Change number field signature display from [r1, r2] to (r1, r2)

lmfdb/number_fields/number_field.py

@@ -465,7 +465,7 @@ def render_field_webpage(args):
     data['class_group'] = nf.class_group()
     data['narrow_class_group'] = nf.narrow_class_group()
     data['class_group_invs'] = nf.class_group_invariants()
-    data['signature'] = nf.signature()
+    data['signature'] = nf.signature_display()
     data['coefficients'] = nf.coeffs()
     nf.make_code_snippets()
     D = nf.disc()
@@ -850,7 +850,7 @@ def number_field_jump(info):
                  lambda label: '<a href="%s">%s</a>' % (url_for_label(label), nf_label_pretty(label))),
     PolynomialCol("coeffs", "nf.defining_polynomial", "Polynomial"),
     MathCol("degree", "nf.degree", "Degree", align="center", default=False),
-    MultiProcessedCol("signature", "nf.signature", "Signature", ["r2", "degree"], lambda r2, degree: '[%s,%s]' % (degree - 2*r2, r2 ), apply_download=False, align="center", default=False),
+    MultiProcessedCol("signature", "nf.signature", "Signature", ["r2", "degree"], lambda r2, degree: '(%s, %s)' % (degree - 2*r2, r2 ), apply_download=False, align="center", default=False),
     DiscriminantCol("disc", "nf.discriminant", "Discriminant", ['disc_sign', 'disc_abs'], func=None, align="left"),
     MathCol("num_ram", "nf.ramified_primes", "Ram. prime count", short_title="ramified prime count", default=False),
     MathCol("rd", "nf.root_discriminant", "Root discriminant", default=False),

lmfdb/number_fields/test_numberfield.py

@@ -77,6 +77,11 @@ def test_signature_search(self):
         self.check_args('/NumberField/?start=0&degree=6&signature=%5B0%2C3%5D&count=100', '6.0.61131.1')
         self.check_args('/NumberField/?start=0&degree=7&signature=%5B3%2C2%5D&count=100', '7.3.1420409.1')
 
+    def test_signature_display(self):
+        # Verify that signatures are displayed with parentheses, not square brackets
+        self.check_args('/NumberField/6.0.61131.1', '(0, 3)')  # degree 6 field with signature (0, 3)
+        self.check_args('/NumberField/7.3.1420409.1', '(3, 2)')  # degree 7 field with signature (3, 2)
+
     def test_relative_class_number(self):
         self.check_args('/NumberField/4.0.1327873600.2', '2108')
 

lmfdb/number_fields/web_number_field.py

@@ -555,6 +555,11 @@ def signature(self):
         n = self._data['degree']
         return [n-2*r2, r2]
 
+    def signature_display(self):
+        """Return signature formatted for display with parentheses."""
+        r1, r2 = self.signature()
+        return '(%s, %s)' % (r1, r2)
+
     def degree(self):
         return self._data['degree']