Re: the minimal polynomial over the composite field

[macsyma <macsyma@yahoo.co.jp>]

Thank you, Bill.

Your method uses galoisinit(), but at least for my purposes, 
the speed of it is not enough.
For example, the timing for only galoisinit(nfsplitting()) are


? for(n=2,16,galoisinit(nfsplitting(x^n-2)));
time = 4,165 ms.

and


? galoisinit(nfsplitting(x^17-2));
time = 33min, 16,082 ms.


On the other hand, the timing of the whole processing by my code are


http://macsyma.starfree.jp/maxima/post20190827.txt


and


[17] x^17-2 
0 
1 
using a factor (-51272*c17^15)-12104*c17^14-11016*c17^13-60996*c17^12
-7616*c17^11-12342*c17^10-37128*c17^9+12376*c17^8-12410*c17^7
-17136*c17^6+36244*c17^5-13736*c17^4-12648*c17^3+26520*c17^2-24752*c17+A^17-12376 
over the cyclotomic_17

272 17 [17] 4.641 0.011 
[[A-e1,A],
 [e1^17-51272*c17^15-12104*c17^14-11016*c17^13-60996*c17^12-7616*c17^11
       -12342*c17^10-37128*c17^9+12376*c17^8-12410*c17^7-17136*c17^6
       +36244*c17^5-13736*c17^4-12648*c17^3+26520*c17^2-24752*c17-12376,e1],
 [c17^16+c17^15+c17^14+c17^13+c17^12+c17^11+c17^10+c17^9+c17^8+c17^7+c17^6
        +c17^5+c17^4+c17^3+c17^2+c17+1,c17]]

Evaluation took 0.1550 seconds (4.6530 elapsed) using 73.874 MB.

macsyma