Re: efficient foursquare() and/or threesquare1m4() functions

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

On Sun, Oct 08, 2023 at 12:01:16PM +0200, hermann@stamm-wilbrandt.de wrote:
> On 2023-10-08 10:19, Bill Allombert wrote:
> > On Sun, Oct 08, 2023 at 01:25:07AM +0200, hermann@stamm-wilbrandt.de
> > wrote:
> > > Because I already implemented generation of ternary quadratic form Q
> > > for n
> > > - that represents n
> > > - and has determinant 1.
> > 
> > > Now I need to figure out how to determine matrix M, such that
> > > M~*Q*M is diagonal matrix. The diagonal entries of M~*Q*M
> > > are three square representation of n.
> > 
> > See qfgaussred
> > 
> > Cheers,
> > Bill.
> > 
> Thanks, but that matrix is not the matrix M I search for.

Yes, you need to read the documentation...

? Q=[41,50,1;50,61,0;1,0,62]
%1 = [41,50,1;50,61,0;1,0,62]
? M=qfgaussred(Q)
%2 = [41,50/41,1/41;0,1/41,-50;0,0,1]
? D=matrix(#M,#M,i,j,if(i==j,M[i,j]))
%3 = [41,0,0;0,1/41,0;0,0,1]
? R=matrix(#M,#M,i,j,if(i==j,1,M[i,j]))
%4 = [1,50/41,1/41;0,1,-50;0,0,1]
? R~*D*R == Q
%5 = 1
? R~^-1*Q*R^-1
%6 = [41,0,0;0,1/41,0;0,0,1]

Cheers,
Bill.