3.0.ipv8.attestation.wallet.primitives.value
============================================

.. py:module:: 3.0.ipv8.attestation.wallet.primitives.value


Classes
-------

.. autoapisummary::

   3.0.ipv8.attestation.wallet.primitives.value.FP2Value


Functions
---------

.. autoapisummary::

   3.0.ipv8.attestation.wallet.primitives.value.format_polynomial


Module Contents
---------------

.. py:function:: format_polynomial(a: int, b: int, c: int) -> str

   Formats a polynomial cx^2 + bx + a into non-zero/non-one form.

   Ex. '0x^2 + 1x + 2' becomes 'x + 2'

   :param a: x^0 coefficient
   :param b: x^1 coefficient
   :param c: x^2 coefficient
   :returns: pretty format of polynomial


.. py:class:: FP2Value(mod: int, a: int = 0, b: int = 0, c: int = 0, aC: int = 1, bC: int = 0, cC: int = 0)

   Defines a rational value (a + bx + cx^2)/(aC + bCx + cCx^2)(mod 1 + x + x^2, mod p).


   .. py:attribute:: mod


   .. py:method:: __str__() -> str

      Format this value as a string.



   .. py:method:: __add__(other: FP2Value) -> FP2Value

      Add this value to another value and return a new FP2Value.



   .. py:method:: __sub__(other: FP2Value) -> FP2Value

      Subtract another value from this value and return a new FP2Value.



   .. py:method:: __mul__(other: FP2Value) -> FP2Value

      Multiply this value with another value and return a new FP2Value.



   .. py:method:: __floordiv__(other: FP2Value) -> FP2Value

      Divide this value by another value and return a new FP2Value.



   .. py:method:: __eq__(other: object) -> bool

      Check equality with another value.



   .. py:method:: __hash__() -> int

      Equality is not trivial. We hash everything to 0 for the full equality check.



   .. py:method:: intpow(power: int) -> FP2Value

      Raise this value by a given power (int).

      :param power: the power to raise this value by
      :type power: int



   .. py:method:: normalize() -> FP2Value

      Normalize to aC = 1: this is the best human-readable form.

      Ex. '20/4' becomes '5'
          '4 + 4x/2 + 2x' becomes '2 + 2x/1 + x'



   .. py:method:: inverse() -> FP2Value

      Return the inverse of this value.



   .. py:method:: wp_nominator() -> FP2Value

      Return the '1' and 'x' coefficients as a new value.



   .. py:method:: wp_denom_inverse() -> FP2Value

      Return the '1^-1' and 'x^-1' coefficients modular inverse.



   .. py:method:: wp_compress() -> FP2Value

      Compress this FP2 value into an FP2Value only containing `a` and `b` values.

      This is an expensive operation.