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