class_docstr: A generalized polynomial ring, with objects DMF. 
class_docstr_tok: ["A","generalized","polynomial","ring",",","with","objects","DMF","."]
docstr: Turn an iterable into a sparse distributed module.
  
  Note that the vector is multiplied by a unit first to make all entries
  polynomials.
  
  Examples
  ========
  
  >>> from sympy import ilex, QQ
  >>> from sympy.abc import x, y
  >>> R = QQ.old_poly_ring(x, y, order=ilex)
  >>> f = R.convert((x + 2*y) / (1 + x))
  >>> g = R.convert(x * y)
  >>> R._vector_to_sdm([f, g], ilex)
  [((0, 0, 1), 2), ((0, 1, 0), 1), ((1, 1, 1), 1), ((1,
    2, 1), 1)]
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code: def _vector_to_sdm(self, v, order):
      """
      Turn an iterable into a sparse distributed module.
  
      Note that the vector is multiplied by a unit first to make all entries
      polynomials.
  
      Examples
      ========
  
      >>> from sympy import ilex, QQ
      >>> from sympy.abc import x, y
      >>> R = QQ.old_poly_ring(x, y, order=ilex)
      >>> f = R.convert((x + 2*y) / (1 + x))
      >>> g = R.convert(x * y)
      >>> R._vector_to_sdm([f, g], ilex)
      [((0, 0, 1), 2), ((0, 1, 0), 1), ((1, 1, 1), 1), ((1,
        2, 1), 1)]
      """
      # NOTE this is quite inefficient...
      u = self.one.numer()
      for x in v:
          u *= x.denom()
      return _vector_to_sdm_helper(
          [x.numer() * u / x.denom() for x in v], order
      )
  
imports: from sympy.polys.agca.modules import FreeModulePolyRing
  from sympy.polys.domains.compositedomain import CompositeDomain
  from sympy.polys.domains.old_fractionfield import FractionField
  from sympy.polys.domains.ring import Ring
  from sympy.polys.orderings import monomial_key, build_product_order
  from sympy.polys.polyclasses import DMP, DMF
  from sympy.polys.polyerrors import GeneratorsNeeded, PolynomialError, CoercionFailed, ExactQuotientFailed, NotReversible
  from sympy.polys.polyutils import dict_from_basic, basic_from_dict, _dict_reorder
  from sympy.utilities import public
  from sympy.utilities.iterables import iterable
label_desc: Use image node_id 7 for calling the GeneralizedPolynomialRing obj's underlying member method code with example usage: obj._vector_to_sdm(v, order) and returns: _vector_to_sdm_helper