.. _Basis_Members_Coefficients:

############
Coefficients
############

The core part of the class are the coefficients introduced in Eq. (12) and Eq. (13) in the :ref:`paper<Paper>`:

.. math::

    s_P(n_{P},\lambda)&=\sum_{k=n^{\text{low}}_P}^{n_{P}-1} D_Q(L_P,k)D_Q(\Gamma,n -\lambda-k)

	f_P(\lambda_P+n_{P}) &= D_Q(\Gamma_P,n-\lambda-n_{P})

Here, :math:`P` refers to a subsystem and :math:`D_Q` is the dimension formula given :ref:`here<eq:dim>`.
While :math:`\Gamma_P` is the remaining length to the left of the subsystem :math:`P` and state independent, :math:`\lambda_P` is the number of particles (or magnetization) to the right of the subsystem :math:`P` and depends on the specific state :math:`\vert\Psi\rangle`.
The coefficient are arranged is non-trivial way optimized for the iteration over a specific state.

.. math::

	\lambda_P &=\sum_{T\in\{Q,\dots,Z\}}n_{T}

	\Gamma_P &= L - \sum_{T\in\{Q,\dots,Z\}}L_T


.. doxygenvariable:: danceq::internal::BasisU1::offsets

.. doxygenvariable:: danceq::internal::BasisU1::strides