code: def _det_DOM(M):
      DOM = DomainMatrix.from_Matrix(M, field=True, extension=True)
      K = DOM.domain
      return K.to_sympy(DOM.det())
  
imports: from types import FunctionType
  from sympy.core.cache import cacheit
  from sympy.core.numbers import Float, Integer
  from sympy.core.singleton import S
  from sympy.core.symbol import uniquely_named_symbol
  from sympy.core.mul import Mul
  from sympy.polys import PurePoly, cancel
  from sympy.functions.combinatorial.numbers import nC
  from sympy.polys.matrices.domainmatrix import DomainMatrix
  from sympy.polys.matrices.ddm import DDM
  from .exceptions import NonSquareMatrixError
  from .utilities import _get_intermediate_simp, _get_intermediate_simp_bool, _iszero, _is_zero_after_expand_mul, _dotprodsimp, _simplify
label_desc: Use image node_id 10 for calling a global function with example usage: _det_DOM(M) and returns: K