code: def vander(x, N=None):
      if len(x.shape) < 1:
          raise RuntimeError(
              "Input dim must be greater than or equal to 1."
          )
  
      # pytorch always return int64 for integers
      if "int" in x.dtype:
          x = ivy.astype(x, ivy.int64)
  
      if len(x.shape) == 1:
          # torch always returns the powers in ascending order
          return ivy.vander(x, N=N, increasing=True)
  
      # support multi-dimensional array
      original_shape = x.shape
      if N is None:
          N = x.shape[-1]
  
      # store the vander output
      x = ivy.reshape(x, (-1, x.shape[-1]))
      output = []
  
      for i in range(x.shape[0]):
          output.append(ivy.vander(x[i], N=N, increasing=True))
  
      output = ivy.stack(output)
      output = ivy.reshape(output, (*original_shape, N))
      output = ivy.astype(output, x.dtype)
      return output
  
imports: import math
  import ivy
  import ivy.functional.frontends.torch
  from ivy.functional.frontends.torch.func_wrapper import to_ivy_arrays_and_back
  from ivy.func_wrapper import with_supported_dtypes, with_unsupported_dtypes
  from collections import namedtuple
label_desc: Use image node_id 31 for calling a global function with example usage: vander(x, N) and returns: output, ivy