# [Numpy-discussion] Polynomial evaluation inconsistencies

Eric Wieser wieser.eric+numpy at gmail.com
Mon Jul 2 02:57:24 EDT 2018

```I think the `x` is just noise there, especially if it's ignored (that is,
`T[0](x*2)` doesn't do anything reasonable).

Chebyshev.literal(lambda T: 1*T[0] + 2*T[1] + 3*T[2])

Would work, but honestly I don't think that provides much clarity. I think
the value here is mainly for "simple" polynomials.

On Sun, 1 Jul 2018 at 23:42 Maxwell Aifer <maifer at haverford.edu> wrote:

> Say we add a constructor to the polynomial base class that looks something
> like this:
>
>
> -------------------------------------------------------------------------------------------
>    @classmethod
>     def literal(cls, f):
>         def basis_function_getter(self, deg):
>             coefs = [0]*deg + [1]
>             return lambda _: cls(coefs)
>         basis = type('',(object,),{'__getitem__': basis_function_getter})()
>         return f(basis, None)
>
> -------------------------------------------------------------------------------------------
>
>
> Then the repr for, say, a Chebyshev polynomial could look like this:
>
> >>> Chebyshev.literal(lambda T,x: 1*T[0](x) + 2*T[1](x) + 3*T[2](x))
>
> Does this sound like a good idea to anyone?
>
> Max
>
>
> On Sat, Jun 30, 2018 at 6:47 PM, Charles R Harris <
> charlesr.harris at gmail.com> wrote:
>
>>
>>
>> On Sat, Jun 30, 2018 at 4:42 PM, Charles R Harris <
>> charlesr.harris at gmail.com> wrote:
>>
>>>
>>>
>>> On Sat, Jun 30, 2018 at 3:41 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
>>>>
>>>
>>> IIRC there was a proposal for that. There is the possibility of adding
>>> renderers for latex and html that could be used by Jupyter, and I think the
>>> ordering was an option.
>>>
>>
>> See https://github.com/numpy/numpy/issues/8893 for the proposal. BTW, if
>> someone would like to work on this, go for it.
>>
>> Chuck
>>
>>> ​
>>>>
>>>
>>
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