On Mon, Apr 14, 2025 at 10:58 AM Nils Bruin <nbr...@sfu.ca> wrote:
>
> It looks like a is an element of "Qbar". Elements there are tracked by
> keeping track of a way to compute a polynomial it is a root of as well as a
> complex "ball" that allows one to distinguish it from other roots of the
> polynomial. Certain operations will force the actual computation of the
> minimal polynomial. In the process one may discover information about the
> number. For instance, one may find it is actually rational or that it is
> real. Such info is then kept and may affect how the element prints. The
> representation that you get the first time is consistent with the imaginary
> part being 0. Computing the minimal polynomial then has the side effect of
> discovering that the imaginary part really is 0 rather than "not
> distinguished from 0" that you get the first time.
>
> It looks like the system is working as specified.
One would wish there was a way to tell the system from the beginning
that this particular polynomial has only real roots.
Perhaps there is an easy way to implement is (a class of real-rooted
polynomials), no?
Dima
>
> On Monday, 14 April 2025 at 00:37:12 UTC-7 Georgi Guninski wrote:
>>
>> I think this is at least one bug on 10.5 on linux, attached is testcase
>>
>> F=Graph(SNIP) #90 vertices
>> spe=F.spectrum()
>> a=spe[64]
>> print("(1):a=",a) #(1) -1.717980512878350? + 0.?e-60*I #XXX imaginary part
>> print("(2):a=",a,"poly=",a.minpoly()) #(2): -1.717980512878350? poly=
>> x^4 + 5*x^3 - 19*x - 16 #XXX imaginary part vanishes
>> """
>> 1. The spectrum must be real with no imaginary part
>> 2. Why the imaginary part disappears after only print()
>> """
>
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