add and use new optional argument embedding_forms to modular_curve

and modular_curve_jacobian_{medium,large}

Makefile.form.in

@@ -185,7 +185,7 @@ reduced_dual_pair.gp: reduced_pairing.gp
 	intermediate_polynomials_0 intermediate_polynomials_1 intermediate_polynomials_2 \
 	intermediate_polynomials_3 intermediate_polynomials_4 pairings reduced_pairings
 
-values: primes.gp | form.gp
+values: primes.gp | embedding_forms.gp
 	$(MAKE) $(patsubst %,values_%.gp,$(shell cat $<))
 	$(MAKE) primes.gp
 

modcurve/modular-curve.c

@@ -105,16 +105,11 @@ modular_curve_jacobian_count_points(GEN group, unsigned long p,
   return gerepileupto(av, n);
 }
 
-/*
-  Compute data associated to the modular curve.  Modular forms are
-  computed to sufficient precision to determine the spaces of global
-  sections of  {\cal L}^max_power.
-*/
-GEN
-modular_curve(GEN group, unsigned long p, unsigned long max_power) {
-  unsigned long degree, dim, genus = modular_group_genus (group), weight,
-    prec, r, i, s0, s1;
-  GEN result, forms, V, M, ind, numzeta;
+static GEN
+compute_embedding_forms(GEN group, ulong p, long max_power) {
+  long genus = modular_group_genus(group),
+    degree, dim, weight, prec, r, i;
+  GEN result, forms, V, M;
   char *cache_file;
 
   /*
@@ -171,25 +166,25 @@ modular_curve(GEN group, unsigned long p, unsigned long max_power) {
   for(i = 1; i <= prec - r; i++)
     gel(M, i) = vec_ei(prec, r + i);
   V = intersect(forms, M);
-  V = ZM_to_Flm(lift(V), p);
   if(lg(V) - 1 != genus + 2)
     pari_err(e_MISC, "unexpected dimension");
+  return rowslice(V, r + 1, r + 1 + max_power*(2*genus + 1));
+}
 
-  /* Extract the small subspace we are interested in.  */
-  ind = gel(Flm_indexrank(V, p), 1);
-  if(lg(ind) != lg(V))
-    pari_err(e_MISC, "dimensions do not agree");
-  if(ind[1] != r + 1)
-    pari_err(e_MISC, "strange order of vanishing");
-  err_printf("using pivots %Ps\n", ind);
-  s0 = ind[1]; s1 = s0 + max_power*(2*genus + 1);
-  V = matslice0(V, s0, s1, 1, lg(V) - 1);
-
+/*
+  Compute data associated to the modular curve.  Modular forms are
+  computed to sufficient precision to determine the spaces of global
+  sections of  {\cal L}^max_power.
+*/
+GEN
+modular_curve(GEN group, ulong p, ulong max_power, GEN embedding_forms) {
+  GEN V, numzeta;
+  if (embedding_forms == NULL)
+    embedding_forms = compute_embedding_forms(group, p, max_power);
+  V = ZM_to_Flm(liftint(embedding_forms), p);
   numzeta = modular_curve_numerator_zeta_function (group, p);
-
-  return curve_construct (mkvec2(group, stoi(weight)), p, NULL,
-			  MULTIPLY_POWER_SERIES,
-			  V, max_power, numzeta);
+  return curve_construct(group, p, NULL, MULTIPLY_POWER_SERIES,
+			 V, max_power, numzeta);
 }
 
 GEN

modcurve/modular-curve.gp.in

@@ -3,6 +3,6 @@ install(modular_curve_numerator_zeta_function, "GL", , "libmodcurve@shrext@");
 install(modular_curve_zeta_function, "GL", , "libmodcurve@shrext@");
 install(modular_curve_count_points, "GLD1,L,", , "libmodcurve@shrext@");
 install(modular_curve_jacobian_count_points, "GLD1,L,", , "libmodcurve@shrext@");
-install(modular_curve, "GLD0,L,", , "libmodcurve@shrext@");
-install(modular_curve_jacobian_medium, "GL", , "libmodcurve@shrext@");
-install(modular_curve_jacobian_large, "GL", , "libmodcurve@shrext@");
+install(modular_curve, "GLD0,L,DG", , "libmodcurve@shrext@");
+install(modular_curve_jacobian_medium, "GLDG", , "libmodcurve@shrext@");
+install(modular_curve_jacobian_large, "GLDG", , "libmodcurve@shrext@");

modcurve/modular-curve.h

@@ -7,7 +7,7 @@ GEN modular_curve_zeta_function(GEN group, unsigned long p);
 GEN modular_curve_count_points(GEN group, unsigned long p, unsigned long k);
 GEN modular_curve_jacobian_count_points(GEN group, unsigned long p,
 					unsigned long k);
-GEN modular_curve(GEN group, unsigned long p, unsigned long max_power);
+GEN modular_curve(GEN group, ulong p, ulong max_power, GEN embedding_forms);
 GEN modular_curve_distinguished_point(GEN X);
 
 #endif

modcurve/modular-jacobian.c

@@ -15,14 +15,14 @@
 
 
 GEN
-modular_curve_jacobian_medium(GEN group, unsigned long p) {
-  return curve_jacobian (modular_curve (group, p, 8),
+modular_curve_jacobian_medium(GEN group, ulong p, GEN embedding_forms) {
+  return curve_jacobian (modular_curve(group, p, 8, embedding_forms),
 			 JACOBIAN_TYPE_MEDIUM);
 }
 
 GEN
-modular_curve_jacobian_large(GEN group, unsigned long p) {
-  return curve_jacobian (modular_curve (group, p, 9),
+modular_curve_jacobian_large(GEN group, ulong p, GEN embedding_forms) {
+  return curve_jacobian (modular_curve(group, p, 9, embedding_forms),
 			 JACOBIAN_TYPE_LARGE);
 }
 

modcurve/modular-jacobian.h

 #ifndef MODULAR_JACOBIAN
 #define MODULAR_JACOBIAN
 
-GEN modular_curve_jacobian_medium(GEN group, unsigned long p);
-GEN modular_curve_jacobian_large(GEN group, unsigned long p);
+GEN modular_curve_jacobian_medium(GEN group, ulong p, GEN embedding_forms);
+GEN modular_curve_jacobian_large(GEN group, ulong p, GEN embedding_forms);
 GEN modular_jacobian_normalised_divisor (GEN X, GEN W_D, GEN W_rO);
 
 #endif

modcurve/torsion-subscheme.c

@@ -369,7 +369,7 @@ torsion_subscheme(GEN Gamma, unsigned long l, unsigned long p,
   /*
     Compute the Jacobian and its base change to the right field.
   */
-  J = modular_curve_jacobian_medium(Gamma, p);
+  J = modular_curve_jacobian_medium(Gamma, p, gp_read_file("embedding_forms.gp"));
   err_printf("working with curve of genus %li with projective"
 	     " embedding of degree %li into P^%li\n",
 	     curve_genus(J), curve_degree(J), lg(curve_V(J, 1)) - 2);