Merge pull request #6011 from sarangop1728/main

Added Zigzag functions and plots

lmfdb/hypergm/templates/hgm_family.html

@@ -37,7 +37,15 @@
       <tr><td>{{KNOWL('hgm.levelt_matrices', title="Levelt matrices")}}:<td>${h_{\infty}={{family.hinf_latex}},\;}$ ${h_0={{family.h0_latex}},\;}$ $ {h_1={{family.h1_latex}}}$ 
     </table>
   <p>
+
+
+<p><h2> {{ KNOWL('hgm.zigzagplot', title='Zigzag plot') }} </h2></p>
+<img src="{{ family.zigzag_plot() }}" width="500">
+
+
+
 <p><h2> {{ KNOWL('hgm.defining_parameter_ppart', title='$p$-parts of defining parameters') }} </h2>
+
 <p>
 <table style="margin-left:1%;" border="0" class="ntdata">
   <thead> <th> $p$ <th> {{ KNOWL('hgm.defining_parameter_ppart', title='$A_p$') }} <th> {{ KNOWL('hgm.defining_parameter_ppart', title='$B_p$') }} <th> {{ KNOWL('hgm.defining_parameter_ppart', title='$C_p$') }}

lmfdb/hypergm/web_family.py

@@ -1,10 +1,11 @@
 import re
 from flask import url_for
-from collections import defaultdict
+from collections import defaultdict, Counter
 
 from sage.all import (ZZ, QQ, cached_method, ceil, gcd, lcm,
                       latex, lazy_attribute,
-                      matrix, valuation)
+                      matrix, valuation, I)
+from sage.rings.complex_mpfr import ComplexField
 from sage.geometry.newton_polygon import NewtonPolygon
 
 from lmfdb import db
@@ -13,7 +14,9 @@
     make_bigint, web_latex, integer_divisors, integer_prime_divisors)
 from lmfdb.groups.abstract.main import abstract_group_display_knowl
 from lmfdb.galois_groups.transitive_group import transitive_group_display_knowl_C1_as_trivial
-from .plot import circle_image, piecewise_constant_image, piecewise_linear_image
+# from .plot import circle_image, piecewise_constant_image, piecewise_linear_image
+from sage.plot.all import line, text, point, circle, polygon, Graphics
+from sage.functions.log import exp
 
 HMF_LABEL_RE = re.compile(r'^A(\d+\.)*\d+_B(\d+\.)*\d+$')
 
@@ -176,15 +179,35 @@ def ppart(self):
             row.append(AB_to_url(A,B))
         return p_data
 
+    @cached_method
+    def circle_image(self):
+        alpha = self.alpha
+        beta = self.beta
+        alpha_counter = dict(Counter(alpha))
+        beta_counter = dict(Counter(beta))
+        G = Graphics()
+        G += circle((0, 0), 1, color='gray', thickness=2, zorder=3)
+        G += circle((0, 0), 1.4, color='black', alpha=0, zorder=2)  # Adds invisible framing circle, which protects the aspect ratio from being skewed.
+        C = ComplexField()
+        for a in alpha_counter.keys():
+            P = exp(C(2*3.14159*I*a))
+            P1 = exp(C(2*3.14159*(a + 0.007)*I))
+            P2 = exp(C(2*3.14159*(a - 0.007)*I))
+            P3 = (1+alpha_counter[a]/30)*exp(C(2*3.14159*I*a))
+            G += polygon([P1,P2,P3], color="red", thickness=1)
+            G += line([P,1.3*P], color="red", zorder=1)
+        for b in beta_counter.keys():
+            P = exp(C(2*3.14159*I*b))
+            P1 = exp(C(2*3.14159*(b + 0.007)*I))
+            P2 = exp(C(2*3.14159*(b - 0.007)*I))
+            P3 = (1-beta_counter[b]/30)*exp(C(2*3.14159*I*b))
+            G += polygon([P1,P2,P3], color="blue", thickness=1)
+            G += line([P,0.7*P], color="blue", zorder=1)
+        return G
+
     @cached_method
     def plot(self, typ="circle"):
-        assert typ in ['circle', 'linear', 'constant']
-        if typ == 'circle':
-            G = circle_image(self.A, self.B)
-        elif typ == 'linear':
-            G = piecewise_linear_image(self.A, self.B)
-        else:
-            G = piecewise_constant_image(self.A, self.B)
+        G = self.circle_image()
 
         return encode_plot(
             G.plot(),
@@ -198,6 +221,67 @@ def plot(self, typ="circle"):
     def plot_link(self):
         return '<a href="{0}"><img src="{0}" width="150" height="150"/></a>'.format(self.plot())
 
+    @lazy_attribute
+    def zigzag(self):
+        # alpha is color red
+        # beta is color blue
+        alpha = self.alpha
+        beta = self.beta
+        alpha_dicts = [dict(value=entry,color="red") for entry in alpha]
+        beta_dicts = [dict(value=entry,color="blue") for entry in beta]
+        zigzag_dicts = sorted(alpha_dicts + beta_dicts, key=lambda d: d["value"])
+        y = 0
+        y_values = [y] # zigzag graph will start at (0,0)
+        colors = [entry["color"] for entry in zigzag_dicts]
+        for entry in zigzag_dicts:
+            if entry["color"] == "red":
+                y += 1
+                y_values.append(y)
+            elif entry["color"] == "blue":
+                y += -1
+                y_values.append(y)
+        return [y_values, colors, zigzag_dicts]
+
+    @cached_method
+    def zigzag_plot(self):
+        zz = self.zigzag
+        y_values = zz[0]
+        colors = zz[1]
+        x_labels = zz[2]
+        y_max = max(y_values)
+        y_min = min(y_values)
+        x_values = list(range(0,len(y_values)))
+        x_max = len(y_values)
+        pts = [(i, y_values[i]) for i in x_values]
+        L = Graphics()
+        # grid
+        for x in x_values:
+            L += line([(x, y_min), (x, y_max)], color="grey", zorder=1, thickness=0.4)
+        for y in y_values:
+            L += line([(0, y), (x_max-1, y)], color="grey", zorder=1, thickness=0.4)
+        # zigzag
+        L += line(pts, thickness=1, color="black", zorder=2)
+        # points
+        x_values.pop()
+        for x in x_values:
+            L += point((x, y_values[x]), marker='o', size = 36, color=colors[x], zorder=3)
+
+        j = 0
+        for label in x_labels:
+            if label["color"] == "red":
+                L += text("$"+latex(QQ(label["value"]))+"$", (j,y_max + 0.4), color=label["color"])
+                j += 1
+            else:
+                L += text("$"+latex(QQ(label["value"]))+"$", (j,y_min - 0.4), color=label["color"])
+                j += 1
+        L.axes(False)
+        L.set_aspect_ratio(1)
+        return encode_plot(L, pad=0, pad_inches=0, bbox_inches="tight")
+
+    @lazy_attribute
+    def zigzag_plot_link(self):
+        return '<a href="{0}"><img src="{0}" width="150" height="150"/></a>'.format(self.zigzag_plot())
+
     @lazy_attribute
     def properties(self):
         return [('Label', self.label),