Merge pull request #6456 from SamSchiavone/belyi_plane

Improved Belyi plane equations

Author: AndrewVSutherland

lmfdb/belyi/main.py

@@ -119,11 +119,11 @@ def by_url_belyi_galmap_label(group, sigma0, sigma1, sigmaoo, letnum):
     label = "{}-{}_{}_{}-{}".format(group, sigma0, sigma1, sigmaoo, letnum)
     return render_belyi_galmap_webpage(label)
 
-
-@belyi_page.route("/<group>/<sigma0>/<sigma1>/<sigmaoo>/<letnum>/<triple>/")
-def by_url_embedded_belyi_map_label(group, sigma0, sigma1, sigmaoo, letnum, triple):
-    label = "{}-{}_{}_{}-{}".format(group, sigma0, sigma1, sigmaoo, letnum)
-    return render_embedded_belyi_map_webpage(label, triple)
+# TODO: fix embedded Belyi pages to work with raw and compress
+#@belyi_page.route("/<group>/<sigma0>/<sigma1>/<sigmaoo>/<letnum>/<triple>/")
+#def by_url_embedded_belyi_map_label(group, sigma0, sigma1, sigmaoo, letnum, triple):
+#    label = "{}-{}_{}_{}-{}".format(group, sigma0, sigma1, sigmaoo, letnum)
+#    return render_embedded_belyi_map_webpage(label, triple)
 
 
 @belyi_page.route("/<group>/<sigma0>/<sigma1>/<sigmaoo>/")

lmfdb/belyi/templates/belyi_galmap.html

@@ -111,9 +111,14 @@ <h2>{{ KNOWL('nf.embedding', title="Embeddings") }}</h2>
     </thead>
     <tbody>
       {% for g in data.embeddings_and_triples %}
+       <td>${{g['embedding']}}$</td>
+       <td>${{g['triple']}}$</td>
+       </tr>
+      <!-- TODO: uncomment this when embedded map pages are reactivated
          <td><a href="{{g['triple_link']}}">${{g['embedding']}}$</a></td>
          <td><a href="{{g['triple_link']}}">${{g['triple']}}$</a></td>
          </tr>
+      -->
       {% endfor %}
     </tbody>
     </table>

scripts/belyi/fix-polred-bug.m

@@ -0,0 +1,22 @@
+// fixing wrong base field polynomial
+// currently affecting 8T50-8_4.1.1.1.1_4.4-b and 8T50-8_4.1.1.1.1_6.2-a
+
+load "8T50-8_4.1.1.1.1_4.4-b.m";
+AttachSpec("~/github/CHIMP/CHIMP.spec");
+Kred, mpred:= Polredabs(K);
+f, _ := HyperellipticPolynomials(X);
+// make isomorphic curve over polredabs-ed numfield
+Xred := EllipticCurve(Polynomial([mpred(el) : el in Coefficients(f)]));
+KXred := FunctionField(Xred);
+
+// make homomorphism from KX to KXred
+cf := hom< Kred -> KXred | Kred.1>;
+KXalg, mp_alg := AlgorithmicFunctionField(KX);
+Kx := BaseRing(KXalg);
+//Kx := RationalFunctionField(K);
+c_final := hom< Kx -> KXred | (mpred*cf), [KXred.1] >;
+//hom< Kx -> KXred | (iota*cf), [KXred.1] >;
+
+// final success
+chg_fld := hom< KXalg -> KXred | c_final, [KXred.2]>;
+chg_fld(mp_alg(phi));

scripts/belyi/format_plane_model.py

@@ -37,7 +37,9 @@ def plane_map_constant_factored(rec):
             num_list = [el/n for el in num_list]
             poly = K(num_list)
             # now LaTeX everything
+            s = ''
             if a in QQ:
+                s = '-' if a.sign()==-1 else '' # if a in QQ, keep track of sign
                 poly_lat = ''
             else:
                 if ("+" in str(poly)) or ("-" in str(poly)):
@@ -47,7 +49,7 @@ def plane_map_constant_factored(rec):
             if d == 1:
                 rec['plane_map_constant_factored'] = "%s" % (latex(factor(n))+poly_lat)
             else:
-                rec['plane_map_constant_factored'] = r"\frac{%s}{%s} %s" % (latex(factor(n)), latex(factor(d)), poly_lat)
+                rec['plane_map_constant_factored'] = r"%s\frac{%s}{%s}%s" % (s,latex(factor(n)), latex(factor(d)), poly_lat)
     return rec
 
 def pretty_print_factor(f):