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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




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