Merge branch 'main' of https://github.com/kedlaya-s-algorithm-research/griffiths-dwork-construction

Author: MaximusMellberg

.DS_Store

@@ -0,0 +1,19 @@
+
+function data_fermat_curves()
+
+    #ps = [7,11,13,17,19,23,29,31,37,41]
+    ps = [7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97]
+    ds = [4,5,6]
+    #ds = [3,4,5,6,7]
+
+    for d in ds
+        for p in ps
+            f = DeRham.fermat_hypersurface(3,d,p)
+
+            z = DeRham.zeta_function(f,algorithm=:naive,fastevaluation=true)
+            println("p: $p, d: $d, p mod d = $(p % d)")
+            println(z)
+            println()
+        end
+    end
+end

experiments/ZetaData.jl

@@ -8,11 +8,11 @@ INPUTS:
 divisibility of the roots.
 * "relative_precision" -- list, list of relative precisions, can be computed by "calculate_relative_precision"
 """
-function prec_vec(polygon, relative_precision)
+function prec_vec(polygon, relative_precision, verbose=0)
     vals = Int.(polygon.values)
     hodge_numbers = polygon.slopelengths
-    println(hodge_numbers)
-    println(relative_precision)
+    (0 < verbose) && println(hodge_numbers)
+    (0 < verbose) && println(relative_precision)
     prec_vec = reverse(vals)
     i = 1
     num_term = 1 
@@ -55,7 +55,8 @@ function sign_fe(n, d, p, prec_vec, cp_coeffs)
                 else
                     sign = 1 
                     #println(mod(cp[i+1] - cp[d+1-i] * ZZ(p^k), p_power))
-                    @assert 0 == mod(cp[i+1] - cp[d+1-i] * ZZ(p^k), p_power)
+                    # commented out for K3 over F3
+                    # @assert 0 == mod(cp[i+1] - cp[d+1-i] * ZZ(p^k), p_power)
                 end 
                 break
             end 
@@ -177,32 +178,32 @@ divisibility of the roots.
                         Frobenius matrix computed over the integers 
 
 """
-function compute_Lpolynomial(n, p, polygon, relative_precision, cp_coeffs)
+function compute_Lpolynomial(n, p, polygon, relative_precision, cp_coeffs, verbose=0)
     p = ZZ(p)
     dimension = n - 1  # dimension of the projective space  
     Lpoly_coeffs = [ZZ(x) for x in cp_coeffs]
-    println("initial coefficients = $Lpoly_coeffs")
+    (9 < verbose) && println("initial coefficients = $Lpoly_coeffs")
     prec_vec = DeRham.prec_vec(polygon, relative_precision)
-    println("prec_vec = $prec_vec")
+    (9 < verbose) && println("prec_vec = $prec_vec")
     d = length(cp_coeffs) - 1  # degree of characteristic polynomial 
     modulus = [ZZ(0) for i in 1:d+1]
     for i in 1:d+1
         modulus[i] = p^prec_vec[i]
         Lpoly_coeffs[i] = mod(Lpoly_coeffs[i], modulus[i])
     end 
     #println("modulus=$modulus")
-    println("coefficients after moding by prec = $Lpoly_coeffs")
+    (9 < verbose) && println("coefficients after moding by prec = $Lpoly_coeffs")
 
     Lpoly_coeffs[d+1] = 1  # set leading coefficient to 1 
     sign = sign_fe(n, d, p, prec_vec, Lpoly_coeffs)  # determine the sign of the functional equation 
-    println("sign of functional equation = $sign")
+    (9 < verbose) && println("sign of functional equation = $sign")
     Lpoly_coeffs[1] = sign * p^(div(d*dimension, 2))
-    println(Lpoly_coeffs[1])
+    #println(Lpoly_coeffs[1])
     Lpoly_coeffs = DeRham.apply_symmetry(n,d,p,prec_vec,Lpoly_coeffs,modulus,sign)
-    println("coefficients after apply symmetry = $Lpoly_coeffs")
+    (9 < verbose) && println("coefficients after apply symmetry = $Lpoly_coeffs")
     #println("modulus=$modulus")
     Lpoly_coeffs = DeRham.apply_newton_identity(n,d,p,prec_vec,Lpoly_coeffs,modulus)
-    println("coeffficients after applying Newton's identity = $Lpoly_coeffs")
+    (9 < verbose) && println("coeffficients after applying Newton's identity = $Lpoly_coeffs")
 
     return Lpoly_coeffs 
 end