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Mini Shell
Mini Shell
from sympy import Symbol, pi, symbols, Tuple, S, sqrt, asinh, Rational
from sympy.geometry import Curve, Line, Point, Ellipse, Ray, Segment, Circle, Polygon, RegularPolygon
from sympy.testing.pytest import raises, slow
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) == Curve([-x, x], (x, 0, 1))
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))
@slow
def test_free_symbols():
a, b, c, d, e, f, s = symbols('a:f,s')
assert Point(a, b).free_symbols == {a, b}
assert Line((a, b), (c, d)).free_symbols == {a, b, c, d}
assert Ray((a, b), (c, d)).free_symbols == {a, b, c, d}
assert Ray((a, b), angle=c).free_symbols == {a, b, c}
assert Segment((a, b), (c, d)).free_symbols == {a, b, c, d}
assert Line((a, b), slope=c).free_symbols == {a, b, c}
assert Curve((a*s, b*s), (s, c, d)).free_symbols == {a, b, c, d}
assert Ellipse((a, b), c, d).free_symbols == {a, b, c, d}
assert Ellipse((a, b), c, eccentricity=d).free_symbols == \
{a, b, c, d}
assert Ellipse((a, b), vradius=c, eccentricity=d).free_symbols == \
{a, b, c, d}
assert Circle((a, b), c).free_symbols == {a, b, c}
assert Circle((a, b), (c, d), (e, f)).free_symbols == \
{e, d, c, b, f, a}
assert Polygon((a, b), (c, d), (e, f)).free_symbols == \
{e, b, d, f, a, c}
assert RegularPolygon((a, b), c, d, e).free_symbols == {e, a, b, c, d}
def test_transform():
x = Symbol('x', real=True)
y = Symbol('y', real=True)
c = Curve((x, x**2), (x, 0, 1))
cout = Curve((2*x - 4, 3*x**2 - 10), (x, 0, 1))
pts = [Point(0, 0), Point(S.Half, Rational(1, 4)), Point(1, 1)]
pts_out = [Point(-4, -10), Point(-3, Rational(-37, 4)), Point(-2, -7)]
assert c.scale(2, 3, (4, 5)) == cout
assert [c.subs(x, xi/2) for xi in Tuple(0, 1, 2)] == pts
assert [cout.subs(x, xi/2) for xi in Tuple(0, 1, 2)] == pts_out
assert Curve((x + y, 3*x), (x, 0, 1)).subs(y, S.Half) == \
Curve((x + S.Half, 3*x), (x, 0, 1))
assert Curve((x, 3*x), (x, 0, 1)).translate(4, 5) == \
Curve((x + 4, 3*x + 5), (x, 0, 1))
def test_length():
t = Symbol('t', real=True)
c1 = Curve((t, 0), (t, 0, 1))
assert c1.length == 1
c2 = Curve((t, t), (t, 0, 1))
assert c2.length == sqrt(2)
c3 = Curve((t ** 2, t), (t, 2, 5))
assert c3.length == -sqrt(17) - asinh(4) / 4 + asinh(10) / 4 + 5 * sqrt(101) / 2
def test_parameter_value():
t = Symbol('t')
C = Curve([2*t, t**2], (t, 0, 2))
assert C.parameter_value((2, 1), t) == {t: 1}
raises(ValueError, lambda: C.parameter_value((2, 0), t))
def test_issue_17997():
t, s = symbols('t s')
c = Curve((t, t**2), (t, 0, 10))
p = Curve([2*s, s**2], (s, 0, 2))
assert c(2) == Point(2, 4)
assert p(1) == Point(2, 1)
Zerion Mini Shell 1.0