tests/functions/test_comb_factorials.py

4                      binomial, exp, expand_func, factorial, factorial2, ff,
258     assert binomial(0, 0) == 1
259     assert binomial(1, 1) == 1
260     assert binomial(10, 10) == 1
261     assert binomial(n, z) == 1
262     assert binomial(1, 2) == 0
263     assert binomial(1, -1) == 0
264     assert binomial(-1, 1) == -1
265     assert binomial(-1, -1) == 1
266     assert binomial(Rational(1, 2), Rational(1, 2)) == 1
267     assert binomial(-10, 1) == -10
268     assert binomial(-10, 7) == -11440
269     assert binomial(n, -1).func == binomial
270     assert binomial(kp, -1) == 0
271     assert binomial(nz, 0) == 1
272     assert expand_func(binomial(n, 1)) == n
273     assert expand_func(binomial(n, 2)) == n*(n - 1)/2
274     assert expand_func(binomial(n, n - 2)) == n*(n - 1)/2
275     assert expand_func(binomial(n, n - 1)) == n
276     assert binomial(n, 3).func == binomial
277     assert binomial(n, 3).expand(func=True) == n**3/6 - n**2/2 + n/3
278     assert expand_func(binomial(n, 3)) == n*(n - 2)*(n - 1)/6
279     assert expand_func(binomial(1, 2, evaluate=False)) == 0
280     assert expand_func(binomial(n, 0, evaluate=False)) == 1
281     assert isinstance(expand_func(binomial(n, -1, evaluate=False)), binomial)
282     assert isinstance(expand_func(binomial(n, k)), binomial)
283     assert binomial(n, n) == 1
284     assert binomial(n, n + 1).func == binomial  # e.g. (-1, 0) == 1
285     assert binomial(kp, kp + 1) == 0
286     assert binomial(n, u).func == binomial
287     assert binomial(kp, u) == 0
288     assert binomial(n, p).func == binomial
289     assert binomial(n, k).func == binomial
290     assert binomial(n, n + p).func == binomial
291     assert binomial(kp, kp + p) == 0
293     assert expand_func(binomial(n, n - 3)) == n*(n - 2)*(n - 1)/6
295     assert binomial(n, k).is_integer
296     assert binomial(p, k).is_integer is None
303     assert binomial(n, k).diff(n) == \
304         (-polygamma(0, 1 + n - k) + polygamma(0, 1 + n))*binomial(n, k)
305     assert binomial(n**2, k**3).diff(n) == \
307             0, 1 + n**2 - k**3) + polygamma(0, 1 + n**2))*binomial(n**2, k**3)
309     assert binomial(n, k).diff(k) == \
310         (-polygamma(0, 1 + k) + polygamma(0, 1 + n - k))*binomial(n, k)
311     assert binomial(n**2, k**3).diff(k) == \
313             0, 1 + k**3) + polygamma(0, 1 + n**2 - k**3))*binomial(n**2, k**3)
315     pytest.raises(ArgumentIndexError, lambda: binomial(n, k).fdiff(3))
322     assert binomial(n, k).rewrite(
324     assert binomial(