On Mar 2, 2011, at 1:27 PM, Alexey U. Gudchenko wrote: > 01.03.2011 00:34, Vinzent Steinberg пишет: >>> A. My fears that it will be hard to maintain behavior of O((x-x0)**n) >>> > for pure "asymptotic expansions" expression in general case (without >>> > knowledge of series structure). In this case O((x-x0)**n) must detect >>> > and catch (x-x0)**k terms in a whole expression for every operation. And >>> > detect and do not permit operations between expressions which contain >>> > O((x-x1)**n) and O((x-x2)**n) respectively (x1<> x2). >> It would be a "for-the-moment" fix which is likely to be changed (and >> should be marked as such). I think it is still better than no O() term >> at all. >> >>> > B. I realize only maintaining of O behavior "asymptotic expansions" with >>> > knowing series structure ( 2) in [1] ) >>> > >>> > Nevertheless, I observe consensus that A*or* B must be implemented >>> > obligatory. >>> > And what is more, both A*and* B implementations better. >> Could you please explain what you mean with the last sentence? >> >> Vinzent >> > > Well, It will be easer to explain from the point of view of programmer. > > It is clear that "A" is sympy Add class which consists of polynomials terms > "a_n (x-x0)**n" and O((x-x0)**n). > > In "B" is imagined class TaylorExpansion that implement the "n-th order > Taylor expansion" so it track his precision (n), the list of [a_n], variable > x, and point x0. > [a_n] may by any sympy expression, not necessarily numbers. > > It has self-depended method for representation it in sympy (print) to print > "a0 + a1*(x - x0) + ... + O(x - x0)" > > It has method "asExpr()" to shape "A" variant for general propose. > > It has method "truncate" to form Taylor polynomial. May be another class too > if it has not analog in polynomials module yet. > > The reason of this class - that manipulations with its objects will be easer. > > F.e. the derivative of it will bring to the same object but the list of [a_n] > will be shifted throu its index by one and precision will be decremented. > > Summation equivalent to summation of lists (c_i = a_i + b_i), with alignment > of precision to minimal value of both. > > Multiplication will be a little complex, but still without analyzing > (x-x0)**k parts of expression. > > May be I became entangled now it with similar "exponential generating > function", but the last one is not derived from function (opposite to > Taylor), and it is not expansion (it is series). > > -- > Alexey U.
It sounds like a special TaylorExpansion class should be implemented as a wrapper around Poly. Aaron Meurer -- You received this message because you are subscribed to the Google Groups "sympy" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. For more options, visit this group at http://groups.google.com/group/sympy?hl=en.
