## a question on proot

Librairie C++ de calcul formel/ C++ symbolic computation library

jocaps
Messages : 118
Inscription : lun. avr. 17, 2017 4:32 pm

### a question on proot

Hi,

I am trying to understand the code behind proot. But I don't think I would understand it in a very short time. I just want to confirm one thing, maybe someone could help answering this question:

Suppose I have an irreducible polynomial of degree 2d in one variable (coefficients are all integers) and such that roots are all non-real and have multiplicity 1. Is it true that proot outputs the roots as conjugate pairs in sequence. What I mean is that is it true that the output of proot is:

Code : Tout sélectionner

``[z1,conj(z1),z2,conj(z2),..., zd,conj(zd)]``
where zi, i=1,..,d are distinct complex roots. I have the impression that this is true (if so I do not need to write an extra code finding where the imaginary conjugates are).

Jose

parisse
Messages : 5084
Inscription : mar. déc. 20, 2005 4:02 pm
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### Re: a question on proot

The code of proot is unfortunately hard to read, because there are several algorithms involved, mixing symbolic methods (for multiplicities), numeric with library calls (GSL, PARI) and numeric built-in. I can not warrant that you will always get pairs of conjugate one after the other one...