[Numpy-discussion] Polynomial evaluation inconsistencies

[Eric Wieser]

“the intuitive way” is the decreasing powers.

An argument against this is that accessing the ith power of x is spelt:

   - x.coeffs[i] for increasing powers
   - x.coeffs[-i-1] for decreasing powers

The former is far more natural than the latter, and avoids a potential
off-by-one error

If I ask someone to write down the coefficients of a polynomial I don’t
think anyone would start from c[2]

You wouldn’t? I’d expect to see

[image: f(x) = a_3x^3 + a_2x^2 + a_1x + a_0]

rather than

[image: f(x) = a_0x^3 + a_1x^2 + a_2x + a_3]

Sure, I’d write it starting with the highest power, but I’d still number my
coefficients to match the powers.


Eric
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