nfgaloisconj() bug

[Igor Schein <igor@txc.com>]

Hi,

? p=polcyclo(40);
? v1=nfgaloisconj(polcyclo(40))
[x, x^9, x^13 - x^9 + x^5 - x, -x^13, 5383471/1024000000*x^14 + 5383471/1024000000*x^12 - 5383471/1024000000*x^10 + 5383471/1024000000*x^8 - 1/2*x^7 + 5383471/1024000000*x^6 + 1/2*x^3 - 5383471/512000000*x^2, -5383471/1024000000*x^14 - 5383471/1024000000*x^12 + 5383471/1024000000*x^10 - 5383471/1024000000*x^8 - 1/2*x^7 - 5383471/1024000000*x^6 + 1/2*x^3 + 5383471/512000000*x^2, 1/2*x^15 + 5383471/1024000000*x^14 + 5383471/1024000000*x^12 - 5383471/1024000000*x^8 + 1/2*x^7 - 5383471/1024000000*x^6 + 5383471/512000000*x^4 - 1/2*x^3 - 5383471/1024000000, 1/2*x^15 - 5383471/1024000000*x^14 - 5383471/1024000000*x^12 + 5383471/1024000000*x^8 + 1/2*x^7 + 5383471/1024000000*x^6 - 5383471/512000000*x^4 - 1/2*x^3 + 5383471/1024000000, -x^15 + x^11 - x^7 + x^3, -x^11, -x^3, x^7, 5383471/1024000000*x^14 - 5383471/1024000000*x^12 - 5383471/1024000000*x^10 + 1/2*x^9 - 5383471/1024000000*x^8 + 5383471/1024000000*x^6 - 1/2*x^5 - 5383471/512000000*x^2 + 1/2*x, -5383471/1024000000*x^14 + 5383471/1024000000*x^12 + 5383471/1024000000*x^10 + 1/2*x^9 + 5383471/1024000000*x^8 - 5383471/1024000000*x^6 - 1/2*x^5 + 5383471/512000000*x^2 + 1/2*x, 5383471/1024000000*x^14 - 5383471/1024000000*x^12 - 1/2*x^9 + 5383471/1024000000*x^8 - 5383471/1024000000*x^6 - 5383471/512000000*x^4 - 1/2*x + 5383471/1024000000, -5383471/1024000000*x^14 + 5383471/1024000000*x^12 - 1/2*x^9 - 5383471/1024000000*x^8 + 5383471/1024000000*x^6 + 5383471/512000000*x^4 - 1/2*x - 5383471/1024000000]~
? v2=nfgaloisconj(nfinit(polcyclo(40)))
[x, x^9, x^13 - x^9 + x^5 - x, -x^13, x^3, -x^7, x^11, x^15 - x^11 + x^7 - x^3, -x^15 + x^11 - x^7 + x^3, -x^11, -x^3, x^7, -x^13 + x^9 - x^5 + x, x^13, -x^9, -x]~
? vector(16,k,subst(p,x,Mod(v1[k],p))==0)
[1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0]
? vector(16,k,subst(p,x,Mod(v2[k],p))==0)
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]

In other words, some of the conjugates are wrong if the argument to
nfgaloisconj() is the polynomial itself, but everything is correct if
the argument is nf.

This bug was introduced sometime between 2.0.17 and 2.0.18 releases.

Thanks

Igor