# [Numpy-discussion] Polynomial evaluation inconsistencies

Maxwell Aifer maifer at haverford.edu
Sat Jun 30 18:06:46 EDT 2018

```*shouldn't the constructor call the lambda with Polynomial([0,1[)

On Sat, Jun 30, 2018 at 6:05 PM, Maxwell Aifer <maifer at haverford.edu> wrote:

> Oh, clever... yeah I think that would be very cool. But shouldn't it call
> the constructor with Polynomial([0,1])?
>
> On Sat, Jun 30, 2018 at 5:41 PM, Eric Wieser <wieser.eric+numpy at gmail.com>
> wrote:
>
>> Since the one of the arguments for the decreasing order seems to just be
>> textual representation - do we want to tweak the repr to something like
>>
>> Polynomial(lambda x: 2*x**3 + 3*x**2 + x + 0)
>>
>> (And add a constructor that calls the lambda with Polynomial(1))
>>
>> Eric
>> ​
>>
>> On Sat, 30 Jun 2018 at 14:30 Eric Wieser <wieser.eric+numpy at gmail.com>
>> wrote:
>>
>>> “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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>>
>
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