GAP中的Radiroot包生成错误

Question

当我运行以下命令时

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

我收到这个错误

***   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安装程序安装，以及PARI/GP 2.9.1 64位(稳定安装程序)。我也尝试过手动下载和使用最新版本的Alnuth和Radiroot，但我仍然会遇到同样的错误。有人知道怎么解决这个问题吗？

Answer 1

这现在适用于GAP 4.11.0，Alnuth 3.1.2、RadiRoot 2.8和Pari/GP 2.9.3，在macOS:下

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

启动显示结果的xdvi查看器。它很难作为图像读取，所以我为它提供了LaTeX源，它可能更有用：

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
$left( - frac{2}{11}zeta_{5} - frac{1}{11}zeta_{5}^{2} + frac{4}{11}zeta_{5}^{3} - frac{4}{11}zeta_{5}^{4}right)omega_2 + left( - frac{42}{121}zeta_{5} + frac{34}{121}zeta_{5}^{2} - frac{92}{121}zeta_{5}^{3} + frac{15}{121}zeta_{5}^{4}right)omega_2^2 + left(frac{91}{605}zeta_{5} + frac{7}{605}zeta_{5}^{2} + frac{38}{605}zeta_{5}^{3} + frac{149}{605}zeta_{5}^{4}right)omega_1omega_2^2 + left(frac{175}{1331}zeta_{5} + frac{302}{1331}zeta_{5}^{2} + frac{706}{1331}zeta_{5}^{3} + frac{482}{1331}zeta_{5}^{4}right)omega_2^3 + left(frac{255}{1331}zeta_{5} + frac{364}{1331}zeta_{5}^{2} + frac{40}{1331}zeta_{5}^{3} + frac{246}{1331}zeta_{5}^{4}right)omega_1omega_2^3 + left( - frac{11480}{14641}zeta_{5} + frac{420}{14641}zeta_{5}^{2} + frac{7725}{14641}zeta_{5}^{3} - frac{740}{14641}zeta_{5}^{4}right)omega_2^4 + left(frac{786}{14641}zeta_{5} + frac{6399}{14641}zeta_{5}^{2} + frac{45}{14641}zeta_{5}^{3} + frac{1275}{14641}zeta_{5}^{4}right)omega_1omega_2^4$
end{document}

很难说最初的问题是什么，这两个包都有很多变化，现在托管在GitHub上——源代码存储库https://github.com/gap-packages/radiroot和https://github.com/gap-packages/alnuth.