Re: Re D-001182: GUI for PARI

[Bill Allombert <allomber@math.u-bordeaux.fr>]

On Thu, Sep 13, 2001 at 11:28:05AM +0100, Cherry Kearton wrote:
> Thanks to Bill Allombert and Kevin Buzzard for their replies.  I am
> thinking of a GUI for Linux, using the KDE or Gnome desktop.  I have in
> mind an application containing a window into which one can type an
> irreducible polynomial and then click on a button which does the
> equivalent of running, say, bnfinit, and then displays the results in
> various windows, i.e. class number, class group, ring of integers, etc.
> If the results could be displayed in standard mathematical notation, so
> much the better.

First, do you know the 'member function' feature of PARI ?

? B=bnfinit(x^4+17);
? B.pol
%3 = x^4 + 17
? B.disc
%10 = 1257728
? B.zk
%4 = [1, x, x^2, x^3]
? B.roots
%5 = [1.435810855512950311149300687 + 1.435810855512950311149300687*I, -1.435810855512950311149300687 + 1.435810855512950311149300687*I]
? B.sign
%9 = [0, 2]
? B.no
%6 = 16
? B.cyc
%8 = [8, 2]
? B.gen
%7 = [[6, 1, 5, 1; 0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1], [26, 7, 3, 5; 0, 1, 0, 0; 0, 0, 1, 0; 0, 0, 0, 1]]
? B.reg
%13 = 6.994161412762274752239133381
? B.tu
%14 = [2, -1]
? B.fu
%15 = [x^3 + x^2 - 7*x + 16]

How do you want to print out ideals in B.gen in standard mathematical notation ?
using idealfactor I can say that B.gen is [P_2*P_3,P_2*P_13]
where P_2 is a prime ideal ideal above P_2, etc...
However there are several prime ideal above 3 and 13.

My experience using PARI is that usually I only want to know a single information
about, say , a number field, but I need to make several computation to get it.
However I only want to see the final result.

For example if I want to know the action of the complex conjugacy on the class
group, I will do

? concat(vector(2,i,Mat(bnfisprincipal(B,nfgaloisapply(B,-x,B.gen[i]))[1])))
%22 =
[5 0]

[0 1]

I don't need to see other informations than B.cyc and this matrix.
However I agree that having a way to print out results like B.clgp in nice form
would be great!

Cheers,

Bill.