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)
assert c.arbitrary_point(None) == Point(2 * s, s**2)
assert c.plot_interval() == [t, 0, 2]
assert c.plot_interval(z) == [z, 0, 2]
raises(ValueError, 'Curve((s), (s, 1, 2))')
raises(ValueError, 'Curve((x, x * 2), (1, x))')
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)
assert c.arbitrary_point(None) == Point(2*s, s**2)
assert c.plot_interval() == [t, 0, 2]
assert c.plot_interval(z) == [z, 0, 2]
raises(ValueError, 'Curve((s), (s, 1, 2))')
raises(ValueError, 'Curve((x, x * 2), (1, x))')
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():
x = Symbol("x", real=True)
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")
# the t returned as assumptions
assert c.arbitrary_point() != Point(2 * t, t ** 2)
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)
assert c.arbitrary_point(None) == Point(2 * s, s ** 2)
assert c.plot_interval() == [t, 0, 2]
assert c.plot_interval(z) == [z, 0, 2]
assert (
Curve([x, x], (x, 0, 1))
.rotate(pi / 2, (1, 2))
.scale(2, 3)
.translate(1, 3)
.arbitrary_point(s)
== Line((0, 0), (1, 1))
.rotate(pi / 2, (1, 2))
.scale(2, 3)
.translate(1, 3)
.arbitrary_point(s)
== Point(-2 * s + 7, 3 * s + 6)
)
raises(ValueError, lambda: Curve((s), (s, 1, 2)))
raises(ValueError, lambda: Curve((x, x * 2), (1, x)))
raises(ValueError, lambda: Curve((s, s + t), (s, 1, 2)).arbitrary_point())
raises(ValueError, lambda: 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)
assert c.arbitrary_point(None) == Point(2*s, s**2)
assert c.plot_interval() == [t, 0, 2]
assert c.plot_interval(z) == [z, 0, 2]
assert Curve([x, x], (x, 0, 1)
).rotate(pi/2, (1, 2)).scale(2, 3).translate(1, 3).arbitrary_point(s
) == \
Line((0, 0), (1, 1)
).rotate(pi/2, (1, 2)).scale(2, 3).translate(1, 3).arbitrary_point(s
) == Point(-2*s + 7, 3*s + 6)
raises(ValueError, lambda: Curve((s), (s, 1, 2)))
raises(ValueError, lambda: Curve((x, x * 2), (1, x)))
raises(ValueError, lambda: Curve((s, s + t), (s, 1, 2)).arbitrary_point())
raises(ValueError, lambda: Curve((s, s + t), (t, 1, 2)).arbitrary_point(s))
