roundoff(?) bug

[Igor Schein <igor@txc.com>]

Hi, 

here's the problem:

? A=x^12+16;
? B=x^12+4*x^9+22*x^6+12*x^3+2;
? C=x^12-4*x^9+22*x^6-12*x^3+2;
? setsearch(Set(polred(B)),A)
2
? setsearch(Set(polred(B)),C)
3
? setsearch(Set(polredabs(A,4)),B)
2
? setsearch(Set(polredabs(B,4)),C)
4
? setsearch(Set(polredabs(A,4)),C)
0

First two setsearch() commands verify that all three polynomials
define the same number field.

The 3rd setsearch() command indicates that B has the same t2-norm as A. 
The 4th setsearch() command indicates that C has the same t2-norm as B.
However, 
The 5th setsearch() command indicates that C *does not* have the same
t2-norm as A.

I'll allow myself to speculate that a round-off error occurred
somewhere, probably during the polroots() stage.

Thanks

Igor