OrionNav's profile - activity

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.

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).

Here's a fun little problem: determine the exponential curve f(x) = c + ba^x defined by three points, (2,10), (4,6), and (5,5).

The system of three equations and three unknowns is

10 = c + ba^2

6 = c + ba^4

5 = c + ba^5

It's not that hard to solve numerically. With a little algebraic substitution and iteration, the answer turns out to be

a = 0.640388203

b = 16.53456516

c = 3.219223594

But is there a more elegant way to use Sage to arrive at this result? I'm stumped.