def test_arit4():
x = Symbol("x")
y = Symbol("y")
assert x * x == x**2
assert x * y == y * x
assert x * x * x == x**3
assert x * y * x * x == x**3 * y
def test_abs_diff():
x = Symbol("x")
y = Symbol("y")
e = abs(x)
assert e.diff(x) != e
assert e.diff(x) != 0
assert e.diff(y) == 0
def test_var_return():
raises(ValueError, lambda: var(''))
v2 = var('q')
v3 = var('q p')
assert v2 == Symbol('q')
assert v3 == (Symbol('q'), Symbol('p'))
def test_conv1b():
x = sympy.Symbol("x")
assert sympify(x) == Symbol("x")
assert sympify(x) != Symbol("y")
x = sympy.Symbol("y")
assert sympify(x) != Symbol("x")
assert sympify(x) == Symbol("y")
def test_conv1():
x = Symbol("x")
assert x._sympy_() == sympy.Symbol("x")
assert x._sympy_() != sympy.Symbol("y")
x = Symbol("y")
assert x._sympy_() != sympy.Symbol("x")
assert x._sympy_() == sympy.Symbol("y")
def test_args():
x = Symbol("x")
y = Symbol("y")
assert (x**2).args == (x, 2)
assert (x**2 + 5).args == (5, x**2)
assert set((x**2 + 2 * x * y + 5).args) == set((x**2, 2 * x * y, 5))
assert (2 * x**2).args == (2, x**2)
assert set((2 * x**2 * y).args) == set((2, x**2, y))
def test_conv2b():
x = sympy.Symbol("x")
y = sympy.Symbol("y")
z = sympy.Symbol("z")
e = x * y
assert sympify(e) == Symbol("x") * Symbol("y")
e = x * y * z
assert sympify(e) == Symbol("x") * Symbol("y") * Symbol("z")
def test_conv3():
x = Symbol("x")
y = Symbol("y")
z = Symbol("z")
e = x+y
assert e._sympy_() == sympy.Symbol("x")+sympy.Symbol("y")
e = x+y+z
assert e._sympy_() == sympy.Symbol("x")+sympy.Symbol("y")+sympy.Symbol("z")
def test_conv2():
x = Symbol("x")
y = Symbol("y")
z = Symbol("z")
e = x*y
assert e._sympy_() == sympy.Symbol("x")*sympy.Symbol("y")
e = x*y*z
assert e._sympy_() == sympy.Symbol("x")*sympy.Symbol("y")*sympy.Symbol("z")
def test_conv3b():
x = sympy.Symbol("x")
y = sympy.Symbol("y")
z = sympy.Symbol("z")
e = x + y
assert sympify(e) == Symbol("x") + Symbol("y")
e = x + y + z
assert sympify(e) == Symbol("x") + Symbol("y") + Symbol("z")
def test_conv9b():
x = Symbol("x")
y = Symbol("y")
assert sympify(sympy.I) == I
assert sympify(2*sympy.I+3) == 2*I+3
assert sympify(2*sympy.I/5+sympy.S(3)/5) == 2*I/5+Integer(3)/5
assert sympify(sympy.Symbol("x")*sympy.I + 3) == x*I+3
assert sympify(sympy.Symbol("x") + sympy.I*sympy.Symbol("y")) == x+I*y
def test_conv9():
x = Symbol("x")
y = Symbol("y")
assert (I)._sympy_() == sympy.I
assert (2*I+3)._sympy_() == 2*sympy.I+3
assert (2*I/5+Integer(3)/5)._sympy_() == 2*sympy.I/5+sympy.S(3)/5
assert (x*I+3)._sympy_() == sympy.Symbol("x")*sympy.I + 3
assert (x+I*y)._sympy_() == sympy.Symbol("x") + sympy.I*sympy.Symbol("y")
def test_conv4b():
x = sympy.Symbol("x")
y = sympy.Symbol("y")
z = sympy.Symbol("z")
e = x**y
assert sympify(e) == Symbol("x")**Symbol("y")
e = (x + y)**z
assert sympify(e) == (Symbol("x") + Symbol("y"))**Symbol("z")
def test_conv6():
x = Symbol("x")
y = Symbol("y")
assert (x / 3)._sympy_() == sympy.Symbol("x") / 3
assert (3 * x)._sympy_() == 3 * sympy.Symbol("x")
assert (3 + x)._sympy_() == 3 + sympy.Symbol("x")
assert (3 - x)._sympy_() == 3 - sympy.Symbol("x")
assert (x / y)._sympy_() == sympy.Symbol("x") / sympy.Symbol("y")
def test_conv4():
x = Symbol("x")
y = Symbol("y")
z = Symbol("z")
e = x**y
assert e._sympy_() == sympy.Symbol("x")**sympy.Symbol("y")
e = (x+y)**z
assert e._sympy_() == (sympy.Symbol("x")+sympy.Symbol("y"))**sympy.Symbol("z")
def test_Subs():
x = Symbol("x")
y = Symbol("y")
_x = Symbol("_x")
f = function_symbol("f", 2 * x)
assert f.diff(x) == 2 * Subs(Derivative(function_symbol("f", _x), [_x]),
[_x], [2 * x])
assert Subs(Derivative(function_symbol("f", x, y), [x]), [x, y], [_x, x]) \
== Subs(Derivative(function_symbol("f", x, y), [x]), [y, x], [x, _x])
def test_arit1():
x = Symbol("x")
y = Symbol("y")
e = x + y
e = x * y
e = Integer(2) * x
e = 2 * x
e = x + 1
e = 1 + x
def test_arit7():
x = Symbol("x")
y = Symbol("y")
assert x - x == 0
assert x - y != y - x
assert 2 * x - x == x
assert 3 * x - x == 2 * x
assert 2 * x * y - x * y == x * y
def test_arit5():
x = Symbol("x")
y = Symbol("y")
e = (x + y)**2
f = e.expand()
assert e == (x + y)**2
assert e != x**2 + 2 * x * y + y**2
assert isinstance(e, Pow)
assert f == x**2 + 2 * x * y + y**2
assert isinstance(f, Add)
def test_sin():
x = Symbol("x")
y = Symbol("y")
e = sin(x)
assert e.subs({x: y}) == sin(y)
assert e.subs({x: y}) != sin(x)
e = cos(x)
assert e.subs({x: 0}) == 1
assert e.subs(x, 0) == 1
def test_expand1():
x = Symbol("x")
y = Symbol("y")
z = Symbol("z")
assert ((2 * x + y)**2).expand() == 4 * x**2 + 4 * x * y + y**2
assert (x**2)**3 == x**6
assert ((2 * x**2 +
3 * y)**2).expand() == 4 * x**4 + 12 * x**2 * y + 9 * y**2
assert ((2 * x / 3 +
y / 4)**2).expand() == 4 * x**2 / 9 + x * y / 3 + y**2 / 16
def test_conv8():
e1 = function_symbol("f", Symbol("x"))
e2 = function_symbol("g", Symbol("x"), Symbol("y"))
assert e1._sympy_() == sympy.Function("f")(sympy.Symbol("x"))
assert e2._sympy_() != sympy.Function("f")(sympy.Symbol("x"))
assert e2._sympy_() == sympy.Function("g")(sympy.Symbol("x"), sympy.Symbol("y"))
e3 = function_symbol("q", Symbol("t"))
assert e3._sympy_() == sympy.Function("q")(sympy.Symbol("t"))
assert e3._sympy_() != sympy.Function("f")(sympy.Symbol("t"))
assert e3._sympy_() != sympy.Function("q")(sympy.Symbol("t"), sympy.Symbol("t"))
def test_arit6():
x = Symbol("x")
y = Symbol("y")
e = x + y
assert str(e) == "x + y" or "y + x"
e = x * y
assert str(e) == "x*y" or "y*x"
e = Integer(2) * x
assert str(e) == "2*x"
e = 2 * x
assert str(e) == "2*x"
def test_conv8():
e1 = sympy.Function("f")(sympy.Symbol("x"))
e2 = function_symbol("f", Symbol("x"))
assert e2._sympy_() == e1
assert sympify(e1) == e2
e3 = sympy.Function("q")(sympy.Symbol("t"))
e4 = function_symbol("q", Symbol("t"))
assert e4._sympy_() == e3
assert e4._sympy_() != e1
assert sympify(e3) == e4
assert sympify(e3) != e2
def test_f():
x = Symbol("x")
y = Symbol("y")
f = function_symbol("f", x)
g = function_symbol("g", x)
assert f.subs({function_symbol("f", x): function_symbol("g", x)}) == g
assert (f+g).subs({function_symbol("f", x): function_symbol("g", x)}) == 2*g
e = (f+x)**3
assert e.subs({f: y}) == (x+y)**3
e = e.expand()
assert e.subs({f: y}) == ((x+y)**3).expand()
def test_arit8():
x = Symbol("x")
y = Symbol("y")
z = Symbol("z")
assert x**y * x**x == x**(x + y)
assert x**y * x**x * x**z == x**(x + y + z)
assert x**y - x**y == 0
assert x**2 / x == x
assert y * x**2 / (x * y) == x
assert (2 * x**3 * y**2 * z)**3 / 8 == x**9 * y**6 * z**3
assert (2 * y**(-2 * x**2)) * (3 * y**(2 * x**2)) == 6
def test_arit2():
x = Symbol("x")
y = Symbol("y")
assert x + x == Integer(2) * x
assert x + x != Integer(3) * x
assert x + y == y + x
assert x + x == 2 * x
assert x + x == x * 2
assert x + x + x == 3 * x
assert x + y + x + x == 3 * x + y
assert not x + x == 3 * x
assert not x + x != 2 * x
def test_f():
x = Symbol("x")
y = Symbol("y")
f = function_symbol("f", x)
g = function_symbol("g", x)
assert f != g
f = function_symbol("f", x)
g = function_symbol("f", x)
assert f == g
f = function_symbol("f", x)
assert f.diff(y) == 0
def test_derivative():
x = Symbol("x")
y = Symbol("y")
f = function_symbol("f", x)
assert f.diff(x) == function_symbol("f", x).diff(x)
assert f.diff(x).diff(x) == function_symbol("f", x).diff(x).diff(x)
assert f.diff(y) == 0
g = function_symbol("f", y)
assert g.diff(x) == 0
assert g.diff(y) == function_symbol("f", y).diff(y)
assert g.diff(y).diff(y) == function_symbol("f", y).diff(y).diff(y)
assert f - function_symbol("f", x) == 0
def test_abs():
x = Symbol("x")
e1 = abs(sympy.Symbol("x"))
e2 = abs(x)
assert sympify(e1) == e2
assert e1 == e2._sympy_()
e1 = abs(2*sympy.Symbol("x"))
e2 = 2*abs(x)
assert sympify(e1) == e2
assert e1 == e2._sympy_()
y = Symbol("y")
e1 = abs(sympy.Symbol("y")*sympy.Symbol("x"))
e2 = abs(y*x)
assert sympify(e1) == e2
assert e1 == e2._sympy_()
def test_conv11():
x = sympy.Symbol("x")
y = sympy.Symbol("y")
x1 = Symbol("x")
y1 = Symbol("y")
e1 = sympy.Subs(sympy.Derivative(sympy.Function("f")(x, y), x), [x, y],
[y, y])
e2 = Subs(Derivative(function_symbol("f", x1, y1), [x1]), [x1, y1],
[y1, y1])
e3 = Subs(Derivative(function_symbol("f", x1, y1), [x1]), [y1, x1],
[x1, y1])
assert sympify(e1) == e2
assert sympify(e1) != e3
assert e2._sympy_() == e1
assert e3._sympy_() != e1
