Merge pull request #6896 from roed314/alpha

main -> alpha

Author: roed314

lmfdb/api/templates/database_options.html

@@ -4,7 +4,7 @@
 
 <div style="max-width:700px;">
 <p>
-  The LMFDB contains two types of underlying data: the main PostgreSQL database and a collection of <a href="{{url_for('datasets')}}">auxiliary datasets</a>.  There are three options available for accessing large parts of the main database.
+  The LMFDB contains two types of underlying data: the main PostgreSQL database and a collection of <a href="{{url_for('datasets')}}">auxiliary datasets</a>; all data is <a href="{{url_for('license')}}">licensed</a> under <a href="https://creativecommons.org/licenses/by-sa/4.0/deed.en">CC-BY-SA</a>.  There are three options available for accessing large parts of the main database.
 </p>
 </div>
 

lmfdb/app.py

@@ -544,6 +544,12 @@ def citation():
     b = [(t, url_for("citation"))]
     return render_template('citation.html', title=t, body_class='', bread=b)
 
+@app.route("/license")
+def license():
+    t = "LMFDB Data and Code Licenses"
+    b = [("LMFDB Licenses", " ")]
+    return render_template('license.html', title=t, bread=b)
+
 
 @app.route("/contact")
 def contact():

lmfdb/elliptic_curves/elliptic_curve.py

@@ -466,6 +466,7 @@ def make_modcurve_link(label):
                   short_title="j-invariant", align="center", default=False),
     FloatCol("abc_quality", "ec.q.abc_quality", "$abc$ quality", short_title="abc quality", prec=5, default=False),
     FloatCol("szpiro_ratio", "ec.q.szpiro_ratio", "Szpiro ratio", prec=5, default=False),
+    MathCol("intrinsic_torsion", "ec.intrinsic_torsion", "Intrinsic torsion order", align="center", default=False),
     MathCol("ainvs", "ec.weierstrass_coeffs", "Weierstrass coefficients", short_title="Weierstrass coeffs", align="left", default=False),
     ProcessedCol("equation", "ec.q.minimal_weierstrass_equation", "Weierstrass equation", latex_equation, short_title="Weierstrass equation", align="left", orig="ainvs", download_col="ainvs"),
     ProcessedCol("modm_images", "ec.galois_rep", r"mod-$m$ images", lambda v: "<span>" + ", ".join([make_modcurve_link(s) for s in v[:5]] + ([r"$\ldots$"] if len(v) > 5 else [])) + "</span>",
@@ -563,6 +564,7 @@ def elliptic_curve_search(info, query):
     parse_floats(info,query,'faltings_height','faltings_height')
     parse_floats(info,query,'abc_quality')
     parse_floats(info,query,'szpiro_ratio')
+    parse_ints(info,query,'intrinsic_torsion')
     if info.get('reduction'):
         if info['reduction'] == 'semistable':
             query['semistable'] = True
@@ -1242,7 +1244,8 @@ class ECSearchArray(SearchArray):
              ("adelic_genus", "adelic genus", ["adelic_genus", "adelic_level", "adelic_index"]),
              ("faltings_height", "Faltings height", ["faltings_height", "conductor", "iso_nlabel", "lmfdb_number"]),
              ("abc_quality", "$abc$ quality", ["abc_quality", "conductor", "iso_nlabel", "lmfdb_number"]),
-             ("szpiro_ratio", "Szpiro ratio", ["szpiro_ratio", "conductor", "iso_nlabel", "lmfdb_number"])]
+             ("szpiro_ratio", "Szpiro ratio", ["szpiro_ratio", "conductor", "iso_nlabel", "lmfdb_number"]),
+             ("intrinsic torsion", "Intrinsic torsion order", ["intrinsic_torsion", "conductor", "iso_nlabel", "lmfdb_number"])]
     jump_example = "11.a2"
     jump_egspan = "e.g. 11.a2 or 389.a or 11a1 or 389a or [0,1,1,-2,0] or [-3024, 46224] or y^2 = x^3 + 1"
     jump_prompt = "Label or coefficients"
@@ -1437,6 +1440,12 @@ def __init__(self):
             knowl="ec.q.szpiro_ratio",
             example="8-",
             advanced=True)
+        intrinsic_torsion = TextBox(
+            name="intrinsic_torsion",
+            label="Intrinsic torsion order",
+            knowl="ec.intrinsic_torsion",
+            example="3",
+            advanced=True)
 
         manin_constant = TextBox(
             name="manin_constant",
@@ -1460,7 +1469,8 @@ def __init__(self):
             [adelic_level, adelic_index],
             [adelic_genus, faltings_height],
             [abc_quality, szpiro_ratio],
-            [count, manin_constant]
+            [intrinsic_torsion, manin_constant],
+            [count]
             ]
 
         self.refine_array = [
@@ -1470,4 +1480,5 @@ def __init__(self):
             [sha, sha_primes, regulator, reduction, faltings_height],
             [galois_image, adelic_level, adelic_index, adelic_genus],
             [nonmax_primes, abc_quality, szpiro_ratio, manin_constant],
+            [intrinsic_torsion]
             ]

lmfdb/elliptic_curves/templates/ec-curve.html

@@ -251,6 +251,12 @@ <h2> Invariants </h2>
         <td>{{ place_code('szpiro_ratio') }}</td>
         </tr>
 
+        <tr>
+        <td>{{ KNOWL('ec.intrinsic_torsion', title='Intrinsic torsion order') }}:</td>
+        <td>$\#E(\mathbb Q)_\text{tors}^\text{is}$</td><td>&nbsp;=&nbsp;</td><td colspan=3>${{ data.intrinsic_torsion }}$</td>
+        <td>{{ place_code('intrinsic_torsion') }}</td>
+        </tr>
+
        </table>
 
     <h2> {{ KNOWL('ec.q.bsdconjecture', title='BSD invariants') }}</h2>

lmfdb/galois_groups/code.yaml

@@ -1,58 +1,128 @@
 prompt:
-    magma:  'magma'
+  magma: 'magma'
+  sage:  'sage'
+  oscar: 'oscar'
 
 logo:
-    magma: <img src = "https://i.stack.imgur.com/0468s.png" width="50px">
+  magma: <img src = "https://i.stack.imgur.com/0468s.png" width="50px">
+  sage: <img src ="https://www.sagemath.org/pix/sage_logo_new.png" width = "50px">
+  oscar: <img src = "https://oscar-system.github.io/Oscar.jl/stable/assets/logo.png" width="50px">
+
+comment:
+  sage: |
+    #
+  magma: |
+    //
+  oscar: |
+    #
+
+not-implemented:
+  sage: |
+    # (not yet implemented)
+  magma: |
+    // (not yet implemented)
+  oscar: |
+    # (not yet implemented)
+
+frontmatter:
+  all: |
+    {lang} code for working with transitive group {label}
 
 gg:
-    magma: G := TransitiveGroup(%s, %s);
+  comment: Define the Galois group
+  magma: G := TransitiveGroup({n}, {t});
+  sage: G = TransitiveGroup({n}, {t})  
+  oscar: G = transitive_group({n}, {t})
 
 n:
-    magma: t, n := TransitiveGroupIdentification(G); n;
+  comment: Degree
+  magma: t, n := TransitiveGroupIdentification(G); n;
+  sage: G.degree()
+  oscar: degree(G)
 
 t:
-    magma: t, n := TransitiveGroupIdentification(G); t;
+  comment: Transitive number
+  magma: t, n := TransitiveGroupIdentification(G); t;
+  sage: G.transitive_number()
+  oscar: transitive_group_identification(G)[2]
 
 primitive:
-    magma: IsPrimitive(G);
+  comment: Determine if group is primitive
+  magma: IsPrimitive(G);
+  sage: G.is_primitive()
+  oscar: is_primitive(G)
 
 even:
-    magma: IsEven(G);
+  comment: Parity
+  magma: IsEven(G);
+  sage: all(g.SignPerm() == 1 for g in libgap(G).GeneratorsOfGroup())
+  oscar: is_even(G)
 
 nilpotent:
-    magma: NilpotencyClass(G);
+  comment: Nilpotency class
+  magma: NilpotencyClass(G);
+  sage: libgap(G).NilpotencyClassOfGroup() if G.is_nilpotent() else -1
+  oscar: if is_nilpotent(G) nilpotency_class(G) end
 
 auts:
-    magma: Order(Centralizer(SymmetricGroup(n), G));
+  comment: Order of the centralizer of G in S_n
+  magma: Order(Centralizer(SymmetricGroup(n), G));
+  sage: SymmetricGroup({n}).centralizer(G).order()
+  oscar: order(centralizer(symmetric_group({n}), G)[1])
 
 gens:
-    magma: Generators(G);
+  comment: Generators
+  magma: Generators(G);
+  sage: G.gens()
+  oscar: gens(G)
 
 ccs:
-    magma: ConjugacyClasses(G);
+  comment: Conjugacy classes
+  magma: ConjugacyClasses(G);
+  sage: G.conjugacy_classes()
+  oscar: conjugacy_classes(G)
 
 order:
-    magma: Order(G);
+  comment: Order
+  magma: Order(G);
+  sage: G.order()
+  oscar: order(G)
 
 cyclic:
-    magma: IsCyclic(G);
+  comment: Determine if group is cyclic
+  magma: IsCyclic(G);
+  sage: G.is_cyclic()
+  oscar: is_cyclic(G)
 
 abelian:
-    magma: IsAbelian(G);
+  comment: Determine if group is abelian
+  magma: IsAbelian(G);
+  sage: G.is_abelian()
+  oscar: is_abelian(G)
 
 solvable:
-    magma: IsSolvable(G);
+  comment: Determine if group is solvable
+  magma: IsSolvable(G);
+  sage: G.is_solvable()
+  oscar: is_solvable(G)
 
 id:
-    magma: IdentifyGroup(G);
+  comment: Abstract group ID
+  magma: IdentifyGroup(G);
+  sage: G.id()
 
 char_table:
-    magma: CharacterTable(G);
+  comment: Character table
+  magma: CharacterTable(G);
+  sage: G.character_table()
+  oscar: character_table(G)
 
+
+# specify which code snippets to test
 snippet_test:
   test4T2: 
     label: 4T2
     url: GaloisGroup/4T2/download/{lang}
-  test11T6: 
-    label: 11T6
-    url: GaloisGroup/11T6/download/{lang}
+  test11T5: 
+    label: 11T5
+    url: GaloisGroup/11T5/download/{lang}

lmfdb/galois_groups/main.py

@@ -13,7 +13,7 @@
     clean_input, prep_ranges, parse_bool, parse_ints, parse_galgrp,
     SearchArray, TextBox, TextBoxNoEg, YesNoBox, ParityBox, CountBox,
     StatsDisplay, totaler, proportioners, prop_int_pretty, Downloader,
-    sparse_cyclotomic_to_mathml, search_wrap, redirect_no_cache)
+    sparse_cyclotomic_to_mathml, search_wrap, redirect_no_cache, CodeSnippet)
 from lmfdb.utils.interesting import interesting_knowls
 from lmfdb.utils.search_columns import SearchColumns, LinkCol, MultiProcessedCol, MathCol, CheckCol, SearchCol
 from lmfdb.api import datapage
@@ -341,7 +341,7 @@ def render_group_webpage(args):
         data['malle_a'] = wgg.malle_a
         downloads = []
         for lang in [("Magma", "magma"), ("Oscar", "oscar"), ("SageMath", "sage")]:
-            downloads.append(('{} commands'.format(lang[0]), url_for(".gg_code", label=label, download_type=lang[1])))
+            downloads.append(('{} commands'.format(lang[0]), url_for(".gg_code_download", label=label, download_type=lang[1])))
         downloads.append(('Underlying data', url_for(".gg_data", label=label)))
         # split the label so that breadcrumbs point to a search for this object's degree
         parent_id, child_id = label.split("T")
@@ -360,20 +360,22 @@ def render_group_webpage(args):
             KNOWL_ID="gg.%s" % label,
             learnmore=learnmore_list()+[('Picture description', url_for('.pictures'))])
 
+
+sorted_code_names = ['gg', 'id', 'order', 'cyclic', 'abelian', 'solvable', 'nilpotent',
+                     'n', 't', 'even', 'primitive', 'auts', 'gens', 'ccs', 'char_table']
+
+def gg_code(label, download_type):
+    gg = WebGaloisGroup(label)
+    gg.make_code_snippets()
+    code = CodeSnippet(gg.code)
+    return code.export_code(label, download_type, sorted_code_names)
+
 @galois_groups_page.route('/<label>/download/<download_type>')
-def gg_code(label,download_type):
-    if download_type == "magma":
-        s = "// Magma code for creating transitive group " + label + "\n\n"
-        s += "G := TransitiveGroup(%s,%s);\n" % tuple(label.split("T"))
-    elif download_type == "oscar":
-        s = "# Oscar code for creating transitive group " + label + "\n\n"
-        s += "G = transitive_group(%s,%s)\n" % tuple(label.split("T"))
-    elif download_type == "sage":
-        s = "# Sage code for creating transitive group " + label + "\n\n"
-        s += "G = TransitiveGroup(%s,%s)\n" % tuple(label.split("T"))
-    else:
-        return abort(404, f"Invalid download type {download_type}")
-    response = make_response(s)
+def gg_code_download(**args):
+    try:
+        response = make_response(gg_code(**args))
+    except Exception as err:
+        return abort(404, str(err))
     response.headers['Content-type'] = 'text/plain'
     return response
 

lmfdb/galois_groups/transitive_group.py

@@ -304,8 +304,10 @@ def make_code_snippets(self):
         # read in code.yaml from galois_groups directory:
         _curdir = os.path.dirname(os.path.abspath(__file__))
         self.code = yaml.load(open(os.path.join(_curdir, "code.yaml")), Loader=yaml.FullLoader)
-        for lang in self.code['gg']:
-            self.code['gg'][lang] = self.code['gg'][lang] % (self.n(),self.t())
+
+        for prop in ['gg', 'auts']:
+            for lang in self.code[prop]:
+                self.code[prop][lang] = self.code[prop][lang].format(**{'n':self.n(), 't':self.t()})
         self.code['show'] = { lang:'' for lang in self.code['prompt'] }
 
 ############  Misc Functions

lmfdb/groups/abstract/templates/character_table.html

@@ -43,9 +43,9 @@
       <td></td><td class="right">{{KNOWL('group.conjugacy_class.power_classes',"{} P".format(p))}}</td>
       {% for c in ccs %}
        {% if loop.index ==  highlight_i %}
-      <td class="highlighted">{{ ccs[c['powers'][ploop.index-1]-1].label }}</td>
+      <td class="highlighted">{{ ccs[c.prime_powers()[ploop.index-1]-1].label }}</td>
       {% else %}
-<td class="right">{{ ccs[c['powers'][ploop.index-1]-1].label }}</td>
+<td class="right">{{ ccs[c.prime_powers()[ploop.index-1]-1].label }}</td>
       {% endif %}
       {% endfor %}
     </tr>

lmfdb/groups/abstract/templates/rational_character_table.html

@@ -24,7 +24,7 @@
     <tr>
       <td></td><td>{{KNOWL('group.conjugacy_class.power_classes',"{} P".format(p))}}</td>
       {% for c in gp.conjugacy_class_divisions %}
-        <td>{{ gp.conjugacy_classes[c.classes.0.powers[ploop.index0]-1].division.label }}</td>
+        <td>{{ gp.conjugacy_classes[c.classes.0.prime_powers()[ploop.index0]-1].division.label }}</td>
       {% endfor %}
     </tr>
   {% endfor %}

lmfdb/groups/abstract/web_groups.py

@@ -24,6 +24,7 @@
     is_prime,
     cartesian_product_iterator,
     exists,
+    euler_phi,
 )
 from sage.libs.gap.libgap import libgap
 from sage.libs.gap.element import GapElement
@@ -3763,6 +3764,14 @@ def force_repr(self, newrep):
         self.representative = newrep
         self.force_repr_elt = True
 
+    # extract from powers list the ones corresponding to ones dividing the order
+    def prime_powers(self):
+        plist = [z[0] for z in ZZ(self.group_order).factor()]
+        Nphi = self.group_order*euler_phi(self.group_order)
+        plist_long = [z[0] for z in ZZ(Nphi).factor()]
+        assert len(plist_long) == len(self.powers)
+        return [self.powers[plist_long.index(p)] for p in plist]
+
     def display_knowl(self, name=None):
         if not name:
             name = self.label