1.5.D.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

half = S(1)/2
if symbolic:
    # quantity = symbol:
    a = var("a")
    mass = var("m")
    g = var("g")
    M = var("M")
else:
    # Derived units:
    N = kg*m/s/s

    # factors:
    a_val = half
    mass_val = 10
    g_val = 10
    M_val = 10
    #
    # quantity =  factor times unit:
    a = a_val * m
    mass = mass_val * kg
    g = g_val * m/s/s
    M = M_val * N*m

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

# Unknowns:
Ah, Av, B, N1, N2, N3, S = var("A_h, A_v, B, N1, N2, N3, S")

# pie = 2 pi:
# 45 deg = pie/8
alpha = pie/8

# for printing equations:
# alpha = var("alpha")
ca = cos(alpha)
sa = sin(alpha)

# 1:
eq1 = Eq(0, N1 - S*sa)
eq2 = Eq(0, S*ca- mass*g)

# 2:
eq3 = Eq(0, N2 - N1)
eq4 = Eq(0, N3 - mass*g)

# 3:
eq5 = Eq(0, Ah - N2)
eq6 = Eq(0, Av + B - N3)
eq7 = Eq(0, M + 2*a*B + half*a*N2 - 5*a/2*N3)

eqs=[eq1, eq2, eq3, eq4, eq5, eq6, eq7]
for eq in eqs:
    pprint(latex(eq))

print("\n--- b: -------------------------------")
sol = solve(eqs, [Ah, Av, B, N1, N2, N3, S])

for x in sorted(sol,key=default_sort_key):
    pprint(x)
    pprint(sol[x])

--- User input ----------------------- --- a: ------------------------------- 0 = N_{1} - \frac{\sqrt{2} S}{2} 0 = \frac{\sqrt{2} S}{2} - \frac{100 kg}{s^{2}} m 0 = - N_{1} + N_{2} 0 = N_{3} - \frac{100 kg}{s^{2}} m 0 = A_{h} - N_{2} 0 = A_{v} + B - N_{3} 0 = B m + \frac{N_{2} m}{4} - \frac{5 N_{3}}{4} m + \frac{10 kg}{s^{2}} m^{2} --- b: ------------------------------- A_h 100*kg*m -------- 2 s A_v 10*kg*m ------- 2 s B 90*kg*m ------- 2 s N1 100*kg*m -------- 2 s N2 100*kg*m -------- 2 s N3 100*kg*m -------- 2 s S ___ 100*\/ 2 *kg*m -------------- 2 s