telescope_workshop_04.txt

AttachSpec("packages.spec");

P<x>:=PolynomialRing(Integers());
f:=x^6 - 3*x^4 - 4*x^3 - 15*x^2 + 125;
is_weil, q := IsWeil(f);
is_ordinary:=IsOrdinary(f);
g := Degree(f)/2;
K:= AssociativeAlgebra(f);
F:= PrimitiveElement(K);
V:= q/F;
R:= Order([F,q/F]);
OK := MaximalOrder(R);
//This is the basis that we are using for the LMFDB
std_beta := Reverse([V^i : i in [0..g-1]]) cat [F^i : i in [1..g] ]; //lmfdb-basis as power basis
chg_of_basis:=Transpose(Matrix(std_beta)); //lmfdb-basis to power-basis 
inverse_chg_of_basis:=chg_of_basis^-1;

load "graph_maker.m";

icmR := ICM(R);
icmR_sorted := Sort(icmR,CompareLattice);

function FakeLabel(I);
    i:=0;
	found_it := False;
	while found_it eq False do
	    i+:=1;
		J:=icmR_sorted[i];
        found_it = IsIsomorphic2(I,J);
	end while;
	return i;
end function;

num_ab := #icmR_sorted;

function RationalPointsLMFDB(I,r)
//elementary divisors for rational points
     ab_group := RationalPoints(I,r);
	 elt_divs := ElementaryDivisors(ab_group);
	 return elt_divs;
end function;

function Dual(I)
    Idual := TraceDual(ComplexConjugate(I));
	return Idual;
end function;

/*
function FrobeniusTwist(I)
    Iprime + (1/p) Iprimeprime    
end function;
*/


//for J in icmR_sorted

//*********************************************************************************
// Things to pre-compute 
//*********************************************************************************

OJ := MultiplicatorRing(J);
Jdual := Dual(J);
NSJ := Colon(J,Jdual); //Neron-Sevari lattice, containing all polarizations
Jftwist := FrobeniusTwist(J);
Jvtwist := VershiebungTwist(J);


//*********************************************************************************
// TUPLE MAKER
//*********************************************************************************

    g;

    q;
	
	dJ,AJ,DMJ,TJ := HNFify(J); //third entry is the Deligne_Module in HNF coordinates
	
	hw_matrix := Matrix(2,[2,2,2,2]) //There is code for this
	
	dual_label := FakeLabel(Jdual);
	
	frob_twist_label := FrobTwistLabel(Jftwist);
	
	ver_twist_label := VerTwistLabel(Jvtwist);
	
	//prin_polarizations, period_lattices
	prin_polarizations := 0;
	
	//period_lattice := PeriodMatrix(J,x0,phi); //x0 polarization, phi CMtype
	period_lattice :=0;
	
	points := [* RationalPointsLMFDB(I,j) : j in [1..g] *];
	
	//kernel of Frobenius is a good one
	
	big_tuple := [* label,g,q, DMJ, hw_matrix, dual_label,frob_twist_label,ver_twist_label, NS_label, , endo_order, points  *] 
	
	print big tuple;
	
//end for;