scuq.arithmetic

scuq.arithmetic.Coerce(x, y)

scuq.arithmetic.gcd(m, n)

Calculate the greatest common divisor.

Parameters:

• n – First integer value (greater or equal to zero).

• m – Second value (greater or equal to zero).

Returns:

The greatest common divisor of the inputs.

scuq.arithmetic.rational(n, d)

This function provides an interface for rational numbers creation, as suggested in PEP 239.

Parameters:

• d – The denominator (must be an interger type).

• n – The nominator (must be an integer type).

Returns:

An instance of RationalNumber

scuq.arithmetic.complex_to_matrix(c)

Convert a complex number to its 2x2 NumPy array representation.

class scuq.arithmetic.RationalNumber(dividend, divisor=1)

Bases: object

Represent a rational number with integer dividend and divisor. The arithmetic operators emulate rational arithmetic where possible. For unsupported mixed-type operations, methods may fall back to floating-point behavior.

__init__(dividend, divisor=1)

Default constructor. This initializes the rational number.

Parameters:

dividend – An integer representing the dividend of this

rational number.

Parameters:

divisor – An integer representing the divisor of this

rational number. If this parameter is obmitted it is initialized to 1.

__str__()

This method returns a string representing this rational number.

Returns:

A string representing this rational number.

normalize()

This method maintains the canonical form of this rational number and avoids negative divisors.

__complex__()

Cast this rational number to a complex number.

Returns:

A complex number, having a zero imaginary part.

__int__()

Cast this rational number to an integer. integer overflow.

Returns:

An integer.

__float__()

Cast this rational number to a floating point number.

Returns:

An integer.

__add__(value)

Add a number and return the result.

Parameters:

value – The number to add.

Returns:

The sum of this instance and the argument.

__sub__(value)

Substract a number and return the result.

Parameters:

value – The number to substract.

Returns:

The difference of this instance and the argument.

__mul__(value)

Multiply a number and return the result.

Parameters:

value – The number to multiply.

Returns:

The product of this instance and the argument.

__pow__(value)

Raise this rational number to the given power and return the result. a floating point number will be returned. Note that this may result in a loss of accuracy.

Parameters:

value – A numeric value representing the power.

Returns:

A new rational number representing power of this instance.

__rpow__(value)

Raise another value to the power of this rational number. the result.

Parameters:

value – A value to be raised to the power.

Returns:

A new rational number representing power of this instance.

__truediv__(value)

Divide by another number and return the result.

Parameters:

value – A number.

Returns:

The fraction of this instance and the number.

__neg__()

This method returns the negative of this instance.

Returns:

A new rational number.

__pos__()

This method returns a copy of this instance.

Returns:

A new rational number.

__abs__()

This method returns the absolute value of this instance.

Returns:

A new rational number.

__invert__()

This method returns a new rational number that swapped dividend and divsor of this instance.

Returns:

A new rational number.

get_dividend()

Returns the dividend of this instance.

Returns:

The dividend of this instance.

get_divisor()

Returns the divisor of this instance.

Returns:

The divisor of this instance.

__eq__(value)

Checks if this instance is equal to a number.

Parameters:

value – The value to compare to.

Returns:

If this rational number is equal to the argument.

__lt__(value)

Checks if this instance is less than another number.

Parameters:

value – The value to compare to.

Returns:

True, if this rational number is less than the argument.

__ne__(value)

Checks if this instance unequal to another number.

Parameters:

value – The value to compare to.

Returns:

True, if this rational number unequal to the argument.

__gt__(value)

Checks if this instance is greater than another number.

Parameters:

value – The value to compare to.

Returns:

True, if this rational number is greater than the argument.

__ge__(value)

Checks if this instance is greater or equal to another number.

Parameters:

value – The value to compare to.

Returns:

True, if this rational number is greater or equal to the argument.

__le__(value)

Checks if this instance is less or equal to another number.

Parameters:

value – The value to compare to.

Returns:

True, if this rational number is less or equal to the argument.

__cmp__(value)

Compares this instance to another number.

Parameters:

value – The value to compare to.

Returns:

-1: if this instance is less…; +1: if this is greater than the argument; 0 otherwise

__bool__()

Check if this instance is nonzero.

Returns:

True, if the dividend is nonzero.

__radd__(value)

Left addition of a numeric value.

Parameters:

value – A value to left from this instance.

__rsub__(value)

Right substraction of a numeric value.

Parameters:

value – A value to left from this instance.

__rmul__(value)

Right multiplication of a numeric value.

Parameters:

value – A value to left from this instance.

__rtruediv__(value)

Right division of a numeric value.

Parameters:

value – A value to left from this instance.

__getstate__()

Serialization using pickle.

Returns:

A string that represents the serialized form of this instance.

__setstate__(state)

Deserialization using pickle.

Parameters:

state – The state of the object.

static value_of(number)

Return a RationalNumber for an integer-like input.

Raises:

TypeError – If number is neither integer-like nor a

RationalNumber.

is_integer()

Check wether this instance could be be casted to long accurately.

Returns:

True, if the divisor is equal to one.

arccos()

This method provides the broadcast interface for numpy.arccos.

Returns:

The inverse Cosine of this number.

arccosh()

This method provides the broadcast interface for numpy.arccosh.

Returns:

The inverse hyperbolic Cosine of this number.

arcsin()

This method provides the broadcast interface for numpy.arcsin.

Returns:

The inverse Sine of this number.

arcsinh()

This method provides the broadcast interface for numpy.arcsinh.

Returns:

The inverse hyperbolic Sine of this number.

arctan()

This method provides the broadcast interface for numpy.arctan.

Returns:

The inverse Tangent of this number.

arctanh()

This method provides the broadcast interface for numpy.arctanh.

Returns:

The inverse hyperbolic Tangent of this number.

cos()

This method provides the broadcast interface for numpy.cos.

Returns:

The Cosine of this number.

cosh()

This method provides the broadcast interface for numpy.cosh.

Returns:

The hyperbolic Cosine of this number.

tan()

This method provides the broadcast interface for numpy.tan.

Returns:

The Tangent of this number.

tanh()

This method provides the broadcast interface for numpy.tanh.

Returns:

The hyperbolic Tangent of this number.

log10()

This method provides the broadcast interface for numpy.log10.

Returns:

The decadic Logarithm of this number.

sin()

This method provides the broadcast interface for numpy.sin.

Returns:

The Sine of this number.

sinh()

This method provides the broadcast interface for numpy.sinh.

Returns:

The hyperbolic Sine of this number.

sqrt()

This method provides the broadcast interface for numpy.sqrt.

Returns:

The Square Root of this number.

fabs()

This method provides the broadcast interface for numpy.fabs.

Returns:

The absolute value of this number.

absolute()

This method provides the broadcast interface for numpy.absolute.

Returns:

The absolute value of this number.

floor()

This method provides the broadcast interface for numpy.floor.

Returns:

The largest integer less than or equal to this number.

ceil()

This method provides the broadcast interface for numpy.ceil.

Returns:

The largest integer greater than or equal to this number.

exp()

This method provides the broadcast interface for numpy.exp.

Returns:

The Exponential of this number.

log()

This method provides the broadcast interface for numpy.log.

Returns:

The Natural Logarithm of this number.

log2()

This method provides the broadcast interface for numpy.log2.

Returns:

The binary logarithm of this number.

square()

This method provides the broadcast interface for numpy.square.

Returns:

The binary logarithm of this number.

arctan2(other)

This method provides the broadcast interface for numpy.arctan2.

Parameters:

other – Another rational number.

Returns:

The binary logarithm of this number.

hypot(other)

This method provides the broadcast interface for numpy.hypot.

Parameters:

other – Another rational number.

Returns:

The binary logarithm of this number.

fmod(other)

Return numpy.fmod(float(self), other). Note: This operation is intentionally one-way and may fail when called via reverse dispatch from other numeric types.

conjugate()

This method provides the broadcast interface for numpy.conjugate.

Returns:

This number.

coerce(other)

Implementation of coercion rules. See also the “Coercion” documentation page.