Subject: Question regarding detecting roots of polynom
From: Stavros Macrakis
Date: Sun, 14 Aug 2011 13:49:26 -0400
This appears to be a bug in solve. As a workaround, first factor the
polynomial with gfactor, e.g. solve(gfactor( p ), x). This will get you all
the gaussian integer roots.
-s
PS Unlike a previous similar problem, solve(),algebraic:true does not help
here.
On Sun, Aug 14, 2011 at 09:25, Wilfried Kral <wilfried.kral at gmx.net> wrote:
> 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
>
>
>
>
>
>
>
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