1from sympy.concrete.guess import (
2            find_simple_recurrence_vector,
3            find_simple_recurrence,
4            rationalize,
5            guess_generating_function_rational,
6            guess_generating_function,
7            guess
8        )
9from sympy import (Function, Symbol, sympify, Rational, symbols, S,
10                   fibonacci, factorial, exp, Product, RisingFactorial)
11
12
13def test_find_simple_recurrence_vector():
14    assert find_simple_recurrence_vector(
15            [fibonacci(k) for k in range(12)]) == [1, -1, -1]
16
17
18def test_find_simple_recurrence():
19    a = Function('a')
20    n = Symbol('n')
21    assert find_simple_recurrence([fibonacci(k) for k in range(12)]) == (
22        -a(n) - a(n + 1) + a(n + 2))
23
24    f = Function('a')
25    i = Symbol('n')
26    a = [1, 1, 1]
27    for k in range(15): a.append(5*a[-1]-3*a[-2]+8*a[-3])
28    assert find_simple_recurrence(a, A=f, N=i) == (
29        -8*f(i) + 3*f(i + 1) - 5*f(i + 2) + f(i + 3))
30    assert find_simple_recurrence([0, 2, 15, 74, 12, 3, 0,
31                                    1, 2, 85, 4, 5, 63]) == 0
32
33
34def test_rationalize():
35    from mpmath import cos, pi, mpf
36    assert rationalize(cos(pi/3)) == S.Half
37    assert rationalize(mpf("0.333333333333333")) == Rational(1, 3)
38    assert rationalize(mpf("-0.333333333333333")) == Rational(-1, 3)
39    assert rationalize(pi, maxcoeff = 250) == Rational(355, 113)
40
41
42def test_guess_generating_function_rational():
43    x = Symbol('x')
44    assert guess_generating_function_rational([fibonacci(k)
45        for k in range(5, 15)]) == ((3*x + 5)/(-x**2 - x + 1))
46
47
48def test_guess_generating_function():
49    x = Symbol('x')
50    assert guess_generating_function([fibonacci(k)
51        for k in range(5, 15)])['ogf'] == ((3*x + 5)/(-x**2 - x + 1))
52    assert guess_generating_function(
53        [1, 2, 5, 14, 41, 124, 383, 1200, 3799, 12122, 38919])['ogf'] == (
54        (1/(x**4 + 2*x**2 - 4*x + 1))**S.Half)
55    assert guess_generating_function(sympify(
56       "[3/2, 11/2, 0, -121/2, -363/2, 121, 4719/2, 11495/2, -8712, -178717/2]")
57       )['ogf'] == (x + Rational(3, 2))/(11*x**2 - 3*x + 1)
58    assert guess_generating_function([factorial(k) for k in range(12)],
59       types=['egf'])['egf'] == 1/(-x + 1)
60    assert guess_generating_function([k+1 for k in range(12)],
61       types=['egf']) == {'egf': (x + 1)*exp(x), 'lgdegf': (x + 2)/(x + 1)}
62
63
64def test_guess():
65    i0, i1 = symbols('i0 i1')
66    assert guess([1, 2, 6, 24, 120], evaluate=False) == [Product(i1 + 1, (i1, 1, i0 - 1))]
67    assert guess([1, 2, 6, 24, 120]) == [RisingFactorial(2, i0 - 1)]
68    assert guess([1, 2, 7, 42, 429, 7436, 218348, 10850216], niter=4) == [
69        2**(i0 - 1)*(Rational(27, 16))**(i0**2/2 - 3*i0/2 +
70        1)*Product(RisingFactorial(Rational(5, 3), i1 - 1)*RisingFactorial(Rational(7, 3), i1
71        - 1)/(RisingFactorial(Rational(3, 2), i1 - 1)*RisingFactorial(Rational(5, 2), i1 -
72        1)), (i1, 1, i0 - 1))]
73    assert guess([1, 0, 2]) == []
74    x, y = symbols('x y')
75    guess([1, 2, 6, 24, 120], variables=[x, y]) == [RisingFactorial(2, x - 1)]
76