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Extension of Factor



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




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