from sympy.series.kauers import finite_diff
from sympy.series.kauers import finite_diff_kauers
from sympy.abc import x, y, z, m, n, w
from sympy.core.numbers import pi
from sympy.functions.elementary.trigonometric import (cos, sin)
from sympy.concrete.summations import Sum


def test_finite_diff():
    assert finite_diff(x**2 + 2*x + 1, x) == 2*x + 3
    assert finite_diff(y**3 + 2*y**2 + 3*y + 5, y) == 3*y**2 + 7*y + 6
    assert finite_diff(z**2 - 2*z + 3, z) == 2*z - 1
    assert finite_diff(w**2 + 3*w - 2, w) == 2*w + 4
    assert finite_diff(sin(x), x, pi/6) == -sin(x) + sin(x + pi/6)
    assert finite_diff(cos(y), y, pi/3) == -cos(y) + cos(y + pi/3)
    assert finite_diff(x**2 - 2*x + 3, x, 2) == 4*x
    assert finite_diff(n**2 - 2*n + 3, n, 3) == 6*n + 3

def test_finite_diff_kauers():
    assert finite_diff_kauers(Sum(x**2, (x, 1, n))) == (n + 1)**2
    assert finite_diff_kauers(Sum(y, (y, 1, m))) == (m + 1)
    assert finite_diff_kauers(Sum((x*y), (x, 1, m), (y, 1, n))) == (m + 1)*(n + 1)
    assert finite_diff_kauers(Sum((x*y**2), (x, 1, m), (y, 1, n))) == (n + 1)**2*(m + 1)