Ciro Santilli @cirosantilli  40

from sympy import *
sympify(2)/3 + sympify(1)/2

7/6

from sympy import *
x, y = symbols('x y')
expr = x/3 + y/2
print(expr)

x/3 + y/2

expr.subs({x: 1, y: 2})

4/3

x = sqrt(2)
print(x)

sqrt(2)

sqrt(2)**2

sqrt(-1)

I

I*I

-1

cos(pi)

-1

cos(pi/4)

sqrt(2)/2

exp(I*pi)

-1

from sympy import *
x = symbols('x')
print(diff(ln(x), x))

1/x

print(integrate(1/x, x))

log(x)

y''(t) - 2y'(t) + y(t) = sin(t)

from sympy import *
x = symbols('x')
f, g = symbols('f g', cls=Function)
diffeq = Eq(f(x).diff(x, x) - 2*f(x).diff(x) + f(x), sin(x)**4)
print(dsolve(diffeq, f(x)))

Eq(f(x), (C1 + C2*x)*exp(x) + cos(x)/2)

diffeq = Eq(f(x).diff(x, x)**2 + f(x), 0)

NotImplementedError: solve: Cannot solve f(x) + Derivative(f(x), (x, 2))**2

from sympy import *
x, a, b, c = symbols('x a b c d e f')
eq = Eq(a*x**2 + b*x + c, 0)
sol = solveset(eq, x)
print(sol)

FiniteSet(-b/(2*a) - sqrt(-4*a*c + b**2)/(2*a), -b/(2*a) + sqrt(-4*a*c + b**2)/(2*a))

sol.subs({a: 1, b: 2, c: 3})

FiniteSet(-1 + sqrt(2)*I, -1 - sqrt(2)*I)

x, a, b, c, d, e, f = symbols('x a b c d e f')
eq = Eq(e*x**4 + d*x**3 + c*x**2 + b*x + a, 0)
solveset(eq, x)

x, a, b, c, d, e, f = symbols('x a b c d e f')
eq = Eq(f*x**5 + e*x**4 + d*x**3 + c*x**2 + b*x + a, 0)
solveset(eq, x)

ConditionSet(x, Eq(a + b*x + c*x**2 + d*x**3 + e*x**4 + f*x**5, 0), Complexes)

m = Matrix([[1, 2], [3, 4]])

m**-1

Matrix([
[ -2,    1],
[3/2, -1/2]])