Subject: Question regarding detecting roots of polynom
From: Wilfried Kral
Date: Sun, 14 Aug 2011 15:25:59 +0200
Hi,
I am using Maxima 5.20.1 http://maxima.sourceforge.net using Lisp GNU
Common Lisp (GCL) GCL 2.6.7 (a.k.a. GCL) on Ubuntu 10.04 LTS
I was building an 18 degree polynom like
x^18-36*%i*x^17+83*x^17-2818*%i*x^16+2591*x^16-95676*%i*x^15+31291*x^15
-1829926*%i*x^14-222415*x^14-21043560*%i*x^13-13429735*x^13
-134373950*%i*x^12-221505091*x^12-162118764*%i*x^11-2100454047*x^11
+5328348982*%i*x^10-12519554958*x^10+54789418068*%i*x^9-44078314424*x^9
+287090759824*%i*x^8-50671326176*x^8+912058259616*%i*x^7+322740608816*x^7
+1651930704544*%i*x^6+1945453962592*x^6+873591016128*%i*x^5
+5209884712576*x^5-3122885337856*%i*x^4+7794942136576*x^4
-7959302616576*%i*x^3+5886979568640*x^3-8129574092800*%i*x^2
+690482554880*x^2-3774525235200*%i*x-1846961971200*x-585326592000*%i
-841015296000$
with roots that have always integers for real an imaginary part
If I am using solve(polynom,x) I always end up in:
[x = - 3, x = - 1, x = - 4, x = - 8, x = - 6,
13 12 11 10
0 = x + (61 - 36 %i) x + (1070 - 2026 %i) x + (- 44660 %i - 3830) x
9 8
+ (- 460920 %i - 371147) x + (- 1529088 %i - 5353727) x
7 6
+ (13544402 %i - 35943060) x + (168139960 %i - 102170200) x
5 4
+ (740595920 %i + 109209296) x + (1349765824 %i + 1597658416) x
3 2
+ (4170648640 - 226610976 %i) x + (3755946880 - 4231612800 %i) x
+ (- 4647635200 %i - 468851200) x - 1016192000 %i - 1460096000]
so Maxima seems to get the pure real values and then stops.
If a freind uses Matlab or in Online Mathematica I get the exact solutions.
Is the implementation of Berlekamp/Kronecker etc. in Maxima not so good
or I am using wrong settings?
Solutions can be guessed with algsys, but that is of course not so nice.
Thx and Best regards,
Wilfried