import sympy

x = sympy.Symbol("x")
y = sympy.Symbol("y")

m = sympy.Matrix([[sympy.cos(x), sympy.sin(x)], [-sympy.sin(x), sympy.cos(x)]])
m = sympy.Matrix([[1, x], [y, 1]])
m = sympy.Matrix([[0, 1], [-1, 0]])
print(m)
print(repr(m))
print(sympy.simplify(m.det()))
print(m.inv())
print(m ** -1)
f = sympy.Matrix(m.inv()).row(0)[0]
print(sympy.simplify(f))
print(m ** 2)
print(sympy.simplify(m ** 4))
print(sympy.simplify(m.eigenvals()))
print(sympy.simplify(m.eigenvects()))
p, d = m.diagonalize()
print(m.charpoly())
print(p)
print(d)
print(sympy.simplify(p * d * p.inv()))

i = sympy.solve(x**4 - 1, x)[3]
print(type(sympy.solve(x**4 - 1, x)[3]))

e = sympy.Eq((x-2)**3, x - y)
print(sympy.solve(e, x))
print(sympy.solve(x ** 4 - 1, x))
print(sympy.factor(x ** 4 - 3 * x**2 + 1, modulus=11))
print(sympy.solve(x * x + x ** 3 < 3))
print(sympy.solve(x**3 + x**2 - 3, x))
print(sympy.satisfiable((x | y) & (x | ~y) & y))

f = sympy.Symbol("f")
print(sympy.latex(f(x, y).diff(*[x, 3])))

f = x ** 4 + x ** 2 + sympy.exp(x ** 4)
g = f.subs(x ** 2, y)
print(g.diff(y))