def test_curve():
s = Symbol("s")
z = Symbol("z")
# this curve is independent of the indicated parameter
C = Curve([2 * s, s ** 2], (z, 0, 2))
assert C.parameter == z
assert C.functions == (2 * s, s ** 2)
assert C.arbitrary_point() == Point(2 * s, s ** 2)
assert C.arbitrary_point(z) == Point(2 * s, s ** 2)
# this is how it is normally used
C = Curve([2 * s, s ** 2], (s, 0, 2))
assert C.parameter == s
assert C.functions == (2 * s, s ** 2)
t = Symbol("t")
assert C.arbitrary_point() != Point(2 * t, t ** 2) # the t returned as assumptions
t = Symbol("t", real=True) # now t has the same assumptions so the test passes
assert C.arbitrary_point() == Point(2 * t, t ** 2)
assert C.arbitrary_point(z) == Point(2 * z, z ** 2)
assert C.arbitrary_point(C.parameter) == Point(2 * s, s ** 2)
raises(ValueError, "Curve((s, s + t), (s, 1, 2)).arbitrary_point()")
raises(ValueError, "Curve((s, s + t), (t, 1, 2)).arbitrary_point(s)")
def test_curve():
s = Symbol('s')
z = Symbol('z')
# this curve is independent of the indicated parameter
C = Curve([2*s, s**2], (z, 0, 2))
assert C.parameter == z
assert C.functions == (2*s, s**2)
assert C.arbitrary_point() == Point(2*s, s**2)
assert C.arbitrary_point(z) == Point(2*s, s**2)
# this is how it is normally used
C = Curve([2*s, s**2], (s, 0, 2))
assert C.parameter == s
assert C.functions == (2*s, s**2)
t = Symbol('t')
assert C.arbitrary_point() != Point(2*t, t**2) # the t returned as assumptions
t = Symbol('t', real=True) # now t has the same assumptions so the test passes
assert C.arbitrary_point() == Point(2*t, t**2)
assert C.arbitrary_point(z) == Point(2*z, z**2)
assert C.arbitrary_point(C.parameter) == Point(2*s, s**2)
raises(ValueError, 'Curve((s, s + t), (s, 1, 2)).arbitrary_point()')
raises(ValueError, 'Curve((s, s + t), (t, 1, 2)).arbitrary_point(s)')
