| 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 | |