code: def validate_tucker_tensor(tucker_tensor):
      core, factors = tucker_tensor
  
      if len(factors) < 2:
          raise ValueError(
              "A Tucker tensor should be composed of at least two factors and a core."
              f"However, {len(factors)} factor was given."
          )
  
      if len(factors) != len(core.shape):
          raise ValueError(
              "Tucker decompositions should have one factor per mode of the core"
              f" tensor.However, core has {len(core.shape)} modes but"
              f" {len(factors)} factors have been provided"
          )
  
      shape = []
      rank = []
      for i, factor in enumerate(factors):
          current_shape, current_rank = factor.shape
          if current_rank != ivy.shape(core)[i]:
              raise ValueError(
                  "Factor `n` of Tucker decomposition should"
                  " verify:\nfactors[n].shape[1] = core.shape[n].However,"
                  f" factors[{i}].shape[1]={ivy.shape(factor)[1]} but"
                  f" core.shape[{i}]={ivy.shape(core)[i]}."
              )
          shape.append(current_shape)
          rank.append(current_rank)
  
      return tuple(shape), tuple(rank)
  
imports: from .base import FactorizedTensor
  import ivy
  from copy import deepcopy
  import warnings
label_desc: Use image node_id 13 for calling the TuckerTensor obj's underlying member method code with example usage: obj.validate_tucker_tensor(tucker_tensor) and returns: tuple,  tuple