Re: Question about Normal[] and O[]

*To*: mathgroup at smc.vnet.net*Subject*: [mg8578] Re: [mg8537] Question about Normal[] and O[]*From*: "w.meeussen" <meeussen.vdmcc at vandemoortele.be>*Date*: Sun, 7 Sep 1997 22:13:00 -0400*Sender*: owner-wri-mathgroup at wolfram.com

hi Stefan, look at the "raw" series object with FullForm: In[3]:= ser=Series[1+3x^2+x^5,{x,-1,5}] In[19]:=ser//FullForm Out[19]//FullForm= SeriesData[x, -1, List[3, -1, -7, 10, -5, 1], 0, 6, 1] this allows a representation of the truncated series as: In[37]:= (#3 (HoldForm[(#1-#2)//Evaluate] ^Range[#4,#5-1]))&@@ser Out[37]= 2 3 4 {3, -(1 + x), -7 (1 + x) , 10 (1 + x) , -5 (1 + x) , 5 (1 + x) } this is a list that allows picking what you need, and keeps "-(1+x)" in held form; if you want the sum then,of course, In[38]:=Plus@@(#3 (HoldForm[(#1-#2)//Evaluate] ^Range[#4,#5-1]))&@@ser Out[38]= 2 3 4 5 3 - 1 + x - 7 (1 + x) + 10 (1 + x) - 5 (1 + x) + (1 + x) but the brackets are gone ! using Hold shows this self-effacing function en lieu of brackets: In[40]:=Plus@@(#3 (Hold[(#1-#2)//Evaluate] ^Range[#4,#5-1]))&@@ser Out[40]= 2 3 3 - Hold[1 + x] - 7 Hold[1 + x] + 10 Hold[1 + x] - 4 5 5 Hold[1 + x] + Hold[1 + x] not pretty, I know. Real gurus might have better advice ... wouter. At 23:16 6-09-97 -0400, Stefan.Becuwe wrote: >The purpose of Normal[] is to "truncate a power series to give an >ordinary expression". I hoped it would just remove the O[] term, >but, for one reason or another, it does a bit more (as you can see in >Out[24]). > >Question: is there a function that only removes the O[] term >(in Mathematica 2.2? 3.0?) >(I need that "3 - (1 + x)" and not "2 - x" ...) > >If it would have been possible to do a substitution ( /. ) before the >Normal[] function, then the problem would have been solved, but >/. doesn't seem to work when there's an O[] term... > > > > In[23]:= Series[1+3x^2+x^5,{x,-1,5}] > > 2 3 4 5 > Out[23]= 3 - (1 + x) - 7 (1 + x) + 10 (1 + x) - 5 (1 + x) + (1 + x) + > > 6 > > O[1 + x] > > In[24]:= Normal[Series[1+3x^2+x^5,{x,-1,5}]] > > 2 3 4 5 > Out[24]= 2 - x - 7 (1 + x) + 10 (1 + x) - 5 (1 + x) + (1 + x) > > > > >Stefan Becuwe > > > > Dr. Wouter L. J. MEEUSSEN eu000949 at pophost.eunet.be w.meeussen.vdmcc at vandemoortele.be