def test_conv10():
A = densematrix(1, 4, [Integer(1), Integer(2), Integer(3), Integer(4)])
assert A._sympy_() == sympy.Matrix(1, 4, [
sympy.Integer(1),
sympy.Integer(2),
sympy.Integer(3),
sympy.Integer(4)
])
B = densematrix(4, 1, [Symbol("x"), Symbol("y"), Symbol("z"), Symbol("t")])
assert B._sympy_() == sympy.Matrix(4, 1, [
sympy.Symbol("x"),
sympy.Symbol("y"),
sympy.Symbol("z"),
sympy.Symbol("t")
])
C = densematrix(
2, 2,
[Integer(5),
Symbol("x"),
function_symbol("f", Symbol("x")), 1 + I])
assert C._sympy_() == sympy.Matrix(
[[5, sympy.Symbol("x")],
[sympy.Function("f")(sympy.Symbol("x")), 1 + sympy.I]])
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_conv10b():
A = sympy.Matrix([[sympy.Symbol("x"), sympy.Symbol("y")],
[sympy.Symbol("z"), sympy.Symbol("t")]])
assert sympify(A) == densematrix(2, 2, [Symbol("x"), Symbol("y"),
Symbol("z"), Symbol("t")])
B = sympy.Matrix([[1, 2], [3, 4]])
assert sympify(B) == densematrix(2, 2, [Integer(1), Integer(2), Integer(3),
Integer(4)])
C = sympy.Matrix([[7, sympy.Symbol("y")],
[sympy.Function("g")(sympy.Symbol("z")), 3 + 2*sympy.I]])
assert sympify(C) == densematrix(2, 2, [Integer(7), Symbol("y"),
function_symbol("g", Symbol("z")), 3 + 2*I])
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_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_abs():
x = Symbol("x")
e = abs(x)
assert e == abs(x)
assert e != cos(x)
assert abs(5) == 5
assert abs(-5) == 5
assert abs(Integer(5)/3) == Integer(5)/3
assert abs(-Integer(5)/3) == Integer(5)/3
assert abs(Integer(5)/3+x) != Integer(5)/3
assert abs(Integer(5)/3+x) == abs(Integer(5)/3+x)
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_bigfloat_invalid():
i = Integer(13333333333333333.5)
def test_integer_string():
i = Integer("133")
def test_smallfloat_valid():
i = Integer(7.5)
assert str(i) == "7"
def test_conv5():
x = Integer(5)
y = Integer(6)
assert x._sympy_() == sympy.Integer(5)
assert (x / y)._sympy_() == sympy.Integer(5) / sympy.Integer(6)
def test_integer_long():
i = Integer(123434444444444444444)
assert str(i) == "123434444444444444444"
def test_sympify1():
assert sympify(1) == Integer(1)
assert sympify(2) != Integer(1)
assert sympify(-5) == Integer(-5)
assert sympify(Integer(3)) == Integer(3)
def test_conv5b():
x = sympy.Integer(5)
y = sympy.Integer(6)
assert sympify(x) == Integer(5)
assert sympify(x / y) == Integer(5) / Integer(6)
def test_integer_string():
raises(TypeError, lambda: Integer("133"))
def test_integer():
i = Integer(5)
assert str(i) == "5"
def test_bigfloat_invalid():
raises(ValueError, lambda: Integer(13333333333333333.5))
def test_conv5():
x = Integer(5)
y = Integer(6)
assert x._sympy_() == sympy.Integer(5)
assert (x/y)._sympy_() == sympy.Integer(5) / sympy.Integer(6)
def legendre(n, x):
e = Integer(1)/(Integer(2)**n * fact(Integer(n))) * diff((x**2-1)**n, x, n)
return e.expand()