Interesting, I wasn't aware that both conventions were widely used. Speaking of series with inverse powers (i.e. Laurent series), I wonder how useful it would be to create a class to represent expressions with integral powers from -m to n. These come up in my work sometimes, and I usually represent them with coefficient arrays ordered like this:
c[0]*x^0 + ... + c[n]*x^n + c[n+1]x^-m + ... + c[n+m+1]*x^-1 Because then with negative indexing you have: c[-m]*x^-m + ... + c[n]*x^n Still, these objects can't be manipulated as nicely as polynomials because they aren't closed under integration and differentiation (you get log terms). Max On Sat, Jun 30, 2018 at 4:56 PM, Charles R Harris <charlesr.har...@gmail.com > wrote: > > > On Sat, Jun 30, 2018 at 1:08 PM, Ilhan Polat <ilhanpo...@gmail.com> wrote: > >> I think restricting polynomials to time series is not a generic way and >> quite specific. >> > > I think more of complex analysis and it's use of series. > > >> Apart from the series and certain filter design actual usage of >> polynomials are always presented with decreasing order (control and signal >> processing included because they use powers of s and inverse powers of z if >> needed). So if that is the use case then probably it should go under a >> namespace of `TimeSeries` or at least require an option to present it in >> reverse. In my opinion polynomials are way more general than that domain >> and to everyone else it seems to me that "the intuitive way" is the >> decreasing powers. >> >> > In approximation, say by Chebyshev polynomials, the coefficients will > typically drop off sharply above a certain degree. This has two effects, > first, the coefficients that one really cares about are of low degree and > should come first, and second, one can truncate the coefficients easily > with c[:n]. So in this usage ordering by increasing degree is natural. This > is the series idea, fundamental to analysis. > > Algebraically, interest centers on the degree of the polynomial, which > determines the number of zeros and general shape, consequently from the > point of view of the algebraist, working with polynomials of finite > predetermined degree, arranging the coefficients in order of decreasing > degree makes sense and is traditional. > > That said, I am not actually sure where the high to low ordering of > polynomials came from. It could even be like the Arabic numeral system, > which when read properly from right to left, has its terms arranged from > small to greater. It may even be that the polynomial convention derives > that of the Arabic numerals. > > <snip> > > Chuck > > _______________________________________________ > NumPy-Discussion mailing list > NumPy-Discussion@python.org > https://mail.python.org/mailman/listinfo/numpy-discussion > >
_______________________________________________ NumPy-Discussion mailing list NumPy-Discussion@python.org https://mail.python.org/mailman/listinfo/numpy-discussion
