1.5.F.sagews

from sympy.physics.units import *
from sympy import *
from sympy import N as Num

# pie is better than pi
pie = 2*pi
one = S(1)
two = S(2)

print("\n--- User input -----------------------")
symbolic = True
symbolic = False

if symbolic:
    # quantity = symbol:
    a = var("a")
    alpha = var("alpha")
    F = var("F")
else:
    # variable = quantity:
    a = one *meter
    # pie = 2 pi
    # pie/8 = 45 deg
    alpha = pie/8
    F = one *newton

print("\n--- a: -------------------------------")

Ah, Av, Bv = var("A_h, A_v, B_v")

# shortcuts:
ca = cos(alpha)
sa = sin(alpha)
Fv = sqrt(2)*F*sa

# equilibrium conditions:
eq1 = Eq(0, Ah)
eq2 = Eq(0, Av + Bv - two*F - 2*Fv)
eq3 = Eq(0, 2*a*Av - 2*a*Bv)

# solve linear system:
sol = solve([eq1, eq2, eq3], [Ah, Av, Bv])
for x in sol:
    print
    pprint(x)
    pprint(sol[x])

--- User input ----------------------- --- a: ------------------------------- A_h 0 A_v 2*kg*m ------ 2 s B_v 2*kg*m ------ 2 s