code: def posify(eq):
      """Return ``eq`` (with generic symbols made positive) and a
      dictionary containing the mapping between the old and new
      symbols.
  
      Explanation
      ===========
  
      Any symbol that has positive=None will be replaced with a positive dummy
      symbol having the same name. This replacement will allow more symbolic
      processing of expressions, especially those involving powers and
      logarithms.
  
      A dictionary that can be sent to subs to restore ``eq`` to its original
      symbols is also returned.
  
      >>> from sympy import posify, Symbol, log, solve
      >>> from sympy.abc import x
      >>> posify(x + Symbol('p', positive=True) + Symbol('n', negative=True))
      (_x + n + p, {_x: x})
  
      >>> eq = 1/x
      >>> log(eq).expand()
      log(1/x)
      >>> log(posify(eq)[0]).expand()
      -log(_x)
      >>> p, rep = posify(eq)
      >>> log(p).expand().subs(rep)
      -log(x)
  
      It is possible to apply the same transformations to an iterable
      of expressions:
  
      >>> eq = x**2 - 4
      >>> solve(eq, x)
      [-2, 2]
      >>> eq_x, reps = posify([eq, x]); eq_x
      [_x**2 - 4, _x]
      >>> solve(*eq_x)
      [2]
      """
      eq = sympify(eq)
      if iterable(eq):
          f = type(eq)
          eq = list(eq)
          syms = set()
          for e in eq:
              syms = syms.union(e.atoms(Symbol))
          reps = {}
          for s in syms:
              reps.update({v: k for k, v in posify(s)[1].items()})
          for i, e in enumerate(eq):
              eq[i] = e.subs(reps)
          return f(eq), {r: s for s, r in reps.items()}
  
      reps = {
          s: Dummy(s.name, positive=True, **s.assumptions0)
          for s in eq.free_symbols
          if s.is_positive is None
      }
      eq = eq.subs(reps)
      return eq, {r: s for s, r in reps.items()}
  
imports: from collections import defaultdict
  from sympy.concrete.products import Product
  from sympy.concrete.summations import Sum
  from sympy.core import Basic, S, Add, Mul, Pow, Symbol, sympify, expand_func, Function, Dummy, Expr, factor_terms, expand_power_exp, Eq
  from sympy.core.exprtools import factor_nc
  from sympy.core.parameters import global_parameters
  from sympy.core.function import expand_log, count_ops, _mexpand, nfloat, expand_mul, expand
  from sympy.core.numbers import Float, I, pi, Rational
  from sympy.core.relational import Relational
  from sympy.core.rules import Transform
  from sympy.core.sorting import ordered
  from sympy.core.sympify import _sympify
  from sympy.core.traversal import bottom_up, walk
  from sympy.functions import gamma, exp, sqrt, log, exp_polar, re
  from sympy.functions.combinatorial.factorials import CombinatorialFunction
  from sympy.functions.elementary.complexes import unpolarify, Abs, sign
  from sympy.functions.elementary.exponential import ExpBase
  from sympy.functions.elementary.hyperbolic import HyperbolicFunction
  from sympy.functions.elementary.integers import ceiling
  from sympy.functions.elementary.piecewise import Piecewise, piecewise_fold, piecewise_simplify
  from sympy.functions.elementary.trigonometric import TrigonometricFunction
  from sympy.functions.special.bessel import BesselBase, besselj, besseli, besselk, bessely, jn
  from sympy.functions.special.tensor_functions import KroneckerDelta
  from sympy.integrals.integrals import Integral
  from sympy.matrices.expressions import MatrixExpr, MatAdd, MatMul, MatPow, MatrixSymbol
  from sympy.polys import together, cancel, factor
  from sympy.polys.numberfields.minpoly import _is_sum_surds, _minimal_polynomial_sq
  from sympy.simplify.combsimp import combsimp
  from sympy.simplify.cse_opts import sub_pre, sub_post
  from sympy.simplify.hyperexpand import hyperexpand
  from sympy.simplify.powsimp import powsimp
  from sympy.simplify.radsimp import radsimp, fraction, collect_abs
  from sympy.simplify.sqrtdenest import sqrtdenest
  from sympy.simplify.trigsimp import trigsimp, exptrigsimp
  from sympy.utilities.decorator import deprecated
  from sympy.utilities.iterables import has_variety, sift, subsets, iterable
  from sympy.utilities.misc import as_int
  import mpmath
label_desc: Use image node_id 4 for calling a global function with example usage: posify(eq) and returns: eq,  unknown, f,  unknown