fractions

Fraction, infinite-precision, real numbers.

Classes

Decimal

Construct a new Decimal object. 'value' can be an integer, string, tuple,
or another Decimal object. If no value is given, return Decimal('0'). The
context does not affect the conversion and is only passed to determine if
the InvalidOperation trap is active.

adjusted(self, /)

  Return the adjusted exponent of the number.  Defined as exp + digits - 1.

as_integer_ratio(self, /)

  Decimal.as_integer_ratio() -> (int, int)

  Return a pair of integers, whose ratio is exactly equal to the original
  Decimal and with a positive denominator. The ratio is in lowest terms.
  Raise OverflowError on infinities and a ValueError on NaNs.

as_tuple(self, /)

  Return a tuple representation of the number.

canonical(self, /)

  Return the canonical encoding of the argument.  Currently, the encoding
  of a Decimal instance is always canonical, so this operation returns its
  argument unchanged.

compare(self, /, other, context=None)

  Compare self to other.  Return a decimal value:

      a or b is a NaN ==> Decimal('NaN')
      a < b           ==> Decimal('-1')
      a == b          ==> Decimal('0')
      a > b           ==> Decimal('1')

compare_signal(self, /, other, context=None)

  Identical to compare, except that all NaNs signal.

compare_total(self, /, other, context=None)

  Compare two operands using their abstract representation rather than
  their numerical value.  Similar to the compare() method, but the result
  gives a total ordering on Decimal instances.  Two Decimal instances with
  the same numeric value but different representations compare unequal
  in this ordering:

      >>> Decimal('12.0').compare_total(Decimal('12'))
      Decimal('-1')

  Quiet and signaling NaNs are also included in the total ordering. The result
  of this function is Decimal('0') if both operands have the same representation,
  Decimal('-1') if the first operand is lower in the total order than the second,
  and Decimal('1') if the first operand is higher in the total order than the
  second operand. See the specification for details of the total order.

  This operation is unaffected by context and is quiet: no flags are changed
  and no rounding is performed. As an exception, the C version may raise
  InvalidOperation if the second operand cannot be converted exactly.

compare_total_mag(self, /, other, context=None)

  Compare two operands using their abstract representation rather than their
  value as in compare_total(), but ignoring the sign of each operand.

  x.compare_total_mag(y) is equivalent to x.copy_abs().compare_total(y.copy_abs()).

  This operation is unaffected by context and is quiet: no flags are changed
  and no rounding is performed. As an exception, the C version may raise
  InvalidOperation if the second operand cannot be converted exactly.

conjugate(self, /)

  Return self.

copy_abs(self, /)

  Return the absolute value of the argument.  This operation is unaffected by
  context and is quiet: no flags are changed and no rounding is performed.

copy_negate(self, /)

  Return the negation of the argument.  This operation is unaffected by context
  and is quiet: no flags are changed and no rounding is performed.

copy_sign(self, /, other, context=None)

  Return a copy of the first operand with the sign set to be the same as the
  sign of the second operand. For example:

      >>> Decimal('2.3').copy_sign(Decimal('-1.5'))
      Decimal('-2.3')

  This operation is unaffected by context and is quiet: no flags are changed
  and no rounding is performed. As an exception, the C version may raise
  InvalidOperation if the second operand cannot be converted exactly.

exp(self, /, context=None)

  Return the value of the (natural) exponential function e**x at the given
  number.  The function always uses the ROUND_HALF_EVEN mode and the result
  is correctly rounded.

fma(self, /, other, third, context=None)

  Fused multiply-add.  Return self*other+third with no rounding of the
  intermediate product self*other.

      >>> Decimal(2).fma(3, 5)
      Decimal('11')

from_float(f, /)

  Class method that converts a float to a decimal number, exactly.
  Since 0.1 is not exactly representable in binary floating point,
  Decimal.from_float(0.1) is not the same as Decimal('0.1').

      >>> Decimal.from_float(0.1)
      Decimal('0.1000000000000000055511151231257827021181583404541015625')
      >>> Decimal.from_float(float('nan'))
      Decimal('NaN')
      >>> Decimal.from_float(float('inf'))
      Decimal('Infinity')
      >>> Decimal.from_float(float('-inf'))
      Decimal('-Infinity')

is_canonical(self, /)

  Return True if the argument is canonical and False otherwise.  Currently,
  a Decimal instance is always canonical, so this operation always returns
  True.

is_finite(self, /)

  Return True if the argument is a finite number, and False if the argument
  is infinite or a NaN.

is_infinite(self, /)

  Return True if the argument is either positive or negative infinity and
  False otherwise.

is_nan(self, /)

  Return True if the argument is a (quiet or signaling) NaN and False
  otherwise.

is_normal(self, /, context=None)

  Return True if the argument is a normal finite non-zero number with an
  adjusted exponent greater than or equal to Emin. Return False if the
  argument is zero, subnormal, infinite or a NaN.

is_qnan(self, /)

  Return True if the argument is a quiet NaN, and False otherwise.

is_signed(self, /)

  Return True if the argument has a negative sign and False otherwise.
  Note that both zeros and NaNs can carry signs.

is_snan(self, /)

  Return True if the argument is a signaling NaN and False otherwise.

is_subnormal(self, /, context=None)

  Return True if the argument is subnormal, and False otherwise. A number is
  subnormal if it is non-zero, finite, and has an adjusted exponent less
  than Emin.

is_zero(self, /)

  Return True if the argument is a (positive or negative) zero and False
  otherwise.

ln(self, /, context=None)

  Return the natural (base e) logarithm of the operand. The function always
  uses the ROUND_HALF_EVEN mode and the result is correctly rounded.

log10(self, /, context=None)

  Return the base ten logarithm of the operand. The function always uses the
  ROUND_HALF_EVEN mode and the result is correctly rounded.

logb(self, /, context=None)

  For a non-zero number, return the adjusted exponent of the operand as a
  Decimal instance.  If the operand is a zero, then Decimal('-Infinity') is
  returned and the DivisionByZero condition is raised. If the operand is
  an infinity then Decimal('Infinity') is returned.

logical_and(self, /, other, context=None)

  Return the digit-wise 'and' of the two (logical) operands.

logical_invert(self, /, context=None)

  Return the digit-wise inversion of the (logical) operand.

logical_or(self, /, other, context=None)

  Return the digit-wise 'or' of the two (logical) operands.

logical_xor(self, /, other, context=None)

  Return the digit-wise 'exclusive or' of the two (logical) operands.

max(self, /, other, context=None)

  Maximum of self and other.  If one operand is a quiet NaN and the other is
  numeric, the numeric operand is returned.

max_mag(self, /, other, context=None)

  Similar to the max() method, but the comparison is done using the absolute
  values of the operands.

min(self, /, other, context=None)

  Minimum of self and other. If one operand is a quiet NaN and the other is
  numeric, the numeric operand is returned.

min_mag(self, /, other, context=None)

  Similar to the min() method, but the comparison is done using the absolute
  values of the operands.

next_minus(self, /, context=None)

  Return the largest number representable in the given context (or in the
  current default context if no context is given) that is smaller than the
  given operand.

next_plus(self, /, context=None)

  Return the smallest number representable in the given context (or in the
  current default context if no context is given) that is larger than the
  given operand.

next_toward(self, /, other, context=None)

  If the two operands are unequal, return the number closest to the first
  operand in the direction of the second operand.  If both operands are
  numerically equal, return a copy of the first operand with the sign set
  to be the same as the sign of the second operand.

normalize(self, /, context=None)

  Normalize the number by stripping the rightmost trailing zeros and
  converting any result equal to Decimal('0') to Decimal('0e0').  Used
  for producing canonical values for members of an equivalence class.
  For example, Decimal('32.100') and Decimal('0.321000e+2') both normalize
  to the equivalent value Decimal('32.1').

number_class(self, /, context=None)

  Return a string describing the class of the operand.  The returned value
  is one of the following ten strings:

      * '-Infinity', indicating that the operand is negative infinity.
      * '-Normal', indicating that the operand is a negative normal number.
      * '-Subnormal', indicating that the operand is negative and subnormal.
      * '-Zero', indicating that the operand is a negative zero.
      * '+Zero', indicating that the operand is a positive zero.
      * '+Subnormal', indicating that the operand is positive and subnormal.
      * '+Normal', indicating that the operand is a positive normal number.
      * '+Infinity', indicating that the operand is positive infinity.
      * 'NaN', indicating that the operand is a quiet NaN (Not a Number).
      * 'sNaN', indicating that the operand is a signaling NaN.

quantize(self, /, exp, rounding=None, context=None)

  Return a value equal to the first operand after rounding and having the
  exponent of the second operand.

      >>> Decimal('1.41421356').quantize(Decimal('1.000'))
      Decimal('1.414')

  Unlike other operations, if the length of the coefficient after the quantize
  operation would be greater than precision, then an InvalidOperation is signaled.
  This guarantees that, unless there is an error condition, the quantized exponent
  is always equal to that of the right-hand operand.

  Also unlike other operations, quantize never signals Underflow, even if the
  result is subnormal and inexact.

  If the exponent of the second operand is larger than that of the first, then
  rounding may be necessary. In this case, the rounding mode is determined by the
  rounding argument if given, else by the given context argument; if neither
  argument is given, the rounding mode of the current thread's context is used.

radix(self, /)

  Return Decimal(10), the radix (base) in which the Decimal class does
  all its arithmetic. Included for compatibility with the specification.

remainder_near(self, /, other, context=None)

  Return the remainder from dividing self by other.  This differs from
  self % other in that the sign of the remainder is chosen so as to minimize
  its absolute value. More precisely, the return value is self - n * other
  where n is the integer nearest to the exact value of self / other, and
  if two integers are equally near then the even one is chosen.

  If the result is zero then its sign will be the sign of self.

rotate(self, /, other, context=None)

  Return the result of rotating the digits of the first operand by an amount
  specified by the second operand.  The second operand must be an integer in
  the range -precision through precision. The absolute value of the second
  operand gives the number of places to rotate. If the second operand is
  positive then rotation is to the left; otherwise rotation is to the right.
  The coefficient of the first operand is padded on the left with zeros to
  length precision if necessary. The sign and exponent of the first operand are
  unchanged.

same_quantum(self, /, other, context=None)

  Test whether self and other have the same exponent or whether both are NaN.

  This operation is unaffected by context and is quiet: no flags are changed
  and no rounding is performed. As an exception, the C version may raise
  InvalidOperation if the second operand cannot be converted exactly.

scaleb(self, /, other, context=None)

  Return the first operand with the exponent adjusted the second.  Equivalently,
  return the first operand multiplied by 10**other. The second operand must be
  an integer.

shift(self, /, other, context=None)

  Return the result of shifting the digits of the first operand by an amount
  specified by the second operand.  The second operand must be an integer in
  the range -precision through precision. The absolute value of the second
  operand gives the number of places to shift. If the second operand is
  positive, then the shift is to the left; otherwise the shift is to the
  right. Digits shifted into the coefficient are zeros. The sign and exponent
  of the first operand are unchanged.

sqrt(self, /, context=None)

  Return the square root of the argument to full precision. The result is
  correctly rounded using the ROUND_HALF_EVEN rounding mode.

to_eng_string(self, /, context=None)

  Convert to an engineering-type string.  Engineering notation has an exponent
  which is a multiple of 3, so there are up to 3 digits left of the decimal
  place. For example, Decimal('123E+1') is converted to Decimal('1.23E+3').

  The value of context.capitals determines whether the exponent sign is lower
  or upper case. Otherwise, the context does not affect the operation.

to_integral(self, /, rounding=None, context=None)

  Identical to the to_integral_value() method.  The to_integral() name has been
  kept for compatibility with older versions.

to_integral_exact(self, /, rounding=None, context=None)

  Round to the nearest integer, signaling Inexact or Rounded as appropriate if
  rounding occurs.  The rounding mode is determined by the rounding parameter
  if given, else by the given context. If neither parameter is given, then the
  rounding mode of the current default context is used.

to_integral_value(self, /, rounding=None, context=None)

  Round to the nearest integer without signaling Inexact or Rounded.  The
  rounding mode is determined by the rounding parameter if given, else by
  the given context. If neither parameter is given, then the rounding mode
  of the current default context is used.

imag = <attribute 'imag' of 'decimal.Decimal' objects>

real = <attribute 'real' of 'decimal.Decimal' objects>

Fraction

This class implements rational numbers.

    In the two-argument form of the constructor, Fraction(8, 6) will
    produce a rational number equivalent to 4/3. Both arguments must
    be Rational. The numerator defaults to 0 and the denominator
    defaults to 1 so that Fraction(3) == 3 and Fraction() == 0.

    Fractions can also be constructed from:

      - numeric strings similar to those accepted by the
        float constructor (for example, '-2.3' or '1e10')

      - strings of the form '123/456'

      - float and Decimal instances

      - other Rational instances (including integers)

as_integer_ratio(self)

  Return the integer ratio as a tuple.

          Return a tuple of two integers, whose ratio is equal to the
          Fraction and with a positive denominator.

conjugate(self)

  Conjugate is a no-op for Reals.

from_decimal(dec)

  Converts a finite Decimal instance to a rational number, exactly.

from_float(f)

  Converts a finite float to a rational number, exactly.

          Beware that Fraction.from_float(0.3) != Fraction(3, 10).

limit_denominator(self, max_denominator=1000000)

  Closest Fraction to self with denominator at most max_denominator.

          >>> Fraction('3.141592653589793').limit_denominator(10)
          Fraction(22, 7)
          >>> Fraction('3.141592653589793').limit_denominator(100)
          Fraction(311, 99)
          >>> Fraction(4321, 8765).limit_denominator(10000)
          Fraction(4321, 8765)

denominator = <property object at 0x7f75e0ca84a0>

imag = <property object at 0x7f75e1394680>
  Real numbers have no imaginary component.

numerator = <property object at 0x7f75e0ca8400>

real = <property object at 0x7f75e1394630>
  Real numbers are their real component.

Modules