hermann on Fri, 09 Feb 2024 20:17:46 +0100


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Re: Best way to determine horizontal plane ℤ³ that contains most vectors of given vector of vectrs 

On 2024-02-09 18:19, Gareth Ma wrote:

Try this:

? z = vecsort(matreduce([v[3] | v <- S])~, 2, 4)[1, 1]; z
%21 = -1
?
Thank you, that is definitely more compact and nicer than my 3 lines before. 

I simplified my code, now these 6 lines of PARI/GP compute everything:

https://github.com/Hermann-SW/GP3D/blob/main/tqf_3D.2.gp#L38-L43

    Q=qflllgram(get_tqf(n))^-1;
    M=Q~*Q;
    S=[x|x<-Vec(qfminim(M,n)[3]),qfeval(M,x)<=n];
    P=[(Q*v)~|v<-S,v[3]==vecsort(matreduce([v[3]|v<-S])~,2,4)[1,1]];
    v=matker(Mat(apply(x->concat(x,1),P~)))[,1];
    PO=-v[4]/(norml2(v[1..3]))*v[1..3]~;
Q is the matrix to multiply [0,0,1]~ with to result in sum of three squares of n (Dirichlet 1850) 

S are all points in ℤ³ with norml2()==n,n-1,...,1
P is the mapped by Q plane determined now with mapreduce (for -3, the purple vertices) 

v is a normal vector of plane through all P
PO is point on plane with minimal distance to origin (small black sphere) 

https://stamm-wilbrandt.de/images/tqf_3D.2.gp.n_37.jpg

Interactive:
https://stamm-wilbrandt.de/tqf_3D.2.gp.n_37.html


Regards,

Hermann.