/usr/lib/python3/dist-packages/mpmath/tests/test_calculus.py is in python3-mpmath 0.18-1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 | from mpmath import *
def test_approximation():
mp.dps = 15
f = lambda x: cos(2-2*x)/x
p, err = chebyfit(f, [2, 4], 8, error=True)
assert err < 1e-5
for i in range(10):
x = 2 + i/5.
assert abs(polyval(p, x) - f(x)) < err
def test_limits():
mp.dps = 15
assert limit(lambda x: (x-sin(x))/x**3, 0).ae(mpf(1)/6)
assert limit(lambda n: (1+1/n)**n, inf).ae(e)
def test_polyval():
assert polyval([], 3) == 0
assert polyval([0], 3) == 0
assert polyval([5], 3) == 5
# 4x^3 - 2x + 5
p = [4, 0, -2, 5]
assert polyval(p,4) == 253
assert polyval(p,4,derivative=True) == (253, 190)
def test_polyroots():
p = polyroots([1,-4])
assert p[0].ae(4)
p, q = polyroots([1,2,3])
assert p.ae(-1 - sqrt(2)*j)
assert q.ae(-1 + sqrt(2)*j)
#this is not a real test, it only tests a specific case
assert polyroots([1]) == []
try:
polyroots([0])
assert False
except ValueError:
pass
def test_pade():
one = mpf(1)
mp.dps = 20
N = 10
a = [one]
k = 1
for i in range(1, N+1):
k *= i
a.append(one/k)
p, q = pade(a, N//2, N//2)
for x in arange(0, 1, 0.1):
r = polyval(p[::-1], x)/polyval(q[::-1], x)
assert(r.ae(exp(x), 1.0e-10))
mp.dps = 15
def test_fourier():
mp.dps = 15
c, s = fourier(lambda x: x+1, [-1, 2], 2)
#plot([lambda x: x+1, lambda x: fourierval((c, s), [-1, 2], x)], [-1, 2])
assert c[0].ae(1.5)
assert c[1].ae(-3*sqrt(3)/(2*pi))
assert c[2].ae(3*sqrt(3)/(4*pi))
assert s[0] == 0
assert s[1].ae(3/(2*pi))
assert s[2].ae(3/(4*pi))
assert fourierval((c, s), [-1, 2], 1).ae(1.9134966715663442)
def test_differint():
mp.dps = 15
assert differint(lambda t: t, 2, -0.5).ae(8*sqrt(2/pi)/3)
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