remove obsolete GP functions

functions.gp

@@ -77,37 +77,6 @@ scalar_multiplication_subgroup_traces(V, H) =
 
 scalar_multiplication_traces(V) = apply(vecsum, values_by_scalar_multiplication_orbit(V));
 
-projective_polynomial(p) =
-{
-   V = readvec(filename("values", p))[1];
-   liftall(roots_to_pol(scalar_multiplication_traces(V), 't));
-}
-
-projectivisation(p) =
-{
-   V = readvec(filename("values", p))[1];
-   x = varhigher("x", variable(V));
-   l = matsize(V)[1];
-   T = scalar_multiplication_traces(V);
-   W = matrix(l, l, i, j,
-	      if(j == 1, if(i == 1, 0, T[l + 1]),
-		 T[(i - 1)/(j - 1) % l + 1]));
-   liftall(polinterpolate(concat(Vec(V))[2..l^2],
-			  concat(Vec(W))[2..l^2], x));
-}
-
-relative_polynomial(p) =
-{
-   [g, a] = readvec("projective_polynomial_reduced.gp");
-   V = readvec(filename("values", p))[1];
-   x = variable(V);
-   z = varhigher("z", x);
-   y = varhigher("y", z);
-   T = scalar_multiplication_traces(V);
-   R = [roots_to_pol(v, z) | v <- values_by_scalar_multiplication_orbit(V)];
-   liftall(subst(polinterpolate(T, R, y), y, a));
-}
-
 /* Compute a maximal chain of subgroups of  G.  */
 subgroup_chain_maximal(G) =
 {
@@ -213,43 +182,6 @@ reduced_bases() =
    vector(#c, j, red_basis(n, [nfinit(variable(f[j])), K[j]], [c[j], alpha[j]]));
 }
 
-addition(p) =
-{
-   V = readvec(filename("values", p))[1];
-   x = variable(V);
-   z = varhigher("z", x);
-   y = varhigher("y", z);
-   l = matsize(V)[1];
-   A = matrix(l, l, i0, j0,
-	      W = matrix(l, l, i, j,
-			 V[(i + i0 - 2) % l + 1, (j + j0 - 2) %l + 1]);
-	      polinterpolate(concat(Vec(V)), concat(Vec(W)), z));
-   liftall(polinterpolate(concat(Vec(V)), concat(Vec(A)), y));
-}
-
-scalar_multiplication(p, r) =
-{
-   V = readvec(filename("values", p))[1];
-   z = varhigher("z", variable(V));
-   l = matsize(V)[1];
-   Vr = matrix(l, l, i, j,
-	       V[(i - 1)*r % l + 1, (j - 1)*r % l + 1]);
-   liftall(polinterpolate(concat(Vec(V)), concat(Vec(Vr)), z));
-}
-
-scalar_multiplication_relative(p, r) =
-{
-   [g, a] = readvec("projective_polynomial_reduced.gp");
-   V = readvec(filename("values", p))[1];
-   z = varhigher("z", variable(V));
-   y = varhigher("y", z);
-   l = matsize(V)[1];
-   W = values_by_scalar_multiplication_orbit(V);
-   F = [polinterpolate(v, vector(l - 1, i, v[i*r % l]), z) | v <- W];
-   T = scalar_multiplication_traces(V);
-   liftall(subst(polinterpolate(T, F, y), y, a));
-}
-
 pairing(p) =
 {
    my(V = readvec(filename("values", p)),
@@ -310,26 +242,6 @@ suitable_primes() =
    return(vecextract(P, ind));
 }
 
-/*
-  Return the list of suitable primes  p  for which in addition
-  the polynomial modulo  p  is square-free.
-*/
-suitable_primes_poly() =
-{
-   [p | p <- readvec("suitable_primes.gp"),
-    issquarefree(Mod(readvec(filename("poly", p))[1], p))];
-}
-
-/*
-  Return the list of suitable primes  p  for which in addition
-  the projective polynomial modulo  p  is square-free.
-*/
-suitable_primes_ppoly() =
-{
-   [p | p <- readvec("suitable_primes.gp"),
-    issquarefree(Mod(read(filename("ppoly", p)), p))];
-}
-
 /*
   Return the list of suitable primes  p  for which in addition
   both  k-th intermediate polynomials modulo  p  are square-free.
@@ -350,18 +262,6 @@ suitable_primes_ipoly(k) =
 			    | i <- [1..#f]]))];
 }
 
-/*
-  Return the primes  p in suitable_primes_ppoly  for which in addition
-  the change of variables to the reduced projective polynomial has no
-  p  in the denominator.
-*/
-suitable_primes_rpoly() =
-{
-   v = Vec(lift(readvec("projective_polynomial_reduced.gp")[2]));
-   [p | p <- readvec("suitable_primes_ppoly.gp"),
-    iferr(v % p; 1, e, 0)];
-}
-
 /*
   Return the primes  p in suitable_primes_ipoly(k)  for which in addition
   the changes of variables to both  k-th intermediate polynomials have no
@@ -420,58 +320,6 @@ polheight(f) =
       log(max(abs(numerator(f)), denominator(f))));
 }
 
-height_polynomial() = polheight(read("polynomial.gp"));
-
-height_projective_polynomial() = polheight(read("projective_polynomial.gp"));
-
-height_relative_polynomial() = polheight(read("relative_polynomial.gp"));
-
-height_addition() = polheight(read("addition.gp"));
-
-height_scalar_mul() = polheight(read("scalar_mul.gp"));
-
-info() =
-{
-   rnfeq = read("relative_equation.gp");
-   K = read("projective_field.gp");
-   polabs = rnfeq[1];
-   pol = rnfeq[5];
-   r1 = polsturm(polabs);
-   r2 = (poldegree(polabs) - r1) / 2;
-   print("[K:Q] = ", poldegree(K.pol));
-   print("[L:K] = ", poldegree(pol));
-   print("disc(Z_K/Z) = ", K.disc);
-   iferr(L = read("relative_field.gp");
-	 D_abs = (-1)^r2 * abs(K.disc)^poldegree(pol) * idealnorm(K, L.disc[1]);
-	 print("disc(Z_L/Z_K) = ", L.disc[1]);
-	 print("factorisation of |disc(Z_L/Z)| = ", factor(D_abs)),
-	 err,
-	 /* do nothing */);
-   print("sign(projective field) = ", K.sign);
-   print("sign(absolute field) = ", [r1, r2]);
-   print("projective polynomial = ", K.pol);
-   print("relative polynomial = ", pol);
-   print("absolute polynomial = ", polabs);
-   print("h(projective_polynomial) = ", polheight(read("projective_polynomial.gp")));
-   print("h(relative_polynomial) = ", polheight(lift(read("relative_polynomial.gp"))));
-   print("h(projective_polynomial_reduced) = ", polheight(K.pol));
-   print("h(relative_polynomial_reduced) = ", polheight(pol));
-   print("h(absolute_polynomial) = ", polheight(polabs));
-   iferr(F = readvec("absolute_polynomial_reduced.gp")[1];
-	 print("h(absolute_polynomial_reduced) = ", polheight(F)),
-	 err,
-	 /* do nothing */);
-   iferr(print("h(pairing) = ", matheight(read("pairing.gp"))),
-	 err,
-	 /* do nothing */);
-   iferr(print("h(addition) = ", polheight(read("addition.gp"))),
-	 err,
-	 /* do nothing */);
-   print("h(scalar_mul_rel) = ", polheight(liftall(read("scalar_mul_rel.gp"))));
-   print("h(scalar_mul_rel_reduced) = ", polheight(liftall(read("scalar_mul_rel_reduced.gp"))));
-   print("h(scalar_mul_absolute) = ", polheight(lift(read("scalar_mul_absolute.gp"))));
-}
-
 summary() =
 {
    my(D = readvec("reduced_dual_pair.gp"),
@@ -535,20 +383,6 @@ chinese_from_files(prefix, P) =
    Mod(x, N);
 }
 
-/*
-  Reconstruct a polynomial  P  whose splitting field is
-  the field of definition of the Galois representation.
-*/
-reconstruct_polynomial() =
-{
-   my(P = readvec("suitable_primes.gp"),
-      Fp = [Mod(readvec(filename("poly", p))[1], p) | p <- P],
-      F = bestappr_shift(chinese(Fp)));
-   if(F == [],
-      error("cannot reconstruct polynomial"));
-   F;
-}
-
 reconstruct_polynomials() =
 {
    my(P = readvec("suitable_primes.gp"),
@@ -559,26 +393,6 @@ reconstruct_polynomials() =
    f;
 }
 
-reconstruct_projective_polynomial() =
-{
-   P = readvec("suitable_primes.gp");
-   Fp = [Mod(read(filename("ppoly", p)), p) | p <- P];
-   F = bestappr_shift(chinese(Fp));
-   if(F == [],
-      error("cannot reconstruct projective polynomial"));
-   F;
-}
-
-reconstruct_relative_polynomial() =
-{
-   P = readvec("suitable_primes_rpoly.gp");
-   Gp = [Mod(read(filename("rpoly", p)), p) | p <- P];
-   G = bestappr(chinese(Gp));
-   if(G == [],
-      error("cannot reconstruct relative polynomial"));
-   Mod(G, readvec("projective_polynomial_reduced.gp")[1]);
-}
-
 reconstruct_intermediate_polynomials(k) =
 {
    if(k == 0,
@@ -619,57 +433,6 @@ reconstruct_origins() =
    L;
 }
 
-reconstruct_addition() =
-{
-   P = readvec("suitable_primes_poly.gp");
-   L = [Mod(read(filename("addition", p)), p) | p <- P];
-   alpha0 = chinese(L);
-   alpha = bestappr(alpha0);
-   if(alpha == [],
-      error("cannot reconstruct addition"));
-   f = read("polynomial.gp");
-   x = variable(f);
-   [y, z] = variables(alpha);
-   if(substvec(alpha, [y, z], [z, y]) != alpha,
-      error("addition is not commutative"));
-   \\ The check below is very slow for  l >= 7.
-   if(subst(f, x, Mod(Mod(alpha, subst(f, x, y)), subst(f, x, z))) != 0,
-      error("alpha does not operate on the roots of f"));
-   alpha;
-}
-
-reconstruct_scalar_mul() =
-{
-   P = readvec("suitable_primes_poly.gp");
-   L = [Mod(read(filename("scalar_mul", p)), p) | p <- P];
-   mu0 = chinese(L);
-   mu = bestappr_shift(mu0);
-   if(mu == [],
-      error("cannot reconstruct scalar multiplication"));
-   f = read("polynomial.gp");
-   x = variable(f);
-   z = variable(mu);
-   if(subst(f, x, Mod(mu, subst(f, x, z))) != 0,
-      error("mu does not operate on the roots of f"));
-   mu;
-}
-
-reconstruct_projectivisation() =
-{
-   P = readvec("suitable_primes_poly.gp");
-   L = [Mod(read(filename("projectivisation", p)), p) | p <- P];
-   iota0 = chinese(L);
-   iota = bestappr_shift(iota0);
-   if(iota == [],
-      error("cannot reconstruct projectivisation"));
-   iota = Mod(iota, read("polynomial_star.gp"));
-   g = read("projective_polynomial.gp");
-   t = variable(g);
-   if(subst(g, t, iota) != 0,
-      error("projectivisation inconsistent"));
-   iota;
-}
-
 reconstruct_pairing() =
 {
    my(P = readvec("suitable_primes_dual.gp"),
@@ -700,17 +463,6 @@ reduced_dual_pair() =
        [variable(K[2]), K[2].pol], [Mat(1), K[2][8]], T]);
 }
 
-projectivisation_to_reduced() =
-{
-   iota = read("projectivisation.gp");
-   [g, a] = readvec("projective_polynomial_reduced.gp");
-   t = variable(g);
-   kappa = subst(lift(modreverse(a)), t, iota);
-   if(subst(g, t, kappa) != 0,
-      error("projectivisation_to_reduced inconsistent"));
-   kappa;
-}
-
 relative_polynomial_reduced() =
 {
    G = read("relative_polynomial.gp");
@@ -781,46 +533,3 @@ intermediate_fields(k) =
    F = if(#F == 3, [F[1]], [F[1], F[4]]);
    [nfinit([f, P]) | f <- F];
 }
-
-reconstruct_scalar_mul_rel() =
-{
-   f = read("relative_polynomial.gp");
-   g = readvec("projective_polynomial_reduced.gp")[1];
-   P = readvec("suitable_primes_strict.gp");
-   L = [Mod(read(filename("scalar_mul_rel", p)), p) | p <- P];
-   mu0 = chinese(L);
-   mu = bestappr(mu0);
-   if(mu == [],
-      error("cannot reconstruct scalar multiplication"));
-   mu = Mod(Mod(mu, g), f);
-   z = variable(f);
-   if(subst(f, z, mu) != 0,
-      error("mu does not operate on the roots of f"));
-   mu;
-}
-
-scalar_mul_rel_reduced() =
-{
-   [f, a] = readvec("relative_polynomial_reduced.gp");
-   [z, t] = variables(f);
-   mu = read("scalar_mul_rel.gp");
-   mu = Mod(subst(lift(modreverse(a)), z, subst(lift(mu), z, a)), f);
-   if(subst(f, z, mu) != 0,
-      error("mu does not operate on the roots of f"));
-   mu;
-}
-
-scalar_mul_absolute() =
-{
-   rnfeq = read("relative_equation.gp");
-   f = rnfeq[1];
-   mu = read("scalar_mul_rel_reduced.gp");
-   \\ K = \Q(alpha),  L = K(beta),
-   \\ L = \Q(beta + k alpha)
-   \\ mu(beta + k alpha) = mu(beta) + k alpha
-   mu = Mod(eltreltoabs(rnfeq, liftpol(mu)) + rnfeq[3] * rnfeq[2], f);
-   z = variable(f);
-   if(subst(f, z, mu) != 0,
-      error("mu does not operate on the roots of f"));
-   mu;
-}