MathGroup Archive 1998

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: Extension of Factor



Fred Lang wrote:
> 
> Dear MathGroup users,
> 
> I am a Mathematica user since 1988, I choose it for the beautiful plots
> and the coherent language.
> 
> But sometimes, it seems to me, Mathematica is not so coherent, for
> example, let's look to the commands
> 
> "Factor" "Apart" and "Integrate":
> 
> 1) The Mathematica (3.0) command "Factor" have the option "Extension ->
> Automatic", but
> 
> In[1] = Factor[ x^4 + 1 , Extension -> Automatic ] is unable to factor
> x^4 + 1.
> 
> I have to use
> 
> In[2] = Factor[ x^4 + 1 , Extension -> {Sqrt[2]} ] to have a result.
> 
> 2) I cannot put a pattern in the Extension:
> 
> In[3] = Factor[ x^4 + 1 , Extension -> {Sqrt[z_]} ]
> 
> 3) Something like the following take a too long time:
> 
> In[4] = list = Table[ Sqrt[ Prime[i] ] , {i,1,100} ]
> 
> In[5] = Factor[ x^4 + 1 , Extension -> list ]
> 
> 4) If a want to use Apart, I have no options like "Extension", I must
> enter something like:
> 
> In[6] = Apart[ 1/Factor[ x^4 + 1 , Extension -> {Sqrt[2]} ] ]
> 
> 5) But Integrate can factor 1/(x^4+1) very well :
> 
> In[7] = Integrate[1/(x^4+1) , x]
> 
> I am waiting for your comments.
> 
> Fred Lang


Fred:
'
I throw in the following - its inefficiant, of limited applicablity and
amounts to getting Factor to sidestep multiplying factors from
conjugate roots - but it works on occasions


In[1]:=
ExactRealFactor[expr_]:=
	Factor[ expr , Extension ->
	Re[x/.Solve[expr==0,x]]]

In[2]:=
ExactRealFactor[x^4+1]

Out[1369]=
                     2                    2 -((-1 + Sqrt[2] x - x ) (1 +
Sqrt[2] x + x )) -- 
Allan Hayes
Training and Consulting
Leicester, UK
hay@haystack.demon.co.uk
http://www.haystack.demon.co.uk
voice: +44 (0)116 271 4198
fax: +44 (0)116 271 8642




  • Prev by Date: Re: Help with fonts
  • Next by Date: Re: Data Extraction from List {{x1,y1}..{xn,yn}}where ##<x<##
  • Prev by thread: Extension of Factor
  • Next by thread: Extension of MatrixExp