factor(x^8+1)



Experimenting with this: 

%i11) factor(x^8+a+1,a^4+a+1);
			          2	       2	    4	   2
(%o11) 			  (x  - a) (x  + a) (x  + a )
(%i12) factor(x^8+a+1,a^8+a+1);
Maxima encountered a Lisp error:

 Error in MACSYMA-TOP-LEVEL [or a callee]: Caught fatal error [memory may be
damaged]

Automatically continuing.
To reenable the Lisp debugger set *debugger-hook* to nil.
(%i13) factor(x^7+a+1,a^7+a+1);
		              6	   5	  2  4    3  3    4  2	  5	   6
(%o13) 	    (x - a) (x  + a x  + a  x  + a  x  + a  x  + a  x + a )
(%i14) 

I hope the powers show up correctly.

RRogers


-----Original Message-----
From: Stavros Macrakis [mailto:macrakis at gmail] 
Sent: Monday, October 31, 2005 10:33 AM
To: Lodder, Josje
Cc: maxima@math.utexas.edu
Subject: Re: [Maxima] factor(x^8+1)


You can factor x^8+1 by adjoining a root of unity, e.g.

    factor(x^8+1,a^2+1) gives a product of two quartics
    factor(x^8+1,a^4+1) gives a product of four quadratics

In both cases, 1/... is integrable.  You can then substitute back in the
value of a.

But the result is rather messy.