

Represent in LaTeX.

conjugate() → AbstractNumber

Compute the complex conjugate.

property numerator: AbstractNumber

Numerator.

property denominator: Integer

Denominator.

__int__() → int

__float__() → float

__complex__() → complex

_to_same_type(other: Any) → GaussianRational

Convert other to the same type as self.

_add(other: Self) → AbstractNumber

Add something of the same type to this.

_sub(other: Self) → AbstractNumber

Subtract something of the same type from this.

_mul(other: Self) → AbstractNumber

Multiply something of the same type by this.

_truediv(other: Self) → AbstractNumber

Divide this by something of the same type.

_eq(other: Self) → bool

Check if something of the same type is equal to this.

arctans.numbers._simplify_type(i: AbstractNumber) → AbstractNumber

Convert i to a simpler type if possible.

arctans.numbers._as_common_type(a: AbstractNumber, b: Any) → tuple[AbstractNumber, AbstractNumber]

Convert a and b to the same type.

arctans.numbers.j

arctans.numbers.zero

arctans.numbers.one