How to use the sympy.core.compatibility.range function in sympy

v = {}
        v[(0, 0)] = [self._print(a) for a in e.an]
        v[(0, 1)] = [self._print(a) for a in e.aother]
        v[(1, 0)] = [self._print(b) for b in e.bm]
        v[(1, 1)] = [self._print(b) for b in e.bother]

        P = self._print(e.argument)
        P.baseline = P.height()//2

        vp = {}
        for idx in v:
            vp[idx] = self._hprint_vec(v[idx])

        for i in range(2):
            maxw = max(vp[(0, i)].width(), vp[(1, i)].width())
            for j in range(2):
                s = vp[(j, i)]
                left = (maxw - s.width()) // 2
                right = maxw - left - s.width()
                s = prettyForm(*s.left(' ' * left))
                s = prettyForm(*s.right(' ' * right))
                vp[(j, i)] = s

        D1 = prettyForm(*vp[(0, 0)].right('  ', vp[(0, 1)]))
        D1 = prettyForm(*D1.below(' '))
        D2 = prettyForm(*vp[(1, 0)].right('  ', vp[(1, 1)]))
        D = prettyForm(*D1.below(D2))

        # make sure that the argument `z' is centred vertically
        D.baseline = D.height()//2

        # insert horizontal separator

if n&(n - 1): # not a power of 2
        b += 1
        n = 2**b

    a += [S.Zero]*(n - len(a))
    for i in range(1, n):
        j = int(ibin(i, b, str=True)[::-1], 2)
        if i < j:
            a[i], a[j] = a[j], a[i]

    ang = -2*pi/n if inverse else 2*pi/n

    if dps is not None:
        ang = ang.evalf(dps + 2)

    w = [cos(ang*i) + I*sin(ang*i) for i in range(n // 2)]

    h = 2
    while h <= n:
        hf, ut = h // 2, n // h
        for i in range(0, n, h):
            for j in range(hf):
                u, v = a[i + j], expand_mul(a[i + j + hf]*w[ut * j])
                a[i + j], a[i + j + hf] = u + v, u - v
        h *= 2

    if inverse:
        a = [(x/n).evalf(dps) for x in a] if dps is not None \
                            else [x/n for x in a]

    return a

seq_dmp = recurrence.recurrence.listofpoly
        R = recurrence.recurrence.parent.base
        K = R.get_field()
        seq = []

        for i, j in enumerate(seq_dmp):
            seq.append(K.new(j.rep))

        sub = [-seq[i] / seq[k] for i in range(k)]
        sol = [i for i in recurrence.u0]

        if l + 1 >= n:
            pass
        else:
            # use the initial conditions to find the next term
            for i in range(l + 1 - k, n - k):
                coeff = S(0)
                for j in range(k):
                    if i + j >= 0:
                        coeff += DMFsubs(sub[j], i) * sol[i + j]
                sol.append(coeff)

        if coefficient:
            return sol

        ser = S(0)
        for i, j in enumerate(sol):
            ser += x**(i + constantpower) * j
        if order:
            ser += Order(x**(n + int(constantpower)), x)
        if x0 != 0:
            return ser.subs(x, x - x0)

========

        >>> from sympy.physics.vector import ReferenceFrame, Vector
        >>> N = ReferenceFrame('N')
        >>> A = ReferenceFrame('A')
        >>> V = 10 * N.x
        >>> A.set_ang_vel(N, V)
        >>> A.ang_vel_in(N)
        10*N.x

        """

        _check_frame(otherframe)
        flist = self._dict_list(otherframe, 1)
        outvec = Vector(0)
        for i in range(len(flist) - 1):
            outvec += flist[i]._ang_vel_dict[flist[i + 1]]
        return outvec

pinv_solve
        LUdecomposition
        """
        if rhs.rows != self.rows:
            raise ShapeError("`self` and `rhs` must have the same number of rows.")

        A, perm = self.LUdecomposition_Simple(iszerofunc=_iszero)
        n = self.rows
        b = rhs.permuteFwd(perm).as_mutable()
        # forward substitution, all diag entries are scaled to 1
        for i in range(n):
            for j in range(i):
                scale = A[i, j]
                b.zip_row_op(i, j, lambda x, y: x - y*scale)
        # backward substitution
        for i in range(n - 1, -1, -1):
            for j in range(i + 1, n):
                scale = A[i, j]
                b.zip_row_op(i, j, lambda x, y: x - y*scale)
            scale = A[i, i]
            b.row_op(i, lambda x, _: x/scale)
        return rhs.__class__(b)

This is called from the enumeration/counting routines, so
        there is no need to call it separately."""

        num_components = len(multiplicities)
        # cardinality is the total number of elements, whether or not distinct
        cardinality = sum(multiplicities)

        # pstack is the partition stack, which is segmented by
        # f into parts.
        self.pstack = [PartComponent() for i in
                       range(num_components * cardinality + 1)]
        self.f = [0] * (cardinality + 1)

        # Initial state - entire multiset in one part.
        for j in range(num_components):
            ps = self.pstack[j]
            ps.c = j
            ps.u = multiplicities[j]
            ps.v = multiplicities[j]

        self.f[0] = 0
        self.f[1] = num_components
        self.lpart = 0

det
        det_bareis
        berkowitz_det
        """
        if not self.is_square:
            raise NonSquareMatrixError()
        if not self:
            return S.One

        M, n = self.copy(), self.rows
        p, prod = [], 1
        l, u, p = M.LUdecomposition()
        if len(p) % 2:
            prod = -1

        for k in range(n):
            prod = prod*u[k, k]*l[k, k]

        return prod.expand()

def _all_roots(cls, poly):
        """Get real and complex roots of a composite polynomial. """
        (_, factors) = poly.factor_list()

        reals = cls._get_reals(factors)
        reals = cls._reals_sorted(reals)
        reals_count = cls._count_roots(reals)

        roots = []

        for index in range(0, reals_count):
            roots.append(cls._reals_index(reals, index))

        complexes = cls._get_complexes(factors)
        complexes = cls._complexes_sorted(complexes)
        complexes_count = cls._count_roots(complexes)

        for index in range(0, complexes_count):
            roots.append(cls._complexes_index(complexes, index))

        return roots

for j in range(i):
                    L[i, j] = (1 / L[j, j])*expand_mul(self[i, j] -
                        sum(L[i, k]*L[j, k].conjugate() for k in range(j)))
                Lii2 = expand_mul(self[i, i] -
                    sum(L[i, k]*L[i, k].conjugate() for k in range(i)))
                if Lii2.is_positive is False:
                    raise NonPositiveDefiniteMatrixError(
                        "Matrix must be positive-definite")
                L[i, i] = sqrt(Lii2)
        else:
            for i in range(self.rows):
                for j in range(i):
                    L[i, j] = (1 / L[j, j])*(self[i, j] -
                        sum(L[i, k]*L[j, k] for k in range(j)))
                L[i, i] = sqrt(self[i, i] -
                    sum(L[i, k]**2 for k in range(i)))
        return self._new(L)