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State Handling
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The :ref:`Basis class<BasisU1>` has to fulfill three different methods:

.. admonition:: Functionality

    1. Retrieve basis index :math:`i` from a given :ref:`state<State>` :math:`\vert \Psi_i \rangle`

    2. An efficient iteration by mapping :math:`\vert \Psi_i \rangle` to :math:`\vert \Psi_{i+1} \rangle`

    3. Generate the :ref:`state<State>` :math:`\vert \Psi_i \rangle` for a given index :math:`i`

Below is a complete list of all necessary functions:

.. _Basis_get_index:

1. .. doxygenfunction:: danceq::internal::BasisU1::get_index(const state_class & state) const

.. _Basis_increment:

2. .. doxygenfunction:: danceq::internal::BasisU1::increment(state_class& state, bool* overflow = nullptr) const

.. _Basis_decrement:

2. .. doxygenfunction:: danceq::internal::BasisU1::decrement(state_class& state, bool* underflow = nullptr) const

.. _Basis_get_state:

3. .. doxygenfunction:: danceq::internal::BasisU1::get_state(uint64_t index) const