\\ Centered vector for cyclic indices.
t_center (v) = {my (n=#v,d=n\2);
vector(n,i,v[(i+d)%n+1])}

\\ Fourier transform on a cyclic group.
t_ft (v,realpart=0) = {my (n,m,Omstar);
n=#v; w=exp(2*Pi*I/n);
Omstar=matrix(n,n,j,k,w^(-(j-1)*(k-1)));
t=(v*Omstar)/n; if (!realpart,t,apply(real,t))}

t_ftabs (v,center=1) = {my (w);
w=t_ft(v); if (center, w=t_center(w)); apply(abs,w)}

t_ftarg (v,center=1) = {my (w);
w=t_ft(v); if (center, w=t_center(w)); apply(arg,w)}

\\ Perhaps obsolete.
t_ftstrabs (v,d=2,center=1) = {my (w);
w=t_ft(v); if (center, w=t_center(w)); \\apply(abs,w)}
apply(x->Strprintf("%.*f",d,abs(x)),w)}

\\ Perhaps obsolete.
t_ftstrarg (v,d=2,center=1) = {my (w);
w=t_ft(v); if (center, w=t_center(w));
apply(x->Strprintf("%.*f",d,arg(x)),w)}

\\Inverse Fourier transform on a cyclic group.
t_fti (v,realpart=0) = {my (n,m,Om);
n=#v; w=exp(2*Pi*I/n);
Om=matrix(n,n,j,k,w^((j-1)*(k-1)));
t=v*Om; if (!realpart,t,apply(real,t))}

\\ Walsh transform.
t_ftw (f) = {my (fW);
fW=t_ftwi(f); vector(#f,i,fW[i]/#f)}

\\ Inverse Walsh transform.
t_ftwi (f) = {my (n,j,falfa,fbeta,p,q,u,v);
n=#f; if (n==1, return(f));
j=n\2; falfa=vecextract(f,[1..j]); fbeta=vecextract(f,[j+1..n]);
p=self()(falfa); q=self()(fbeta);
u=vector(j,i,p[i]+q[i]); v=vector(j,i,p[i]-q[i]);
concat(u,v)}

\\ Perhaps inconsistencies.
t_ftwrite (F,X,name,G=F) = {my (u,v);
u=apply(G,X); v=apply(F,X);
t_writeplotpairs(Strprintf("%s.fun",name),u);
\\ t_writeplotpairs(Strprintf("%s.abs",name),t_ftstrabs(v));
\\ t_writeplotpairs(Strprintf("%s.arg",name),t_ftstrarg(v));
}

t_ftwritev (v,name,u=v,m=200,fase=0) = {m=min(m,#v); u=u[1..m]; v=v[1..m];
t_writeplotpairs(Strprintf("%s.fun",name),u);
t_writeplotpairs(Strprintf("%s.abs",name),t_ftstrabs(v));
if (fase, t_writeplotpairs(Strprintf("%s.arg",name),t_ftstrarg(v)))}