Question

当我运行以下命令时

g := UnivariatePolynomial(Rationals, [12,-5,0,0,0,1]);
RootsOfPolynomialAsRadicals(g);

我收到此错误

  ***   too many arguments: ...;,nf=nfinit([f,nfbasis(f,1)]);fac=lift(nffact
  ***                                                   ^--------------------
  ***   at top-level: for(i=1,#fac[,1],for(j=1,fac[i,2
  ***                             ^--------------------
  ***   incorrect type in _[,_] OCcompoC [not a matrix] (t_POL).
Error, List Element: <list>[1] must have an assigned value in
  faktoren[1] := lcoeff * faktoren[1]; at /proc/cygdrive/C/gap486/pkg/Alnuth-3.0.0/gap/factors.gi:99 called from
FactorsPolynomialPari( AlgExtEmbeddedPol( H, poly )
 ) at /proc/cygdrive/C/gap486/pkg/Alnuth-3.0.0/gap/factors.gi:51 called from
FactorsPolynomialAlgExt( erw.H, poly ) at /proc/cygdrive/C/gap486/pkg/radiroot/lib/SplittField.gi:237 called from
RR_Zerfaellungskoerper( poly, rec(
    roots := [  ],
    degs := [  ],
    coeffs := [  ],
    K := FieldByMatrices( [ [ [ 1 ] ] ] ),
    H := Rationals ) ) at /proc/cygdrive/C/gap486/pkg/radiroot/lib/Radicals.gi:293 called from
CallFuncList( RootsOfPolynomialAsRadicalsNC, arg
 ) at /proc/cygdrive/C/gap486/pkg/radiroot/lib/Radicals.gi:253 called from
<function "RootsOfPolynomialAsRadicals">( <arguments> )
 called from read-eval loop at line 2 of *stdin*
you can 'return;' after assigning a value

我在Windows 10上使用GAP 4.8.6，从GAP下载页面上的Windows安装程序和64位PARI / GP 2.9.1（稳定安装程序）安装。我也试过手动下载和使用Alnuth和Radiroot的最新版本，但我仍然得到同样的错误。有谁知道如何解决这个问题？

Answer 1

在macOS下，该版本现在可用于GAP 4.11.0，Alnuth 3.1.2，RadiRoot 2.8和Pari / GP 2.9.3：

g := UnivariatePolynomial(Rationals, [12,-5,0,0,0,1]);
RootsOfPolynomialAsRadicals(g);

启动xdvi查看器，显示结果。很难以图像的形式读取，因此我为其提供了LaTeX源，这可能会更有用：

\documentclass[fleqn]{article} 
\setlength{\paperwidth}{84cm} 
\setlength{\textwidth}{80cm} 
\setlength{\paperheight}{59.5cm} 
\setlength{\textheight}{57cm} 
\begin{document} 
\noindent
An expression by radicals for the roots of the polynomial $x^{5} - 5x + 12$ with the $n$-th root of unity $\zeta_n$ and
\\
$\omega_1 = \sqrt[2]{ - 10}$,\\
$\omega_2 = \sqrt[5]{\left( - \frac{421}{5}\zeta_{5} - \frac{449}{5}\zeta_{5}^{2} - \frac{49}{5}\zeta_{5}^{3} + \frac{229}{5}\zeta_{5}^{4}\right) + \left( - \frac{168}{25}\zeta_{5} - \frac{849}{25}\zeta_{5}^{2} - \frac{1101}{25}\zeta_{5}^{3} - \frac{582}{25}\zeta_{5}^{4}\right)\omega_1}$,\\
\\
is:
\\
\noindent
$\left( - \frac{2}{11}\zeta_{5} - \frac{1}{11}\zeta_{5}^{2} + \frac{4}{11}\zeta_{5}^{3} - \frac{4}{11}\zeta_{5}^{4}\right)\omega_2 + \left( - \frac{42}{121}\zeta_{5} + \frac{34}{121}\zeta_{5}^{2} - \frac{92}{121}\zeta_{5}^{3} + \frac{15}{121}\zeta_{5}^{4}\right)\omega_2^2 + \left(\frac{91}{605}\zeta_{5} + \frac{7}{605}\zeta_{5}^{2} + \frac{38}{605}\zeta_{5}^{3} + \frac{149}{605}\zeta_{5}^{4}\right)\omega_1\omega_2^2 + \left(\frac{175}{1331}\zeta_{5} + \frac{302}{1331}\zeta_{5}^{2} + \frac{706}{1331}\zeta_{5}^{3} + \frac{482}{1331}\zeta_{5}^{4}\right)\omega_2^3 + \left(\frac{255}{1331}\zeta_{5} + \frac{364}{1331}\zeta_{5}^{2} + \frac{40}{1331}\zeta_{5}^{3} + \frac{246}{1331}\zeta_{5}^{4}\right)\omega_1\omega_2^3 + \left( - \frac{11480}{14641}\zeta_{5} + \frac{420}{14641}\zeta_{5}^{2} + \frac{7725}{14641}\zeta_{5}^{3} - \frac{740}{14641}\zeta_{5}^{4}\right)\omega_2^4 + \left(\frac{786}{14641}\zeta_{5} + \frac{6399}{14641}\zeta_{5}^{2} + \frac{45}{14641}\zeta_{5}^{3} + \frac{1275}{14641}\zeta_{5}^{4}\right)\omega_1\omega_2^4$
\end{document}

很难说出最初的问题是什么，两个软件包都有很多变化，它们现在都托管在GitHub上-源代码存储库是https://github.com/gap-packages/radiroot和https://github.com/gap-packages/alnuth。

GAP中的Radiroot包生成错误

1 个答案: