A very nonlinear system of three equations

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Thanks! That works well enough. My first attempt gave an unexpected answer: model(x) = c+b*a^x find_fit([(2,10), (4,6), (5,5)], model) [a == -0.39038820320220763, b == 30.965434844830888, c == 5.2807764064044145] which is correct as far as it goes, but raising -0.39 to non-integer values of x results in a complex number. Giving it a non-default initial guess sussed out the expected answer: model(x) = c+b*a^x find_fit([(2,10), (4,6), (5,5)], model, initial_guess=(1,1,3)) [a == 0.6403882032022076, b == 16.534565155169098, c == 3.219223593595585] and I'm pleased with the accuracy of the result. Since this can be done with only two lines of code, I consider it more elegant than the fsolve approach (above).

Yes, sometimes you do need to give it a little help! That's typical of such numerical routines.

Thanks. I suspect that some or all of this is Python code, and I know absolutely nothing about Python. (I'm a decent Perl coder, though.) The Sage Reference Manual has information about maple.fsolve and qfsolve, but nothing about plain old fsolve.