T3Tangent.to_t3
===============

.. py:method:: t3toolbox.manifold.T3Tangent.to_t3(include_shift = False)

   .. code-block:: python

      def to_t3(
              self,
              include_shift:  bool = False,  # False: tangent vector v. True: base point + v.
      ) -> t3.TuckerTensorTrain:  # doubled-rank Tucker tensor train


   Doubled-rank :py:class:`TuckerTensorTrain` representation of this tangent vector.

   The Tucker and TT ranks are (roughly) doubled. With ``include_shift=True`` the result
   represents ``base point + v`` (the standard shifted embedding used by :py:meth:`retract`).

   This is the doubled-rank representation of Appendix A.3.1 (equations (50)-(53) and Figure 20)
   in Alger et al. (2026), "Tucker Tensor Train Taylor Series" (arXiv:2603.21141).