1.5.B.sagews

from sympy import *
from sympy import N as Num

# pie is better than pi
pie = 2*pi

# SI units:
m  = Symbol("m",  positive=True)
s  = Symbol("s",  positive=True)
kg = Symbol("kg", positive=True)

print("\n--- User input -----------------------")

symbolic = True
symbolic = False

if symbolic:
    # quantity = symbol:
    F, a, alpha, q = var("F, a, alpha, q")
else:
    # Derived units:
    N = kg*m/s/s

    # factors:
    F_val = 2
    a_val = 1
    #
    # pie = 2 pi = 360 deg
    alpha_val = pie/4
    #
    q_val = 1
    #
    # quantity =  factor times unit:
    a = a_val *m
    F = F_val *N
    alpha = alpha_val
    q = q_val *N/m

print("--- a: Resultant force -------------------")

R = S(3)/2*a*q

print("--- b: Reaction forces -------------------")

# unknowns:
A_h, A_v, B_v, C_v, G_h, G_v = var("A_h, A_v, B_v, C_v, G_h, G_v")
unknowns = [A_h, A_v, B_v, C_v, G_h, G_v]

# shortcuts:
ca = cos(alpha)
sa = sin(alpha)

# equilibrium conditions:
eq1 = Eq(0, A_h + F*ca - G_h)
eq2 = Eq(0, A_v + G_v - F*sa)
eq3 = Eq(0, 2*a*G_v - a*F*sa)

eq4 = Eq(0, G_h)
eq5 = Eq(0, B_v + C_v - R - G_v)
eq6 = Eq(0, a*B_v + 5*a*C_v - 4*a*R)

# solve linear system:
eqs = [eq1, eq2, eq3, eq4, eq5, eq6]
sol = solve(eqs, unknowns)

print("--- c: Use quantities --------------------")
# Set symbolic = True or
#     symbolic = False
# at the beginning of this file!

# print solution:
pprint(sol)