How to combine different equations automatically

Question

I have 9 different equations that contain only 7 unknowns. I would like to generate a code that creates all the possible systems of 7 equations and return the cases in which all the variables have a positive result. The 9 equations are:

    eq1 = 14*x+7*z-21.71
    eq2 = 15*x+11*z+w-38.55
    eq3=12*x+8*y+12*z+w-52.92
    eq4=12*x+8*y+14*z+t-61.7
    eq5=13*x+8*y+15*z+t-69.37
    eq6=4*x+17*y+14*r+s-98.32
    eq7=4*x+18*y+12*w+s-130.91
    eq8=4*x+18*y+15*w+2*t-165.45
    eq9=4*x+18*y+12*w+2*s-168.16

please make an effort before asking as SO is not a coding service — depperm, Apr 18 '22 at 14:00

score 0 · Accepted Answer · answered Apr 18 '22 at 18:15

Adapted from this answer

What you want to do is iterate through all the combinations that only have 7 equations. You can do this with nested loops but it will get very ugly as you will have 7 nests.

itertools library in python (standard library) has a built in method for looping like this, so if you create a list of equations, you can iterate through all unique systems by doing the following

import itertools
eq = [eq1,eq2eq3,eq4,eq5,eq6,eq7,eq8,eq9]

for system in itertools.combinations(eq, 7):
    # do stuff to solve equations however you want

system is going to be a tuple containing the 7 equations in the system. From there use whatever solving technique you want to solve them and determine if all outputs are positive (i.e. numpy and matrix equations)

the problem is to declare each of the equations that make up the system before 'eq'. Thanks in advance. — Arangul, Apr 19 '22 at 09:39

How to combine different equations automatically

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