83 lines
3.3 KiB
Python
83 lines
3.3 KiB
Python
from sympy.concrete.guess import (
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find_simple_recurrence_vector,
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find_simple_recurrence,
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rationalize,
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guess_generating_function_rational,
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guess_generating_function,
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guess
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)
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from sympy.concrete.products import Product
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from sympy.core.function import Function
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from sympy.core.numbers import Rational
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from sympy.core.singleton import S
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from sympy.core.symbol import (Symbol, symbols)
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from sympy.core.sympify import sympify
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from sympy.functions.combinatorial.factorials import (RisingFactorial, factorial)
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from sympy.functions.combinatorial.numbers import fibonacci
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from sympy.functions.elementary.exponential import exp
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def test_find_simple_recurrence_vector():
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assert find_simple_recurrence_vector(
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[fibonacci(k) for k in range(12)]) == [1, -1, -1]
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def test_find_simple_recurrence():
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a = Function('a')
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n = Symbol('n')
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assert find_simple_recurrence([fibonacci(k) for k in range(12)]) == (
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-a(n) - a(n + 1) + a(n + 2))
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f = Function('a')
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i = Symbol('n')
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a = [1, 1, 1]
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for k in range(15): a.append(5*a[-1]-3*a[-2]+8*a[-3])
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assert find_simple_recurrence(a, A=f, N=i) == (
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-8*f(i) + 3*f(i + 1) - 5*f(i + 2) + f(i + 3))
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assert find_simple_recurrence([0, 2, 15, 74, 12, 3, 0,
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1, 2, 85, 4, 5, 63]) == 0
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def test_rationalize():
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from mpmath import cos, pi, mpf
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assert rationalize(cos(pi/3)) == S.Half
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assert rationalize(mpf("0.333333333333333")) == Rational(1, 3)
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assert rationalize(mpf("-0.333333333333333")) == Rational(-1, 3)
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assert rationalize(pi, maxcoeff = 250) == Rational(355, 113)
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def test_guess_generating_function_rational():
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x = Symbol('x')
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assert guess_generating_function_rational([fibonacci(k)
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for k in range(5, 15)]) == ((3*x + 5)/(-x**2 - x + 1))
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def test_guess_generating_function():
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x = Symbol('x')
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assert guess_generating_function([fibonacci(k)
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for k in range(5, 15)])['ogf'] == ((3*x + 5)/(-x**2 - x + 1))
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assert guess_generating_function(
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[1, 2, 5, 14, 41, 124, 383, 1200, 3799, 12122, 38919])['ogf'] == (
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(1/(x**4 + 2*x**2 - 4*x + 1))**S.Half)
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assert guess_generating_function(sympify(
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"[3/2, 11/2, 0, -121/2, -363/2, 121, 4719/2, 11495/2, -8712, -178717/2]")
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)['ogf'] == (x + Rational(3, 2))/(11*x**2 - 3*x + 1)
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assert guess_generating_function([factorial(k) for k in range(12)],
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types=['egf'])['egf'] == 1/(-x + 1)
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assert guess_generating_function([k+1 for k in range(12)],
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types=['egf']) == {'egf': (x + 1)*exp(x), 'lgdegf': (x + 2)/(x + 1)}
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def test_guess():
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i0, i1 = symbols('i0 i1')
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assert guess([1, 2, 6, 24, 120], evaluate=False) == [Product(i1 + 1, (i1, 1, i0 - 1))]
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assert guess([1, 2, 6, 24, 120]) == [RisingFactorial(2, i0 - 1)]
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assert guess([1, 2, 7, 42, 429, 7436, 218348, 10850216], niter=4) == [
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2**(i0 - 1)*(Rational(27, 16))**(i0**2/2 - 3*i0/2 +
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1)*Product(RisingFactorial(Rational(5, 3), i1 - 1)*RisingFactorial(Rational(7, 3), i1
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- 1)/(RisingFactorial(Rational(3, 2), i1 - 1)*RisingFactorial(Rational(5, 2), i1 -
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1)), (i1, 1, i0 - 1))]
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assert guess([1, 0, 2]) == []
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x, y = symbols('x y')
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assert guess([1, 2, 6, 24, 120], variables=[x, y]) == [RisingFactorial(2, x - 1)]
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