CODEWITHSUNDEEP
python-3.xnumpyscipy-optimize
Charlie Shuffler
Charlie Shuffler

Reputation: 175

Having issues solving pair of nonlinear equations using Python

So I know there have been plenty of questions/answers on this topic, but I haven't been able to locate exactly what is going wrong in my attempts. I have two nonlinear function f(x,y) and g(x,y) and I am trying to solve the system 

f(x,y) - g(x,y) = 0
f(x,y) + g(x,y) = c

where c is some positive constant. I have been using the snippet described in the answer to this question: How to solve a pair of nonlinear equations using Python?, but I am facing issues. If I run that snippet for my code, it returns the x and y values such that only the second equation in the system is satisfied, i.e. it returns x and y such that f(x,y) + g(x,y) = c, while for the other equation it holds that f(x,y) - g(x,y) != 0. I get the exact same issues when using the scipy.optimize.root function. I'm quite lost as to what could be causing this issue. Could it mean that there do not exist x, y such that both equations are satisfied?

Thanks in advance for any help!

Upvotes: 0

Views: 61

Answers (1)

asylumax
asylumax

Reputation: 845

It is very possible that there is no solution. x + y = 10, x + y = 20 has no solution, for example. This isn't an issue of non-linearity; this is an issue of math. Also, it might be possible, if this can't be solved algebraically, that the first equation has f(x,y) - g(x,y) is approximately zero. If f(x,y)-g(x,y)=0.0001, would you consider this close enough?

For completeness: Check out the math, as noted by @tstanisl. If you add the equations together, you solve f(x,y)=c/2 or g(x,y)=c/2, which is easier.

Upvotes: 1

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