For this challenge, when given a list of (x,y) points your submission needs to output a polynomial function that goes through all of them.
For example, if your points were
[(0,0), (2,5)], you could return
y = 2.5*x or
y = x + 1/4x^2.
- All points passed in will consist only of integers
- Two points will never have the same
- Your function be of the form
y = a*x^n + ... b*x^m. Reducing of terms is allowed.
- Constants (the exponent and coefficient) can either be in decimal or fractional form. Decimals should be accurate to at least 3 decimal places
- You should be able to handle an arbitrary number of points
- Output must be a string starting with "y=". Whitespace anywhere in the string is fine.
Note, the given output is not the only valid output, just one of the possibilities.
(1,4) -> y=x+3 (0,0), (1,8) -> y=8x (0,6), (-1,90) -> y=-84x+6 (6,4), (70,4), (-1,-6) -> y=−10/497x^2+760/497x−316/71 (4,5), (5,6), (6,7) -> y=x+1 (20,1), (-20,1), (0,5), (10, 4), (11,12), (17,4), (2,4) -> y=488137/10424165400x^6−643187/473825700x^5−87561839/10424165400x^4+550999039/1042416540x^3−21590713027/5212082700x^2+300110420/52120827x+5
This is a code-golf, so make your answers as short as possible in your favorite language!