code: def sum_add(self, other, method=0):
      """Helper function for Sum simplification"""
  
      # we know this is something in terms of a constant * a sum
      # so we temporarily put the constants inside for simplification
      # then simplify the result
      def __refactor(val):
          args = Mul.make_args(val)
          sumv = next(x for x in args if isinstance(x, Sum))
          constant = Mul(*[x for x in args if x != sumv])
          return Sum(constant * sumv.function, *sumv.limits)
  
      if isinstance(self, Mul):
          rself = __refactor(self)
      else:
          rself = self
  
      if isinstance(other, Mul):
          rother = __refactor(other)
      else:
          rother = other
  
      if type(rself) is type(rother):
          if method == 0:
              if rself.limits == rother.limits:
                  return factor_sum(
                      Sum(
                          rself.function + rother.function,
                          *rself.limits,
                      )
                  )
          elif method == 1:
              if simplify(rself.function - rother.function) == 0:
                  if len(rself.limits) == len(rother.limits) == 1:
                      i = rself.limits[0][0]
                      x1 = rself.limits[0][1]
                      y1 = rself.limits[0][2]
                      j = rother.limits[0][0]
                      x2 = rother.limits[0][1]
                      y2 = rother.limits[0][2]
  
                      if i == j:
                          if x2 == y1 + 1:
                              return factor_sum(
                                  Sum(rself.function, (i, x1, y2))
                              )
                          elif x1 == y2 + 1:
                              return factor_sum(
                                  Sum(rself.function, (i, x2, y1))
                              )
  
      return Add(self, other)
  
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 12 for calling a global function with example usage: sum_add(other, method) and returns: Add, Sum, factor_sum, factor_sum, factor_sum