grassmann_number

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() instead.

Parameters:

• data: numpy.ndarray

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

• generator: a list of str

  A list of symbols for Grassmann generators \(\theta_1,\theta_2,\cdots,\theta_n\).

Returns:

• out: grassmann_number

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

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().