1.3.H.sagews

from sympy import *
from sympy import N as Num

# 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:
    a, F, G = var("a, F, G")
else:
    # Derived units:
    N = kg*m/s/s
    # factors:
    a_val = 1
    F_val = 1
    G_val = 1
    # quantity =  factor times unit:
    a = a_val * m
    F = F_val * N
    G = G_val * N

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

# Unknowns:
Ax, Ay, Az, Bx, By, Cy = var("A_x, A_y, A_z, B_x, B_y, C_y")

F, G = var("F, G")

rA = Matrix([ -a, 0,   0 ])
rB = Matrix([  0, 0, 2*a ])
rC = Matrix([ -a, 0, 2*a ])
rF = Matrix([ -a, 0,   a ])
rG = Matrix([  0, 0,   a ])

FA = Matrix([ Ax, Ay, Az ])
FB = Matrix([ Bx, By, 0  ])
FC = Matrix([  0, Cy, 0  ])
FF = Matrix([  F,  0, 0 ])
FG = Matrix([  0,  G, 0 ])

MA = rA.cross(FA)
MB = rB.cross(FB)
MC = rC.cross(FC)
MF = rF.cross(FF)
MG = rG.cross(FG)

sum_F = FA + FB + FC + FF + FG
sum_M = MA + MB + MC + MF + MG

Zero = Matrix([ 0, 0, 0 ])

eq_F = Eq(Zero, sum_F)
eq_M = Eq(Zero, sum_M)

sol=solve([eq_F, eq_M], [Ax, Ay, Az, Bx, By, Cy])

pprint(sol)

--- User input ----------------------- --- a: ------------------------------- -F -G -F G {A_x: ---, A_y: ---, A_z: 0, B_x: ---, B_y: -G, C_y: -} 2 2 2 2