class_docstr: Class for the manifold of multinomial distributions.
  
  This is the set of `n+1`-tuples of positive reals that sum up to one,
  i.e. the `n`-simplex. Each point is the parameter of a multinomial
  distribution, i.e. gives the probabilities of $n$ different outcomes
  in a single experiment.
  
  Attributes
  ----------
  dim : int
      Dimension of the parameter manifold of multinomial distributions.
      The number of outcomes is dim + 1.
  embedding_manifold : Manifold
      Embedding manifold.
docstr: Project a vector to the tangent space.
  
  Project a vector in Euclidean space on the tangent space of
  the simplex at a base point.
  
  Parameters
  ----------
  vector : array-like, shape=[..., dim + 1]
      Vector in Euclidean space.
  base_point : array-like, shape=[..., dim + 1]
      Point on the simplex defining the tangent space,
      where the vector will be projected.
  
  Returns
  -------
  vector : array-like, shape=[..., dim + 1]
      Tangent vector in the tangent space of the simplex
      at the base point.
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code: def to_tangent(self, vector, base_point=None):
      """Project a vector to the tangent space.
  
      Project a vector in Euclidean space on the tangent space of
      the simplex at a base point.
  
      Parameters
      ----------
      vector : array-like, shape=[..., dim + 1]
          Vector in Euclidean space.
      base_point : array-like, shape=[..., dim + 1]
          Point on the simplex defining the tangent space,
          where the vector will be projected.
  
      Returns
      -------
      vector : array-like, shape=[..., dim + 1]
          Tangent vector in the tangent space of the simplex
          at the base point.
      """
      component_mean = gs.mean(vector, axis=-1)
      tangent_vec = gs.transpose(gs.transpose(vector) - component_mean)
  
      return repeat_out(
          self.point_ndim,
          tangent_vec,
          vector,
          base_point,
          out_shape=self.shape,
      )
  
imports: from scipy.stats import dirichlet, multinomial
  import geomstats.backend
  from geomstats.algebra_utils import from_vector_to_diagonal_matrix
  from geomstats.geometry.base import LevelSet
  from geomstats.geometry.euclidean import Euclidean
  from geomstats.geometry.hypersphere import Hypersphere
  from geomstats.geometry.riemannian_metric import RiemannianMetric
  from geomstats.information_geometry.base import InformationManifoldMixin, ScipyMultivariateRandomVariable
  from geomstats.vectorization import repeat_out
label_desc: Use image node_id 8 for calling the MultinomialDistributions obj's underlying member method code with example usage: obj.to_tangent(vector, base_point) and returns: repeat_out