\\ Copyright (c) 2003 Henri Darmon and Adam Logan
fpcoefs(nf,v,p)=
	{
	local(i,t,w2,w3);
	t=reductions(nf,v,p);
	print(t);
	w2=[];
	for(i=1,length(t),if(poldegree(t[i][2])==1,w2=concat(w2,[t[i][1]]),));
	/* Now we've built the list of things to count. */
	w3=[vector(length(w2),i,q=w2[i];ellap(ellinit(q),p)),p];
	return(w3);
	}

	
reductions(nf,v,p)=
	{
	local(nfpdec,nfredp,nfmodppols,i,a,j,w);
	nfpdec=idealprimedec(nf,p);
	nfredp=vector(length(nfpdec),i,nfmodprinit(nf,nfpdec[i]));
	/* Time to extract the polynomials to mod out by from the
	nfmodprinit information. */
	nfmodppols=vector(length(nfpdec),i,a=nfeltpowmodpr(nf,nf[7][2],nfpdec[i][4],nfredp[i]);x^nfpdec[i][4]-sum(j=1,nfpdec[i][4],x^(j-1)*lift(a[j])));
	w=vector(length(nfpdec),i,[Mod(modpol(v,p),nfmodppols[i]),nfmodppols[i]]);
	for(i=1,length(w),if(poldegree(nfmodppols[i])==1,w[i]=lift(w[i]),));
	return(w);
	}

modpol(v,p)=
	vector(length(v),i,if(poldegree(v[i])==0,Mod(v[i],p),sum(j=0,poldegree(v[i]),Mod(polcoeff(v[i],j),p)*variable(v[i])^j)));

fptest(nf,p)=
	{
	local(w,w1,w2,w3,z);
	w=simplify(lift(reductions(nf,[1,0,5*x+11,0,0],p)));
	w1= lift([[[Mod(1, p), 0, Mod(1, p), 0, 0], x - 2], [[Mod(1, p), 0, Mod(1, p), 0, 0], x - 4]]);
	if(w1[1][1]==w[1][1],print("equal"),print("not equal"));
	print(w1);
	print(w);
	w2=[];
	for(i=1,length(w),if(poldegree(w[i][2])==1,w2=concat(w2,[w[i][1]]),));
	z=[[1, 0, 1, 0, 0], [1, 0, 1, 0, 0]];
	if(w2==z,print("equal"),print("not equal"));
	w3=[vector(length(w2),i,ellap(ellinit(w2[i]),p)),p];
	return(w3);
	}