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- from sympy.core.numbers import Rational
- from sympy.functions.combinatorial.numbers import fibonacci
- from sympy.core import S, symbols
- from sympy.testing.pytest import raises
- from sympy.discrete.recurrences import linrec
- def test_linrec():
- assert linrec(coeffs=[1, 1], init=[1, 1], n=20) == 10946
- assert linrec(coeffs=[1, 2, 3, 4, 5], init=[1, 1, 0, 2], n=10) == 1040
- assert linrec(coeffs=[0, 0, 11, 13], init=[23, 27], n=25) == 59628567384
- assert linrec(coeffs=[0, 0, 1, 1, 2], init=[1, 5, 3], n=15) == 165
- assert linrec(coeffs=[11, 13, 15, 17], init=[1, 2, 3, 4], n=70) == \
- 56889923441670659718376223533331214868804815612050381493741233489928913241
- assert linrec(coeffs=[0]*55 + [1, 1, 2, 3], init=[0]*50 + [1, 2, 3], n=4000) == \
- 702633573874937994980598979769135096432444135301118916539
- assert linrec(coeffs=[11, 13, 15, 17], init=[1, 2, 3, 4], n=10**4)
- assert linrec(coeffs=[11, 13, 15, 17], init=[1, 2, 3, 4], n=10**5)
- assert all(linrec(coeffs=[1, 1], init=[0, 1], n=n) == fibonacci(n)
- for n in range(95, 115))
- assert all(linrec(coeffs=[1, 1], init=[1, 1], n=n) == fibonacci(n + 1)
- for n in range(595, 615))
- a = [S.Half, Rational(3, 4), Rational(5, 6), 7, Rational(8, 9), Rational(3, 5)]
- b = [1, 2, 8, Rational(5, 7), Rational(3, 7), Rational(2, 9), 6]
- x, y, z = symbols('x y z')
- assert linrec(coeffs=a[:5], init=b[:4], n=80) == \
- Rational(1726244235456268979436592226626304376013002142588105090705187189,
- 1960143456748895967474334873705475211264)
- assert linrec(coeffs=a[:4], init=b[:4], n=50) == \
- Rational(368949940033050147080268092104304441, 504857282956046106624)
- assert linrec(coeffs=a[3:], init=b[:3], n=35) == \
- Rational(97409272177295731943657945116791049305244422833125109,
- 814315512679031689453125)
- assert linrec(coeffs=[0]*60 + [Rational(2, 3), Rational(4, 5)], init=b, n=3000) == \
- Rational(26777668739896791448594650497024, 48084516708184142230517578125)
- raises(TypeError, lambda: linrec(coeffs=[11, 13, 15, 17], init=[1, 2, 3, 4, 5], n=1))
- raises(TypeError, lambda: linrec(coeffs=a[:4], init=b[:5], n=10000))
- raises(ValueError, lambda: linrec(coeffs=a[:4], init=b[:4], n=-10000))
- raises(TypeError, lambda: linrec(x, b, n=10000))
- raises(TypeError, lambda: linrec(a, y, n=10000))
- assert linrec(coeffs=[x, y, z], init=[1, 1, 1], n=4) == \
- x**2 + x*y + x*z + y + z
- assert linrec(coeffs=[1, 2, 1], init=[x, y, z], n=20) == \
- 269542*x + 664575*y + 578949*z
- assert linrec(coeffs=[0, 3, 1, 2], init=[x, y], n=30) == \
- 58516436*x + 56372788*y
- assert linrec(coeffs=[0]*50 + [1, 2, 3], init=[x, y, z], n=1000) == \
- 11477135884896*x + 25999077948732*y + 41975630244216*z
- assert linrec(coeffs=[], init=[1, 1], n=20) == 0
- assert linrec(coeffs=[x, y, z], init=[1, 2, 3], n=2) == 3
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