added valued of the Hurwitz zeta function at pairs of rational numbers

data/Special_values/Values_of_the_Hurwitz_zeta_function_at_pairs_of_rational_numbers/generate.sage

@@ -0,0 +1,57 @@
+import yaml
+import os
+from utils.utils import numbers_to_yaml
+from utils.utils import real_interval_to_sage_string
+
+path = 'data/Special_values/Values_of_the_Hurwitz_zeta_function_at_pairs_of_rational_numbers/'
+
+prec10 = 100 #relative precision in base 10
+b_range = [1..10]
+a_range = [-10..10]
+
+d_range = [1..5]
+c_range = [1..5]
+
+
+RIFprec = RealIntervalField(prec10 * 3.4 * 2)
+
+
+numbers = {}
+for d in d_range:
+	for c in c_range:
+		if gcd(c,d) != 1:
+			continue
+		x = c/d
+		if x > 1:
+			continue
+		if x == 1:
+			numbers_x = {
+				#'equals': 'HREF{T14}',
+				'equals': 'HREF{Values_of_the_Riemann_zeta_function_at_rational_numbers}',
+			}
+		else:
+			numbers_x = {}
+			for b in b_range:
+				for a in a_range:
+					if gcd(a,b) != 1:
+						continue
+					s = a/b
+					if s == 1:
+						continue
+
+					if s == 0:
+						n = 1/2 - x #use this as hurwitz_zeta returns a real, not an integer...
+					else:
+						n = hurwitz_zeta(s,x)
+
+					if n in QQ:
+						n_str = str(n)
+					else:
+						#n is so far symbolic
+						n = RIFprec(n)
+						n_str = real_interval_to_sage_string(n,max_digits = prec10).replace('?','')
+					numbers_x[str(s)] = n_str
+		numbers[str(x)] = numbers_x
+
+filename = os.path.join(path, 'numbers.yaml')
+yaml.dump(numbers, stream = open(filename, 'w'), sort_keys = False)