[Numpy-discussion] [ANN]: Taylorpoly, an implementation of vectorized Taylor polynomial operations and request for opinions

[Friedrich Romstedt]

2010/2/27 Sebastian Walter <sebastian.walter@gmail.com>:
> IMO this kind of discussion is not offtopic since it is directly
> related to the original question.

Ok, but I say it's not my responsibility now if the numpy-discussion
namespace is polluted now.

>> 2010/2/27 Sebastian Walter <sebastian.walter@gmail.com>:
>>> On Sat, Feb 27, 2010 at 3:59 PM, Friedrich Romstedt
>>> <friedrichromstedt@gmail.com> wrote:
>>>> I'm working currently on upy, uncertainty-python, dealing with real
>>>> numbers. github.com/friedrichromstedt/upy .  I want in mid-term extend
>>>> it to complex numbers, where the concepts of "uncertainty" are
>>>> necessarily more elaborate.  Do you think the concept of truncated
>>>> Taylor polynomials could help in understanding or even generalising
>>>> the uncertainties?
>>> I'm not sure what you mean by uncertainties. Could you elaborate?
>>> For all I know you can use Taylor series for nonlinear error propagation.
>>
>> I mean Gaussian error propagation.  I currently am not intending to
>> cover regimes where one has to consider "higher order" effects.  If it
>> is not very easy.  On the contrary, I want to find a way to describe
>> complex numbers which consist of a deterministic value and as many
>> superposed "complex Gaussian variables" as needed.
>
> what is a Gaussian variable? a formula would help ;)

Oh, I wasn't precise: en.wikipedia.org/wiki/Gaussian_random_variable
(aka normal distribution)

>>>>  Are complex numbers and truncated Taylor
>>>> polynomials in some way isomorphic or something similar?
>>>
>>> Taylor polynomials are not a field but just a commutative ring (there
>>> are zero divisors) so I guess it's not possible to find an
>>> isomorphism.
>>
>> Ok.
>>
>> The other things I will post back to the list, where they belong to.
>> I just didn't want to have off-topic discussion there.

Friedrich