grassmann_number
========================================

.. py:class:: grassmanntn.arith.grassmann_number(data,generator)

An object representing a Grassmann number.

.. note::
  This is a class definition function. To define a new Grassmann variable, use `set_anticommutative() <set_ac.html>`__ instead.


**Parameters:**

- **data:** ``numpy.ndarray``

  A vector containing all the coefficients. :math:`C_{i_1i_2\cdots i_n}` (vectorized).

- **generator:** a list of ``str``

  A list of symbols for Grassmann generators :math:`\theta_1,\theta_2,\cdots,\theta_n`.

**Returns:**

- **out:** `grassmann_number <grassmann_number.html>`__

  A Grassmann number :math:`\psi=\sum_{i_1,i_2,\cdots,i_n}C_{i_1i_2\cdots i_n}\theta_1^{i_1},\theta_2^{i_2},\cdots,\theta_n^{i_n}`.

Attributes
++++++++++

- **size:** ``int``

  Returns the size of the Grassmann algebra containing this variable.

- **basis:** ``list``

  Returns an ordered list of ``str`` representing the generators. For data protection, this list is not modifiable.

Unary and binary operations
+++++++++++++++++++++++++++
- **Addition**: `<self>+<other>` and `<other>+<self>`

  Returns the sum of two Grassmann numbers (or scalars).

- **Multiplication**: `<self>*<other>` and `<other>*<self>`
  
  Returns a multiplication of two Grassmann numbers (or scalars). This is **not** commutative in general! 

- **Subtraction**: `<self>-<other>` and `<other>-<self>`
  
  Returns the difference of two Grassmann numbers (or scalars).

- **Scalar division**: `<self>/<other>`
  
  Returns the divisiion of `<self>` by a scalar.

- **Power**: `<self>^<other>`
  
  Raising to a power of some integer. Real and complex powers are not supported.

- **Exponentiation**: `<other>^<self>`
  
  Returns `exp(log(<other>)*<self>)`. The base `<other>` can be any non-Grassmann scalar.

- **Unary plus**: `+<self>`
  
  Returns `<self>`

- **Negation**: `-<self>`
  
  Returns `(-1)*<self>`

Methods
+++++++
- **is_grassmann()**: 

  Returns `True` if it contains Grassmann numbers (even or odd).

- **is_even()**: 

  Returns `True` if every term is Grassmann even.

- **is_odd()**: 

  Returns `True` if every term is Grassmann odd.

- **get_coeff(basis=`None`)**: 

  See `get_coeff() <get_coeff.html>`__.