def test_mobius_transform():
assert all(
tf(ls, subset=subset) == ls for ls in ([], [S(7) / 4])
for subset in (True, False)
for tf in (mobius_transform, inverse_mobius_transform))
w, x, y, z = symbols('w x y z')
assert mobius_transform([x, y]) == [x, x + y]
assert inverse_mobius_transform([x, x + y]) == [x, y]
assert mobius_transform([x, y], subset=False) == [x + y, y]
assert inverse_mobius_transform([x + y, y], subset=False) == [x, y]
assert mobius_transform([w, x, y, z]) == [w, w + x, w + y, w + x + y + z]
assert inverse_mobius_transform([w, w + x, w + y, w + x + y + z]) == \
[w, x, y, z]
assert mobius_transform([w, x, y, z], subset=False) == \
[w + x + y + z, x + z, y + z, z]
assert inverse_mobius_transform([w + x + y + z, x + z, y + z, z], subset=False) == \
[w, x, y, z]
ls = [S(2) / 3, S(6) / 7, S(5) / 8, 9, S(5) / 3 + 7 * I]
mls = [
S(2) / 3,
S(32) / 21,
S(31) / 24,
S(1873) / 168,
S(7) / 3 + 7 * I,
S(67) / 21 + 7 * I,
S(71) / 24 + 7 * I,
S(2153) / 168 + 7 * I
]
assert mobius_transform(ls) == mls
assert inverse_mobius_transform(mls) == ls + [S.Zero] * 3
mls = [
S(2153) / 168 + 7 * I,
S(69) / 7,
S(77) / 8, 9,
S(5) / 3 + 7 * I, 0, 0, 0
]
assert mobius_transform(ls, subset=False) == mls
assert inverse_mobius_transform(mls, subset=False) == ls + [S.Zero] * 3
ls = ls[:-1]
mls = [S(2) / 3, S(32) / 21, S(31) / 24, S(1873) / 168]
assert mobius_transform(ls) == mls
assert inverse_mobius_transform(mls) == ls
mls = [S(1873) / 168, S(69) / 7, S(77) / 8, 9]
assert mobius_transform(ls, subset=False) == mls
assert inverse_mobius_transform(mls, subset=False) == ls
raises(TypeError, lambda: mobius_transform(x, subset=True))
raises(TypeError, lambda: inverse_mobius_transform(y, subset=False))
def test_mobius_transform():
assert all(tf(ls, subset=subset) == ls
for ls in ([], [S(7)/4]) for subset in (True, False)
for tf in (mobius_transform, inverse_mobius_transform))
w, x, y, z = symbols('w x y z')
assert mobius_transform([x, y]) == [x, x + y]
assert inverse_mobius_transform([x, x + y]) == [x, y]
assert mobius_transform([x, y], subset=False) == [x + y, y]
assert inverse_mobius_transform([x + y, y], subset=False) == [x, y]
assert mobius_transform([w, x, y, z]) == [w, w + x, w + y, w + x + y + z]
assert inverse_mobius_transform([w, w + x, w + y, w + x + y + z]) == \
[w, x, y, z]
assert mobius_transform([w, x, y, z], subset=False) == \
[w + x + y + z, x + z, y + z, z]
assert inverse_mobius_transform([w + x + y + z, x + z, y + z, z], subset=False) == \
[w, x, y, z]
ls = [S(2)/3, S(6)/7, S(5)/8, 9, S(5)/3 + 7*I]
mls = [S(2)/3, S(32)/21, S(31)/24, S(1873)/168,
S(7)/3 + 7*I, S(67)/21 + 7*I, S(71)/24 + 7*I,
S(2153)/168 + 7*I]
assert mobius_transform(ls) == mls
assert inverse_mobius_transform(mls) == ls + [S.Zero]*3
mls = [S(2153)/168 + 7*I, S(69)/7, S(77)/8, 9, S(5)/3 + 7*I, 0, 0, 0]
assert mobius_transform(ls, subset=False) == mls
assert inverse_mobius_transform(mls, subset=False) == ls + [S.Zero]*3
ls = ls[:-1]
mls = [S(2)/3, S(32)/21, S(31)/24, S(1873)/168]
assert mobius_transform(ls) == mls
assert inverse_mobius_transform(mls) == ls
mls = [S(1873)/168, S(69)/7, S(77)/8, 9]
assert mobius_transform(ls, subset=False) == mls
assert inverse_mobius_transform(mls, subset=False) == ls
raises(TypeError, lambda: mobius_transform(x, subset=True))
raises(TypeError, lambda: inverse_mobius_transform(y, subset=False))
def test_mobius_transform():
assert all(tf(ls, subset=subset) == ls
for ls in ([], [Rational(7, 4)]) for subset in (True, False)
for tf in (mobius_transform, inverse_mobius_transform))
w, x, y, z = symbols('w x y z')
assert mobius_transform([x, y]) == [x, x + y]
assert inverse_mobius_transform([x, x + y]) == [x, y]
assert mobius_transform([x, y], subset=False) == [x + y, y]
assert inverse_mobius_transform([x + y, y], subset=False) == [x, y]
assert mobius_transform([w, x, y, z]) == [w, w + x, w + y, w + x + y + z]
assert inverse_mobius_transform([w, w + x, w + y, w + x + y + z]) == \
[w, x, y, z]
assert mobius_transform([w, x, y, z], subset=False) == \
[w + x + y + z, x + z, y + z, z]
assert inverse_mobius_transform([w + x + y + z, x + z, y + z, z], subset=False) == \
[w, x, y, z]
ls = [Rational(2, 3), Rational(6, 7), Rational(5, 8), 9, Rational(5, 3) + 7*I]
mls = [Rational(2, 3), Rational(32, 21), Rational(31, 24), Rational(1873, 168),
Rational(7, 3) + 7*I, Rational(67, 21) + 7*I, Rational(71, 24) + 7*I,
Rational(2153, 168) + 7*I]
assert mobius_transform(ls) == mls
assert inverse_mobius_transform(mls) == ls + [S.Zero]*3
mls = [Rational(2153, 168) + 7*I, Rational(69, 7), Rational(77, 8), 9, Rational(5, 3) + 7*I, 0, 0, 0]
assert mobius_transform(ls, subset=False) == mls
assert inverse_mobius_transform(mls, subset=False) == ls + [S.Zero]*3
ls = ls[:-1]
mls = [Rational(2, 3), Rational(32, 21), Rational(31, 24), Rational(1873, 168)]
assert mobius_transform(ls) == mls
assert inverse_mobius_transform(mls) == ls
mls = [Rational(1873, 168), Rational(69, 7), Rational(77, 8), 9]
assert mobius_transform(ls, subset=False) == mls
assert inverse_mobius_transform(mls, subset=False) == ls
raises(TypeError, lambda: mobius_transform(x, subset=True))
raises(TypeError, lambda: inverse_mobius_transform(y, subset=False))