Re: Rearranging terms - user-defined

*To*: mathgroup at smc.vnet.net*Subject*: [mg127173] Re: Rearranging terms - user-defined*From*: akoz at mimuw.edu.pl*Date*: Wed, 4 Jul 2012 03:30:51 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com

Well, in this particular case the "normal expression" is just the polynomial whose terms coincide with the terms of the power series in degrees less than the degree of the O -term. Whether calling this the "normal" expression is a good choice of words is not quite clear to me. The "normal" use of "Normal" is to denote some canonical form of an expression to which special forms of expressions (of the same kind) can be reduced but which itself can't be reduced any more. So, for example, in the case of a graphic object, Normal will express any GraphicsComplex in terms of the usual graphics primitives. In other words, a graphic object expressed in a special form is replaced by an equivalent graphic object expressed in a standard form. Similarly, a matrix can be expressed in a special form of a SparseArray. There is no point doing so for an ordinary matrix but if the matrix is "sparse", working with SparseArray form may lead to a considerable gain in efficiency. Again, Normal will replace a matrix in SparseArray form as a standard matrix. But what about Series? Most people seem to think that Mathematica's series represents, well, a series, but then how come the "normal" form of a series is a polynomial? There is something fundamentally illogical here unless we decide that Series[f,{x,x0,n}} does not represent a series at all (contrary to the documentation) but only the polynomial made up of the first n terms of the series. The O part serves only to remind one that the actual series has (possibly) more terms but still the output of Series is a polynomial in a special form and not a different kind of mathematical object altogether. If you adopt this interpretation (that the result of Series is a polynomial) then there is nothing strange in Normal[Seriesâ?¦.] returning "he same" polynomial in "normal form". Andrzej Kozlowski On 2 Jul 2012, at 10:53, Alexei Boulbitch wrote: Well, in my opinion the best way is: a + b x - b y + O[x, y]^2 // Normal a+b (x-y) Dear Andrzej, That is a nice method. Could you please kindly comment, what stays behind. From the documentation it is not quite clear to me. It only states â??Normal[expr] converts a power series to a normal expression by truncating higher-order terms.â?? but does not state, what expression is considered to be normal. Best, Alexei Alexei BOULBITCH, Dr., habil. IEE S.A. ZAE Weiergewan, 11, rue Edmond Reuter, L-5326 Contern, LUXEMBOURG Office phone : +352-2454-2566 Office fax: +352-2454-3566 mobile phone: +49 151 52 40 66 44 e-mail: alexei.boulbitch at iee.lu