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| from sympy.ntheory.multinomial import (binomial_coefficients, binomial_coefficients_list, multinomial_coefficients) | |
| from sympy.ntheory.multinomial import multinomial_coefficients_iterator | |
| def test_binomial_coefficients_list(): | |
| assert binomial_coefficients_list(0) == [1] | |
| assert binomial_coefficients_list(1) == [1, 1] | |
| assert binomial_coefficients_list(2) == [1, 2, 1] | |
| assert binomial_coefficients_list(3) == [1, 3, 3, 1] | |
| assert binomial_coefficients_list(4) == [1, 4, 6, 4, 1] | |
| assert binomial_coefficients_list(5) == [1, 5, 10, 10, 5, 1] | |
| assert binomial_coefficients_list(6) == [1, 6, 15, 20, 15, 6, 1] | |
| def test_binomial_coefficients(): | |
| for n in range(15): | |
| c = binomial_coefficients(n) | |
| l = [c[k] for k in sorted(c)] | |
| assert l == binomial_coefficients_list(n) | |
| def test_multinomial_coefficients(): | |
| assert multinomial_coefficients(1, 1) == {(1,): 1} | |
| assert multinomial_coefficients(1, 2) == {(2,): 1} | |
| assert multinomial_coefficients(1, 3) == {(3,): 1} | |
| assert multinomial_coefficients(2, 0) == {(0, 0): 1} | |
| assert multinomial_coefficients(2, 1) == {(0, 1): 1, (1, 0): 1} | |
| assert multinomial_coefficients(2, 2) == {(2, 0): 1, (0, 2): 1, (1, 1): 2} | |
| assert multinomial_coefficients(2, 3) == {(3, 0): 1, (1, 2): 3, (0, 3): 1, | |
| (2, 1): 3} | |
| assert multinomial_coefficients(3, 1) == {(1, 0, 0): 1, (0, 1, 0): 1, | |
| (0, 0, 1): 1} | |
| assert multinomial_coefficients(3, 2) == {(0, 1, 1): 2, (0, 0, 2): 1, | |
| (1, 1, 0): 2, (0, 2, 0): 1, (1, 0, 1): 2, (2, 0, 0): 1} | |
| mc = multinomial_coefficients(3, 3) | |
| assert mc == {(2, 1, 0): 3, (0, 3, 0): 1, | |
| (1, 0, 2): 3, (0, 2, 1): 3, (0, 1, 2): 3, (3, 0, 0): 1, | |
| (2, 0, 1): 3, (1, 2, 0): 3, (1, 1, 1): 6, (0, 0, 3): 1} | |
| assert dict(multinomial_coefficients_iterator(2, 0)) == {(0, 0): 1} | |
| assert dict( | |
| multinomial_coefficients_iterator(2, 1)) == {(0, 1): 1, (1, 0): 1} | |
| assert dict(multinomial_coefficients_iterator(2, 2)) == \ | |
| {(2, 0): 1, (0, 2): 1, (1, 1): 2} | |
| assert dict(multinomial_coefficients_iterator(3, 3)) == mc | |
| it = multinomial_coefficients_iterator(7, 2) | |
| assert [next(it) for i in range(4)] == \ | |
| [((2, 0, 0, 0, 0, 0, 0), 1), ((1, 1, 0, 0, 0, 0, 0), 2), | |
| ((0, 2, 0, 0, 0, 0, 0), 1), ((1, 0, 1, 0, 0, 0, 0), 2)] | |